- Email: [email protected]
Capital cost of compressors for conceptual design
Accepted Manuscript Title: Capital Cost of Compressors for Conceptual Design Author: William L. Luyben PII: DOI: Reference:
S0255-2701(17)31316-8 https://doi.org/10.1016/j.cep.2018.01.020 CEP 7175
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
24-12-2017 19-1-2018 25-1-2018
Please cite this article as: William L.Luyben, Compressors for Conceptual Design, Chemical Processing https://doi.org/10.1016/j.cep.2018.01.020
Capital Cost of Engineering and
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Paper submitted to Chemical Engineering and Processing: Process Intensification CEP_2017_1148
SC RI PT
Capital Cost of Compressors for Conceptual Design
M
A
N
U
William L. Luyben* Department of Chemical Engineering Lehigh University Bethlehem, PA 18015
EP
TE
D
December 24, 2017 Revised January 19, 2018
A
CC
* [email protected]; 610-758-4256; FAX 610-758-5057
1
Highlights
SC RI PT
Published compressor capital cost predictions shows large variability and use only compressor power to estimate capital cost. Aspen Economic predictions are larger for low suction pressures. A simple method to incorporate the effect of pressure is presented. Optimum compression ratios in multistage compression trains do not follow the conventional heuristic of keeping the compression ratio the same in all stages.
Abstract
U
Many process intensification techniques involve the use of gas compressors. Gas
N
recycles are typically used to improve yield and selectivity in reactor/separation
A
processes. Vapor recompression in distillation systems are becoming more widely
M
applied, particularly with complex separations such as divided-wall, reactive, extractive
D
and azeotropic distillation systems.
TE
At the conceptual design stage it is vital to have reasonable estimates of the capital cost of compressors involved in these processes. The literature correlations use
EP
only the compressor power to estimate capital cost, and there are significant differences in the published methods. However, in addition to power, it appears that suction pressure
CC
also must be considered in cost estimation. The proprietary Aspen Economics program
A
gives results that show a strong dependency of cost on the pressure of the gas being compressed. The purpose of this paper is to provide a simple method to estimate compressor capital cost that incorporates both compressor power and compressor suction pressure. A
2
case study illustrates that the conventional heuristic of using equal compression ratios in multistage compression trains does not give the optimum economic design.
Compressor cost; vapor recompression; conceptual design
1. Introduction
SC RI PT
Key Words
Reliable and easy-to-use methods for estimating the cost of equipment are vital at the conceptual design stage of chemical plant design. All design textbooks provide
U
graphs and/or equations for making these estimates. The capital costs of pressure vessels
A
available and are in fairly good agreement.
N
and heat exchangers are two of the most important, and existing published methods are
M
However, the situation with compressor cost estimation is quite different. The
D
published methods show significant differences in their predicted results. In addition the
estimation.
TE
published methods use the single parameter of compressor power requirements for cost
EP
Aspen Economics is a proprietary software package that predicts much larger compressor capital costs than the published methods. More importantly it shows a strong
CC
dependence of cost on compressor suction conditions in addition to compressor power.
A
For the same compressor power (same compression ratio, inlet temperature, gas composition and molar throughput), Aspen Economics predicts that compressor capital investment increases as compressor suction pressure decreases. Compressors are volumetric devices, and they handle volumetric flowrates. As suction pressure decreases, more volume of gas must be captured by the turbine blades
3
for the same mass or molar throughput. Therefore the size of the compressor must increase. Nothing has been found in the published literature that quantifies this effect. The purpose of this paper is to provide a simple method to estimate compressor
SC RI PT
capital cost that incorporates both compressor power and compressor suction pressure.
2. Published Methods
The chemical engineering design textbooks all present methods for estimating compressor capital costs. Douglas1 give a widely used correlation.
N
U
Compressor Cost ($) 5840(kW )0.82
A
For a numerical example, consider the compression 1000 kmol/h of nitrogen at suction
M
conditions of 1 bar and 50 oC. Assuming an ASTM polytropic efficiency of 80% and
D
using Peng-Robinson physical properties, Aspen Plus predicts a power requirement of
TE
1010 kW for a typical compression ratio of 2.5. The Douglas method gives a compressor and drive capital cost of $1,700,000 using stainless steel materials of construction.
