Mixing and Combining Rules for SAFT

The last type of equation of state that we will consider is the Statistical Associating-Fluid Theory (SAFT) first proposed by Chapman et and Huang and Radosz, and for which there are now many variants as discussed in Chapter 8. 

In the SAFT model, a molecule is considered to consist of a collection of segments, and the Helmholtz function is written as  

The association term from Wertheim s theory is given by 

The application of this equation of state to mixtures requires the replacement of the Carnahan-Starling term with the expression reported by Mansoori et and more complicated chain and association terms. In the SAFT equation, and other equations of this type, each of the terms has its own theoretically-based mixing rule that is different from the mixing rules for other terms in the same equation. For example, the mean attractive energy associated with the first rder perturbation is treated by Galindo et al SAFT and the related methods can be considered molecular-based equations of state for associating fluids. SAFT is reviewed in Chapter 8 and by Muller and Gubbins.  

For mixtures, only the dispersion part of the segment Flelmholtz energy requires the use of combining rules the composition dependence is built into the chain and association terms by the statistical thermodynamics. Gross and Sadowski presented a new parameterization of SAFT with constants for a wide range of substances that does not suffer from the numerical inconsistencies of the Huang-Radosz model.  

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