Sensitivity analysis and design optimization - Revision history

Jian: /* References */

2015-03-02T04:19:16Z

References

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	=References=		=References=
	:Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.		Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.

	:Seider WD, Seader JD, Lewin DR. Process Design Principles: Synthesis, Analysis, and Evaluation. 3rd ed. New York: Wiley; 2004.		Seider WD, Seader JD, Lewin DR. Process Design Principles: Synthesis, Analysis, and Evaluation. 3rd ed. New York: Wiley; 2004.

	:Towler G. Chemical Engineering Design. PowerPoint presentation; 2012.		Towler G. Chemical Engineering Design. PowerPoint presentation; 2012.

	:Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.		Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.

	:Turton R, Bailie RC, Whiting WB, Shaewitz JA, Bhattacharyya D. Analysis, Synthesis, and Design of Chemical Processes. 4th ed. Upper Saddle River: Prentice-Hall; 2012.		Turton R, Bailie RC, Whiting WB, Shaewitz JA, Bhattacharyya D. Analysis, Synthesis, and Design of Chemical Processes. 4th ed. Upper Saddle River: Prentice-Hall; 2012.

	:Ulrich GD. A Guide to Chemical Engineering Process Design and Economics. New York: Wiley; 1984.		Ulrich GD. A Guide to Chemical Engineering Process Design and Economics. New York: Wiley; 1984.

Jian: /* References */

2015-02-26T19:41:30Z

References

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	=References=		=References=
	~~#Towler~~, G.P. ~~and Sinnot~~, R. ~~(2012). Chemical Engineering~~ Design: ~~Principles~~, ~~Practice~~ and ~~Economics of Plant and Process Design~~. ~~Elsevier~~.		:Peters MS, Timmerhaus KD. Plant Design and Economics for Chemical Engineers. 5th ed. New York: McGraw Hill; 2003.
	#Towler, G~~.P. (2012)~~. Chemical Engineering Design, PowerPoint presentation.
	~~#Peters, M.S. (2003) Plant Design and Economics for Chemical Engineers, 5th Ed. McGraw-Hill~~: ~~New York.~~		:Seider WD, Seader JD, Lewin DR. Process Design Principles: Synthesis, Analysis, and Evaluation. 3rd ed. New York: Wiley; 2004.
	~~#Ulrich~~, ~~G.D~~. ~~(1984) A Guide to~~ Chemical Engineering ~~Process~~ Design and Economics. ~~Wiley~~: ~~New York~~.
	~~#Seider, W.D. (2004). Process Design Principles~~: ~~Synthesis~~, ~~Analysis~~, ~~and Evaluation~~, ~~Wiley: New York.~~		:Towler G. Chemical Engineering Design. PowerPoint presentation; 2012.
	~~#Turton~~, ~~R.T. (2003)~~. Analysis, Synthesis, and Design of Chemical Processes, Prentice Hall: ~~Upper Saddle River~~.
			:Towler G, Sinnott R. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston: Elsevier; 2013.

			:Turton R, Bailie RC, Whiting WB, Shaewitz JA, Bhattacharyya D. Analysis, Synthesis, and Design of Chemical Processes. 4th ed. Upper Saddle River: Prentice-Hall; 2012.

			:Ulrich GD. A Guide to Chemical Engineering Process Design and Economics. New York: Wiley; 1984.

Jian: /* Statistical Methods of Risk Analysis */

2015-02-26T19:40:45Z

Statistical Methods of Risk Analysis

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	<math> S_x = \frac {H-L} {2.65} </math>		<math> S_x = \frac {H-L} {2.65} </math>

	It is important to recognize that values of this statistical method will likely be skewed if the distribution is incorrect. The mean and standard deviation of other parameters can be calculated as a function of the equations above. This allows relatively easy estimation of the overall error in a completed cost estimate, and can be extended to economic criteria such as NPV, TAC, or ROI. Commercial programs are available for more sophisticated analyses such as the Monte Carlo method ~~[1]~~.		It is important to recognize that values of this statistical method will likely be skewed if the distribution is incorrect. The mean and standard deviation of other parameters can be calculated as a function of the equations above. This allows relatively easy estimation of the overall error in a completed cost estimate, and can be extended to economic criteria such as NPV, TAC, or ROI. Commercial programs are available for more sophisticated analyses such as the Monte Carlo method (Towler and Sinnott, 2013).