EP
Changing the suction pressure and keeping the same compression ratio does not significantly change the power requirement. So the Douglas method does not have any
CC
dependence of capital cost on suction pressure. The design textbook by Turton et al2 gives separate cost curves for the
A
compressor and for the drive. Only compressor power is used to estimate capital cost Using the numerical example considered above, Turton predicts a carbon-steel compressor cost of $280 per kW at 1000 kW and an electric drive cost of $120 per kW.
4
Using a SS-to-CS ratio of 5.8/2.7 for the compressor, the total capital cost predicted is $722,000. This is less than half the cost predicted by Douglas. Peters et al3 predict a cost of $2,000,000 using only compressor power as the
SC RI PT
costing parameter. Seider et al4 also use only compressor power to predict a cost of $1,000,000.
The only reference that hints at the effect of suction pressure is Ulrich5. Figure 529 in Ulrich gives a plot in which the abscissa is the volumetric flowrate of the gas, not
the normal power. But this flowrate is given at standard conditions (1 atm), so the effect
U
of suction pressure is not included. Ulrich predicts a cost of $417,000.
N
Calado6 explores compression trains for sequestration of carbon dioxide and
A
proposes the following correlations for stainless steel compressors and electric motor
M
drives.
D
Compressor Cost ($) 2.5 exp 7.58 0.8 ln(hp)
TE
Motor Cost ($) 2049 668.16(hp)
EP
The Calado capital cost prediction for the numerical example is $1,530,000. No effect of suction pressure on capital cost is included.
CC
Table 1 summarizes the comparison of the several published capital cost predictions. The parameters are 1000 kmol/h of nitrogen gas at 1 bar and 50 oC with a
A
compression ratio of 2.5. The variability among the several methods is clearly very large and introduces too much uncertainty for even conceptual design evaluations. As we demonstrate in the next section, the prediction of Aspen Economics is the largest, so it should be used for conservative design (highest capital cost).
5
3. Aspen Economics Predictions The Lehigh Chemical Engineering senior design course uses a wide variety of process design projects to expose students to the basic principles of design and plantwide
SC RI PT
control. Each three-student group works on the conceptual design of different processes, so 15 to 20 projects are explored each year. Many of these processes include multi-train compressors. The conventional engineering heuristic of selecting the same compression ratio in each stage is used with the number of stages selected to avoid discharge
U
temperatures greater than 200 oC as recommended by Walas7. With interstage cooling,
N
the power requirements in each stage are approximately the same.
A
Up until a few years ago the capital cost was estimated using the Douglas
M
Correlation. Then Aspen Economics became available and is now used since its estimates are more conservative (higher capital investment).
D
However we observed in many projects that the Aspen Economics predictions did
TE
not give the same capital cost for each stage even though the power requirements were the same. The first compressor cost was often much larger than the second and third.
EP
One logical physical reason for the higher cost is the larger size required at low
CC
pressure and density. However, we have been unable to find any quantitative discussion of this in the published literature. Private communications with a number of compressor
A
design experts came up empty. Clearly the compressor sizing and the costing methods used in Aspen Economics include these concepts. Another insight into why low suction pressure increases compressor cost is gained by comparing the power to compress an ideal gas with that to compress a real gas. The
1 P 2 (8.326 kJ / kmol K ) T1 ( K ) 1 Power (kW ) Flowrate (kmol / sec) P1 1
6
thermodynamic equation for the power to adiabatically and reversibly compress an ideal
SC RI PT
gas is given in the following equation.
The ratio of heat capacities is 1.4 for an ideal gas. For the numerical case considered above, the power to compress an ideal gas is 1410 kW, which is 40% larger than the
power calculated for the real gases. As suction pressure decreases, gases become more ideal. So we would expect that there should be an effect of pressure on compressor
U
design.
