A revisit of the vapor-liquid equilibrium calculation with cubic equations of state

Abstract

Based on the roots-coefficient relations for a cubic function, quadratic functions are constructed that strictly relate the saturated volumes of liquid and vapor phases and the third solution from a cubic equation of state (EoS). The vapor-liquid equilibrium (VLE) calculation with a cubic EoS is thus reduced to solving a single nonlinear equation. In light of a recent finding that the “unphysical” third solution, namely the Maxwell crossover or the M-line, plays a central role as the dividing interface in the density gradient theory, here we show that it can also be used to derive analytically approximate solutions to a VLE problem. The van der Waals EoS and the Soave-Redlich-Kwong (SRK) EoS are discussed as examples. The method proposed in this work simplifies the calculations of the traditional VLE calculations with a cubic EoS. With one-time-only effort for a given system, simple analytical solutions can be obtained to avoid the repetitively iterative computations for a VLE problem. Finally, the relationship between the Widom line in the supercritical region and the M-line is briefly discussed with the SRK EoS.