Cubic mixing rules

The accurate description of thermodynamic properties of asymmetric multicomponent fluid systems of industrial interest, over a wide range of conditions, requires the availability of models that are both consistent and mathematically flexible. Specially suited models are those of the equation-of-state (EOS) type, which are built to represent the properties of liquids, vapors, and supercritical fluids. The composition dependence of EOSs is typically pairwise additive, with binary interaction parameters conventionally fit to match experimental information on binary systems. This is the case for the well-known van der Waals quadratic mixing rules (QMRs), which assume multicomponent system describability from binary parameters. In contrast, cubic mixing rules (CMRs) depend on binary and ternary interaction parameters. Thus, CMRs offer the possibility of increasing the model flexibility, i.e., CMRs are ternionwise additive. This means that, through ternary parameters, CMRs make it possible to influence the model behavior for ternary systems while leaving invariant the description of the corresponding binary subsystems. However, the increased flexibility implies the need for experimental information on ternary systems. This is so, unless we have a method to predict values for ternary parameters from values of binary parameters for the ternary subsystems not having ternary experimental information available, when we want to model the behavior of multicomponent fluids. Mathias, Klotz, and Prausnitz (MKP) [Fluid Phase Equilib. 1991, 67, 31-44] put forward this problem. In this work, we provide a possible solution, i.e., an equation to predict three index ternary parameters from three index binary parameters within the context of CMRs. Our equation matches the Michelsen-Kistenmacher invariance constraint and, in a way, has the pair-based MKP mixing rule in its genesis. The present approach can be extended also to models that are not of the EOS type.