9 Mixing and combining rules

Abstract

Equations of state have been used for the accurate description of the P-v-T behavior and thermodynamic properties of fluids for decades. It is mixing and combining rules that allow an equation of state developed for pure fluids to be used for mixtures. Historically, there have been many examples in which an equation of state could be used to describe the properties of two or more pure fluids, but not of their mixtures. This is clearly a failure of the mixing and/or combining rules used. For almost a century, only the simplest mixing rules were widely used; the classical van der Waals one-fluid rules for cubic equations of state, and mixing rules based on the virial equation for more complicated equations of state. In recent years, there has been a great deal of research on mixing rules and some real advances. Perhaps the most important has been the combination of equation of state and free energy models. These mixing rules, discussed in this chapter, have resulted in simple cubic equations of state providing accurate descriptions of the phase behavior of highly nonideal mixtures over large ranges of temperature and pressure with temperature-independent parameters. Further, these new mixing rules can incorporate mixture group contribution methods, such as UNIFAC, allowing for a simple extension of these models to high temperatures and high pressures with the existing parameter tables. New mixing rules have also been developed for other classes of equations of state. In this area, the progress has been slow and less noteworthy. One interesting feature that has emerged, largely from molecular theory, is the use of different mixing rules for the attractive and repulsive contributions to the equation of state.