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		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3526</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3526"/>
		<updated>2015-03-17T16:29:23Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
AspenTech. Appendix A - Property Methods and Calculations. Simulation Basics. 2014;A-3 - A-26.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. 1983 Aug 2.&lt;br /&gt;
&lt;br /&gt;
Britannica.com. Methane (Chemical Compound) [Internet]. Encyclopædia Britannica Online; c2015 [cited 13 Mar 2015]. Available from: http://www.britannica.com/EBchecked/topic/378264/methane.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal Today. 2007;125:111–119.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; n.d. [cited 13 Mar 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; c2014 [cited 13 Mar 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/.&lt;br /&gt;
&lt;br /&gt;
Epa.gov. Summary of the Clean Air Act, 2015 [Internet]. United States Environmental Protection Agency; c2015 [cited 13 Mar. 2015]. Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 2012 Dec;6:101-115.&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct 4-7; Houston, TX. Houston: Texas A&amp;amp;M University; 2010.&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84.&lt;br /&gt;
&lt;br /&gt;
Statista.com. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons) [Internet]. American Chemistry Council; c2014 [cited 15 Jan 2015]. Available from: http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems [Internet]. The University of Missouri-Columbia, Dept of Chemical Engineering; c2002 [cited 13 Mar 2015]. Available from: http://web.missouri.edu/~suppesg/paper28.pdf.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979.&lt;br /&gt;
&lt;br /&gt;
US Energy Information Administration. Today in Energy - Daily Prices [Internet]. US EIA; c2015 [cited 3 Mar 2015]. Available from: http://www.eia.gov/todayinenergy/prices.cfm.&lt;br /&gt;
&lt;br /&gt;
Weddle N. ICIS Pricing: Ethylene (Europe) [Internet]. Reed Business Limited; c2015 [cited 10 Mar 2015]. Available from: http://www.icis.com/chemicals/ethylene/europe/&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; c2012 [cited 13 Mar 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf.&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3524</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3524"/>
		<updated>2015-03-17T07:50:39Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics. 2014; A-3 - A-26.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. 1983 Aug 2.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today. 2007;125:111–119.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; n.d. [cited 13 Mar 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; c2014 [cited 13 Mar 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 2012 December;6:101-115.&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct.&lt;br /&gt;
&lt;br /&gt;
Britannica.com. Methane (Chemical Compound) [Internet]. Encyclopædia Britannica Online; c2015 [cited 13 Mar 2015]. Available from: http://www.britannica.com/EBchecked/topic/378264/methane.&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84.&lt;br /&gt;
&lt;br /&gt;
Statista.com. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons) [Internet]. American Chemistry Council; c2014 [cited 15 Jan 2015]. Available from: http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/.&lt;br /&gt;
&lt;br /&gt;
Epa.gov. Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems [Internet]. The University of Missouri-Columbia, Dept of Chemical Engineering; c2002 [cited 13 Mar 2015]. Available from: http://web.missouri.edu/~suppesg/paper28.pdf.&lt;br /&gt;
&lt;br /&gt;
US Energy Information Administration. Today in Energy - Daily Prices [Internet]. US EIA; c2015 [cited 3 Mar 2015]. Available from: http://www.eia.gov/todayinenergy/prices.cfm.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; c2012 [cited 13 Mar 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf.&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3523</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3523"/>
		<updated>2015-03-17T07:50:15Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
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&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics. 2014; A-3 - A-26.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. 1983 Aug 2.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today. 2007;125:111–119.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; [cited 13 Mar 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; 2014 [cited 13 Mar 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 2012 December;6:101-115.&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct.&lt;br /&gt;
&lt;br /&gt;
Britannica.com. Methane (Chemical Compound) [Internet]. Encyclopædia Britannica Online; c2015 [cited 13 Mar 2015]. Available from: http://www.britannica.com/EBchecked/topic/378264/methane.&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84.&lt;br /&gt;
&lt;br /&gt;
Statista.com. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons) [Internet]. American Chemistry Council; c2014 [cited 15 Jan 2015]. Available from: http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/.&lt;br /&gt;
&lt;br /&gt;
Epa.gov. Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems [Internet]. The University of Missouri-Columbia, Dept of Chemical Engineering; c2002 [cited 13 Mar 2015]. Available from: http://web.missouri.edu/~suppesg/paper28.pdf.&lt;br /&gt;
&lt;br /&gt;
US Energy Information Administration. Today in Energy - Daily Prices [Internet]. US EIA; c2015 [cited 3 Mar 2015]. Available from: http://www.eia.gov/todayinenergy/prices.cfm.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; c2012 [cited 13 Mar 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf.&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3522</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3522"/>
		<updated>2015-03-17T07:48:53Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics. 2014; A-3 - A-26.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. 1983 Aug 2.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today. 2007;125:111–119.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; [cited 13 Mar 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; 2014 [cited 13 Mar 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 2012 December;6:101-115.&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct.&lt;br /&gt;
&lt;br /&gt;
Britannica.com. Methane (Chemical Compound). Encyclopædia Britannica Online; c2015 [cited 13 Mar. 2015] Available from: http://www.britannica.com/EBchecked/topic/378264/methane.&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84.&lt;br /&gt;
&lt;br /&gt;
Statista.com. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons) [Internet]. American Chemistry Council; c2014 [cited 15 Jan 2015]. Available from: http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/.&lt;br /&gt;
&lt;br /&gt;
Epa.gov. Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems [Internet]. The University of Missouri-Columbia, Dept of Chemical Engineering; c2002 [cited 13 Mar 2015]. Available from: http://web.missouri.edu/~suppesg/paper28.pdf.&lt;br /&gt;
&lt;br /&gt;
US Energy Information Administration. Today in Energy - Daily Prices [Internet]. US EIA; c2015 [cited 3 Mar 2015]. Available from: http://www.eia.gov/todayinenergy/prices.cfm.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; c2012 [cited 13 Mar 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf.&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3509</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3509"/>
		<updated>2015-03-16T17:00:52Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics; A-3 - A-26. 2014.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. August 2, 1983.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today 2007, 125, 111–119.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; [cited 13 Mar 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; 2014 [cited 13 Mar 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 6, 101-115. doi: 10.3390/ma6010101.&lt;br /&gt;
&lt;br /&gt;
Hadawey A, Ge Y, Tassou TSA. Energy Savings Through Liquid Pressure Amplification In A Dairy Plant Refrigeration System. The Centre for Energy and Built Environment Research [cited 13 Mar. 2015].&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct 4-7; Houston, TX. Houston: Texas A&amp;amp;M University; 2010.&lt;br /&gt;
&lt;br /&gt;
Methane (Chemical Compound). 2015. Encyclopædia Britannica Online. [cited 13 Mar. 2015] Available from: http://www.britannica.com/EBchecked/topic/378264/methane.&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84.&lt;br /&gt;
&lt;br /&gt;
Statista.com. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons) [Internet]. American Chemistry Council; c2014 [cited 15 Jan 2015]. Available from: http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/.&lt;br /&gt;
&lt;br /&gt;
Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems. The University of Missouri-Columbia, Dept of Chemical Engineering. [cited 13 Mar. 2015].&lt;br /&gt;
&lt;br /&gt;
Today in Energy - Daily Prices. US Energy Information Administration website. http://www.eia.gov/todayinenergy/prices.cfm. Accessed March 3rd 2015.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; 2012 [cited 13 Mar 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf.&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3508</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3508"/>
		<updated>2015-03-16T16:54:01Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
American Chemistry Council. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons). In Statista - The Statistics Portal [Internet]. August 2014. Available at http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/, Accessed January 15, 2015.&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics; A-3 - A-26. 2014.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012. - Aspen HYSYS help file used for troubleshooting and assistance on economic analysis.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. August 2, 1983. - Primary background for process design.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today 2007, 125, 111–119. - Paper introducing research on modified alumina catalyst for ethanol dehydration.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; [cited 13 Mar. 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html. -- Composition of air.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; 2014 [cited 13 Mar. 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene -- Plant size ranges.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar. 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/. -- Information on ethanol production in Iowa.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 6, 101-115. doi: 10.3390/ma6010101. - Comparison of types of catalysts used in the dehydration of ethanol and current research into new catalysts.&lt;br /&gt;
&lt;br /&gt;
Hadawey A, Ge Y, Tassou TSA. Energy Savings Through Liquid Pressure Amplification In A Dairy Plant Refrigeration System. The Centre for Energy and Built Environment Research [cited 13 Mar. 2015].&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct 4-7; Houston, TX. Houston: Texas A&amp;amp;M University; 2010. -- Use of turboexpander for cryogenic separations&lt;br /&gt;
&lt;br /&gt;
Methane (Chemical Compound). 2015. Encyclopædia Britannica Online. [cited 13 Mar. 2015] Available from: http://www.britannica.com/EBchecked/topic/378264/methane -- Composition of Methane&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84. – Overview of bioethanol dehydration process development.&lt;br /&gt;
&lt;br /&gt;
Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act -- Emissions requirements of chemical plants.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems. The University of Missouri-Columbia, Dept of Chemical Engineering. [cited 13 Mar. 2015]. -- Use of NRTL in alcohol separations.&lt;br /&gt;
&lt;br /&gt;
Today in Energy - Daily Prices. US Energy Information Administration website. http://www.eia.gov/todayinenergy/prices.cfm. Accessed March 3rd 2015. - Bulk market price for 95% ethanol.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013. -- General Reference Book&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979. – Patent for catalytic dehydration of ethylene in a fluidized bed reactor.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014. - Bulk market price for chemical grade ethylene.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514. – Technical information on ethanol to ethylene conversion via dehydration.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; 2012 [cited 13 Mar. 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf -- Information regarding 95% ethanol&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3493</id>
		<title>Ethanol to Ethylene (B1)</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Ethanol_to_Ethylene_(B1)&amp;diff=3493"/>
		<updated>2015-03-15T06:45:18Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:BFD_B1.png|600px|thumbnail|alt=Alt text|Conversion of Ethanol to Ethylene]]&lt;br /&gt;
&lt;br /&gt;
Team B1 Final Report&lt;br /&gt;
&lt;br /&gt;
Authors: Harry Poppick, Emm Fulk and Scott Smith&lt;br /&gt;
&lt;br /&gt;
Instructors: Fengqi You, David Wegerer&lt;br /&gt;
&lt;br /&gt;
March 13, 2015&lt;br /&gt;
&lt;br /&gt;
=Executive Summary=&lt;br /&gt;
&lt;br /&gt;
The following report outlines the design and analysis of a process converting ethanol to chemical-grade ethylene via catalytic dehydration. This process consumers 100,000 kg/hr of 95 wt% ethanol, 5 wt% water feedstock and produces 53,000 kg/hr of 99.7 wt% chemical-grade ethylene. The ethanol feed passes through two fixed-bed reactors, each packed with an aluminum oxide catalyst, and the resulting ethylene is purified by two flash tanks and by absorption with water. The process was modeled using Aspen HYSYS simulation software to estimate mass and energy flows and equipment sizing requirements. Based on results of this initial simulation, several alternatives are discussed for increasing the process efficiency and profitability. The use of a fluidized bed reactor or a more ethylene-selective catalyst could increase the production of ethylene per ethanol basis. Additionally, several methods of purification to more valuable polymer-grade ethylene are proposed. &lt;br /&gt;
&lt;br /&gt;
