Mixing Rules from Models for Excess Gibbs Energy

5 MIXING RULES FROM MODELS FOR EXCESS GIBBS ENERGY 

We have noted that historically PvTx models and fugadty coefficients were restricted to gas-phase mixtures, while models and activity coefficients were restricted to condensed-phase mixtures. But these restrictions are not thermodynamic instead, they arose because of limitations in the models themselves and because of computational difficulties that occur in solving sets of nonlinear algebraic equations. But with continuing improvements in models, as well as in the power and availability of digital computers, we can contrive complicated models for nearly any system. In particular, FFF 1 is now being applied to virtually all types of mixtures and phases. 

Use of FFF 1 requires a PvTx equation of state for the mixture and each standard state, and we noted in 4.5.12 that the outstanding problems in applying PvTx equations to mixtures are the choices for mixing rules and combining rules. C e approach to this problem is to base mixing rules on models for g. The motivation is to combine the composition-dependence in g models with the pressure-dependence in PvTx 

Formally, this could be used to coimect a PvTx model for p, (Ihs) with a model for the activity coefficient (rhs). However, this approach is unattractive because it would require us to deal separately with each component. 

A better approach is to start from a particular model for g (T, P, x) A ), such as the Porter, Margules, or Wilson models introduced in 5.6. Here the A) are the model parameters, whose values are usually obtained by fits to phase-equilibrium data. We then select a PvTx model often a cubic is used. In this discussion, we consider the Redlich-Kwong equation ( 4.5.8). This model contains parameters a, b that depend on composition via some mixing rules ( 4.5.12). Our strategy is to find those mixing rules by matching the model to given by the PvTx equation. 

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