N
At the conceptual design stage it would be useful to have a simple way to
A
quantitatively incorporate the effect of suction pressure on capital cost. That is the
D
M
provided in this paper.
TE
4. Correction Factor
A number of cases were run using Aspen Plus to simulate the compressor and
EP
Aspen Economics to evaluate capital costs. Throughput was fixed at 1000 kmol/h with a suction temperature of 50 oC. Compression ratio was fixed at 2.5 and cases were run with
CC
different suction pressures. Different gases have different ratios of heat capacities, so
A
power requirements change with the gas compressed. Figure 1 gives results from Aspen Economics for several gases. Capital cost of a
stainless steel compressor and the associated motor drive are shown as a function of the suction pressure. The pressure dependence of cost is clearly shown.
7
Figure 2 suggests the use of a correction factor as a simple method for adjusting the capital cost. Using the convenient Douglas correlation as the basis, compressor cost is multiplied by the appropriate correction factor for a specified suction pressure and type of
SC RI PT
gas.
5. Multistage Compressor Design
The conventional design method for multistage compression systems is to select
the required number of stages such that the discharge temperature does not exceed 200 oC
U
(Walas7). Then the compression ratio in each stage is selected to be the same. For
N
example, suppose the overall compression ratio for the system is 8, going from the initial
A
feed gas pressure to the final discharge pressure at the end of the compressor train.
M
Assuming that the temperature limitation dictates that three stages should be used, the compression ratio CR in each stage is (8)0.3333. The general relationship is the following. 1/ N
TE
D
CR in each stage CR Total
However, the results given above in this paper demonstrate that the capital cost of
EP
the early stages in the train, which are at lower pressures, will be larger than those with higher suction pressures. Therefore, the consequence of having higher capital costs with
CC
low suction pressure is that the conventional heuristic used for multistage compressor
A
design is no longer valid. To illustrate this, we take a case in which the following design parameters are
given: 1. Gas flowrate is 1000 kmol/h of nitrogen. 2. Inlet temperature is 50 oC.
8
3. Feed pressure is 0.5 bar. 4. The final desired pressure is 3.125 bar, which corresponds to an overall compression ratio of 6.25.
SC RI PT
5. The maximum discharge temperature in any stage is 200 oC.
A single-stage compressor gives a discharge temperature of 343 oC and requires 2405 kW of power. This exceeds the temperature limitation, so a two-stage compressor system
must be used. Using the conventional design approach with equal compression ratio in
U
each stage (CR = 2.5) with interstage cooling back down to 50 oC gives discharge
N
temperatures of 175 oC and requires 1011 kW in each stage. This is a feasible design, but
A
is it the economic optimum with the lowest total annual cost?
M
Table 2 gives the capital and energy costs of several cases. The first column gives detailed design parameters and economic results for the conventional 2-stage
D
compression train with equal compression ratios (CR = 2.5) in the two compressors. The
TE
capital cost of the first compressor is much larger than that of the second ($6,193,000
EP
versus $2,574,000). This suggests that a lower compression ratio in the first compressor and a higher compression in the second might lower capital investment. The total energy
CC
cost of this conventional design is $1,020,000 per year (using $16 per GJ electricity cost).
A
The total annual cost is $3,981,000 per year using a 3-year payback period. The second column in Table 2 gives results for a modified design with adjusted
compression ratios. The first step is to find the compression ratio for the second stage that would just satisfy the 200 oC maximum temperature limitation. A compression ratio CR = 2.9 produces the desired discharge temperature. Since the discharge pressure in the
9
second compressor is 3.125 bar, the suction pressure in the second compressor must be 1.078 bar. The first stage in this modified design now has a lower compression ratio CR = 2.135 instead of CR = 2.5 in the original. The result is a lower capital cost of the first
SC RI PT
compressor ($4,638,000) while only a slightly higher capital cost of the second compressor ($2,608,000). Total capital cost is $7,358,000. Total energy cost increases
only slightly to $1,031,000 per year. Total annual cost is reduced 12% to $3,484,000 per year.