	==Contingency Costs==		==Contingency Costs==

Jian: /* Sensitivity Analysis */

2015-02-26T19:40:24Z

Sensitivity Analysis

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	=Sensitivity Analysis=		=Sensitivity Analysis=
	A sensitivity analysis is a way of examining the effects of uncertainties in the forecasts on the viability of a project ~~[1]~~. First a base case for analysis is established from the investment and cash flows. Various parameters in the cost model are then modified, measuring the range of error in the forecast figures; this shows how sensitive the cash flows and economic criteria are to errors in the forecast figures. The results are usually presented as plots of economic criterion, and give some idea of the risk involved in making judgments on the forecast performance of the project.		A sensitivity analysis is a way of examining the effects of uncertainties in the forecasts on the viability of a project (Towler and Sinnott, 2013). First a base case for analysis is established from the investment and cash flows. Various parameters in the cost model are then modified, measuring the range of error in the forecast figures; this shows how sensitive the cash flows and economic criteria are to errors in the forecast figures. The results are usually presented as plots of economic criterion, and give some idea of the risk involved in making judgments on the forecast performance of the project.

	==Parameters to Study==		==Parameters to Study==

Jian: /* Optimization in Process Design */

2015-02-26T19:40:03Z

Optimization in Process Design

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	#Safety, operability, reliability, and flexibility are top priorities in design. A safe, operable, plant will often require be more expensive then the economically optimal design.		#Safety, operability, reliability, and flexibility are top priorities in design. A safe, operable, plant will often require be more expensive then the economically optimal design.

	Experienced design engineers usually think through constraints, trade-offs, major cost components, and the objective function to satisfy themselves that their design is “good ~~enough~~.~~” [1]~~		Experienced design engineers usually think through constraints, trade-offs, major cost components, and the objective function to satisfy themselves that their design is “good enough” (Towler and Sinnott, 2013).

	=Sensitivity Analysis=		=Sensitivity Analysis=

Jian: /* Search Methods */

2015-02-26T19:39:37Z

Search Methods

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	==Search Methods==		==Search Methods==
	Search methods are at the core of the solution algorithms for complex multivariable objective functions. The four main search functions are unrestricted search, three-point interval search, golden-section search, and quasi-newton method ~~[1]~~.		Search methods are at the core of the solution algorithms for complex multivariable objective functions. The four main search functions are unrestricted search, three-point interval search, golden-section search, and quasi-newton method (Towler and Sinnott, 2013).

	===Unrestricted Search===		===Unrestricted Search===

Jian: /* Defining the Optimization Problem and Objective Function */

2015-02-26T19:38:22Z

Defining the Optimization Problem and Objective Function

Jian: /* Design Optimization */

2015-02-26T19:32:19Z

Design Optimization

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	Although profitability or cost is generally the basis for optimization, practical and intangible factors usually need to be included as well in the final investment decision. Such factors are often difficult or impossible to quantify, and so decision maker judgment must weigh such factors in the final analysis ~~[3]~~, ~~[4]~~.		Although profitability or cost is generally the basis for optimization, practical and intangible factors usually need to be included as well in the final investment decision. Such factors are often difficult or impossible to quantify, and so decision maker judgment must weigh such factors in the final analysis (Peters and Timmerhaus, 2003; Ulrich, 1984).

	=Defining the Optimization Problem and Objective Function=		=Defining the Optimization Problem and Objective Function=

Jian: /* Introduction */

2015-02-26T19:29:19Z

Introduction

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	=Introduction=		=Introduction=
	Optimization and sensitivity analysis are key aspects of successful process design. Optimizing a process maximizes project value and plant performance, minimizes project cost, and facilitates the selection of the best components ~~[1]~~.		Optimization and sensitivity analysis are key aspects of successful process design. Optimizing a process maximizes project value and plant performance, minimizes project cost, and facilitates the selection of the best components (Towler and Sinnott, 2013).

