Development of an accurate and practical equation of state based on perturbation theory and random-closest-packed born spheres

Abstract

Equation of state calculations are used by engineers in all phases of chemical process design and control. New processes often are designed to operate under conditions for which insufficient experimental data exist, and equations of state are used to predict the behavior of the process fluids. Additionally, equations of state are well suited to the numerical methods used in modern computer based simulation programs which currently are used in the design and control of chemical processes. Historically, equations of state have suffered from several difficulties, including the inability to make accurate predictions of the high density liquid and the saturation regions simultaneously. There are three main causes for these problems. First, a lack of extensive, accurate data for a wide variety of fluids over their full range of temperature and pressure has resulted in equations that can predict the few properties used in their development, but lack accuracy in the prediction of other properties. Second, most of these equations are analytic and cubic in density, and as a result cannot predict the proper behavior in the critical region. Finally, in most of these equations the pressure diverges at too high a density compared to real fluids, and, therefore, the equations do not exhibit a sufficiently fast change in pressure with a change in density in the dense liquid region. This work presents a practical, accurate equation of state for use with natural gas components and other simple fluids. The new equation is based on perturbation theory, making use of an empirical hard body repulsion term with a pole at the random-closest-packed density. The Born potential is used for the reference fluid, and a perturbation expansion similar to the virial series is used for the attractive term. Additionally, this work makes use of a new exponential term to improve predictions in the critical region. This equation can predict accurately the thermophysical behavior of methane, propane, argon and carbon dioxide over nearly the entire range of fluid conditions. Although the new equation is fourth order in density, it has only three real positive roots. Computation times are, therefore, comparable to those for the commonly used cubic equations.