Another alternative suggests itself at this point. Suppose we use a 3-stage
U
compression train that would give even lower compression ratios in the low-pressure
N
stages. This design is expected to give a lower total annual energy cost, but it would have
A
three compressors and two interstage coolers, which might increase capital cost. The third
M
column in Table 2 shows that the capital cost of the first compressor drops to $3,969,000 using a compression ratio of 1.6. The second compressor is $2,315,000 with a
D
compression ratio of 1.7 and the third compressor is $1,826,000 with a compression ratio
TE
of 2.3. Total capital investment increases to $8,299,000. Energy cost is lower ($983,200
EP
per year) as expected, but not enough to offset the increase in capital cost. Total annual cost increases to $3,750,000 per year.
CC
So the 2-stage design with a lower compression ratio in the first stage is the
A
economic optimum.
6. Conclusion A method for adjusting compressor capital costs using both power and suction pressure is proposed to give more realistic estimates for conceptual design of compression system. A case study illustrates that the conventional heuristic of equal
10
compression ratios in each stage of a multistage compression train does not give the economic optimum design.
SC RI PT
References
1. Douglas, J. M. Conceptual Design of Chemical Processes McGraw-Hill (1988) 2. Turton, R., Bailie, R. C., Whiting, W, B., Shaeiwitz, J. A., Bhattacharyya, D. Analysis, Synthesis and Design of Chemical Processes, 4th Ed. Prentice Hall
Peters, M., Timmerhaus, K. D., West, R. E. Plant Design and Economics for
N
3.
U
(2012)
A
Chemical Engineers, 5th Ed. McGraw-Hill (2003)
D
2nd Ed.Wiley (2003)
M
4. Seider, W. D., Seader, J. D., Lewin, D. R. Product & Process Design Principles
TE
5. Ulrich, G. D. A Guide to Chemical Engineering Process Design and Economics Wiley (1984)
EP
6. Calado, M. P. A. “Modeling and design synthesis of a CCS compression train system via MINLP optimization” MS Thesis (2012) Tecnico, Lisboa
CC
7. Walas, S. M. Chemical Process Equipment: Selection and Design Butterworth-
A
Heinemann (1988)
11
M
A
N
U
SC RI PT
Figure Captions
A
CC
EP
TE
D
Figure 1 – Effect of suction pressure on capital cost.
12
SC RI PT U
A
CC
EP
TE
D
M
A
N
Figure 2 – Correction factor
13
Table 1 – Comparison of Compressor Cost Predictions Douglas
$1,700,000
Turton
$722,000
Peters
$2,000,000
Seider
$1,000,000
Ulrich
$417,000
Calado
$1,530,000
Aspen Economics
$2,580,000
SC RI PT
Capital Investment
A
CC
EP
TE
D
M
A
N
U
Basis: 1000 kmol/h nitrogen gas at 1 bar and 50 oC; 2.5 compression ratio
14
Table 2 – Case Studies Conventional Modified Two-Stage Two-Stage
InterCooler
CR
2.5
2.155
1.6
Power (kW) Tout (oC) Capital Cost (106 $) Pin (bar) Pout (bar)
1011 175 6.193
824.4 152 4.638
471 109 3.969
1.25 3.125
1.078 3.125
0.8 1.36
CR
2.5
2.9
1.7
Power (kW) Tout (oC) Capital Cost (106 $) Pin (bar) Pout (bar) CR Power (kW) Tout (oC) Capital Cost (106 $) Capital Cost (106 $) (kW)
1011 175 2.574
1220 200 2.608
559 119 2.315
(106 $/y)
CC
U N
1.36 3.125
0.1170
0.1134
0.189
2022
2044
1949
1.020
1.031
0.9832
(106 $)
8.883
7.358
8.299
(106 $/y)
3.981
3.484
3.750
A
-
2.3 912.8 162 1.826
A
TAC
-
SC RI PT
0.5 0.8
EP
Total Energy Total Energy Cost Total Capital
0.5 1.078
M
Stage 3
0.5 1.25
D
Stage 2
Pin (bar) Pout (bar)
TE
Stage 1
Three Stage
15
S0255-2701(17)31316-8 https://doi.org/10.1016/j.cep.2018.01.020 CEP 7175
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
24-12-2017 19-1-2018 25-1-2018
Please cite this article as: William L.Luyben, Compressors for Conceptual Design, Chemical Processing https://doi.org/10.1016/j.cep.2018.01.020
Capital Cost of Engineering and
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Paper submitted to Chemical Engineering and Processing: Process Intensification CEP_2017_1148
SC RI PT
Capital Cost of Compressors for Conceptual Design
M
A
N
U
William L. Luyben* Department of Chemical Engineering Lehigh University Bethlehem, PA 18015
EP
TE
D
December 24, 2017 Revised January 19, 2018
A
CC
* [email protected]; 610-758-4256; FAX 610-758-5057
