Second derivative of alpha functions in cubic equations of state

Abstract

In this paper, a mathematical study of the second derivatives of five well-established alpha functions (Mathias–Copeman, Coquelet et al., Twu et al., Stryjek–Vera and Heyen) for cubic equation of state, CEoS, is performed. For alpha functions having different formulations in the subcritical and supercritical temperature ranges, like those by Mathias–Copeman and Coquelet et al., undesired discontinuities are highlighted at the critical temperature. A method for fixing such discontinuities is presented and its validity is tested by predicting Cv and Cp values.Moreover, an exponential form of Soave alpha function with consistent derivatives by means of Taylor series expansion is proposed.In a second step, 21 thermodynamic packages (combination of a cubic EoS and an alpha function) are tested to predict sub and super critical properties of a series of pure components. Our study makes it possible to conclude that the Mathias–Copeman and Coquelet et al. alpha functions have the best accuracy. At supercritical temperatures Soave alpha function is superior to studied exponential alpha functions.