On the temperature dependence of the α function in the cubic equation of state. (31st December 2018) - Yang, Fufang; Liu, Qiang; Duan, Yuanyuan; Yang, Zhen
Graphical abstract: Highlights: Improved the supercritical consistency of the cubic equation of state. Derived the temperature dependence of the α function. Presented a set of requirements for the α function supercritical extrapolation. Revised the predictive Soave and Twu α functions correcting the physical behavior. Abstract: The cubic equation of state (EoS) is widely applied for modeling fluid thermodynamic properties in chemical processes. However, in the absence of a distinguishable reference property, the supercritical extrapolation of its only temperature-dependent parameter, the α function, resulted in nonphysical prediction of supercritical virial coefficients and heat capacities. From a theoretical perspective, we here rigorously derive the universal temperature-dependent behavior of the α function, using the generalized van der Waals theory without specifying the interaction potential. To isolate the behavior of the α function from the EoS structure, we examine the thermodynamic functions of realistic fluids at low densities. Our study reveals that the α function is finite, positive, and monotonically decreases with increasing temperature. We present a set of thermodynamic requirements and accordingly revise the predictive Soave and Twu α functions for the Redlich-Kwong and Peng-Robinson EoSs. Our study shows that the revised α functions avoid the divergent virial coefficients at infinite temperature, and the nonphysical bump on the heat capacity isobars immediately above the critical temperature, demonstrating the imperative need for thermodynamic requirements for the temperature dependence of the α function. Joule-Thomson inversion curve and vapor-liquid equilibria are also investigated.