	=Design Optimization=		=Design Optimization=

Group G1 at 17:35, 28 February 2014

2014-02-28T17:35:57Z

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	==Contingency Costs==		==Contingency Costs==
	A minimum contingency charge of 10% is normally added to ISBL plus OSBL fixed capital to account for variations in capital cost. If the confidence interval of the estimate is known, the contingency charges can be estimated based on the desired level of certainty that the project will not exceed projected costs.		A minimum contingency charge of 10% is normally added to ISBL plus OSBL fixed capital to account for variations in capital cost. If the confidence interval of the estimate is known, the contingency charges can be estimated based on the desired level of certainty that the project will not exceed projected costs.

			=Conclusion=
			Design optimization and sensitivity analysis are essential to designing and operating a successful chemical process. Optimization can be tricky due to high levels of uncertainty and magnitude of variables, but can help minimize costs and increase efficiency. Chemical engineers need to understand the optimization methods, the role of constraints in limiting designs, recognize design trade-offs, and understand the pitfalls of their analysis. In a similar respect, sensitivity analysis is a way of examining the effects of uncertainties in the forecasts on the viability of a project. If an engineer can optimize a process and perform a sensitivity analysis, the project will be cost effective and run more smoothly.

	=References=		=References=

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	<math> z = f(x_1 , x_2 , ... x_n) </math>		<math> z = f(x_1 , x_2 , ... x_n) </math>

	The decision variables may be independent or they may be related via constraint equations. Examples of process variables include operating conditions such as temperature and pressure, and equipment specifications such as the number of trays in a distillation column. The conventional name and strategy of this optimization method varies between texts; Turton et al suggests creating a base case prior to defining the objective function and Seider et al classifies the objective function as a piece of a nonlinear program (NLP) ~~[5]~~, ~~[6]~~.		The decision variables may be independent or they may be related via constraint equations. Examples of process variables include operating conditions such as temperature and pressure, and equipment specifications such as the number of trays in a distillation column. The conventional name and strategy of this optimization method varies between texts; Turton et al suggests creating a base case prior to defining the objective function and Seider et al classifies the objective function as a piece of a nonlinear program (NLP) (Seider et al., 2004; Turton et al., 2012).

	A second type of process variable is the dependent variable; a group of variables influenced by process constraints. Common examples of process constraints include process operability limits, reaction chemical species dependence, and product purity and production rate. Towler & Sinnott define equality and inequality constraints ~~[2]~~. Equality constraints are the laws of physics and chemistry, design equations, and mass/energy balances:		A second type of process variable is the dependent variable; a group of variables influenced by process constraints. Common examples of process constraints include process operability limits, reaction chemical species dependence, and product purity and production rate. Towler & Sinnott define equality and inequality constraints (Towler, 2012). Equality constraints are the laws of physics and chemistry, design equations, and mass/energy balances:

	<math> h(x_1 , x_2 , ... x_n ) = b_1 </math>		<math> h(x_1 , x_2 , ... x_n ) = b_1 </math>

	For example, a distillation column that is modeled with stages assumed to be in phase equilibrium often has several hundred MESH (material balance, equilibrium, summation of mole fractions, and heat balance) equations. However, in the implementation of most simulators, these equations are solved for each process unit, given equipment parameters and steam variables. Hence, when using these simulators, the equality constraints for the process units are not shown explicitly in the nonlinear program. Given values for the design variables, the simulators call upon these subroutines to solve the appropriate equations and obtain the unknowns that are needed to perform the optimization ~~[5]~~.		For example, a distillation column that is modeled with stages assumed to be in phase equilibrium often has several hundred MESH (material balance, equilibrium, summation of mole fractions, and heat balance) equations. However, in the implementation of most simulators, these equations are solved for each process unit, given equipment parameters and steam variables. Hence, when using these simulators, the equality constraints for the process units are not shown explicitly in the nonlinear program. Given values for the design variables, the simulators call upon these subroutines to solve the appropriate equations and obtain the unknowns that are needed to perform the optimization (Seider et al., 2004).

