Gamma-Phi Method for Vapor-Liquid Phase Equilibrium

Gamma-Phi Method for Vapor-Liquid Phase Equilibrium 

From the relation between the fugacity, the Gibbs free energy, and an equation of state, the fugacity in a vapor can be computed from 

In this equation V is total volume, and Z = PV/RT is the compressibility factor computed from an equation of state, and V is the molar volume of the mixture. Most equations of state used in engineering are pressure explicit, that is, they arc in a form in which the pressure is explicit and the volume dependence is more complicated. One such example is the virial equation 

Here B, C, D, and so forth, are the second, third, fouith, and so forth, virial coefficients, which in a pure fluid are only a function of temperature, and in a mixture are functions of only temperature and mole fraction. Another class of commonly used equations of state is based on the van der Waals equation. One member of this class is the Peng-Robinson (1976) equation 

Redlich-Kwong-Soave, and others that are reviewed elsewhere (Sandler, Orbey, and Lee 1994, Chap. 2). 

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