The economic feasibility of this process was evaluated using Aspen Economic Analyzer with the Icarus economics package. Capital cost is approximately $16.4 million total with an operating cost of $465 million per year. The current market prices of the ethanol feed and ethylene sales price are $1.44/gallon and $1350/metric ton respectively. The cost of feed ethanol, process utilities and miscellaneous operational costs total to about $427 million/year. At full operation, revenue at current prices would be approximately $640 million per year. The predicted 10-year net present value of the process is approximately $391 million with an IRR of 79% and a payback period of 2.7 years. A sensitivity analysis indicates that the process is most sensitive to feed prices, product prices and operation cost.&lt;br /&gt;
&lt;br /&gt;
Several recommendations are made for both cost reduction and profit maximization, including the design of a heat exchanger network and the optimization of fired heaters that require high capital investment and large amounts of fuel. A safety review of the process is recommended, as well as the minimization of flue gas effluent and wastewater. It is also suggested that the construction of an onsite wastewater treatment center be considered. Overall, the initial analysis indicates this to be a profitable process and it is recommended the project move forward.&lt;br /&gt;
&lt;br /&gt;
=Introduction=&lt;br /&gt;
&lt;br /&gt;
Ethylene is a critical chemical precursor to a number of different industrial products. It is often derived from petroleum sources and polymerized to polyethylene, one of the most ubiquitous plastics today. (American Chemistry Council, 2013) Recently there has been a significant effort to develop production pathways utilizing biologically-derived feedstocks, such as corn or cellulosic ethanol, rather than traditional fossil-fuel sources. Ethylene can be produced from bioethanol via catalytic dehydration over an aluminum oxide catalyst. The proposed process converts 100,000 kg/hr of 95 wt% ethanol, 5% water feed to 53,000 kg/hr of 99.7% chemical-grade ethylene when operating at full capacity. This process was found to be economically viable with a 10-year net present value (NPV) of $131 million (2014 USD) and a payback period of approximately 2.7 years. This memo will detail the proposed process, as well as outline potential alternatives and economic viability of the project.&lt;br /&gt;
&lt;br /&gt;
=Technical Approach=&lt;br /&gt;
&lt;br /&gt;
Many bioethanol plants are located in the Midwest where large amounts of feedstock crops, such as corn, are grown. As such, this plant will be located in Story county, Iowa, near a large-scale bioethanol production plant. (DuPont Nevada Site, 2012) It is assumed that the supply of bioethanol is consistent and readily available. It is also assumed that other reagents - namely, the aluminum oxide catalyst, heater fuel, utility water and freon refrigerant - are readily available, and that wastewater treatment facilities are located near enough to facilitate the off-site treatment of wastewater. Plant capacity was based on current mid-sized industrial ethylene plants. (Designing Ethylene Plants, 2014)&lt;br /&gt;
&lt;br /&gt;
HYSYS simulations were performed with the NRTL fluid package and Peng-Robinson vapor model. The NRTL fluid package is an activity coefficient model that is especially useful to model the separations of alcohols in aqueous solutions. (Suppes, 2015) In addition, NRTL uses models of binary pairs of components, much like the Wilson equation, to predict chemical interactions at the molecular level. The NRTL package can thus be easily extended to ternary and higher order chemical systems, making it ideal for this type of simulation. The Peng-Robinson vapor model was selected as it is well-suited to account for the non-idealities of the vapor phase reactions and separations integral to this process. (ASPENtech, 2014)&lt;br /&gt;
&lt;br /&gt;
It was assumed that the feed enters the process at ambient temperature and pressure (25 °C, 1 atm) and at a consistent rate and composition with negligible quantities of impurities. The ethanol feed was assumed to be 95% ethanol and 5% water by mass, which is the commercial standard for industrial ethanol. (190 Proof Ethanol, 2012) Storage vessels for the feed ethanol, waste streams and products are assumed to be located nearby to the process. An initial feed pump compensates for pressure drops through the process and reduces the duty on downstream compressors. (Hadawey, 2015)&lt;br /&gt;
&lt;br /&gt;
Natural gas, assumed to consist of 83% methane, 16% ethane and 1% nitrogen by mass, was supplied to two fired heaters at a flow rate estimated by HYSYS. (Methane, 2015) Air fed to the process to enable combustion was assumed to be 23% oxygen and 77% nitrogen by mass. (Composition of Air, 2015) Air streams were fed at 50% molar excess in order to ensure complete combustion and prevent the formation of carbon monoxide in the heater exhaust. Total flue gases are assumed to be 230,000 kg/hr, or 2.2 million tons annually, and consist of 73.8% nitrogen gas, 10.5% carbon dioxide, 8.2% water vapor, and 7.5% oxygen by mass. The only compound of concern in these emissions is the carbon dioxide, a known greenhouse gas. At the time of this report, the quantities of carbon dioxide emitted by this plant annually are within acceptable EPA specifications. (Summary of the Clean Air Act, 2015)&lt;br /&gt;
&lt;br /&gt;
Due to the difficulty of simulation equilibrium and conversion reactions in a single vessel in HYSYS, these two reaction types were simulated in separate equilibrium reactor and conversion reactor units in series. In addition, while HYSYS indicated that reactor units would output separate vapor and liquid streams, it was assumed that in practice this would take the form of a single, two phase stream between each unit. To account for this, mixers were installed downstream of each reactor to combine the liquid and vapor phases of the reactor effluent. The three consequent reactions considered are as follows:&lt;br /&gt;
[[File:Equation.PNG|300px|center]]&lt;br /&gt;
The optimal reaction temperature was determined to be 400 °C, which promotes the equilibrium reaction of ethanol to ethylene while minimizing byproducts. (Zhang and Yu, 2013) While other byproducts may be produced in this process, these reactions are typically taken to comprise of the bulk of the dehydration reaction. Heat losses over these reactors were assumed to be negligible. (Zhang and Yu, 2013)All major process equipment is assumed to be constructed of high strength carbon steel. (AspenTech, 2012)&lt;br /&gt;
&lt;br /&gt;
The “Sizing Utility” within the Icarus Economic Evaluation module was used to estimate sizes of major equipment based on the process simulation. These values can serve as a benchmark for an initial plant design. Icarus KbaseTM implements a wide variety of mechanical design standards, including ASME and BS5500, in order to calculate accurate equipment sizing. The Icarus sizing module combines equipment prices for standard chemical processing equipment as well as correlations and sizing factors. The advantage of using a software package such as HYSYS to price out individual equipment is that it utilizes up-to-date prices from vendors and distributors when estimating costs. A more in-depth overview of the correlations included in this software can be found in Towler and Sinnott (2009).&lt;br /&gt;
&lt;br /&gt;
=Process Flowsheet=&lt;br /&gt;
[[File:Squarepfd_B1.PNG|thumb|400px|alt=Alt text|Fig 1: PFD of the Proposed Process]]&lt;br /&gt;
&lt;br /&gt;
The following process is based primarily on a 1983 US patent titled “Process for dehydration of a low molecular weight alcohol.” (Barrocas and Baratelli, 1983) The process flow diagram can be seen in Figure 1. A larger version of the PFD is included in Appendix I and the HYSYS simulation setup in Appendix II.&lt;br /&gt;
&lt;br /&gt;
The feed enters the process at a rate of 100,000 kg/hr, a temperature and pressure of a 25 °C and 1 atm and at a composition of 95 wt% ethanol and 5 wt% water.It is initially pressurized to 4335 kPa by centrifugal pump P-101 and subsequently heated to 400 °C by fired heater F-101. The heated and pressurized feed enters fixed bed reactor R-101 and contacts with the aluminum oxide catalyst. At this point it dehydrates to form the product, ethylene, as well as the byproducts water, hydrogen, diethyl ether and acetaldehyde. Fired heater F-102 and reactor R-102 increase the overall conversion of the process. Both fired heaters F-101 and F-102 are fueled with natural gas and fed with excess air. The composition of the reactor train effluent is 54.5 wt% ethylene, 37.1 wt% water, 8.1 wt% unreacted ethanol and trace amounts of diethyl ether, acetaldehyde, and hydrogen contaminants. &lt;br /&gt;
&lt;br /&gt;
The pressure of the reactor train effluent is increased to 4500 kPa by compressor K-102 and the temperature decreased to 100 °C by exchange with cold water in heat exchanger E-201. The stream then expands and flashes in flash vessel FL-201, which separates out 82.3% of the unreacted ethanol, 96.6% of the water and virtually all of the acetaldehyde contaminant in the bottoms while sending the ethylene-rich vapor phase out of the top. The top product of FL-202 is compressed to 3500 kPA by K-202 and cooled to 0.0 °C by a freon refrigerant in E-202. At this point the stream is flashed for a second time in vessel FL-202 to remove additional impurities. The top outlet stream consists of 99.5 wt% ethylene, which is fed to the bottom of a 10-tray absorption column that removes a fraction of the residual diethyl ether as well as the remainder of the unreacted ethanol. A stream of absorbent water is fed to the top of the column at 10,000 kg/hr.  The product exits the top of the column at a rate of 54,600 kg/hr and has a purity of 99.7% ethylene. Diethyl ether makes up 0.2% of the remaining product stream and is the primary contaminant. Trace amounts of residual water and hydrogen are also present.&lt;br /&gt;
&lt;br /&gt;
Full tables of material and energy streams can be found in Appendices III and IV respectively. &lt;br /&gt;
&lt;br /&gt;
==Process Alternatives==&lt;br /&gt;
===Reactor Alternatives===&lt;br /&gt;
Two fixed bed reactors, alternating with fired heaters, are used in the dehydration reaction of ethanol to ethylene. However, a fluidized bed reactor can offer better mixing and temperature control than a fixed bed reactor and thus provide the highest possible conversion of ethanol with the greatest selectivity to ethylene. (Tsao and Zasloff, 1979) Fluidized bed reactors also provide a lower rate of catalyst coking and byproduct formation, minimizing separation and catalyst regeneration costs. (Morschbacker, 2009) The major downside of fluidized bed reactors is that few large-scale processes have been built since the technology was developed in the late 1970s. (Tsao and Zasloff, 1979; Morschbacker, 2009) Although implementation of fluidized bed reactors could potentially increase the purity of the ethylene product and/or decrease costs, a small scale pilot process would need to be built and tested before it would be possible to develop an industrial-scale facility.&lt;br /&gt;
&lt;br /&gt;
===Catalyst Alternatives===&lt;br /&gt;
Aluminum oxide, specifically gamma alumina, is the most industrially-common catalyst and has been historically used due to its low cost and high stability. (Tsao and Zasloff, 1979; Fan and Dai, n.d.) Recent improvements in selectivity and catalyst stability of activated alumina have been achieved by incorporating titanium oxide into the catalyst, although this increases reaction temperature by approximately 50 °C and decreases catalyst lifespan. (Chen and Li, et. al. 2007) There is also significant ongoing research into HZSM-5 zeolite and heteropolyacids, which are being explored as potential alternatives to alumina oxide. A nanoscale HZSM-5 zeolite catalyst has been shown to operate at the relatively low temperature of 200-300°C, with a 100% ethanol conversion and 99.7% selectivity to ethylene. Initial research has also indicated that it maintains greater than 98% selectivity for 630 operational hours. (Fan and Dai, n.d.) However, the current low cost and ready availability of unmodified alumina oxide makes it a better choice for a process of this scale.&lt;br /&gt;
&lt;br /&gt;
===Purification Alternatives===&lt;br /&gt;
As specified in this process, the reactor effluent is purified by two flash drums and absorption with water to produce chemical-grade ethylene. If chemical-grade ethylene is indeed the desired product, other purification options include caustic washing of the reactor effluent and water removal in a desiccant drying bed. (Morschbacker, 2009) While this purification train is relatively simple and does not require harsh chemical reagents, polymer grade ethylene is more commercially valuable and the additional cost of removing water and diethyl ether contaminants may be justified by increased revenue. Cryogenic distillation was initially simulated to produce polymer-grade ethylene, but utility requirements were found to render this separation economically unviable. (Barrocas and Baratelli, 1983) Further research and optimization may find this purification strategy to be a more valid process. Alternatively, the addition of a cryogenic turboexpander or the use of alternative adsorbents may increase product purity to polymer grade. (Jumonville, 2010) Initial HYSYS simulations indicate that these operations may be feasible with further refinement.&lt;br /&gt;
&lt;br /&gt;
===Wastewater Treatment===&lt;br /&gt;
Due to the large volume of wastewater produced, building an on-site wastewater treatment facility may prove to be more economical than paying for third-party wastewater treatment. Flash vessel FL-201 produces 44,600 L/hr of wastewater contaminated with 18.7 vol% ethanol and 0.6 vol% acetaldehyde, while FL-202 produces 2940 L/hr of an aqueous waste consisting of 56.8 vol% ethanol, 42.0 vol% water and 0.9 vol% diethyl ether. The absorption column produces approximately 10,200 liters/hr of wastewater contaminated with 1.2 vol% ethanol, 0.2% diethyl ether and 0.2% acetaldehyde. Utilizing distillation to separate these streams into clean water and volatile organic waste could ultimately reduce the quantity of waste that requires disposal and reduce the overall costs of the process. &lt;br /&gt;
&lt;br /&gt;
==Process Equipment==&lt;br /&gt;
Relevant sizing information for each unit operation, estimated by the method described in the “Technical Approach,” can be found in Appendix V. Equipment and piping is assumed to be constructed of carbon steel. It should be noted that the two fired heaters are proportionately large enough to heat the entirety of the process stream and are thus larger than standard equipment.&lt;br /&gt;
&lt;br /&gt;
=Economic Analysis=&lt;br /&gt;
[[File:NPV_B1.png|400px|thumb|Fig 2. Projected Cash Flow]]&lt;br /&gt;
[[File:sensitivityanalysis_B1.png|400px|thumb| Fig 3. Results of the Sensitivity Analysis on 10 year NPV]]&lt;br /&gt;
&lt;br /&gt;
