Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

Abstract

In conventional van der Waals type equation of state (EOS) modeling, the denominator of the attractive contribution is regarded as being a necessarily factorable quadratic polynomial for the closed-form expression of the corresponding Helmholtz free energy. This study evaluates the effect of the opposite case, an irreducible quadratic polynomial, on the description of the volumetric behavior of real fluid through a comparison with the critical isotherm data, coexistence curve, and PVT isotherm data. In a generalized cubic EOS, an irreducible quadratic polynomial was found to yield an improved description of the flattened region around the critical density while a nonclosed form of the Helmholtz free energy results. For an improved volumetric description using an irreducible quadratic polynomial and a derivation of the closed form of the Helmholtz free energy, we developed a quintic EOS containing seven parameters, two of which are determined by correlating the critical isotherm data and others, by regressing the sub- and supercritical properties. In the description of the critical isotherms of nine pure compounds, a comparison of the present model with the Benedict–Webb–Robinson–Soave (BWRS) EOS showed that the present model exhibits slightly larger deviations than those with BWRS EOS; however, a good agreement was obtained with the reference model of REFPROP 8.0 in the description of the saturated vapor pressure, saturated density, and PVT isotherm data over a wide range of temperatures.