processdesign - User contributions [en]

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Engineering economic analysis

2014-03-10T03:47:47Z

TJConsidine: /* Conclusion */

Authors: Michael Gleeson, Sean Kelton, Thomas Considine (ChE 352 in Winter 2014)

Steward: David Chen, Fengqi You

Date Presented: Feb. 22, 2014

==Measures of Economic Return==
The following are "back of the envelope" type calculations for economic return of a project. These measures are quick and easy because they ignore some of the more complicated parts of evaluating a project including factors such as depreciation, time value of money and taxes.
===Payback Time===
The payback time is defined as the period of time (in years) required to break even on the initial economic investment. It is given by the equation:

<math>T = I/C</math>

Where <math>T</math> is the payback time for the project, <math>I</math> is the total investment required for the project and <math>C</math> is the average annual cash flow generated by the project. This calculation is used to determine how quickly the project's fixed costs (i.e. land, machinery, etc.) can be recovered from the project. A small payback period is desirable for a new project.

===Return on Investment===
The regular return on investment (ROI) involves complicated tax and depreciation calculations. However, the pre-tax ROI is much simpler. It is given by the equation:

<math>ROI = C/I</math>

Where ROI in this case is the pre-tax ROI, C is the pre-tax cash flow generated by the project and I is the total investment required fro the project. This calculation, as it sounds, is a measure of the percentage return on the initial investment required for a project (typically the fixed costs, explained above). A higher ROI is a more profitable project.

==Project Cash Flows==
Project cash flows, much like it sounds, are the annualized cash flows, or revenue, generated from a new project. The first year of a project's cash flow is typically negative because the money is spent on initial investment. At first there will be a small expenditure on research and design expenses from engineering. Once the design is finished and construction is set to begin the expenditures will rapidly increase. These expenses may include things such as initial cost of renting or purchasing space/land, equipment & materials, initial labor to build a plant, etc. All in all research, design, procurement and construction, all which must be done prior to start up, will typically take 2-4 years. At this point the project will have reached maximum investment and typically has the most negative sum of cash flows.

The first year after start up, cash flows begin to become positive, however, the cash flows in the first year are usually reduced comparatively to years after. This is due to unexpected problems within the project/process. Typically machine down time, maintenance,etc. will be greatest in this year, causing the project to run under capacity. After the first year all of the problems within a process have begun to be discovered and resolved and so the process can run at full capacity with increase cash flows. From this point on, the only improvements in project cash flows come from process improvements (i.e. six sigma analysis, etc.), however, by using these techniques project cash flows can become greater year over year.

Toward the end of the life of a project, cash flows can begin to tail off in magnitude once again due to outdated equipment, new competition, or other increases in operating costs. Finally when a project is terminated there is a small additional cash flow related to the recovery from any assets such as equipment, land, etc. can all be resold or scrapped, however, there will also be some amount of costs related to deconstruction and land remediation (due to pollution or other harmful project outputs). Typically the recovered assets outweighs these costs.

A typical cash flow diagram of a project relating the cumulative cash flows over the life of the project is shown in the figure below.

[[File:Example11.jpg]]

Figure 1: Cash Flows Diagram. Taken from ChE 351 powerpoint slide 11 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 5, 2013.

As seen in Figure 1, the cash flows follow the pattern described in the paragraph above. The break even point of the project is the point at which the cash flows cross the x-axis. The life of the project is given by the duration of the graph.

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>PV=FV*DF</math>.

Where <math>PV</math> is the Present value, <math>FV</math> is the Future value, and <math>DF</math> is the discount factor.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>DF=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. (Towler 407). If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

where i' is the DCFROR. DCFROR is useful for comparing projects of different sizes and for comparing projects to other investments. (Towler 408).

===Discounted Payback Period===
DPP is the time required, after start-up, to recover the fixed capital costs required for a project with all cash flows discount back to time zero. (Turton 268). The project with the shortest discounted payback period is the most desirable.

==Annualized Costs==
Annualized Cost is another way of comparing capital expenses with future cash flows where the capital expense is converted into a recurring annual capital charge. It is useful for comparing the cost of assets with different lifetimes. (Towler 411). This is very similar to the way that mortgages are amortized over a 15 or 30 year lifetime. Annual payment can be represented as:

<math>A = P\,\frac{i\,\left( 1+i \right)^n} {\left(1+i\right)^n - 1}</math>

where P is the principle investment, n is investment period, and i is the discount rate. The annual capital charge ratio can be defined as:

<math>ACCR = A/P</math>

It is the fraction of the principle that must be paid each year to recover the investment at the target interest rate.