==Economics Overview==&lt;br /&gt;
All final values are normalized to June 2014 USD by CEPCI scaling. It is assumed that all products produced are sold at current market prices.&lt;br /&gt;
&lt;br /&gt;
The Aspen Economic Evaluation module within HYSYS v8.0 was used to estimate capital and operating costs for a 10-year plant life span with a construction start date of April 2015. The price of the 95% ethanol feed stream was estimated at $1.44 per gallon,  while the chemical grade ethylene produced is currently selling for approximately $1350 per metric ton. (Today in Energy, 2015; Weddle, 2014)  Mapping and sizing calculations were performed by the economics module and a preliminary economic evaluation was completed. Equipment sizes, also estimated by HYSYS, were reviewed to ensure that height, diameter, and volume specifications were within realistic ranges. &lt;br /&gt;
&lt;br /&gt;
The process was ideally projected to operate 360 days per year with a start-up time of one year. In addition, the tax rate was approximated at 40%, an interest rate at 20%, and a salvage value of 20%. Escalation percentages were compounded yearly for the product, raw material, and operating costs.  The total capital cost for this process is approximately $16.4 million, which includes all equipment and piping described in the process. The most expensive equipment used in this process are the two fired heaters F-101 and F-102, which have an exceptionally large heat exchange area to adequately heat the feed. Standard heaters may not suffice and additional costs may be incurred for the raw materials and manufacture of this equipment. Including a feed preheater or additional fired heaters may reduce this cost in subsequent design iterations.&lt;br /&gt;
&lt;br /&gt;
The total operating cost is approximately $465 million per year, about $427 million of which is the cost of the ethanol feed and natural gas for the two fired heaters. An additional $1.73 million per year is used for utilities including the cooling water and refrigerant. The labor and maintenance costs of this industrial process were also accounted for within the simulation’s economic analysis. The HYSYS simulation software, in conjunction with the Icarus economic analyzer, estimated there should be 5 operators per 8 hour shift with a cost per operator of $20 per hour. This results in a total operating labor cost of approximately $880,000 per year. In addition, the process will require one supervisor per shift with an hourly rate of $35 for total supervisor salaries of $307,000 per year. Finally, a fixed maintenance rate was estimated at $205,000 per 8000 hours of operation for a total cost of $225,000 per year.&lt;br /&gt;
&lt;br /&gt;
Total product sales are roughly $640 million per year at full operation. The estimated income for this process is thus approximately $175 million per year. After ten years, the plant is projected to have a net present value (NPV) of $391 million and an internal rate of return of approximately 79%. In addition the payout period for the initial investment is estimated to be about 2.7 years. Figure 2 shows the projected cash flow for the project.&lt;br /&gt;
&lt;br /&gt;
==Sensitivity Analysis==&lt;br /&gt;
A sensitivity analysis was performed to investigate the effects of fluctuating capital costs, operating costs, raw materials, utility costs and ethylene sales price on the 10-year net present value (NPV) of the project. This analysis was performed by scaling these cost factors according to typical ranges given in Towler and Sinnott and calculating the adjusting the NPV accordingly. The results, illustrated in Figure 3, indicate that the project value is most sensitive to product sales, raw materials costs, and operating costs. Ethylene and ethanol prices are market-determined and cannot be controlled for in the process design, so further optimization should be focused on minimizing the operations cost of the process. (Today in Energy, 2015; Weddle, 2014) However, in feed and product prices do still have a profound effect on profitability and feasibility. A more rigorous market analysis will better inform the profitability outlook.&lt;br /&gt;
&lt;br /&gt;
=Conclusions/Recommendations=&lt;br /&gt;
&lt;br /&gt;
The proposed process produces approximately 460,000 metric tons of 99.7 wt% ethylene annually, with a 10-year net present value of $131 million. If current economic conditions hold, it is recommended that this project proceed to implementation following further design improvements and optimization.&lt;br /&gt;
&lt;br /&gt;
Future design iterations should focus on process optimization, particularly in minimizing operating costs as prescribed by the results of the sensitivity analysis. The development of a heat-exchanger network, potentially with Aspen Energy Analyzer, is one option for decreasing utility requirements and increasing the efficiency of the process overall. Optimization of the fired heaters could also result in decreased operational costs. Although overall profitability is less sensitive to capital costs, reviewing and adjusting equipment sizing would also improve the economic outlook. In particular, exploring alternative heating strategies at the beginning of the process could significantly decrease capital costs. Although there are not any particularly dangerous chemicals utilized in the process, an overall process review should also consider potential failure modes to minimize the safety risk to plant workers and nearby residents.&lt;br /&gt;
&lt;br /&gt;
In addition to economic and safety considerations, harmful emissions and waste streams should be minimized both to bring down the cost of treatment and to decrease environmental effects. The two fired heaters consume a large amount of natural gas per year, emitting about 200,000 tons of CO2 annually, and account for more than half of the capital cost of the process. Although no known toxic gases are produced, carbon capture or other emissions-reduction methods should be considered. Additionally, enough wastewater is produced by this process that building an onsite wastewater treatment center should be considered. This could not only decrease operating costs by eliminating the need for an external contract but also give the plant more control over the final purity of the treated wastewater.&lt;br /&gt;
&lt;br /&gt;
Finally, the current model assumes that all ethylene produced will be sold at a current prices and price or product sales will not be affected by economic variability. A more detailed study of the chemical-grade ethylene market, as well as a more thorough understanding of sales and distribution logistics, would increase the surety of a profitable process.&lt;br /&gt;
&lt;br /&gt;
In summary, the proposed process yields chemical grade ethylene via the catalytic dehydration of ethanol. A 100,000 kg/hr of 95 wt% ethanol, 5% water feed is converted to 53,000 kg/hr of 99.7% chemical-grade ethylene. After 10 years of operation, including a one-year startup time, the process has an NPV of $391 million with an IRR of 79% and a payback period of 2.7 years.&lt;br /&gt;
Pending further optimization, this process was determined to be viable and it is recommended for the project to move forward.&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
&lt;br /&gt;
American Chemistry Council. Production of chemicals and plastics in the U.S. in 2013, by type (in 1,000 metric tons). In Statista - The Statistics Portal. August 2014. Available at http://www.statista.com/statistics/299725/total-us-plastics-and-chemicals-shipments-by-type/, Accessed January 15, 2015. – Relative proportions of plastics production.&lt;br /&gt;
&lt;br /&gt;
ASPENtech. Appendix A - Property Methods and Calculations. Simulation Basics; A-3 - A-26. 2014.&lt;br /&gt;
&lt;br /&gt;
AspenTech. Aspen HYSYS Help File v8.0. Aspen Technology, Inc. 2012. - Aspen HYSYS help file used for troubleshooting and assistance on economic analysis.&lt;br /&gt;
&lt;br /&gt;
Barrocas H, Baratelli F, inventors; Petroleo Brasileiro S.A., assignee. Process for dehydration of a low molecular weight alcohol. US patent 4,396,789 A. August 2, 1983. - Primary background for process design.&lt;br /&gt;
&lt;br /&gt;
Chen G, Li S, Jiao F, Yuan Q. Catalytic dehydration of bioethanol to ethylene over TiO2/γ-Al2O3 catalysts in microchannel reactors. Catal. Today 2007, 125, 111–119. - Paper introducing research on modified alumina catalyst for ethanol dehydration.&lt;br /&gt;
&lt;br /&gt;
Composition of Air [Internet]. Engineering Toolbox; [cited 13 Mar. 2015]. Available from: http://www.engineeringtoolbox.com/air-composition-d_212.html. -- Composition of air.&lt;br /&gt;
&lt;br /&gt;
Designing Ethylene Plants. Ethylene [Internet]. Technip; 2014 [cited 13 Mar. 2015]. Available from: http://www.technip.com/en/our-business/onshore/ethylene -- Plant size ranges.&lt;br /&gt;
&lt;br /&gt;
DuPont Nevada Site Cellulosic Ethanol Facility [Internet]. DuPont Chemical; c2012-2015 [cited 11 Mar. 2015]. Available from: http://biofuels.dupont.com/cellulosic-ethanol/nevada-site-ce-facility/. -- Information on ethanol production in Iowa.&lt;br /&gt;
&lt;br /&gt;
Fan D, Dai DJ, Wu HS. Ethylene Formation by Catalytic Dehydration of Ethanol with Industrial Considerations. Materials. 6, 101-115. doi: 10.3390/ma6010101. - Comparison of types of catalysts used in the dehydration of ethanol and current research into new catalysts.&lt;br /&gt;
&lt;br /&gt;
Hadawey A, Ge Y, Tassou TSA. Energy Savings Through Liquid Pressure Amplification In A Dairy Plant Refrigeration System. The Centre for Energy and Built Environment Research [cited 13 Mar. 2015].&lt;br /&gt;
&lt;br /&gt;
Jumonville, J. Tutorial on Cryogenic Turboexpanders. Proceedings of the Thirty-Ninth Turbomachinery Symposium; 2010 Oct 4-7; Houston, TX. Houston: Texas A&amp;amp;M University; 2010. -- Use of turboexpander for cryogenic separations&lt;br /&gt;
&lt;br /&gt;
Methane (Chemical Compound). 2015. Encyclopædia Britannica Online. [cited 13 Mar. 2015] Available from: http://www.britannica.com/EBchecked/topic/378264/methane -- Composition of Methane&lt;br /&gt;
&lt;br /&gt;
Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews. 2009; 49:79-84. – Overview of bioethanol dehydration process development.&lt;br /&gt;
&lt;br /&gt;
Summary of the Clean Air Act, 2015. United States Environmental Protection Agency. [cited 13 Mar. 2015] Available from: http://www2.epa.gov/laws-regulations/summary-clean-air-act -- Emissions requirements of chemical plants.&lt;br /&gt;
&lt;br /&gt;
Suppes GJ. Selecting Thermodynamic Models for Process Simulation of Organic VLE and LLE Systems. The University of Missouri-Columbia, Dept of Chemical Engineering. [cited 13 Mar. 2015]. -- Use of NRTL in alcohol separations.&lt;br /&gt;
&lt;br /&gt;
Today in Energy - Daily Prices. US Energy Information Administration website. http://www.eia.gov/todayinenergy/prices.cfm. Accessed March 3rd 2015. - Bulk market price for 95% ethanol.&lt;br /&gt;
&lt;br /&gt;
Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013. -- General Reference Book&lt;br /&gt;
&lt;br /&gt;
Tsao U, Zasloff HB, inventors; The Lummus Company, assignee. Production of ethylene from ethanol. US patent 4,134,926. January 16, 1979. – Patent for catalytic dehydration of ethylene in a fluidized bed reactor.&lt;br /&gt;
&lt;br /&gt;
Weddle, N. ICIS Pricing: Ethylene (Europe). Reed Business Limited. January 10 2014. - Bulk market price for chemical grade ethylene.&lt;br /&gt;
&lt;br /&gt;
Zhang M, Yu Y. Dehydration of Ethanol to Ethylene. Industrial Engineering and Chemical Research. 2013; 52:9505-9514. – Technical information on ethanol to ethylene conversion via dehydration.&lt;br /&gt;
&lt;br /&gt;
190 Proof Ethanol: Technical Data Sheet [Internet]. Decon Labs Inc; 2012 [cited 13 Mar. 2015]. Available from: http://www.deconlabs.com/tds/ETHANOL%20190%20%20PROOF.pdf -- Information regarding 95% ethanol&lt;br /&gt;
&lt;br /&gt;
=Appendix I - Process Flow Diagram=&lt;br /&gt;
[[File:PFD B1.JPG|1200px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix II - HYSYS Simulation=&lt;br /&gt;
[[File:HYSYS_B1.PNG|center|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix III - Material Streams=&lt;br /&gt;
[[File:Streams_B1.png|1200px]]&lt;br /&gt;
&lt;br /&gt;
=Appendix IV - Energy Table=&lt;br /&gt;
[[File:Energy_B1.png|600px|center]]&lt;br /&gt;
&lt;br /&gt;
[[File:Utilities.PNG|600px|center]]&lt;br /&gt;
&lt;br /&gt;
=Appendix V - Equipment Sizing=&lt;br /&gt;
[[File:Equipment sizes.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Appendix VI - Economics=&lt;br /&gt;
[[File:Econsummary_B1.png|center]] &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Capcost_B1.png|center]] &amp;lt;br&amp;gt;&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3052</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3052"/>
		<updated>2015-03-07T16:36:24Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler and Sinnott, 2013). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge (Tolwer et al, 1997).]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer and Sinnott, 2013). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer and Sinnott, 2013).]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column (Belter et al., 1998).]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute (Belter et al., 1998). This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3051</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3051"/>
		<updated>2015-03-07T16:35:46Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler and Sinnott, 2013). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge (Tolwer et al, 1997).]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer and Sinnott, 2013). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer and Sinnott, 2013).]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column (Belter et al., 1998).]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute (Belter et al., 1998). This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3050</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3050"/>
		<updated>2015-03-07T16:34:00Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler et al., 1997). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge (Tolwer et al, 1997).]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer et al, 1997). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer et al, 1997).]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column (Belter et al., 1998).]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute (Belter et al., 1998). This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3049</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3049"/>
