(672a) Multiparameter Equation of State Basis Set Selection

Thermodynamic property data for many pure fluids are correlated using equations of state that incorporate tens to hundreds of empirically determined parameters. These equations describe all of the experimentally available data for a particular fluid to within reported uncertainty, which allows the equation to be used directly as a reference. The functional form of the multiparameter equation of state, typically explicit in the Helmholtz free energy, is not derived from theory and has instead evolved from a virial expression to presently include both polynomial and exponential terms in the reduced density. Fundamentally motivated expressions, such as hard-sphere terms or square-well terms have not been found to significantly improve accuracy. Other expressions, such as Gaussian bell-shaped terms or nonanalytic terms are useful in the neighborhood of the vapor-liquid critical point.

Recent work has suggested that terms involving the logarithm of the density can be used to improve equation of state accuracy. Molar volume residuals were calculated for several pressure explicit equations of state; in this context, the residuals were defined as the difference between pure fluid density estimates from multiparameter equations (i.e., reference values) and the estimates from the pressure explicit equations. These residuals demonstrated common trends that were fit to a closed-form expression in temperature and volume that was then used to improve the original pressure explicit equations of state. The modification improved estimation accuracy for other properties as well, although not to the same extent as molar volumes. The difference between Helmholtz free energy expressions derived from the modified and unmodified pressure explicit equations could be expressed using several terms involving the logarithm of the density, suggesting that these terms could be part of a suitable basis for multiparameter equations.