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Compressor Heuristics for Conceptual Process Design William L. Luyben Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States ABSTRACT: Multiple compressors in series with intermediate heat exchangers are frequently used to reduce compressor energy consumption or to limit compressor discharge temperatures when the overall compression ratio (initial suction pressure divided by the required final pressure) is large. The optimum number of stages can be fixed by economics (trade-off between capital investment and energy cost) or by equipment and/or process compressor discharge temperature limitations. The chemical engineering design literature contains several conflicting heuristics for designing multistage gas compression systems, and little information about the rationale behind these heuristics is provided. This paper explores several aspects of multistage compression systems including economics, equipment temperature limitations, and process temperature limitations. New heuristics are presented that give either the economic optimum or the temperature-limited number of stages as a function of the overall compression ratio.
1. INTRODUCTION Compression of gas streams is important in many chemical processes. The capital and operating costs of compressors are typically a very significant part of the economics of the plant. Gaseous fresh feed streams, gas recycles, and gas products can require the use of compressors. A wide range of overall compression ratios (final required downstream pressure divided by the initial upstream pressure) occurs in a variety of industrial applications. Most compressors operate adiabatically. If compressors could be operated isothermally, their energy consumption would be minimized. The practical approach to approximate isothermal compression is to use a series of adiabatic compressors with interstage cooling. Figure 1 shows four different compressor systems with the number of compressor stages varying from one to four. Total energy consumption decreases as more stages are used, but capital investment in equipment (compressors and heat exchangers) increases. The optimum design from an economic standpoint can be determined by balancing energy and capital costs using total annual cost. Section 2 presents this analysis for a wide range of total compression ratios. Another important effect of increasing the number of stages is a reduction in compressor discharge temperature. Maximum temperature limitations for the materials of construction (blades and seals) can often make it necessary to use multiple stages. The temperature limitation (Ross1) for some elastomer O-ring seal materials with hydrocarbon gases is about 477 K (400 °F) and with air is about 533 K (500 °F). More stages may be required if there are process temperature limitations due to potential polymerization or detonation of the gas being compressed. Temperatures in the compression of ethylene must be kept below about 422 K (300 °F) to prevent polymerization of the ethylene.1 Lower temperatures can also decrease maintenance problems. Some of the classical chemical engineering design textbooks give heuristics for selecting the number of compressor stages. Turton et al.2 suggest simply restricting per-stage compression ratios to less than 3. No explanation of the basis for this heuristic is provided. Seider et al.3 give a table of suggested optimum number of stages for different overall compression ratios that is equivalent to using a maximum per-stage compression ratio of 4. Seader4 r 2011 American Chemical Society
provided an explanation of this heuristic. The basis is a discharge temperature of 463 K (375 °F) for the adiabatic reversible compression of a gas with a ratio of heat capacities of 1.4 and an inlet compressor suction temperature of 311 K (100 °F). Walas5 suggests a discharge temperature limit of 450477 K (350400 °F), which corresponds to a per-stage compression ratio of 4 (for diatomic gases with a ratio of heat capacities of 1.4). All of the references recommend the heuristic of using the same compression ratio in each stage. For an N-stage system with an initial upstream pressure of P1 and a final downstream pressure of PN, the per-stage compression ratio is (PN/P1)1/N. None of these textbooks appears to consider economic issues. These are quantitatively explored in section 2.
2. ECONOMIC ANALYSIS 2.1. Alternative Multistage Systems. Figure 1 shows four alternative gas compression systems for 100 kmol/h methane gas supplied at 1 atm and 323 K and compressed to 50 atm. Aspen simulation software is used assuming polytropic compression with an efficiency of 80% and using ChaoSeader physical properties for methane. Results for other gases are discussed later in this paper. A single-stage design requires only a compressor if the high exit gas temperature does not have to be reduced for downstream process concerns. With this high overall compression ratio (50), the discharge temperature is 760 K, which may exceed compressor equipment temperature limitations. The compressor work is also high (593 kW). A two-stage system requires less total compressor work (236 and 238 kW in the two compressors, totaling 474 kW). However, two compressors and a heat exchanger are required. Note that compressor discharge temperatures are reduced to about 456 K, which may be below equipment temperature constraints. Threeand four-stage systems drop the total work to 438 and 421 kW, Received: September 5, 2011 Accepted: November 13, 2011 Revised: November 3, 2011 Published: November 14, 2011 13984
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Figure 1. Multistage compression system.