==Conclusion==
Measures of economic return are vital in the design phase of an engineering project. Companies will perform simulations to project capital and operating cost expenditures along with revenue generation, and use the resulting data to perform economic analyses, such as NPV and payback period. Based on the results of this analysis, the project will either be scrapped or it will be given the go ahead to begin granular design and construction. Measures of economic return provide a quick way for companies to determine the feasibility of a project, and therefore are extremely valuable.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. J.M. Douglas, Conceptual Design of Chemical Processes, McGraw-Hill: New York, 1988

Engineering economic analysis

2014-03-10T03:19:22Z

TJConsidine: /* References */

Authors: Michael Gleeson, Sean Kelton, Thomas Considine (ChE 352 in Winter 2014)

Steward: David Chen, Fengqi You

Date Presented: Feb. 22, 2014

==Measures of Economic Return==
The following are "back of the envelope" type calculations for economic return of a project. These measures are quick and easy because they ignore some of the more complicated parts of evaluating a project including factors such as depreciation, time value of money and taxes.
===Payback Time===
The payback time is defined as the period of time (in years) required to break even on the initial economic investment. It is given by the equation:

<math>T = I/C</math>

Where <math>T</math> is the payback time for the project, <math>I</math> is the total investment required for the project and <math>C</math> is the average annual cash flow generated by the project. This calculation is used to determine how quickly the project's fixed costs (i.e. land, machinery, etc.) can be recovered from the project. A small payback period is desirable for a new project.

===Return on Investment===
The regular return on investment (ROI) involves complicated tax and depreciation calculations. However, the pre-tax ROI is much simpler. It is given by the equation:

<math>ROI = C/I</math>

Where ROI in this case is the pre-tax ROI, C is the pre-tax cash flow generated by the project and I is the total investment required fro the project. This calculation, as it sounds, is a measure of the percentage return on the initial investment required for a project (typically the fixed costs, explained above). A higher ROI is a more profitable project.

==Project Cash Flows==
Project cash flows, much like it sounds, are the annualized cash flows, or revenue, generated from a new project. The first year of a project's cash flow is typically negative because the money is spent on initial investment. At first there will be a small expenditure on research and design expenses from engineering. Once the design is finished and construction is set to begin the expenditures will rapidly increase. These expenses may include things such as initial cost of renting or purchasing space/land, equipment & materials, initial labor to build a plant, etc. All in all research, design, procurement and construction, all which must be done prior to start up, will typically take 2-4 years. At this point the project will have reached maximum investment and typically has the most negative sum of cash flows.

The first year after start up, cash flows begin to become positive, however, the cash flows in the first year are usually reduced comparatively to years after. This is due to unexpected problems within the project/process. Typically machine down time, maintenance,etc. will be greatest in this year, causing the project to run under capacity. After the first year all of the problems within a process have begun to be discovered and resolved and so the process can run at full capacity with increase cash flows. From this point on, the only improvements in project cash flows come from process improvements (i.e. six sigma analysis, etc.), however, by using these techniques project cash flows can become greater year over year.

Toward the end of the life of a project, cash flows can begin to tail off in magnitude once again due to outdated equipment, new competition, or other increases in operating costs. Finally when a project is terminated there is a small additional cash flow related to the recovery from any assets such as equipment, land, etc. can all be resold or scrapped, however, there will also be some amount of costs related to deconstruction and land remediation (due to pollution or other harmful project outputs). Typically the recovered assets outweighs these costs.

A typical cash flow diagram of a project relating the cumulative cash flows over the life of the project is shown in the figure below.

[[File:Example11.jpg]]

Figure 1: Cash Flows Diagram. Taken from ChE 351 powerpoint slide 11 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 5, 2013.

As seen in Figure 1, the cash flows follow the pattern described in the paragraph above. The break even point of the project is the point at which the cash flows cross the x-axis. The life of the project is given by the duration of the graph.

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>PV=FV*DF</math>.

Where <math>PV</math> is the Present value, <math>FV</math> is the Future value, and <math>DF</math> is the discount factor.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>DF=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. (Towler 407). If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

where i' is the DCFROR. DCFROR is useful for comparing projects of different sizes and for comparing projects to other investments. (Towler 408).

===Discounted Payback Period===
DPP is the time required, after start-up, to recover the fixed capital costs required for a project with all cash flows discount back to time zero. (Turton 268). The project with the shortest discounted payback period is the most desirable.

==Annualized Costs==
Annualized Cost is another way of comparing capital expenses with future cash flows where the capital expense is converted into a recurring annual capital charge. It is useful for comparing the cost of assets with different lifetimes. (Towler 411). This is very similar to the way that mortgages are amortized over a 15 or 30 year lifetime. Annual payment can be represented as:

<math>A = P\,\frac{i\,\left( 1+i \right)^n} {\left(1+i\right)^n - 1}</math>

where P is the principle investment, n is investment period, and i is the discount rate. The annual capital charge ratio can be defined as:

<math>ACCR = A/P</math>

It is the fraction of the principle that must be paid each year to recover the investment at the target interest rate.