		<updated>2015-03-07T16:32:52Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Isolation */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler et al., 1997). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge (Tolwer et al, 1997).]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer et al, 1997). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer et al, 1997).]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3048</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3048"/>
		<updated>2015-03-07T16:32:14Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Centrifugation */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler et al., 1997). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge (Tolwer et al, 1997).]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer et al, 1997). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer et al, 1997).]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3047</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3047"/>
		<updated>2015-03-07T16:31:35Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Sedimentation */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler et al., 1997). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult (Belter et al., 1998).&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [(Tolwer et al, 1997)]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer et al, 1997). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer et al, 1997)]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3046</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3046"/>
		<updated>2015-03-07T16:31:01Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass (Towler et al., 1997). &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [(Tolwer et al, 1997)]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth (Tolwer et al, 1997). [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge (Tolwer et al, 1997)]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3045</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3045"/>
		<updated>2015-03-07T16:29:01Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Importance */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification (Belter et al., 1998). This section will provide examples of unit operations in each step. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform (Harrison et al., 2003).&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3044</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3044"/>
		<updated>2015-03-07T16:25:18Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* References */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.&lt;br /&gt;
# Biegler LT, Grossmann IE, Westerberg AW. Systematic Methods of Chemical Process Design. Upper Saddle River: Prentice Hall; 1997.&lt;br /&gt;
# Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison RG, Todd P, Rudge SR, Petrides, DP. Bioseparations Science and Engineering. New York: Oxford University Press; 2003.&lt;br /&gt;
# Belter PA, Cussler EL, Hu WS. Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley; 1998.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3041</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3041"/>
		<updated>2015-03-02T06:00:35Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer is manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3040</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3040"/>
		<updated>2015-03-02T05:59:45Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited  a resin phase before the column is flushed with an elution solvent specific that results in solutes eluted in bands, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3039</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3039"/>
		<updated>2015-03-02T05:58:47Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Bioseparations */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
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The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
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====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The volumetric flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
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====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3037</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3037"/>
		<updated>2015-03-02T05:57:09Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Centrifugation */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle density, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3036</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3036"/>
		<updated>2015-03-02T05:56:37Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Centrifugation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be thought of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3035</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3035"/>
		<updated>2015-03-02T05:55:49Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Centrifugation */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are some of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3033</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3033"/>
		<updated>2015-03-02T05:55:18Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Sedimentation */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive, requires little energy and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3032</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3032"/>
		<updated>2015-03-02T05:54:51Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the solid biomass [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3031</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3031"/>
		<updated>2015-03-02T05:54:14Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution in a homogenizer. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
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The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
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====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3026</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3026"/>
		<updated>2015-03-02T05:49:50Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Importance */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14]. Ultimately, the choice of separation process and unit operations will depend on the specific process and product. The descriptions below are examples of the most common bioseparation operations within the general platform.&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3025</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3025"/>
		<updated>2015-03-02T05:46:01Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged either positively (in cation exchange) or negatively (in anion exchange) and will bind to different solutes depending on their charge. The pH of the elution buffer is change to force a specific solute to wash out, depending on whether the pH of the buffer is above or below the isoelectric point of the solute [14]. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3023</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3023"/>
		<updated>2015-03-02T05:29:01Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
====Sedimentation====&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
====Centrifugation====&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)}{9\mu}}g&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
====Example: Centrifugation Scale-up====&lt;br /&gt;
&lt;br /&gt;
You are trying to separate a cell of radius 0.4 &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;m with a density of 1.05 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; from broth of mostly water (density of 1 g/cm&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; and viscosity of 0.01 g/cm s). The sigma factor of the centrifuge you are using is 1 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. A] What volumetric flow rate should you use? B] If you want to scale up the process to a centrifuge with &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; = 3 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, what flow rate would you use in the larger centrifuge?&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
A] Using the equation for &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt;, and being mindful of units, the sedimentation velocity equals 1.74 x 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt; cm/s. The flow rate, then, equals&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(1.74 x 10^-6)(1,000,000) = 1.74 cm^3/s = 0.104 L/min&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
B] Keeping in mind that for the same process, &amp;lt;math&amp;gt;v_g1 = v_g2,&amp;lt;/math&amp;gt; and rearranging the sigma factor equality, the new flow rate is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q_2 = {\frac{\Sigma_2 x Q_1}{\Sigma_1}} = {\frac{(3 x 10^6)(0.104)}{1 x 10^6}} = 0.313  L/min &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged and will bind to different solutes depending on the pH of the elution buffer. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3010</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=3010"/>
		<updated>2015-03-02T05:11:52Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Importance */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers[8]. &lt;br /&gt;
&lt;br /&gt;
==== Spray Tower vs Ejector Scrubber ====&lt;br /&gt;
&lt;br /&gt;
In both &#039;&#039;&#039;spray tower&#039;&#039;&#039; and the &#039;&#039;&#039;ejector scrubber&#039;&#039;&#039; nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|center|Figure 3. Ejector Scrubber (US EPA, 2006)]]&lt;br /&gt;
&#039;&#039;&#039;Spray towers&#039;&#039;&#039; on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a ejector scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the ejector scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown below in Figure 4[8].&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|center|Figure 4. Spray Tower Absorber (US EPA, 2006)]]&lt;br /&gt;
&lt;br /&gt;
==== Tower Type Absorption Apparatus ====&lt;br /&gt;
&#039;&#039;&#039;Packed column absorbers&#039;&#039;&#039; and &#039;&#039;&#039;tray column absorbers&#039;&#039;&#039; have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in the respective distillation columns. &lt;br /&gt;
&lt;br /&gt;
For a &#039;&#039;&#039;trayed column&#039;&#039;&#039; the plate efficiency can be calculated using O&#039;Connell&#039;s Correlation which invovles the Henry&#039;s Law constant, total system pressure, and solvent viscosity at the operating temperature[2].&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;x=0.062*\frac{\rho_s*P}{\mu_s*H*M_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the tray efficiency,&lt;br /&gt;
&amp;lt;math&amp;gt;\rho_s&amp;lt;/math&amp;gt; is the density of the solvent in &amp;lt;math&amp;gt;kg/m^3&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure of the system in &amp;lt;math&amp;gt;N/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_s&amp;lt;/math&amp;gt; is the solvent&#039;s viscosity in &amp;lt;math&amp;gt;mNs/m^2&amp;lt;/math&amp;gt;,&lt;br /&gt;
&amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the Henry Law constant in &amp;lt;math&amp;gt;1/(Nm^2*(mol fraction))&amp;lt;/math&amp;gt;,&lt;br /&gt;
and &amp;lt;math&amp;gt;M_s&amp;lt;/math&amp;gt; is the molecular weight of the solvent.&lt;br /&gt;
&lt;br /&gt;
A packed towers height can be determined using the equations below when concentration of solute is below 10% so that the assumption that the flow of gas and liquid will be essentially constant throughout the column holds[2]. The height of packing &amp;lt;math&amp;gt;Z&amp;lt;/math&amp;gt; is given by the following equation:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=\frac{L_m}{K_G*a*P}*\int\limits_{y_2}^{y_1} \frac{dy}{y-y_e}\,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the total pressure, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the interfacial surface area per unit volume, &amp;lt;math&amp;gt;y_1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;y_2&amp;lt;/math&amp;gt; are the mol fractions of the solute in the gas stream at the bottom and top of the column respectively, &amp;lt;math&amp;gt;G_m&amp;lt;/math&amp;gt; is the molar gas flow rate per unit cross-sectional area, and &amp;lt;math&amp;gt;y_e&amp;lt;/math&amp;gt; is the mole fraction of solute in the gas that would be in equilibrium with the liquid concentration. &lt;br /&gt;
&lt;br /&gt;
The first half of the equation before the integral can be called the height of an overall gas-phase transfer unit &amp;lt;math&amp;gt;H_G&amp;lt;/math&amp;gt; and the second part of the equation is the number of overall gas-phase transfer units or &amp;lt;math&amp;gt;N_G&amp;lt;/math&amp;gt;. Using these definitions the above equation can be simplified to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Z=H_G*N_G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These equations assist in sizing an absorption column[2]. &lt;br /&gt;
&lt;br /&gt;
==== Film Absorber ====&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Figure 5 below shows the typical setup of an amine plant. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
[[File:AmineTreating.png|thumb|400px|center|Figure 5. Amine Gas Treating Plant Schematic]]&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13,14].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 6: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 7: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 8. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 8: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged and will bind to different solutes depending on the pH of the elution buffer. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
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		<title>Separation processes</title>
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
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Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
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Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
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==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
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Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
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==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
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==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
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Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
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[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
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===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
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[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