1
Highlights
SC RI PT
Published compressor capital cost predictions shows large variability and use only compressor power to estimate capital cost. Aspen Economic predictions are larger for low suction pressures. A simple method to incorporate the effect of pressure is presented. Optimum compression ratios in multistage compression trains do not follow the conventional heuristic of keeping the compression ratio the same in all stages.
Abstract
U
Many process intensification techniques involve the use of gas compressors. Gas
N
recycles are typically used to improve yield and selectivity in reactor/separation
A
processes. Vapor recompression in distillation systems are becoming more widely
M
applied, particularly with complex separations such as divided-wall, reactive, extractive
D
and azeotropic distillation systems.
TE
At the conceptual design stage it is vital to have reasonable estimates of the capital cost of compressors involved in these processes. The literature correlations use
EP
only the compressor power to estimate capital cost, and there are significant differences in the published methods. However, in addition to power, it appears that suction pressure
CC
also must be considered in cost estimation. The proprietary Aspen Economics program
A
gives results that show a strong dependency of cost on the pressure of the gas being compressed. The purpose of this paper is to provide a simple method to estimate compressor capital cost that incorporates both compressor power and compressor suction pressure. A
2
case study illustrates that the conventional heuristic of using equal compression ratios in multistage compression trains does not give the optimum economic design.
Compressor cost; vapor recompression; conceptual design
1. Introduction
SC RI PT
Key Words
Reliable and easy-to-use methods for estimating the cost of equipment are vital at the conceptual design stage of chemical plant design. All design textbooks provide
U
graphs and/or equations for making these estimates. The capital costs of pressure vessels
A
available and are in fairly good agreement.
N
and heat exchangers are two of the most important, and existing published methods are
M
However, the situation with compressor cost estimation is quite different. The
D
published methods show significant differences in their predicted results. In addition the
estimation.
TE
published methods use the single parameter of compressor power requirements for cost
EP
Aspen Economics is a proprietary software package that predicts much larger compressor capital costs than the published methods. More importantly it shows a strong
CC
dependence of cost on compressor suction conditions in addition to compressor power.
A
For the same compressor power (same compression ratio, inlet temperature, gas composition and molar throughput), Aspen Economics predicts that compressor capital investment increases as compressor suction pressure decreases. Compressors are volumetric devices, and they handle volumetric flowrates. As suction pressure decreases, more volume of gas must be captured by the turbine blades
3
for the same mass or molar throughput. Therefore the size of the compressor must increase. Nothing has been found in the published literature that quantifies this effect. The purpose of this paper is to provide a simple method to estimate compressor
SC RI PT
capital cost that incorporates both compressor power and compressor suction pressure.
2. Published Methods
The chemical engineering design textbooks all present methods for estimating compressor capital costs. Douglas1 give a widely used correlation.
N
U
Compressor Cost ($) 5840(kW )0.82
A
For a numerical example, consider the compression 1000 kmol/h of nitrogen at suction
M
conditions of 1 bar and 50 oC. Assuming an ASTM polytropic efficiency of 80% and
D
using Peng-Robinson physical properties, Aspen Plus predicts a power requirement of
TE
1010 kW for a typical compression ratio of 2.5. The Douglas method gives a compressor and drive capital cost of $1,700,000 using stainless steel materials of construction.