==Conclusion==
Hi TJ
==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. J.M. Douglas, Conceptual Design of Chemical Processes, McGraw-Hill: New York, 1988

Engineering economic analysis

2014-03-10T03:14:37Z

TJConsidine: /* References */

Authors: Michael Gleeson, Sean Kelton, Thomas Considine (ChE 352 in Winter 2014)

Steward: David Chen, Fengqi You

Date Presented: Feb. 22, 2014

==Measures of Economic Return==
The following are "back of the envelope" type calculations for economic return of a project. These measures are quick and easy because they ignore some of the more complicated parts of evaluating a project including factors such as depreciation, time value of money and taxes.
===Payback Time===
The payback time is defined as the period of time (in years) required to break even on the initial economic investment. It is given by the equation:

<math>T = I/C</math>

Where <math>T</math> is the payback time for the project, <math>I</math> is the total investment required for the project and <math>C</math> is the average annual cash flow generated by the project. This calculation is used to determine how quickly the project's fixed costs (i.e. land, machinery, etc.) can be recovered from the project. A small payback period is desirable for a new project.

===Return on Investment===
The regular return on investment (ROI) involves complicated tax and depreciation calculations. However, the pre-tax ROI is much simpler. It is given by the equation:

<math>ROI = C/I</math>

Where ROI in this case is the pre-tax ROI, C is the pre-tax cash flow generated by the project and I is the total investment required fro the project. This calculation, as it sounds, is a measure of the percentage return on the initial investment required for a project (typically the fixed costs, explained above). A higher ROI is a more profitable project.

==Project Cash Flows==
Project cash flows, much like it sounds, are the annualized cash flows, or revenue, generated from a new project. The first year of a project's cash flow is typically negative because the money is spent on initial investment. At first there will be a small expenditure on research and design expenses from engineering. Once the design is finished and construction is set to begin the expenditures will rapidly increase. These expenses may include things such as initial cost of renting or purchasing space/land, equipment & materials, initial labor to build a plant, etc. All in all research, design, procurement and construction, all which must be done prior to start up, will typically take 2-4 years. At this point the project will have reached maximum investment and typically has the most negative sum of cash flows.

The first year after start up, cash flows begin to become positive, however, the cash flows in the first year are usually reduced comparatively to years after. This is due to unexpected problems within the project/process. Typically machine down time, maintenance,etc. will be greatest in this year, causing the project to run under capacity. After the first year all of the problems within a process have begun to be discovered and resolved and so the process can run at full capacity with increase cash flows. From this point on, the only improvements in project cash flows come from process improvements (i.e. six sigma analysis, etc.), however, by using these techniques project cash flows can become greater year over year.

Toward the end of the life of a project, cash flows can begin to tail off in magnitude once again due to outdated equipment, new competition, or other increases in operating costs. Finally when a project is terminated there is a small additional cash flow related to the recovery from any assets such as equipment, land, etc. can all be resold or scrapped, however, there will also be some amount of costs related to deconstruction and land remediation (due to pollution or other harmful project outputs). Typically the recovered assets outweighs these costs.

A typical cash flow diagram of a project relating the cumulative cash flows over the life of the project is shown in the figure below.

[[File:Example11.jpg]]

Figure 1: Cash Flows Diagram. Taken from ChE 351 powerpoint slide 11 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 5, 2013.

As seen in Figure 1, the cash flows follow the pattern described in the paragraph above. The break even point of the project is the point at which the cash flows cross the x-axis. The life of the project is given by the duration of the graph.

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>PV=FV*DF</math>.

Where <math>PV</math> is the Present value, <math>FV</math> is the Future value, and <math>DF</math> is the discount factor.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>DF=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. (Towler 407). If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

where i' is the DCFROR. DCFROR is useful for comparing projects of different sizes and for comparing projects to other investments. (Towler 408).

===Discounted Payback Period===
DPP is the time required, after start-up, to recover the fixed capital costs required for a project with all cash flows discount back to time zero. (Turton 268). The project with the shortest discounted payback period is the most desirable.

==Annualized Costs==
Annualized Cost is another way of comparing capital expenses with future cash flows where the capital expense is converted into a recurring annual capital charge. It is useful for comparing the cost of assets with different lifetimes. (Towler 411). This is very similar to the way that mortgages are amortized over a 15 or 30 year lifetime. Annual payment can be represented as:

<math>A = P\,\frac{i\,\left( 1+i \right)^n} {\left(1+i\right)^n - 1}</math>

where P is the principle investment, n is investment period, and i is the discount rate. The annual capital charge ratio can be defined as:

<math>ACCR = A/P</math>

It is the fraction of the principle that must be paid each year to recover the investment at the target interest rate.

==Conclusion==
Hi TJ
==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

Process hydraulics

2014-02-24T01:00:52Z

TJConsidine: /* References */

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg|300px]]

Figure 1: Example Centrifugal Pump [6]

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

[[File:reciprocating piston pump.jpg|300px]]

Figure 2: Example Positive Displacement Pump [7]

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

[[file:compressor.jpg|300px]]

Figure 3: Example Continuous Flow Compressor [8]

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

7. "MARINE ENGINEERING." Reciprocating Positive Displacement Pump with Air Vessel. N.p., n.d. Web. 23 Feb. 2014.

8. "12.4 Multistage Axial Compressors." MIT.edu. N.p., n.d. Web. 23 Feb. 2014.