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[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
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====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
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====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
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===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
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Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
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An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
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&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
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Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
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&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
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===Distillation Applications===&lt;br /&gt;
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Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
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Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
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===Example Case: Ideal Distillation===&lt;br /&gt;
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Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
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Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
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&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
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==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
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The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
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In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
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===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
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The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
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===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
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Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 7. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 7: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged and will bind to different solutes depending on the pH of the elution buffer. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;br /&gt;
# Belter, P.A., Cussler, E.L., Hu, W.-S, (1998). Bioseparations: Downstream Processing for BIotechnology. New York: John Wiley.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2997</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2997"/>
		<updated>2015-03-02T05:00:54Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 7. Different bands are eluted at different times depending on the size of the solute (as in gel filtration chromatography) or the affinity of the solute for the resin (as in ion exchange chromatography). [[File:chromatography.png|frame|center|Fig. 7: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
In gel filtration chromatography, small molecules are &amp;quot;trapped&#039; by the porous resin and take longer to flow through the column. Larger products will elute first, and this operation is often used when there is a distinct difference in size between the desired product and other solutes. In ion-exchange chromatography, the resin beads are charged and will bind to different solutes depending on the pH of the elution buffer. This is especially useful for the separation of protein product (including antibodies), nucleic acids, and other charged molecules. When the solutes have sufficiently different isoelectric points, the pH of the buffer manipulated to affect the solute charge and force the product to elute while the solute remains preferentially bound to the resin, or vice versa [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2987</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2987"/>
		<updated>2015-03-02T04:50:23Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Bioseparations */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
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==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 7.  [[File:chromatography.png|frame|center|Fig. 7: Illustration of product bands in an elution chromatography column [14]]]&lt;br /&gt;
&lt;br /&gt;
 [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]]&lt;br /&gt;
Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
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	<entry>
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		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2981</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2981"/>
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		<summary type="html">&lt;p&gt;Emm: /* Product Purification */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for food-grade and medical products can be extensive, as sterility and high purity are essential. Purification in fuel-producing processes may be less extensive, depending on the process. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Chromatography&amp;lt;/i&amp;gt; is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the substances in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific, as shown in Figure 6. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
 Ion exchange chromatography is a commonly-used &lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2969</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2969"/>
		<updated>2015-03-02T04:25:37Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Sedimentation&amp;lt;/b&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;b&amp;gt;Centrifugation&amp;lt;/b&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;i&amp;gt; Disk-stack centrifuges&amp;lt;/i&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;i&amp;gt;Tubular bowl centrifuges&amp;lt;/i&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2967</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2967"/>
		<updated>2015-03-02T04:23:30Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;b&amp;gt;Tubular bowl centrifuges&amp;lt;/b&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The sedimentation velocity can be calculated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_g={\frac{2a^2(\rho-\rho_0)g}{9\mu}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;v_g&amp;lt;/math&amp;gt; is the sedimentation velocity, &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; is the cell or biomass particle diameter, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the particle, &amp;lt;math&amp;gt;\rho_0&amp;lt;/math&amp;gt; is the fluid density, and &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; is the fluid viscosity. The fluid flow &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; can be estimated by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Q=(v_g)(\Sigma)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2936</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2936"/>
		<updated>2015-03-02T04:05:27Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Product Isolation */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;b&amp;gt;Tubular bowl centrifuges&amp;lt;/b&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2,&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. The exact separations used depend on the nature of the product and the scale of the process. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
These processes are nearly identical to their non-biological counterparts, and their description is left to other sections.&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2926</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2926"/>
		<updated>2015-03-02T03:59:46Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] &amp;lt;b&amp;gt;Tubular bowl centrifuges&amp;lt;/b&amp;gt; are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2,&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2924</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2924"/>
		<updated>2015-03-02T03:58:00Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for processes where a biomass cake is desired. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2,&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2923</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2923"/>
		<updated>2015-03-02T03:57:29Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation are the most common, although filtration is sometimes also used for small volume processes. Both methods utilize density differences to separate the product from the homogenous solution [2]. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2,&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2920</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2920"/>
		<updated>2015-03-02T03:52:59Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by &amp;lt;i&amp;gt;sigma analysis&amp;lt;/i&amp;gt;, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is dependent on the inner and outer radius of the centrifuge, the angular velocity, and the sedimentation velocity of the solid particles being separated. It can be through of as the characteristic cross-sectional area with units of [length]&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;. The equality &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2,&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2896</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2896"/>
		<updated>2015-03-02T03:32:58Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png|frame|center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png|frame|center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 through the equality&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2894</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2894"/>
		<updated>2015-03-02T03:31:29Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: Disk_stack_centrifuge_towler.png |center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2]. [[File: tubular bowl centrifuge towler.png |center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] &lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 through the equality&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2891</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2891"/>
		<updated>2015-03-02T03:30:16Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: tubular bowl centrifuge towler.png |center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to estimate equivalent flow rates between a small-scale centrifuge 1 and larger centrifuge 2 through the equality&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;Sigma&amp;lt;/math&amp;gt; is the sigma factor for each centrifuge and &amp;lt;math&amp;gt;Q&amp;lt;/math&amp;gt; is the volumetric flow rate [13].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2877</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2877"/>
		<updated>2015-03-02T03:05:38Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: tubular bowl centrifuge towler.png |center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to obtain an initial estimate of the capacity of a large centrifuge by the equality&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2875</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2875"/>
		<updated>2015-03-02T03:05:12Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |center|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: tubular bowl centrifuge towler.png |center|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to obtain an initial estimate of the capacity of a large centrifuge by the equality&lt;br /&gt;
&amp;lt;math&amp;gt;{\frac{\Sigma_1}{\Sigma_2}}={\frac{Q_1}{Q_2}}&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
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		<title>Separation processes</title>
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Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
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Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
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Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
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==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
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Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
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[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
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==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
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&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
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==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
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Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
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[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
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===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
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[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
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[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
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====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
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====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
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===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
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Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
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An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
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&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
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Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
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&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
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===Distillation Applications===&lt;br /&gt;
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Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
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Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
