Equations of State for Gas Compressor Design and Testing

Abstract

In the design and testing of gas compressors, the correct determination of the thermodynamic properties of the gas. such as enthalpy, entropy and density from pressure, temperature and composition, plays an important role. Due to the wide range of conditions encountered, pressure, specific volume and temperature (p-v-T) equations of state (EOS) and ideal gas heat capacities, along with measured data, are used to determine the isentropic efficiency of a compressor configuration and to model the actual behavior of real gases and compressors. There are many possible model choices. The final selection should depend on the applicability of the EOS to the gas and the temperature dependence of the heat capacities, as well as the particular process of interest along with the range of pressures and temperatures encountered. This paper compares the thermodynamic properties from five commonly used equations in the gas compressor industry: the Redlich-Kwong (RK), Redlich-Kwong-Soave (RKS), Peog-Robinson (PR), Benedict-Webb-Rubin-Starling (BWRS), and Lee-Kesler-Plocker (LKP) models. It also compares them with a high accuracy EOS for methane from Wagner and Setzmann in the common range for gas compressors. The validity of a linear temperature dependence for ideal gas heat capacities is also evaluated. The objective was to determine if the models give significant differences in their predicted efficiencies. It was found that different EOS gave somewhat different enthalpy changes for methane, ethane and nitrogen for real compressions. This appeared to be connected to the different densities given by the models. Interestingly, the isentropic enthalpy changes are quite similar, suggesting that the effect is canceled out when two properties are involved. However, since the efficiency is the ratio of isentropic enthalpy change to actual enthalpy change, the EOS yield different efficiencies. These differences are on the same order as the typical tolerances allowed for prediction and testing of industrial gas compressors (3 to 5%) and comparisons with the highly accurate equation of state for pure methane from Wagner and Setzmann (1991) showed similar differences. Commonly, the ideal gas heat capacity is assumed linear in temperature from 10 to 150°C (50 to 300°F). Comparison of this form with a quadratic expression from the literature and the highly accurate equation of Wagner and Setzmann for methane, showed insignificant differences among the methods for temperatures up to 600°K (1080°R).