Process hydraulics

2014-02-24T00:59:27Z

TJConsidine: /* Continuous Flow Compressors */

File:Compressor.jpg

2014-02-24T00:59:01Z

TJConsidine:

Process hydraulics

2014-02-24T00:55:16Z

TJConsidine: /* Continuous Flow Compressors */

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg|300px]]

Figure 1: Example Centrifugal Pump [6]

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

[[File:reciprocating piston pump.jpg|300px]]

Figure 2: Example Positive Displacement Pump [7]

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

[[file:flow compressor.jpg|300px]]

Figure 3: Example Continuous Flow Compressor [8]

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

7. "MARINE ENGINEERING." Reciprocating Positive Displacement Pump with Air Vessel. N.p., n.d. Web. 23 Feb. 2014.

File:Flow compressor.jpg

2014-02-24T00:54:15Z

TJConsidine:

Process hydraulics

2014-02-24T00:43:40Z

TJConsidine:

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg|300px]]

Figure 1: Example Centrifugal Pump [6]

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

[[File:reciprocating piston pump.jpg|300px]]

Figure 2: Example Positive Displacement Pump [7]

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

7. "MARINE ENGINEERING." Reciprocating Positive Displacement Pump with Air Vessel. N.p., n.d. Web. 23 Feb. 2014.

Process hydraulics

2014-02-24T00:41:19Z

TJConsidine: /* Positive Displacement Pumps */

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg|300px]]

Figure 1: Example Centrifugal Pump [6]

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

[[File:reciprocating piston pump.jpg|300px]]

Figure 2: Example Positive Displacement Pump [7]

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

Process hydraulics

2014-02-24T00:40:55Z

TJConsidine:

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg|300px]]

Figure 1: Example Centrifugal Pump [6]

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

[[File:reciprocating piston pump.jpg|300px]]

Figure 2: Example Centrifugal Pump [7]

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

Process hydraulics

2014-02-24T00:34:35Z

TJConsidine:

Authors: Thomas Considine, Sean Kelton, Michael Gleeson

Steward: David Chen, Fengqi You

Date Presented: Feb. 2, 2014

==Introduction==

The transportation and storage of fluids is essential to a chemical process plant. Piping, valves, pumps and compressors comprise the major components of fluid handling equipment. The goal of process hydraulics in a design setting is to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. All three objectives must be designed in concert, and before the final controls system is designed. (Towler, 1207).

==Hydraulic systems & Pressure drop==

Overall pressure drops created by pumps and compressors must also include those created by the connecting pipes. These components must be designed in concert, to account for changes in elevation and friction losses in the pipe.

===Total Pressure Drop===

Pressure drops throughout the flow of a fluid can be summed to find the overall pressure drop of a defined system. For example: If a fluid A, initially at zero gauge pressure, is pumped to a pressure of 300 kPa, then flows through 10 meters of pipe resulting in a loss of 50 kPa, the final gauge pressure at the end of the pipe is 250 kPa. This type of analysis is useful when designing pressure systems over many components.

<math>Total Pressure Drop = \sum_i \Delta P_i = +300 kPa - 50 kPa = 250 kPa</math>

===Pressure Drop in Pipes===

When designing pumps and compressors, the loss of pressure due to piping is not negligible, and must be appropriately accounted for (Turton, 537). The <math>\Delta P</math> across a pipe is calculated as follows:

<math>P = (4*c*L/d)*(rho*v^2/2)</math>

where <math>c</math>, is the specific coefficient (typically 0.005 for turbulent flows)
<math>L</math> is the length of piping,
<math>d</math> is the diameter of piping,
<math>rho</math> is the density of the fluid, and
<math>v</math> is the velocity of the fluid.

An added term accounting for the pressure difference due to height is also necessary if there is a change in elevation.

Additionally, the first term in the equation can be altered to include an additional factor:

<math>(n + 4*c*L/d)</math>

where <math>n</math> is an empirical value to account for piping bends, restrictions, and other variables.

===Heuristics===

Both the process hydraulics and the economics of a system is affected by pipe sizing (Peters, 500). Heuristics, or "Rules-of-thumbs" have been developed to assist in optimizing pipe selection. While more detailed optimization techniques are available and commonly used, the rules of thumb provide a good starting point for pipe selection.

Suggested pipe velocities, in ft/s, for gases, liquids, and super-heated steam are approximately 60-100, 6, and 150, respectively (Towler Presentation, 9). Additionally, for liquid flow, the following equation provides a rule-of-thumb for optimal pipe diameter, in inches:

<math>D = \sqrt{Flow/10}</math>

Where D is the optimal diameter, and Flow is in units of gallons/minute.

==Pumps & Compressors==
Pumps and Compressors are used to pressurize liquids and gases, respectively, and to transfer them from one location to another. In general, it is preferable to increase the pressure of a stream by pumping a liquid rather than compressing a gas because it is far less expensive. This is because the power needed to increase the pressure of a stream is:

<math>W = \int\limits_{P_1}^{P_2} V\, dP</math>

where V is the volumetric flow rate. Generally, the volumetric flow rate of a liquid is approximately two orders of magnitude less than the volumetric flow rate of a gas, which means a 10hp pump is comparable in fluid pressurizing capacity to a 1000hp compressor. (Seider 132).

