Generalization Comparison Study of the Performance of Six Different Alpha Functions Coupled to a Peng–Robinson Equation of State

Abstract

A methodology is applied to generalize the parameters of the alpha function of the Peng−Robinson equation of state for polar and nonpolar substances. The method relates the parameters of the alpha function in terms of the first, second, and third derivatives under the critical condition. The parameters of the derivative functions are correlated by using the acentric and Halm−Stiel polar factors to construct a generalized model. Coquelet, Mathias−Copeman, Heyen, Melhem, Soave, and Trebble−Bishnoi are the selected alpha functions within three-to-one fitted parameters. The correlation procedure is done with 82 pure substances, and the test is done with 177 nonself-associating and self-associating substances using the pseudoexperimental data from the Design Institute for Physical Property Data database (2460 data in correlation and 28,620 for testing) and the objective function related to the saturation pressure. The thermodynamical properties associated with heat vaporization, molar liquid volume, and isobaric heat capacity of the liquid are estimated. The statistical comparison shows that the alpha function of Coquelet and Mathias−Copeman presents the lowest values of average absolute relative deviations (AARD) of the vapor pressure of 0.67% and for heat vaporization of 1.69%. On the other hand, the molar liquid volume does not present a statistical difference at a 95% confidence level for all the alpha functions; otherwise, the heat capacity presents statistical differences where the Heyen and Melhem values of deviations are around 6.42 and 6.55%. The prediction is made using the NIST-REFPROP 8 database, which estimates different thermodynamic properties under saturation and single-phase conditions with a total of 51,150 data points per alpha function. Predictive model analysis shows no statistical differences at a 95% confidence level among models (Coquelet, Mathias−Copeman, Melhem, and Soave) with AARD values from 0.57 to 1.10%. Alpha functions for heat vaporization, entropy vaporization, fugacity, and molar volume also showed no differences. However, under T r ≤ 0.9, Trebble−Bishnoi deviated in residual enthalpy and liquid fugacity. For T r ≥ 1, all models' alpha functions were consistent across properties. The well-modeled analyses are done for all of the substances, and the results show that more than 60% of the substances present good modeling behavior. Finally, the consistency test of the derivatives of the alpha function is applied at a reduced temperature (T r ) below and above the critical condition. This test showed that for T r < 1, all the alpha functions, except for Melhem, pass the test; however, Heyen and Trebble−Bishnoi fulfill all the tests above 93% of the substances at 0.5 ≤ T r ≤ 8.