Quest for a Single van der Waals Loop: A Four-Parameter Cubic Equation of State Tailored to a Reference Formulation for Propane

Abstract

Modern multiparameter equations of state (MP EOSs) enable accurate computation of thermodynamic properties of fluids in broad ranges of temperature and pressure. Between the saturated vapor and saturated liquid densities, a pressure vs. density isotherm computed with an MP EOS exhibits several oscillations with large amplitudes. This is not a problem for most engineering computations, because this portion of isotherm is replaced with a horizontal line, representing an equilibrium mixture of the vapor and liquid phases. However, for computing properties in metastable states, modeling phase interfaces with gradient theory, and certain models of fluid mixtures, an isotherm with a single maximum and a single minimum (single van der Waals loop) is needed. As a step toward an accurate, single-loop EOS, we propose a generalized four-parameter cubic (G4C) EOS. The four parameters are temperature functions which are fitted, at subcritical temperatures, to the second virial coefficient, saturation pressure, liquid density and compressibility, and, in the supercritical region, to the second virial coefficient and derivatives of pressure. Fitted data were generated from thermodynamic property formulation for propane (Lemmon et al. J Chem Eng Data 54:3141, 2009). The G4C EOS provides a representation of thermodynamic properties of propane in the gaseous, liquid, and supercritical regions, which is sufficiently accurate for the intended applications. The equation can be extrapolated to high temperatures. Between 85.5 K and 296 K, the density and compressibility of the saturated liquid are represented with an average absolute relative deviation (AARD) of, respectively, 0.04 and 0.25 percent, the density and compressibility of saturated vapor show AARD of 0.31 and 0.39 percent, and the saturation pressure deviates by 0.23 percent. Features to be improved in future are temperature dependencies of the third- and higher-order virial coefficients at low temperatures, the curvature of isotherms in the liquid region, liquid density at very high pressures, and the critical region. Developed G4C EOS was successfully used in a new mixture model (Hrubý Int J Thermophys 44:130, 2023) to model volumetric behavior and vapor–liquid equilibrium in asymmetric mixtures with propane as a low-volatile component.