===Pumps===
As stated above, pumps require relatively little power compared to gas compressors. However, they are easily vapor locked when pumping liquids near the bubble point because small amounts of vapor can become trapped within their rotating blades. Pumps increase the pressure energy of the effluent fluid by the transfer of kinetic energy from the motor to the fluid, through the impeller. (Seider 642). Selection of pumps for specific services requires knowledge of the liquid to be handled, the total dynamic head required, the suction and discharge heads, and in most cases, the temperature, viscosity, vapor pressure, and density of the fluid. The different types of pumps used in industry can be classified as centrifugal pumps, positive displacement pumps, jet pumps, and electromagnetic pumps. (Peters 508).

====Centrifugal Pumps====
This type of pumps is the most widely used in industry. They range in capacity from .5 to 20,000 meters cubed per hour. In the centrifugal pump, the fluid enters the pump are the center of a rotating impeller, where it is thrown outward by centrifugal force. The fluid at the edge of the impeller gains a high kinetic energy, which is then converted into pressure energy, which supplies the pressure difference between the suction side and the delivery side of the pump. (Peters 510).

[[File:centrifugal pump.jpg]]

Figure 1: Example Centrifugal Pump (Taken from source 6)

====Positive Displacement Pumps====
In positive displacement pumps, a fixed volume is alternately filled and emptied of the pump fluid by action of the pump. In general, overall efficiencies of positive displacement pumps are higher than those of centrifugal pumps because internal losses are minimized. However, the range of capacities that these pumps can handle is somewhat limited. There are two classes of positive displacement pump, reciprocating and rotary. Reciprocating pumps use valves that are operated by pressure difference to introduce and discharge the liquid being pumped. They generally can deliver fluids with high efficiency against high pressure. In rotary pumps, two intermeshing gears are fitted into a casing. Fluids becomes trapped between the teeth of the gears and is transported to the discharge side of the pump. (Peters 514).

====Jet Pumps====
Jet pumps use the momentum of one fluid to transport the desired fluid. Efficiency of jet pumps is generally low, and these are mainly useful for situations in which the head to be attained is low and less than the head of the fluid used from pumping. (Peters 515).

====Electromagnetic Pumps====
Electromagnetic pumps use the principle that a conductor in a magnetic field, carrying a current that flows at right angles to the field, has a force exerted on it. These pumps are used to move fluids that exhibit electromagnetic properties. (Peters 515).

===Compressors===
Gas compressors are designed to increase the pressure of gases. Even small amounts of liquids can cause significant amounts of degradation to the compressor blades, so most compressors are designed to avoid condensation. Like pumps, the feed enters the eye of the impeller unit. Compressors are generally much larger than pumps, and they are well insulated to facilitate operation on light gases. To avoid excessively high temperatures, individual compressors are designed to operate at small compressor ratios <math>P_2/P_1</math>, typically less than 5. If the compression ratio is greater than 5, multistage compressors are used. (Seider 644-646). Compressors are generally classified into two major categories; continuous flow compressors and positive displacement compressors.

====Continuous Flow Compressors====
Centrifugal and Axial Compressors are the two main types of continuous flow compressors. Centrifugal compressors are used for higher pressure ratios and lower flow rates, while axial compressors are used for lower stage pressure ratios and high flow rates. The pressure ratio of a single stage centrifugal compressor is roughly 1.2:1, while the pressure ratio of axial flow compressors is between 1.05:1 and 1.15:1. Because of the low pressure ratios for each stage, a single compressor may include a number of stages in one casing to achieve the desired overall pressure ratio. (Peters 521).

====Positive Displacement Compressors====
These units are essentially volume gas movers with variable discharge pressures. They operate in much the same way as positive displacement pumps. (Peters 522).

===Economics of Pumps and Compressors===
Pumps are relatively cheap in terms of processing equipment. In 1997 dollars, they would cost between $390 and $1500 base cost multiplied by a ~2.38 (because pumps usually cost much less than $200,000) factor for the installation costs. Therefore their total installed costs today is $1000-$3500 multiplied by some time correction factor to account for inflation. For this reason it is typically preferable to condense a vapor to liquid, pump up the liquid, then evaporate the liquid, rather than compress a gas. (Biegler, 133-135).

Compressors are one of the most expensive pieces of process equipment. In 1997 dollars they cost about $23,000 as a base cost multiplied by a ~3.11 (because compressors are typically less than $200,000) factor to account for installation costs. Therefore their total installed cost today is ~$71,500 multiplied by a correction factor to account for the inflation over time; nearly 70 times as expensive as a pump! For this reason in industry compressing a gas within your process is avoided if at all possible. (Biegler, 133-135).

==Valves==
A valve is a mechanical tool used to control the flow of material in a system by blocking or restricting the materials flow path; typically used on piping. Valves serve many purposes including but not limited to: beginning or quenching the flow of a material through a system, regulating the flow rate of the material traveling through a system, regulating the pressure of a material flowing through a system, prevent back-flow of a material and changing the flow direction at intersection points. Any valve in a piping system will cause a pressure drop. As a rule of thumb, 10 psi change in pressure should be accounted for across each valve when designing a plant. (Towler)

More specifically, the table below gives the pressure drop of different types of valves in the number of velocity heads lost.