EP
Changing the suction pressure and keeping the same compression ratio does not significantly change the power requirement. So the Douglas method does not have any
CC
dependence of capital cost on suction pressure. The design textbook by Turton et al2 gives separate cost curves for the
A
compressor and for the drive. Only compressor power is used to estimate capital cost Using the numerical example considered above, Turton predicts a carbon-steel compressor cost of $280 per kW at 1000 kW and an electric drive cost of $120 per kW.
4
Using a SS-to-CS ratio of 5.8/2.7 for the compressor, the total capital cost predicted is $722,000. This is less than half the cost predicted by Douglas. Peters et al3 predict a cost of $2,000,000 using only compressor power as the
SC RI PT
costing parameter. Seider et al4 also use only compressor power to predict a cost of $1,000,000.
The only reference that hints at the effect of suction pressure is Ulrich5. Figure 529 in Ulrich gives a plot in which the abscissa is the volumetric flowrate of the gas, not
the normal power. But this flowrate is given at standard conditions (1 atm), so the effect
U
of suction pressure is not included. Ulrich predicts a cost of $417,000.
N
Calado6 explores compression trains for sequestration of carbon dioxide and
A
proposes the following correlations for stainless steel compressors and electric motor
M
drives.
D
Compressor Cost ($) 2.5 exp 7.58 0.8 ln(hp)
TE
Motor Cost ($) 2049 668.16(hp)
EP
The Calado capital cost prediction for the numerical example is $1,530,000. No effect of suction pressure on capital cost is included.
CC
Table 1 summarizes the comparison of the several published capital cost predictions. The parameters are 1000 kmol/h of nitrogen gas at 1 bar and 50 oC with a
A
compression ratio of 2.5. The variability among the several methods is clearly very large and introduces too much uncertainty for even conceptual design evaluations. As we demonstrate in the next section, the prediction of Aspen Economics is the largest, so it should be used for conservative design (highest capital cost).
5
3. Aspen Economics Predictions The Lehigh Chemical Engineering senior design course uses a wide variety of process design projects to expose students to the basic principles of design and plantwide
SC RI PT
control. Each three-student group works on the conceptual design of different processes, so 15 to 20 projects are explored each year. Many of these processes include multi-train compressors. The conventional engineering heuristic of selecting the same compression ratio in each stage is used with the number of stages selected to avoid discharge
U
temperatures greater than 200 oC as recommended by Walas7. With interstage cooling,
N
the power requirements in each stage are approximately the same.
A
Up until a few years ago the capital cost was estimated using the Douglas
M
Correlation. Then Aspen Economics became available and is now used since its estimates are more conservative (higher capital investment).
D
However we observed in many projects that the Aspen Economics predictions did
TE
not give the same capital cost for each stage even though the power requirements were the same. The first compressor cost was often much larger than the second and third.
EP
One logical physical reason for the higher cost is the larger size required at low
CC
pressure and density. However, we have been unable to find any quantitative discussion of this in the published literature. Private communications with a number of compressor
A
design experts came up empty. Clearly the compressor sizing and the costing methods used in Aspen Economics include these concepts. Another insight into why low suction pressure increases compressor cost is gained by comparing the power to compress an ideal gas with that to compress a real gas. The
1 P 2 (8.326 kJ / kmol K ) T1 ( K ) 1 Power (kW ) Flowrate (kmol / sec) P1 1
6
thermodynamic equation for the power to adiabatically and reversibly compress an ideal
SC RI PT
gas is given in the following equation.
The ratio of heat capacities is 1.4 for an ideal gas. For the numerical case considered above, the power to compress an ideal gas is 1410 kW, which is 40% larger than the
power calculated for the real gases. As suction pressure decreases, gases become more ideal. So we would expect that there should be an effect of pressure on compressor
U
design.