	Inequality constraints are technical, safety, and legal limits, economic and current market:		Inequality constraints are technical, safety, and legal limits, economic and current market:
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	<math> g(x_1 , x_2 , ... x_n ) \frac {\geq} {\leq} b_2 </math>		<math> g(x_1 , x_2 , ... x_n ) \frac {\geq} {\leq} b_2 </math>

	Inequality constraints also pertain to equipment; for example, when operating a centrifugal pump, the head developed is inversely related to the throughput. Hence, as the flow rate is varied when optimizing the process, care must be taken to make sure that the required pressure increase does not exceed that available from the pump ~~[5]~~.		Inequality constraints also pertain to equipment; for example, when operating a centrifugal pump, the head developed is inversely related to the throughput. Hence, as the flow rate is varied when optimizing the process, care must be taken to make sure that the required pressure increase does not exceed that available from the pump (Seider et al., 2004).

	It is important that a problem is not under or over-constrained so a possible solution is attainable. A degree-of-freedom (DOF) analysis should be completed to simply the number of process variables, and determine if the system is properly specified.		It is important that a problem is not under or over-constrained so a possible solution is attainable. A degree-of-freedom (DOF) analysis should be completed to simply the number of process variables, and determine if the system is properly specified.
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	[[File:SAO1.PNG\|center\|600px]]		[[File:SAO1.PNG\|center\|600px]]
	Figure 1: Trade-off example ~~[1]~~		Figure 1: Trade-off example (Towler and Sinnott, 2013)

	Some common design trade-offs are more separations equipment versus low product purity, more recycle costs versus increased feed use and increased waste, more heat recovery versus cheaper heat exchange system, and marketable by-product versus more plant expense.		Some common design trade-offs are more separations equipment versus low product purity, more recycle costs versus increased feed use and increased waste, more heat recovery versus cheaper heat exchange system, and marketable by-product versus more plant expense.

	==Parametric Optimization==		==Parametric Optimization==
	Parametric optimization deals with process operating variables and equipment design variables other than those strictly related to structural concerns. Some of the more obvious examples of such decisions are operating conditions, recycle ratios, and steam properties such as flow rates and compositions. Small changes in these conditions or equipment can have a diverse impact on the system, causing parametric optimization problems to contain hundreds of decision variables. It is therefore more efficient to analyze the more influential variables effect on the overall system. Done properly, a balance is struck between increased difficulty of high-variable-number optimization and optimization accuracy. ~~[3]~~		Parametric optimization deals with process operating variables and equipment design variables other than those strictly related to structural concerns. Some of the more obvious examples of such decisions are operating conditions, recycle ratios, and steam properties such as flow rates and compositions. Small changes in these conditions or equipment can have a diverse impact on the system, causing parametric optimization problems to contain hundreds of decision variables. It is therefore more efficient to analyze the more influential variables effect on the overall system. Done properly, a balance is struck between increased difficulty of high-variable-number optimization and optimization accuracy (Seider et al., 2004).

	==Suboptimizations==		==Suboptimizations==
	Simultaneous optimization of the many parameters present in a chemical process design can be a daunting task due to the large number of variables that can be present in both integer and continuous form, the non-linearity of the property prediction relationships and performance models, and frequent ubiquity of recycle. It is therefore common to seek out suboptimizations for some of the variables, so as to reduce the dimensionality of the problem ~~[3]~~. While optimizing sub-problems usually does not lead to overall optimum, there are instances for which it is valid in a practical, economic sense. Care must always be taken to ensure that subcomponents are not optimized at the expense of other parts of the plant.		Simultaneous optimization of the many parameters present in a chemical process design can be a daunting task due to the large number of variables that can be present in both integer and continuous form, the non-linearity of the property prediction relationships and performance models, and frequent ubiquity of recycle. It is therefore common to seek out suboptimizations for some of the variables, so as to reduce the dimensionality of the problem (Seider et al., 2004). While optimizing sub-problems usually does not lead to overall optimum, there are instances for which it is valid in a practical, economic sense. Care must always be taken to ensure that subcomponents are not optimized at the expense of other parts of the plant.

	Equipment optimization is usually treated as a subproblem that is solved after the main process variables such as reactors conversion, recycle ratios, and product recoveries have been optimized.		Equipment optimization is usually treated as a subproblem that is solved after the main process variables such as reactors conversion, recycle ratios, and product recoveries have been optimized.