Table 1: Pressure Drops Across Valves. Taken from ChE 351 powerpoint slide 25 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.
{| class="wikitable"
|-
!Valve or Fitting Type
!No. Velocity Heads, n
!Valve or Fitting Type
!No. Velocity Heads, n
|-
|45 degree ell, standard
|0.35
|Globe valve, bevel seat, open
|6
|-
|90 degree ell, standard
|0.75
|Globe valve, bevel seat, ½ open
|9.5
|-
|180 degree bend, close return
|1.5
|Globe valve, plug disk, open
|9
|-
|Tee, along run, branch blanked off
|0.4
|Globe valve, plug disk, ¾ open
|13
|-
|Tee, entering run or entering branch
|1
|Globe valve, plug disk, ½ open
|36
|-
|Tee, branching flow
|1
|Globe valve, plug disk, ¼ open
|112
|-
|Gate valve, open
|0.17
|Plug valve, 5 degrees open
|0.05
|-
|Gate valve, ¾ open
|0.9
|Plug valve, 20 degrees open
|1.56
|-
|Gate valve, ½ open
|4.5
|Plug valve, 40 degrees open
|17.3
|-
|Gate valve, ¼ open
|24
|Plug valve, 60 degrees open
|206
|-
|Check valve, swing
|2
|Pipe union
|0.04
|}

=== Gate Valve ===
A gate valve is comprised of a wedge that slides up and down perpendicular to the path of fluid flow on screw type mechanism, which spins in opposite directions to open/close the valve, in order to allow and block fluid flow respectively. This type of valve is an ON/OFF valve and therefore should either be operated fully open or fully closed. Operating partially open can degrade the seal on the valve. The fluid path is straight through the valve and therefore minimal pressure drop results. (Towler)

[[File:Example.jpg]]

Figure 1: Gate Valve Example. Taken from ChE 351 powerpoint slide 14 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Ball Valve===
A ball valve is another type of ON/OFF valve that only operates fully opened or closed with the flow path straight through the valve. However, these valves only require a quarter turn to open or close the valve and therefore can quench flow much faster than a gate valve. Rather than blocking flow with a wedge, a ball valve turns so that the opening aligns with the pipe to allow flow or pipe wall to block flow. (Towler)

[[File:Example3.jpg]]

Figure 2: Ball Valve Example. Taken from ChE 351 powerpoint slide 16 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Butterfly Valve===
A butterfly valve also requires only a quarter turn to switch between the open and closed position. A flat plate switches positions between being parallel or perpendicular to flow in order to allow or prevent flow through the valve respectively. This valve does not seal well on its own and, unaided, can be pushed open by fluid flow, therefore extra materials are required for complete shutdown of flow. (Towler)

[[File:Example4.jpg]]

Figure 3: Butterfly Valve Example. Taken from ChE 351 powerpoint slide 17 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Plug Valve===
A plug valve is very similar to a ball valve, except it is used in situations in which a better seal is needed. The valve uses plug stationed in lubricated lining to provide the seal and once again a quarter turn will open/close the valve by aligning the hole within the plug to the pipe/wall respectively. There is an upper limit to the temperature a which a plug valve can be used, ~450 F, because after this point heat expansion differences of the liner and plug ruins the seal. (Towler)

[[File:Example5.jpg]]

Figure 4: Plug Valve Example. Taken from ChE 351 powerpoint slide 18 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Globe Valve===
A globe valve is a type of throttling valve, controlling the fluid flow rate, in which the height of a disk is adjusted between two vertical plates. The gap between the disk and the second vertical plate, known as the seat, can be adjusted to regulate flow rate, however, the valve should not be run at very slow flow rates (<10% open) because the flowing fluid will cause damage to the seat. The two vertical directional changes of the fluid flow path cause greater pressure drops across these valves. This type of valve can be adjusted automatically (using a machine program) or manually by a worker. (Towler)

[[File:Example6.jpg]]

Figure 5: Globe Valve Example. Taken from ChE 351 powerpoint slide 19 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Needle Valve===
A needle valve is much like a globe valve, however, a stem with a conical head is used to control the flow rate. The conical head provides a more accurate and precise flow rate control. Additionally, the conical head does not have problems at low flow rates as the flat disk of a globe valve exhibits. (Towler)

[[File:Example7.jpg]]

Figure 6: Needle Valve Example. Taken from ChE 351 powerpoint slide 21 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Control Valve===
Control valves are a classification of automatic globe valves. These valves use an electric actuator or some type of compressed air system to adjust the flow rate through the valve via signaling from an electric control program. (Towler)

[[File:Example8.png|300px]]

Figure 7: Control Valve Example. Taken from ChE 351 powerpoint slide 22 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