N
At the conceptual design stage it would be useful to have a simple way to
A
quantitatively incorporate the effect of suction pressure on capital cost. That is the
D
M
provided in this paper.
TE
4. Correction Factor
A number of cases were run using Aspen Plus to simulate the compressor and
EP
Aspen Economics to evaluate capital costs. Throughput was fixed at 1000 kmol/h with a suction temperature of 50 oC. Compression ratio was fixed at 2.5 and cases were run with
CC
different suction pressures. Different gases have different ratios of heat capacities, so
A
power requirements change with the gas compressed. Figure 1 gives results from Aspen Economics for several gases. Capital cost of a
stainless steel compressor and the associated motor drive are shown as a function of the suction pressure. The pressure dependence of cost is clearly shown.
7
Figure 2 suggests the use of a correction factor as a simple method for adjusting the capital cost. Using the convenient Douglas correlation as the basis, compressor cost is multiplied by the appropriate correction factor for a specified suction pressure and type of
SC RI PT
gas.
5. Multistage Compressor Design
The conventional design method for multistage compression systems is to select
the required number of stages such that the discharge temperature does not exceed 200 oC
U
(Walas7). Then the compression ratio in each stage is selected to be the same. For
N
example, suppose the overall compression ratio for the system is 8, going from the initial
A
feed gas pressure to the final discharge pressure at the end of the compressor train.
M
Assuming that the temperature limitation dictates that three stages should be used, the compression ratio CR in each stage is (8)0.3333. The general relationship is the following. 1/ N
TE
D
CR in each stage CR Total
However, the results given above in this paper demonstrate that the capital cost of
EP
the early stages in the train, which are at lower pressures, will be larger than those with higher suction pressures. Therefore, the consequence of having higher capital costs with
CC
low suction pressure is that the conventional heuristic used for multistage compressor
A
design is no longer valid. To illustrate this, we take a case in which the following design parameters are
given: 1. Gas flowrate is 1000 kmol/h of nitrogen. 2. Inlet temperature is 50 oC.
8
3. Feed pressure is 0.5 bar. 4. The final desired pressure is 3.125 bar, which corresponds to an overall compression ratio of 6.25.
SC RI PT
5. The maximum discharge temperature in any stage is 200 oC.
A single-stage compressor gives a discharge temperature of 343 oC and requires 2405 kW of power. This exceeds the temperature limitation, so a two-stage compressor system
must be used. Using the conventional design approach with equal compression ratio in
U
each stage (CR = 2.5) with interstage cooling back down to 50 oC gives discharge
N
temperatures of 175 oC and requires 1011 kW in each stage. This is a feasible design, but
A
is it the economic optimum with the lowest total annual cost?
M
Table 2 gives the capital and energy costs of several cases. The first column gives detailed design parameters and economic results for the conventional 2-stage
D
compression train with equal compression ratios (CR = 2.5) in the two compressors. The
TE
capital cost of the first compressor is much larger than that of the second ($6,193,000
EP
versus $2,574,000). This suggests that a lower compression ratio in the first compressor and a higher compression in the second might lower capital investment. The total energy
CC
cost of this conventional design is $1,020,000 per year (using $16 per GJ electricity cost).
A
The total annual cost is $3,981,000 per year using a 3-year payback period. The second column in Table 2 gives results for a modified design with adjusted
compression ratios. The first step is to find the compression ratio for the second stage that would just satisfy the 200 oC maximum temperature limitation. A compression ratio CR = 2.9 produces the desired discharge temperature. Since the discharge pressure in the
9
second compressor is 3.125 bar, the suction pressure in the second compressor must be 1.078 bar. The first stage in this modified design now has a lower compression ratio CR = 2.135 instead of CR = 2.5 in the original. The result is a lower capital cost of the first
SC RI PT
compressor ($4,638,000) while only a slightly higher capital cost of the second compressor ($2,608,000). Total capital cost is $7,358,000. Total energy cost increases
only slightly to $1,031,000 per year. Total annual cost is reduced 12% to $3,484,000 per year.