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===Example Case: Ideal Distillation===&lt;br /&gt;
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Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
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Solving this system of equations:&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
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At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
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&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
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So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
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==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
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The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
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&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
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where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
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In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
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===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
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[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
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Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
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The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
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===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
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Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
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==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
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The stripping factor of component i is&lt;br /&gt;
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&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
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An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
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==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
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Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
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===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
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The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
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&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
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Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |frame|Fig. 5: Diagram of a disk-stack centrifuge [2]]] Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: tubular bowl centrifuge towler.png |frame|Fig. 6: Diagram of a tubular bowl centrifuge centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to obtain an initial estimate of the capacity of a large centrifuge by the equality&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2869</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2869"/>
		<updated>2015-03-02T02:57:53Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |frame|Fig. 4: Diagram of a disk-stack centrifuge [2]]] Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. [[File: tubular bowl centrifuge towler.png |frame|Fig. 5: Diagram of a tubular bowl centrifuge centrifuge [2]]] Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to obtain an initial estimate of the capacity of a large centrifuge by the equality&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2868</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2868"/>
		<updated>2015-03-02T02:56:58Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&lt;div&gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |frame|Fig. 4: Diagram of a disk-stack centrifuge [2]]]&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. &lt;br /&gt;
&lt;br /&gt;
[[File: tubular bowl centrifuge towler.png |frame|Fig. 5: Diagram of a tubular bowl centrifuge centrifuge [2]]]&lt;br /&gt;
Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
Centrifugation scale-up is made easier by sigma analysis, which allows for the estimation of appropriate feed rates for different size centrifuges. The sigma factor is a characterization describing the equivalent cross-sectional area of each centrifuge. It can be an easy way to obtain an initial estimate of the capacity of a large centrifuge by the equality&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
	</entry>
	<entry>
		<id>https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2866</id>
		<title>Separation processes</title>
		<link rel="alternate" type="text/html" href="https://design.cbe.cornell.edu/index.php?title=Separation_processes&amp;diff=2866"/>
		<updated>2015-03-02T02:56:19Z</updated>

		<summary type="html">&lt;p&gt;Emm: /* Biomass Separations */&lt;/p&gt;
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&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Authors: Nick Pinkerton,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Karen Schmidt,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; James Xamplas,&amp;lt;sup&amp;gt; [2014] &amp;lt;/sup&amp;gt; Emm Fulk,&amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt; and Erik Zuehlke &amp;lt;sup&amp;gt; [2015] &amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Stewards: David Chen, Jian Gong, and Fengqi You &lt;br /&gt;
&lt;br /&gt;
Date Presented: February 9, 2014  /Date Revised: February 1, 2014&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Introduction==&lt;br /&gt;
Essentially all chemical processes require the presence of a separation stage. Most chemical plants comprise of a reactor surrounded by many separators. Separators have a countless number of jobs inside of a chemical plant. A separator can process raw materials prior to the reaction, remove incondensable gases, remove undesired side products, purify a product stream, recycle materials back into the process, and many other jobs that are essential to the process.&lt;br /&gt;
&lt;br /&gt;
Chemical engineers must understand the science of separation and the variety of ways that separation can take place. There are many ways to perform a separation some of these including: distillation, absorption, stripping, and extraction. The science of separation revolves around the presence of two phases that are in contact and equilibrium [1].&lt;br /&gt;
&lt;br /&gt;
[[File:Sepmeth.JPG|frame|Figure 1. Separation methods by property]]&lt;br /&gt;
&lt;br /&gt;
==Theory==&lt;br /&gt;
===Vapor-Liquid Equilibrium===&lt;br /&gt;
Separation processes are based on the theory of vapor-liquid equilibrium. This theory states that streams leaving a stage in a separation process are in equilibrium with one another. The idea of equilibrium revolves around the idea that when there is vapor and liquid in contact with one another they are in constantly vaporizing and condensing. Different components in the mixture will condense and vaporize at different rates. There are three types of equilibrium conditions that can be subdivided into thermal, mechanical and chemical potential categories. These separate equilibrium states are given as: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T_{liquid} = T_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_{liquid} = p_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;chemical potential_{liquid} = chemical potential_{vapor}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Distillation==&lt;br /&gt;
===Flash Distillation===&lt;br /&gt;
Flash Distillation is one of the simpler separation processes to be employed in a chemical plant. The main premise of flash distillation is that a portion of a liquid feed stream vaporizes in a flash chamber or a vapor feed condenses. Vapor-liquid equilibrium will cause the vapor phase and the liquid phase to have different compositions. The more volatile component of the mixture will compose of a larger portion of the vapor. This simple separation is easy to manufacture but does not result in large degrees of separation. &lt;br /&gt;
&lt;br /&gt;
Flash distillation requires a feed stream that is pressurized and heated and then passed through a valve into a flash drum. The large pressure drop across the valve will result in a partial vaporization of the fluid. Vapor will be removed overhead from the flash drum while the remaining liquid will collect at the bottom of the drum and be removed. Most flash drums will contain an entrainment eliminator which is a screen that prevents liquid from being carried into the vapor effluent. Figure 2 shows a simple overview of the flash distillation process. As shown, there is a heater that flows into a let-down valve where the two-phase flow begins. Variables y and x are the mole fractions of the more volatile component in the vapor and liquid effluents, respectively. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Flash.gif|center|frame|Figure 2. Flash Distillation Flow Diagram]]&lt;br /&gt;
&lt;br /&gt;
===Column Distillation===&lt;br /&gt;
Distillation columns are the most widely used separation technique used in the chemical industry, accounting for approximately 90% of all separations [1]. Distillations in columns consist of multiple trays that each act at their own equilibrium conditions. Large columns are able to perform complete separations of binary mixtures as well as more complex multi-component mixtures. &lt;br /&gt;
&lt;br /&gt;
[[File:column.jpg|250px|center|]]&lt;br /&gt;
===Stages===&lt;br /&gt;
Columns are separated into stages by the presence of trays. These trays allow for vapor-liquid contact and equilibrium to occur. Typically, the more stages in a column, the larger separation that can be achieved. There are many different types of trays that can be used in a column. &lt;br /&gt;
====Sieve Trays====&lt;br /&gt;
The simplest and least expensive tray type is the sieve tray which is a sheet of metal with holes punched into it to allow vapor flow. Sieve trays can have different hole patterns and sizes that will affect the tray efficiency and flow rates.&lt;br /&gt;
&lt;br /&gt;
[[File:sieve.jpg|200px|center|]]&lt;br /&gt;
&lt;br /&gt;
====Bubble-Cap Trays====&lt;br /&gt;
Bubble-cap trays consist of a weir around each hole in the tray which is covered with a cap that has holes or slots to allow vapor passage. Entrainment is about three times larger than a sieve tray. Bubble-cap trays require larger tray spacing than sieve tray design. Bubble-cap trays have been known to have problems with coking, polymer formation, or high fouling mixtures. Recently, very few new bubble-cap columns are being built due to the expense and marginal benefits. However, engineers will likely encounter bubble-cap columns still currently in operation.&lt;br /&gt;
&lt;br /&gt;
====Flow Patterns====&lt;br /&gt;
Cross flow columns are the most common pattern for distillation columns. For liquid flows between 50 and 500 Gal/min, a cross flow column is appropriate. When liquid flow is increased above 500 Gal/min, an engineer should consider designing a double pass or multi-pass column. This will reduce the liquid gradient on the tray and reduce the downcomer loading [1].&lt;br /&gt;
&lt;br /&gt;
===Column Sizing===&lt;br /&gt;
Column height will be dependent on the amount of trays required and the spacing between the trays. Normally, tray spacing of 0.15 m to 1 m is used. For columns, above 1 meter in diameter, 0.5 m can be used as an initial estimate.&lt;br /&gt;
&lt;br /&gt;
Column diameter is influenced by the vapor flow rate in the column. The trays can not have excess liquid entrainment or high pressure drops; therefore, vapor velocity in the column must be maintained at a reasonable level. &lt;br /&gt;
&lt;br /&gt;
An equation based on the Souders and Brown equation can be used as an estimate for the max allowable superficial vapor velocity, &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\hat u_v = (-0.171l_t^2 + 0.27l_t - 0.047){\frac{\rho_L - \rho_v}{\rho_v}}^{1/2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;l_t&amp;lt;/math&amp;gt; is the plate spacing in meters, &amp;lt;math&amp;gt;\rho_L&amp;lt;/math&amp;gt; is the density of the liquid stream, and &amp;lt;math&amp;gt;\rho_V&amp;lt;/math&amp;gt; is the density of the vapor stream. &lt;br /&gt;
&lt;br /&gt;
Column diameter, &amp;lt;math&amp;gt;D_c&amp;lt;/math&amp;gt;, can then be estimated using the relation,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D_c = \sqrt{\frac{4\hat{V_w}}{\pi\rho_v\hat{u_v}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hat{V_w}&amp;lt;/math&amp;gt; is the maximum vapor rate in kg/s [2].&lt;br /&gt;
&lt;br /&gt;
===Distillation Applications===&lt;br /&gt;
&lt;br /&gt;
Distillation is a process that can be implemented in various scales. There is both laboratory scaled distillation as well as very large industrial distillation. Other applications for distillation include food/alcohol processing and herb distillation for the perfume and medical industries. Typically laboratory scaled distillation occurs in batches whereas industrial distillation (e.g. fractional distillation of crude oil) occurs continuous with a constant distillate and bottom effluent streams. &lt;br /&gt;
&lt;br /&gt;
Some applications of distillation are concerned the top stream only, some the bottom stream only and others both streams can be used for future products. In alcohol distillation for example, the water that is separated from the ethanol/water binary solution is discarded as waste water. In fractional distillation of crude oils, the heavy hydrocarbons at the bottom of the column are collected and sold along with the light hydrocarbons that appear in higher side draws [1]. &lt;br /&gt;
&lt;br /&gt;
===Example Case: Ideal Distillation===&lt;br /&gt;
&lt;br /&gt;