===Check Valve===
Check valves are valves that are used to control the flow direction within the pipe (i.e. prevent back-flow). The three main types are swing valves, lift valves and wafer valves (respectively below). Swing valves push a swinging mechanism forward to allow forward flow, but is blocked in the other direction because the weight of the disc holds itself in place. These valves are most common in industry. These valves are not good when flow rate pulsates or is very high, nor if the fluid is a slurry or a gas. Lift valves use vertical plates, as in a throttling valve, to divert flow in an upward direction to lift a move-able piece that is otherwise held in place by gravity preventing reverse flow. Wafer valves use a circular wafer that can only twist in one direction so that forward flow in the pipe spins the wafer to align with the fluid flow and move forward, however, in the reverse direction the hinge is blocked so the wafer can not spin allow flow. These valves require a smaller pressure drop to open and are generally cheaper however they must be used in a very strict flow rate range (~3-11 ft/s). (Towler)

[[File:Example9.png]]

Figure 8: Swing Check Valve Example. Taken from ChE 351 powerpoint slide 24 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example10.png|300px]]

Figure 9: Lift Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

[[File:Example11.png|300px]]

Figure 10: Wafer Check Valve Example. Taken from ChE 351 powerpoint slide 23 (written by Jennifer Cole) for class instruction. Slides presented on Oct. 28, 2013.

==Conclusion==

The transportation and storage of fluids is a key variable in the design and optimization of a chemical process facility. The major components involved in this step of process design are the piping, valves, pumps and compressors. Process hydraulics design aims to overcome frictional losses in piping and equipment, provide correct operating conditions, and overall assist in the controls of the plant. These three objectives must be designed in concert, as together they effect many variables within both the chemistry, engineering, and economics of the plant.

==References==
1. G.P. Towler, R. Sinnott, ''Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design'', Elsevier, 2012.

2. L.T. Biegler, I.E. Grossmann, A.W. Westerberg, ''Systematic Methods of Chemical Process Design'', Prentice-Hall: Upper Saddle River, 1997.

3. W.D. Sieder, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.

4. R.T. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, ''Analysis, Synthesis, and Design of Chemical Processes'', Prentice Hall: Upper Saddle River, 2003.

5. M.S. Peters, K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 5th Ed., McGraw-Hill: New York, 2003

6. "Pumps." Enggcyclopedia. N.p., n.d. Web. 23 Feb. 2014.

File:Reciprocating piston pump.jpg

2014-02-24T00:34:03Z

TJConsidine:

File:Centrifugal pump.jpg

2014-02-24T00:19:06Z

TJConsidine:

Engineering economic analysis

2014-02-23T22:35:28Z

TJConsidine:

==Introduction==

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>Present value=future value*discount factor</math>.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>Discount factor=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. (Towler 407). If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

where i' is the DCFROR. DCFROR is useful for comparing projects of different sizes and for comparing projects to other investments. (Towler 408).

===Discounted Payback Period===
DPP is the time required, after start-up, to recover the fixed capital costs required for a project with all cash flows discount back to time zero. (Turton 268). The project with the shortest discounted payback period is the most desirable.

==Annualized Costs==
Annualized Cost is another way of comparing capital expenses with future cash flows where the capital expense is converted into a recurring annual capital charge. It is useful for comparing the cost of assets with different lifetimes. (Towler 411). This is very similar to the way that mortgages are amortized over a 15 or 30 year lifetime. Annual payment can be represented as:

<math>A = P\,\frac{i\,\left( 1+i \right)^n} {\left(1+i\right)^n - 1}</math>

where P is the principle investment, n is investment period, and i is the discount rate. The annual capital charge ratio can be defined as:

<math>ACCR = A/P</math>

It is the fraction of the principle that must be paid each year to recover the investment at the target interest rate.

Engineering economic analysis

2014-02-23T22:30:36Z

TJConsidine:

==Introduction==

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>Present value=future value*discount factor</math>.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>Discount factor=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. (Towler 407). If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

where i' is the DCFROR. DCFROR is useful for comparing projects of different sizes and for comparing projects to other investments. (Towler 408).

===Discounted Payback Period===
DPP is the time required, after start-up, to recover the fixed capital costs required for a project with all cash flows discount back to time zero. (Turton 268). The project with the shortest discounted payback period is the most desirable.

==Annualized Costs==
Annualized Cost is another way of comparing capital expenses with future cash flows where the capital expense is converted into a recurring annual capital charge. It is useful for comparing the cost of assets with different lifetimes. (Towler 411). This is very similar to the way that mortgages are amortized over a 15 or 30 year lifetime. Annual payment can be represented as:

<math>P\,\frac{i\,\left( 1+i \right)^n} {\left(1+i\right)^n - 1}</math>

Engineering economic analysis

2014-02-23T22:07:15Z

TJConsidine:

==Introduction==

==Taxes==

Chemical production facilities are subject to the same financial levies by the government as all corporations. Specifically, corporations typically pay income taxes, and may collect incentives based on state and federal regulations. Detailed tax filings are almost always conducted by the accounting or financial department of a corporation. When preparing process economics estimations, taxes should be included, however all final cost estimates reported to management should be prepared by the appropriate specialist (Douglas, 23).

===Corporate Taxes===

The specific tax codes will vary from state to state, and from country to country (Peters, 303). The common factor will be that income is taxed at marginal rates. In the United States, this percentage is 35%, although the effective rate may be lower.

