Mixing Rules for van der Waals-Type Equations of State Based on Activity-Coefficient Models

A new approach for incorporation of the excess free energy from an activity coefficient model (ACM) into an equation of state (EOS) has been proposed. The approach is based on a concept that any ACM is valid at a low but finite value of compressibility factor. This condition allows us to analyze the "infinite pressure" approximation in a general way. It is shown that the "infinite pressure" approach neglects the contribution of the repulsive term of the EOS to the excess free energy of a mixture. This, in turn, introduces inconsistency which results in the difference in the calculated excess free energy of the EOS and the base ACM. The new approach defines parameter a of the EOS as an implicit function of compositions and temperature, thus requiring an iterative procedure using the "infinite pressure limit" as a starting point. The new approach can be modified to provide the correct composition dependence of a mixture second virial coefficient. Applicability of the new method has been tested for binary systems under vapor-liquid and liquid-liquid equilibrium conditions.