Assume an equimolar mixture flowing at 10 mol/s of 20 mol% n-pentane, 30 mol% n-hexane, and 50 mol% n-heptane. Separate the mixture into 3 products: 99% pure n-pentane, 99% pure n-hexane, 99% n-heptane. Assume the feed and products are all liquids at the bubble points. There are two process alternatives to consider in this example. The direct sequence removes the most volatile species, pentane, in the first column, and then separates hexane and heptane in the second column. The indirect sequence separates the heaviest product, heptane, and then separates pentane from hexane in the second column. This example will consider the direct sequence. Next, we must decide if these species exhibit fairly ideal behavior during distillation. Since the n-alkanes have very similar properties, it is safe to assume they will display close to ideal behavior. The next step is to look up the boiling points of the 3 species. In this case, the normal boiling points of pentane, hexane, and heptane are 309 K, 342 K, and 372 K, respectively. Also, it is a good idea to look up relative volatilites, to further verify near-ideality of the mixture, but also to obtain the information necessary for the Underwood method, which we will employ to obtain a solution. The next step is to write out material balances based on molar flows and the design specifications. They go as follows:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) + \mu_{II}(nC5) = 2 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) + \mu_{II}(nC6) + \mu_{III}(nC6) = 3 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) + \mu_{III}(nC7) = 5 mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 99\mu_I(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = (5/990)\mu_{II}(nC6)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 99\mu_{III}(nC7)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; represents the molar flow, and the subscript represents the product stream.&lt;br /&gt;
&lt;br /&gt;
Solving this system of equations:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC5) = 1.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC5) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_I(nC6) = 0.020\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC6) = 2.930\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC6) = 0.050\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{II}(nC7) = 0.015\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mu_{III}(nC7) = 4.985\ mol/s&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
At this point we have enough information to use Underwood&#039;s method to estimate the minimum vapor flows in the column. The following three equations are used in Underwood&#039;s method:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}f_i = (1-q)F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(R_{min}+1)D = \sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}d_i = V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\bar R_{min}B = -\sum_i \frac{\alpha_{ik}}{\alpha_{ik}-\phi}b_i = \bar V_{min}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\alpha_{ik}&amp;lt;/math&amp;gt; is the relative volatility of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; to species &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;f_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the feed, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; the fraction of the feed that joins the liquid stream at the feed tray, &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; the total molar flow of the feed, &amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; the molar flow of the distillate, &amp;lt;math&amp;gt;R_{min}&amp;lt;/math&amp;gt; the minimum reflux ratio &amp;lt;math&amp;gt;(=L_{min}/D)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;d_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the distillate, &amp;lt;math&amp;gt;V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow possible in the top section of the column to accomplish the desired separation, &amp;lt;math&amp;gt;\bar R_{min}&amp;lt;/math&amp;gt; the minimum reboil ratio &amp;lt;math&amp;gt;(=\bar V_{min}/B)&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;b_i&amp;lt;/math&amp;gt; the molar flow of species &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; in the bottoms product, and &amp;lt;math&amp;gt;\bar V_{min}&amp;lt;/math&amp;gt; the minimum vapor flow in the bottom section of the column. The final variable, &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, will be solved for using the first Underwood equation, and it&#039;s value will be decided based on the relative volatilities of the key components in the column. &lt;br /&gt;
&lt;br /&gt;
So, after solving the first Underwood equation, we get two values for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt;, 3.806 and 1.462. Because 3.806 is between the relative volatilities of the key components, we will substitute that value for &amp;lt;math&amp;gt;\phi&amp;lt;/math&amp;gt; into the second Underwood equation. Doing so for both columns gives &amp;lt;math&amp;gt;V_{min} = 6.4\ mol/s&amp;lt;/math&amp;gt; for the first column and &amp;lt;math&amp;gt;V_{min} = 8.9\ mol/s&amp;lt;/math&amp;gt; for the second column, for a total minimum vapor flow of 15.3 mol/s. The process would then be repeated for the indirect sequence, and the decision for which process to use would be justified by the process with the overall minimum vapor flow [3].&lt;br /&gt;
&lt;br /&gt;
==Absorption==&lt;br /&gt;
===Description of Absorption===&lt;br /&gt;
Another separation process used in industry is absorption, which is used to remove a solute from a gas stream. It accomplishes this by contacting the gas mixture with a liquid solvent that readily absorbs the undesirable components from the gas stream, purifying the gas stream. This separation process is determined by the inputs of the liquid flow rate, temperature, and pressure. &lt;br /&gt;
&lt;br /&gt;
The absorption factor, which can be determined mathematically, determines how readily a component will absorb in the liquid phase. The absorption factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;A_i=L/K_iV&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio for component i [4]. Higher absorption factors result in higher absorptivity into the liquid and a decrease in the number of trays required for separation, however a diminishing return occurs after the absorption factor is greater than 2.0. An absorption factor of 1.4 is most commonly used.&lt;br /&gt;
&lt;br /&gt;
In general absorption can be seperated into two overarching categories, physical and chemical absorption. In physical absorption, the unwanted solute in the gas is absorbed into the liquid phase because solubility of the component is higher in the liquid phase than the gas phase. In chemical absorption the solute is removed from the gas via a reaction with the solvent, this reacted product is then transported into the liquid phase[7]. There are two types of chemical absorption reversible and irreversible. Generally reversible chemical absorption is preferred as the solvent can be put through a stripper and regenerated so it can be recycled back to the absorption process[1].&lt;br /&gt;
&lt;br /&gt;
===Absorption Apparatus===&lt;br /&gt;
[[File:Ejectorventuri.jpg|thumb|200px|right|Figure 3. Ejector Scrubber]]&lt;br /&gt;
There are five major apparatus used for absorption in industrial application. These five pieces of equipment are spray absorbers (or towers), ejector (venturi) scrubbers, packed columns, trayed columns, and film absorbers. In both spray tower and the ejector scrubber nozzles are employed to produce small solvent droplets. These small droplets increase the surface area of the liquid to gas contact allowing for the maximum amount of mass transfer to occur between the gas mixture and the liquid. The major difference between the two nozzle equipment designs is the configuration and type of nozzles. In the ejector scrubber shown in Figure 3 there is a single nozzle that is generally a higher pressure spray nozzle that produces finer solvent drops allowing for an even greater amount of mass transfer enabling better physical absorption[8].&lt;br /&gt;
&lt;br /&gt;
[[File:SparyTowerAbsorber.jpg|thumb|200px|right|Figure 4. Spray Tower Absorber]]&lt;br /&gt;
Spray towers on the other hand generally have many nozzle at different heights where the liquid solvent will be sprayed out of to contact the gas running through the tower. This design is used in order to ensure the gas contacts the liquid as throughout the tower. These nozzles are lower pressure than a venturi scrubbers nozzle and thus physical mixing is worse in this configuration. Since physical mixing is generally worse in this configuration it is usually used in conjunction with a chemical absorption process. The other major difference between the venturi scrubber and the spray tower is that gas and liquid flow is cocurrent in the former while it is countercurrent in a spray tower. A spray tower absorber is shown on the right in Figure 4[8].&lt;br /&gt;
&lt;br /&gt;
Packed column absorbers and tray column absorbers have very high efficiencies for the removal of an unwanted solute in the gas stream. The major disadvantage a trayed column has when compared to a packed column is the pressure drop. The pressure drop in a packed column is generally very low, whereas in between each tray of a trayed column pressure drop can be quite large. However the advantages inherent to trayed columns become clear when one needs the solvent to have a high concentration of the component to be removed from the gas stream. This is most important in the case where there is a very low concentration of the component in the gas stream and the specification states the solvent must contain a high concentration of that component. In this case the flow rate of the solvent may not be high enough for a packed column, however in a trayed column the solvent flow rate can be near zero for operation[8]. Packed and trayed column internals are very similar to the setups found in distillation columns. &lt;br /&gt;
&lt;br /&gt;
The final absorber the film absorber is generally used in the case where the heat of absorption must be removed. The film absorber operates by sending the gas and solvent through a heat exchanger where the solvent creates a thin film on the walls of the tubes and the gas flows through the interior allowing for solute transfer. The good heat transfer present in a film absorber makes it preferable for situations where low temperatures are required for a high recovery of the solute[8]. &lt;br /&gt;
&lt;br /&gt;
===Industrial Absorption Processes===&lt;br /&gt;
An industrial example is lean oil absorption, which is used to separate nitrogen and other impurities from natural gas. A lean oil is contacted with low quality natural gas, and the methane is selectively absorbed by the lean oil, leaving the impurities behind. The methane is subsequently regenerated from the rich oil as high quality natural gas [9].&lt;br /&gt;
&lt;br /&gt;
Other common industrial practices of absorption come from sour gas treatment. Amine gas treating is used to remove hydrogen sulfide or carbon dioxide from gas streams via a reversible chemical absorption. In amine gas treating the sour gas is fed to the bottom an absorber where amine solution is fed to the top along with any necessary make up water. The sour gas components are absorbed into the amine via a chemical absorption method. Sweet gas leaves the top of the absorber whereas the amine out of the bottom, now rich with acidic components is sent to a regenerator where the acid gas components are stripped and the acid gas is generally sent to a flare whereas the amine now lean again is recycled back into the first absorber[10]. Another type of sour gas treatment that uses absorption is Merichems LO-CAT process which uses a chelated iron to remove hydrogen sulfide from feed gas in the absorption column[11].&lt;br /&gt;
&lt;br /&gt;
==Stripping==&lt;br /&gt;
This process separates solutes from solvents (often after absorption, to purify the solvent so that it can be recycled to an absorber). Stripping will depend on the vapor and liquid flow rates, as well as the temperature and pressure of the column. There is a temperature drop down the column, so columns generally have either an increased operating temperature or decreased operating pressure. &lt;br /&gt;
&lt;br /&gt;
The stripping factor of component i is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S_i=K_iV/L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;K_i&amp;lt;/math&amp;gt; is the vapor/liquid equilibrium ratio, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the vapor flow rate entering the column, and &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; is the liquid flow rate entering the column, will determine how much of solute i will be stripped from the liquid into the vapor phase [4]. The usual range for the stripping factor is between 1.2 and 2.0, with a stripping factor of 1.4 being most economic.&lt;br /&gt;
&lt;br /&gt;
An example of stripping in industry is the deodorization of food items such as oils. The oil is heated and allowed to trickle down the column while steam flows up from the bottom of the column. At the vapor-liquid interface, volatile components of the oil transfer to the steam and are carried off the top of the column, leaving a purified oil product [12].&lt;br /&gt;
&lt;br /&gt;
==Bioseparations==&lt;br /&gt;
===Importance===&lt;br /&gt;
As our ability to manipulate and engineer biological systems improves, biological products are becoming an increasingly important source of therapeutics and fuels. The production of fuels from biomass via either the enzymatic breakdown of a feedstock or the secretion of usable lipids from algae is a promising new energy source. Additionally, enzymes, antibodies and other therapeutic proteins have been applied to the treatment of a wide range of diseases. Although each process requires its own set of separations, all follow the same basic format: separation of biomass, product isolation, and product purification. This section will provide examples of unit operations in each step [13].&lt;br /&gt;
&lt;br /&gt;
Bioprocesses begin with fermentations or growth operations. In biofuel production processes, this may involve growing algae or breaking down corn or cellulosic biomass. For the production of therapeutics, mammalian or bacterial cells may be grown in a fermentor and the product secreted into the supernatant or harvested from the cells.&lt;br /&gt;
&lt;br /&gt;
===Biomass Separations===&lt;br /&gt;
After fermentation and product production, the solid biomass must first be separated from the desired product. If the product is secreted from the cells, this can be done immediately after fermentation ends. If the product is not secreted, the cells must first be lysed. &lt;br /&gt;
Cell lysis is the process of lysing, or breaking, the cell in open. Mechanical lysis is the simplest, and involves physically breaking the cell either by mashing (think mortar and pestle) or blending the cells into a homogenous solution. Chemical lysis is another method, achieved by introducing an osmotic shock or chemically degrading the cell membrane. Additional separation can be achieved by flocculation, which is the process of aggregating biomaterial by charge neutralization or bridging. These larger complexes are easier to separate from smaller molecules [13].&lt;br /&gt;
&lt;br /&gt;