Corporate income taxes is a yearly expense. The percentage rate is to be applied on the income, not the revenue. See other Economics sections on the difference between income and revenue.

===Investment Incentives===

Local, state, and federal governments generally encourage capital investments by corporations. Financial incentives afforded to corporations include low interest loans, free capital for research and development, and tax holidays for new technologies.

When conducting economic estimates of a chemical process plant, especially if the plant utilizes efficient or "green" technology, it is important to investigate any and all sources of government incentives.

==Depreciation==

Depreciation, in the colloquial sense, is the loss of value of an item. As it pertains to the chemical process industry, depreciation is the loss of value due to "wear and tear" of the components and facilities of the plant. It is important to note that this does not include working capital or land.

===Economics of Depreciation===

Depreciation can be thought of as a yearly expense that the plant incurs. It can then be considered a cost, effectively reducing the income and thus the income tax. However, depreciation is not an actual cash flow. There is no transfer of money.

Note how depreciation lowers the amount of taxes:

<math>T=(P-D)*t</math>

where <math>T</math> is the taxes due;
<math>P</math> is the gross profit;
<math>D</math> is the depreciation; and
<math>t</math> are the taxes due.

Two commons methods of calculating depreciation are discussed in the next sections.

===Straight Line Depreciation===

Straight line depreciation is the most common method of approximating depreciation when calculating profitability measures, such as return on investment (Seider, 392).

In this method, the depreciable value <math>Cd</math> is written off over the total life of <math>n</math> years at a constant linear rate:

<math>Di=Cd/n</math>, where <math>i</math> is each year in the lifetime.

Therefore, the book value <math>Bm</math>, or the initial cost of the item minus the accumulated depreciation charges, at year <math>m</math>, can be defined as:

<math>Bm=C-m*Cd/n</math> where <math>C</math> is the initial cost of the item.

===Depreciation Case Study===

For example, let us find the book value after 3 years of a compressor which originally costs $50,000, has a depreciable value of $5,000, and has a lifetime of 20 years.

<math>Di=5,000/20=250</math>

<math>Bm=$50,000-250*3=$49,250</math>

Therefore we can say that over the three years, the compressor has cost the process a difference of $750, which can be taken out of the taxable income.

==Time Value of Money==

Money that is available now is inherently more valuable than the same amount in the future, because that money could be used as capital for an investment that earns interest.

Capital that is available in the future is said to be "discounted". The present value of money, which is discussed in further detail in the coming sections, is a discounted amount of the future value:

<math>Present value=future value*discount factor</math>.

The discount factor, which takes into account an estimated interest rate gained on present money, is calculated for every year <math>n</math>:

<math>Discount factor=1/(1+i)^n</math>.

This implies that the a given amount of money in the future has less value as the length of future time increases, and as the expected amount of interest that current capital could gain increases. See Net Present Value for more information on this subject.

Of additional interest is the different between the time value of money and inflation. It is important to note that these two concepts are completely different. Inflation is the yearly rate at which the price of a certain good will increase (Biegler, 169). Although the mathematics and calculations are similar, inflation is generally a result of socioeconomic factors increasing the supply of money, and not the potential interest rate gained on current capital.

==Discounted Cash Flow Methods==
As discussed above, the value of money is directly related to time, insofar as $500 today is worth more than $500 in two years. Discounted cash flow methods, such as net present value (NPV) and internal rate of return (IRR) take the time value of money into account. The main difference between nondiscounted and discounted cash flows is that all cash flows are related to time zero in the latter.(Turton 266).

===Net Present Value===
Net Present Value (NPV), also known as Net Present Worth (NPW), gives the present value of all payments and provides a basis of comparison for projects with different payment schedules but similar lifetimes. (Biegler 151). In making comparisons between projects, the larger the net present worth, the more favorable the investment. (Peters 328). It is one of the most widely used economic measures because it captures the time value of money, the value of investment incentives and variations in construction schedule, while allowing for price forecast models that include cyclic behavior. The NPV can be represented as:

<math> NPV = \sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i \right) ^n} </math>

where <math>CF_n</math> = cash flow in year n and <math>t</math> = project lifetime and i is the discount rate as a decimal. If the net present value is equal to zero, the return of the project is equal to the return that the discount rate would provide. (Peters 328). There are several drawbacks to NPV; it does not measure bang for buck, and it cannot be optimized unless an upper bound is set to the plant size.

===Discounted Cash Flow Rate of Return===
The DCFROR is the interest or discount rate for which the NPV is equal to zero. (Turton 270). This means that DCFROR represents the highest after tax interest rate at which the project can break even. Often, corporation management will set an "internal" interest rate, which is the lowest rate of return that a company will accept for any new investment. If the DCFROR is greater than this internal rate, the investment is favorable. NPV and DCFROR are almost always used together. (Peters 328). The DCFROR can be represented as:

<math>\sum_{n=1}^{n=t}\frac{CF_n} {\left( 1+i' \right) ^n} = 0 </math>

Engineering economic analysis

2014-02-23T21:56:25Z