Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case

Abstract

The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.

Interstage Pressures of a Multistage Compressor with Intercooling

“…For the same suction temperature and interstage isentropic efficiency in each compression stage, Equation (12) is analogous to that obtained by Vadasz and Weiner [ 6 ] (see Equation (31)) and Hernández et al [ 12 ] (see Equation (11)), with and without intercooler pressure losses, respectively. Equation (12) also corresponds to the expression for the minimum compression work obtained recently by López-Paniagua et al [ 13 ] (see Equation (34)) for the case in which each compression stage has a different isentropic compression efficiency and the same suction temperature and the intercoolers do not present pressure drops.…”

“…therefore, Equation (13) indicates that ξ 1/x 1 > 1. From Equation ( 13), an expression is obtained to estimate the number of compression stages in terms of the j-th individual and overall compression pressure ratios and the coefficient ξ 1/x j , as shown in the following equation…”

“…These authors also establish a numerical approach to specify the optimal location and number of intercoolers. Recently, López-Paniagua et al [ 13 ] employed Lagrange multipliers to determine the optimum interstage pressures for a multistage compression process with different-stage isentropic efficiencies. Their result is applied to the design of a multistage compression plant with reciprocating compressors.…”

A comparative study of modified Linde and cryogenic cooling for CO 2 separation

“…Because, in the case of adiabatic compression, the heat would coincide exactly with the specific compressor work. 55 Due to this, the compressor cooling load follows the trend of compressor load compressor cooling load also increases with the increase in the compressor work. The trend of refrigeration load is found to be constant.…”

“…60 In adiabatic compression, the heat would coincide exactly with the specific compressor work. 55 Due to this reason, the cooling load of the compressor is also high. Table 10 presents the comparative results of CO 2 separation by the two-stage compression and cooling processes with the two-stage compression modified Linde process.…”