respectively, and compressor discharge temperatures are lower (about 456 and 420 K, respectively). 2.2. Economic and Sizing Basis. Given the flow rate, inlet temperature, inlet pressure, compressor efficiency, compression type (polytropic), and required discharge pressure, Aspen calculates the required work. The cost of electric energy in the compressor motor is assumed to be $16.8/GJ as given by Turton et al.2 The capital cost depends on the horsepower (hp) requirement and is calculated from eq 1 as given by Turton et al.2 compressor capital cost ¼ ð1293Þð517:3Þð3:11ÞðhpÞ0:82 =280 ð1Þ Heat exchangers are sized by assuming that the exit gas is cooled from the upstream compressor discharge temperature to an outlet temperature of 323 K. The Aspen HeatX model gives the heat-transfer rate. An overall heat-transfer coefficient of 0.28 kW m2 K1 is assumed for this gas system. Cooling water at 305 K is fed to each heat exchanger in countercurrent flow. The exit temperature of the cooling water is specified to be 323 K. An Aspen Flowsheet design specification is used to adjust the flow rate of cooling through each heat exchanger to give the specified 323 K exit cooling water temperature for the known heat-transfer rate. Aspen then calculates the required heattransfer area using a log-mean differential temperature driving force. The capital cost of each heat exchanger (area in m2) is calculated from eq 2 based on Douglas.6 capital cost ¼ 7296ðareaÞ0:65
ð2Þ
A pressure drop of 0.1 atm is assumed through each heat exchanger. The cost of providing cooling water is typically very
small compared to compressor energy cost and is neglected in this analysis. 2.3. Effect of Overall Compression Ratio. Figure 2 gives process results for a multistage compressor system for overall compression ratios (CRs) of 6, 25, and 50. Total compressor work, per-stage compression ratio, and discharge temperatures all decrease as more stages are used and as the overall compression ratio decreases. However, the total heat exchanger area increases. Figure 3 gives economic results for the same system. The top two graphs show that, as expected, compressor capital and energy costs increase for larger overall compression ratios and decrease as more stages are used. The bottom left graph gives the capital cost of the heat exchangers as a function of the number of stages and overall compression ratio. The bottom right graph gives total capital investment. Note that the capital cost of the compressors is much larger than capital cost of the heat exchangers (different ordinate scales). The total capital investment curves for the higher compression ratios are not monotonic. There is a minimum in the curve of capital cost versus number of stages. Although a one-stage compressor system does not require a heat exchanger, the power requirement is large, so the compressor cost is high. Using two stages requires a heat exchanger, but the power requirements in the two compressors are much smaller, which results in lower compressor capital investment. However, as more stages are added, more exchangers are needed, and the reduction in compressor power as more stages are added begins to level out. The effect of these economic variables on total annual cost (TAC) is shown in Figure 4. Total annual cost is the annual cost of compressor energy plus the annual capital cost (total capital 13985
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Figure 2. Effect on process variables of overall compression ratio and number of stages.
Figure 3. Effect on economic variables of overall compression ratio and number of stages.
investment divided by a 3-year payback period). A one-stage compressor system gives the minimum TAC for a compression ratio of 6 (marked with a star in Figure 4). A two-stage compressor system gives the minimum TAC for a compression ratio of 25. A three-stage compressor system gives the minimum TAC for a compression ratio of 50 A four-stage compressor system gives the minimum TAC for a compression ratio of 120. Results for a wide range of overall compression ratios are summarized in Figure 5. The ordinate is the economic optimum number of stages. The abscissa is the overall compression ratio. Figure 5 provides a simple heuristic relationship for estimating the optimum number of stages at the conceptual design stage, based on only economics (minimum total annual cost) with no consideration of temperature limitations. A single-stage system
can be used up to an overall compression ratio of 6. A two-stage system is recommended up to an overall compression ratio of 35. A three-stage system should be used for overall compression ratios up to 110. Higher compression ratios require four stages. Note that these compression ratios are much higher than those given in design textbooks. But remember that they do not consider temperature limitations. This aspect is discussed in section 3.
3. TEMPERATURE LIMITATIONS The economics results presented in section 2 do not consider temperature limitations. For example, the compressor discharge temperature of the one-stage compressor in a system with an overall compression ratio of 6 is 507 K, as shown in the upper 13986
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Industrial & Engineering Chemistry Research right graph in Figure 2. If equipment or process temperature limitations are lower than 507 K, a two-stage system may be required, which would give discharge temperatures from the two compressors of about 415 K. This is below the Seader4 heuristic (463 K) and below the Ross1 heuristic (477 K). Now consider the system with an overall compression ratio of 25. The compressor discharge temperature of the one-stage compressor is very high (674 K), as shown in the upper right graph in Figure 2. Using a two-stage system produces compressor discharge temperatures from the two compressors of about 490 K. Using a three-stage system produces compressor discharge temperature of about 430 K. Using a four-stage system produces compressor discharge temperature of about 405 K. Figure 6 shows how compressor discharge temperatures vary with the overall compression ratio and the number of stages in
Figure 4. Number of stages for minimum TAC with different overall compression ratios.
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the methane system. If the Ross temperature limitation of 477 K is used (the horizontal dashed line in Figure 6), a single-stage system would be limited to compression ratios of 3. A two-stage system would be limited to compression ratios less than 20. A three-stage system would be limited to compression ratios less than 100. The proposed heuristic approach is to start with the economic optimum number of stages for a given overall compression ratio, and then check to see if temperature limitations require additional stages. Table 1 compares several heuristics with the economic optimum and the temperature-limited number of stages.
4. OTHER GASES All of the results presented above have used methane. Aspen simulations with a number of other gases were performed to determine compressor power and temperature conditions. Table 2 gives results for methane, nitrogen, carbon dioxide, ethylene, hydrogen, oxygen, and air. Gas flow rates are 100 kmol/h and the overall compression ratio is 50 for all cases. The overall compression ratio is 50, and a three-stage compressor system is assumed. The power and temperatures vary somewhat with the gas being compressed because of differences in the ratios of heat capacities, but the differences compared to methane are not large. Therefore it should be possible to use the heuristics developed from methane for other gases at the conceptual design stage. 5. OTHER FLOW RATES Another important parameter is capacity. All of the results presented above are based on a gas flow rate of 100 kmol/h. How would the results be affected by changing throughput? Compressor power scales in direct proportion with gas flow rate. Energy cost would therefore change in direct ratio to throughput.
Figure 5. Economic optimum number of stages. 13987
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Figure 6. Temperature limitations.
Table 1. Maximum Overall Compression Ratio
Table 3. Effect of Gas Flow Rate (Methane, CR = 50)
minimum TAC
Turton
Seider and Seader
Ross temperature
criterion
criterion
criterion
criterion (477 K)