The next step is removing the unwanted biomass from the product in solution. Separation by centrifugation or sedimentation is most common. Both methods utilize density differences to separate the product from the homogenous solution. &lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Sedimentation&amp;lt;/i&amp;gt;&lt;br /&gt;
Sedimentation relies purely on the force of gravity, while centrifugation speeds the settling process by subjecting the cells to a centrifugal force. Sedimentation in a settling tank is the simplest method of solid-liquid bioseparation. In this process, biomass in a tank is simply allowed to settle to the bottom over time. While this process is inexpensive and can separate out large volumes of biomass, it generally requires long time periods and is only mostly in very large-scale processes where active centrifugation is difficult.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;i&amp;gt;Centrifugation&amp;lt;/i&amp;gt;&lt;br /&gt;
[[File: Disk_stack_centrifuge_towler.png |frame|Fig. 4: Diagram of a disk-stack centrifuge [2]]]&lt;br /&gt;
Centrifuges are widely utilized across many processes, and thus a wide variety of scales and designs have been developed. &amp;lt;b&amp;gt; Disk-stack centrifuges&amp;lt;/b&amp;gt;, in which the solid phase is deposited onto “shelves” in the center of the spinner and liquid phase is pushed to the outside, are one of the most commonly used centrifuges in industry. They are especially suited to biomass separation processes because they can be built on a large scale and are ideal for separating fine solids from liquids. &lt;br /&gt;
&lt;br /&gt;
[[File: tubular bowl centrifuge towler.png |frame|Fig. 5: Diagram of a tubular bowl centrifuge centrifuge [2]]]&lt;br /&gt;
Tubular bowl centrifuges are also common and can reach separation efficiencies of up to 90%.  Heavier products accumulate along the sides of the bowl, while the light phase flows out the top. They separate products by can be used both to separate solids from liquids and immiscible liquids, such as and oil product and an aqueous broth [2].&lt;br /&gt;
&lt;br /&gt;
===Product Isolation===&lt;br /&gt;
Liquid-liquid separation, to extract the product from the aqueous phase, is much less straightforward than liquid-solid extraction. Many methods - especially extraction, adsorption, filtration, and precipitation - are similar in principle to operations found in other, non-biological separations. Particular care needs to be taken with protein products because of their instability, and the selection of an appropriate solvent or adsorbent is crucial to a successful process [13].&lt;br /&gt;
&lt;br /&gt;
===Product Purification===&lt;br /&gt;
The final steps of protein purification and polishing remove any remaining contaminants and bring the concentration of product to an appropriate value for applications. Purification processes for medical proteins can be extensive, as high purity is essential for therapeutic products. Chromatography and crystallization are two common steps in purification and are especially used in industrial scale protein production.&lt;br /&gt;
&lt;br /&gt;
Chromatography is similar to adsorption in that it relies on differences in affinity between solutes and a solid surface. A solution is eluted through a column containing a solid resin with various affinities for the solutes in solution. In adsorption, the solutes are evenly saturated throughout the column. Chromatography differs in that solutes are deposited in bands on a resin phase before the column is flushed with an elution solvent specific for a solute. Alternative chromatography methods are used for specific applications, but elution chromatography is the most common [13].&lt;br /&gt;
&lt;br /&gt;
Crystallization, or the formation of solute crystals from a solution, is especially useful in biomolecule separations because it is possible to obtain a 99.9%+ product purity. In crystallization, a diluent is added to the homogeneous solution that reduces the solubility of the product to the point that it “falls out” of solution and crystallizes. It is similar to precipitation but results in the formation of crystals rather than unordered aggregates.Crystallization can be used on a laboratory scale for determining protein structure, on on the industrial scale for antibody and therapeutic protein productions. Batch crystallizers are often used in industry because of their simplicity and inexpensiveness compared to continuous crystallization [13].&lt;br /&gt;
&lt;br /&gt;
==Other Separation Processes==&lt;br /&gt;
===Extraction===&lt;br /&gt;
Liquid-liquid extraction is a process for components with overlapping boiling points and azeotropes. The process requires a solvent such that some of the components of the mixture are soluble, and then the components will be separated based on this solubility in the liquid. This process can operate at moderate temperatures and pressures, so is not very energy intensive. However, a distillation column is required to extract the solvent for recycle. More recently, supercritical fluids have replaced liquid solvents in some processes for L/L extraction, due to the solute’s ability to more rapidly diffuse through them.  The issue with these fluids, however, is that they must be operated at extremely high pressures and temperatures, increasing both capital and operating expenses of the process [4].&lt;br /&gt;
&lt;br /&gt;
===Crystallization===&lt;br /&gt;
This process recovers solutes that have been dissolved in solution. The resulting product is in the solid phase. Depending on the material properties of the solute and solvent, the solute is recovered by precipitation after cooling, removal of solvent, or adding precipitating agents. Crystallizers are designed based on phase equilibria, solubilities, rates and amounts of nuclei generated, and rates of crystal growth. Every crystallization process is a unique system, so plant evaluation is usually required before complete implementation. Crystallization can be performed in both batch and continuous processes, and design features can control crystal size to an extent [4].&lt;br /&gt;
&lt;br /&gt;
===Membrane Separation===&lt;br /&gt;
This separations process uses selectively permeable membranes to separate components in a mixture. Typically, one of the components will freely pass through the barrier while the other components will not. The stream that passes through the membrane is the permeate and the stream that does not pass is the retentate. The driving force behind this separation is a pressure gradient. Membrane separation is beneficial because it can separate mixtures at the molecular and small particle level. Furthermore, there is no phase change required so the energy input is low. Limitations of this process include achieving high product purity, incompatibility with certain stream components, low operating temperature, and low flow rates. Although membrane separation is generally not scaled up, examples of scaled-up membrane separation include seawater desalination and hydrogen recovery [4].&lt;br /&gt;
&lt;br /&gt;
===Adsorption===&lt;br /&gt;
Adsorption involves an adsorbent and adsorbate. The adsorbent is typically a solid, and will typically separate the adsorbate from the stream. This process usually includes a desorption step that regenerates the adsorbent for further use. Raising the temperature or increasing the concentration of the adsorbate can reverse the adsorption process. Although the recycle of the adsorbent is a very economic design feature, the downside of this step is that it results in a cyclic process, which introduces complexity to the overall process. Industrial applications of this process are for bulk separations and gas purification. The adsorption/desorption process in these situations involves a large amount of heat transfer, which design engineers must take into account when sizing and selecting equipment material [4].&lt;br /&gt;
&lt;br /&gt;
===External Field/Gradient Separation===&lt;br /&gt;
These separations use external force fields or temperature gradients to separate responsive molecules or ions. The use of these processes is fairly limited to a few specialized industrial applications [4].&lt;br /&gt;
&lt;br /&gt;
===Settling and Sedimentation===&lt;br /&gt;
In settling processes, solid particles or liquid drops are separated from a stream by gravity. The stream can be in either the liquid or gas phase. For vapor-liquid mixtures, flash drums are generally used to separate the mixture. The velocity of the vapor must be less than the settling velocity of the liquid drops for this separation to occur. For liquid-liquid separation, the horizontal velocity of the fluid must be low enough to allow the low-density droplets to rise to the interface and the high-density droplets to move away from the interface and coalesce. In sedimentation, the result of the process is a more concentrated slurry. Typically a flocculating agent is used to aid in the settling process. One way to perform this separation is to use a cone-shaped tank with a slowly revolving rake that scrapes and moves the thickened slurry to the center of the cone for removal [4].&lt;br /&gt;
&lt;br /&gt;
===Flotation===&lt;br /&gt;
Flotation is a process designed for specific solid-solid mixtures. It works by generating gas bubbles in a liquid that attach to selected solid particle. Afterwards, the particles rise to the liquid surface where they are removed by an overflow weir or mechanical scraper. The separation depends on the surface properties of the particles and its preference to attach to the gas bubbles. To meet the necessary requirements of the flotation process, a number of additives can be used to control things like the pH of the liquid-solid mixture, the activity of the solid surface, and the froth that can assist in separation. The bubbles can be produced by gaseous dispersion, dissolution, or electrolysis of the liquid [4].&lt;br /&gt;
&lt;br /&gt;
===Centrifugation===&lt;br /&gt;
This process is similar to external field separation in that an external force field is applied to separate a mixture. When gravity separation is too slow due to particle densities, particle size, settling velocity, or the formation of an emulsion, centrifugation is commonly used. Centrifugal force increases the total force acting on the particle and results in faster separation times. This process is generally used to separate solids from liquids, however it can also be used to separate two liquids with very different densities [4].&lt;br /&gt;
&lt;br /&gt;
===Drying===&lt;br /&gt;
Drying is performed to remove liquid from a liquid-solid mixture and produce a dry solid. Water is most often the liquid removed, but organic liquids are removed from solids on occasion as well. The heat required to vaporize the liquid is usually obtained by a series of gas-solid contacting devices. Feed condition and temperature sensitivity of the solid dictate the type of contacting device that is used. There are two groups of dryers that differ by the dependence of either mechanical means or fluid motion for gas solid contact. Another feature of dryers is to use either direct (hot gas) or indirect (conductive surface) heating [4].&lt;br /&gt;
&lt;br /&gt;
===Evaporation===&lt;br /&gt;
Evaporators separate solvents from a solution by evaporation. The difference between evaporation and distillation is that evaporation requires the solute be nonvolatile. Because of this, a high separation can be achieved with one stage. Evaporators are essentially reboilers, so evaporation is a very energy-intensive process with a high thermal economy [4].&lt;br /&gt;
&lt;br /&gt;
===Filtration===&lt;br /&gt;
Filtration is a process that separates a mixture of solid in a liquid or gas by passing the mixture through a porous medium in which the particles do not pass. Filtration is done by either cake filtration (particles found on the surface of the filter) or depth filtration (particles found within the filter). Cake filtration is generally performed with a cloth as the filtration medium [4].&lt;br /&gt;
&lt;br /&gt;
==Conclusion==&lt;br /&gt;
Separation is a key part of most chemical processes, and there is a great variety of techniques to perform separation of compounds based on size, volatility, charge, and many other features. A common technique with which the process engineer should be familiar is distillation, but he or she should also be aware of the other available options. Some techniques may be less expensive, less energy-intensive, or more effective than distillation, depending on the specific separation problem. Therefore, the separation strategy should be carefully considered.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
# Wankat, P.C. (2012). &#039;&#039;Separation Process Engineering.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Towler, G.P. and Sinnot, R. (2012). &#039;&#039;Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design.&#039;&#039;Elsevier.&lt;br /&gt;
# Biegler, L.T., Grossmann, L.E., and Westerberg, A.W. (1997). &#039;&#039;Systematic Methods of Chemical Process Design.&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Peters, M.S. and Timmerhaus, K.D. (2003). &#039;&#039;Plant Design and Economics for Chemical Engineers, 5th Edition.&#039;&#039; New York: McGraw-Hill.&lt;br /&gt;
# Seider, W.D., Seader, J.D., and Lewin, D.R. (2004). &#039;&#039;Process Design Principles: Synthesis, Analysis, and Evaluation.&#039;&#039; New York: Wiley.&lt;br /&gt;
# Turton, R.T., Bailie, R.C., Whiting, W.B., and Shaewitz, J.A. (2003). &#039;&#039;Analysis, Synthesis, and Design of Chemical Processes&#039;&#039; Upper Saddle River: Prentice-Hall.&lt;br /&gt;
# Danckwerts P (1965) The Absorption of Gases in Liquids.  Pure and Applied Chemistry UK 10:625-642.&lt;br /&gt;
# Schmidt Eberhard (2012) Waste Gases, Separation and Purification.  Ullman’s Encyclopedia of Industrial Chemistry Germany 2:174-181.&lt;br /&gt;
# Lean Oil Absorption. PetroGas Systems Web site. Available at: http://petrogassystems.com/technology/natural-gas-processing-and-dew-point-control/lean-oil-absorption. Accessed February 19, 2014.&lt;br /&gt;
# US 4080424, Loren N. Miller &amp;amp; Thomas S. Zawacki, &amp;quot;Process for acid gas removal from gaseous mixtures&amp;quot;, issued 21 Mar 1978, assigned to Institute of Gas Technology&lt;br /&gt;
# Merichem Gas Technologies. ®LO-CAT PROCESS available at http://www.merichem.com/images/casestudies/Desulfurization.pdf Accessed 6 Feb. 2015.&lt;br /&gt;
# Stripping Column. Alfa Laval Web site. Available at: http://www.alfalaval.com/solution-finder/products/soft-column/Documents/Stripping%20Column.pdf. Accessed February 19, 2014.&lt;br /&gt;
# Harrison, R.G., Todd, P., Rudge, S.R. and Petrides, D.P, (2003). Bioseparations Science and Engineering. New York: Oxford University Press.&lt;/div&gt;</summary>
		<author><name>Emm</name></author>
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