Another alternative suggests itself at this point. Suppose we use a 3-stage
U
compression train that would give even lower compression ratios in the low-pressure
N
stages. This design is expected to give a lower total annual energy cost, but it would have
A
three compressors and two interstage coolers, which might increase capital cost. The third
M
column in Table 2 shows that the capital cost of the first compressor drops to $3,969,000 using a compression ratio of 1.6. The second compressor is $2,315,000 with a
D
compression ratio of 1.7 and the third compressor is $1,826,000 with a compression ratio
TE
of 2.3. Total capital investment increases to $8,299,000. Energy cost is lower ($983,200
EP
per year) as expected, but not enough to offset the increase in capital cost. Total annual cost increases to $3,750,000 per year.
CC
So the 2-stage design with a lower compression ratio in the first stage is the
A
economic optimum.
6. Conclusion A method for adjusting compressor capital costs using both power and suction pressure is proposed to give more realistic estimates for conceptual design of compression system. A case study illustrates that the conventional heuristic of equal
10
compression ratios in each stage of a multistage compression train does not give the economic optimum design.
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References
1. Douglas, J. M. Conceptual Design of Chemical Processes McGraw-Hill (1988) 2. Turton, R., Bailie, R. C., Whiting, W, B., Shaeiwitz, J. A., Bhattacharyya, D. Analysis, Synthesis and Design of Chemical Processes, 4th Ed. Prentice Hall
Peters, M., Timmerhaus, K. D., West, R. E. Plant Design and Economics for
N
3.
U
(2012)
A
Chemical Engineers, 5th Ed. McGraw-Hill (2003)
D
2nd Ed.Wiley (2003)
M
4. Seider, W. D., Seader, J. D., Lewin, D. R. Product & Process Design Principles
TE
5. Ulrich, G. D. A Guide to Chemical Engineering Process Design and Economics Wiley (1984)
EP
6. Calado, M. P. A. “Modeling and design synthesis of a CCS compression train system via MINLP optimization” MS Thesis (2012) Tecnico, Lisboa
CC
7. Walas, S. M. Chemical Process Equipment: Selection and Design Butterworth-
A
Heinemann (1988)
11
M
A
N
U
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Figure Captions
A
CC
EP
TE
D
Figure 1 – Effect of suction pressure on capital cost.
12
SC RI PT U
A
CC
EP
TE
D
M
A
N
Figure 2 – Correction factor
13
Table 1 – Comparison of Compressor Cost Predictions Douglas
$1,700,000
Turton
$722,000
Peters
$2,000,000
Seider
$1,000,000
Ulrich
$417,000
Calado
$1,530,000
Aspen Economics
$2,580,000
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Capital Investment
A
CC
EP
TE
D
M
A
N
U
Basis: 1000 kmol/h nitrogen gas at 1 bar and 50 oC; 2.5 compression ratio
14
Table 2 – Case Studies Conventional Modified Two-Stage Two-Stage
InterCooler
CR
2.5
2.155
1.6
Power (kW) Tout (oC) Capital Cost (106 $) Pin (bar) Pout (bar)
1011 175 6.193
824.4 152 4.638
471 109 3.969
1.25 3.125
1.078 3.125
0.8 1.36
CR
2.5
2.9
1.7
Power (kW) Tout (oC) Capital Cost (106 $) Pin (bar) Pout (bar) CR Power (kW) Tout (oC) Capital Cost (106 $) Capital Cost (106 $) (kW)
1011 175 2.574
1220 200 2.608
559 119 2.315
(106 $/y)
CC
U N
1.36 3.125
0.1170
0.1134
0.189
2022
2044
1949
1.020
1.031
0.9832
(106 $)
8.883
7.358
8.299
(106 $/y)
3.981
3.484
3.750
A
-
2.3 912.8 162 1.826
A
TAC
-
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0.5 0.8
EP
Total Energy Total Energy Cost Total Capital
0.5 1.078
M
Stage 3
0.5 1.25
D
Stage 2
Pin (bar) Pout (bar)
TE
Stage 1
Three Stage
15