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Partial Derivative Quantities from Phase Equilibria Relationships for Mixtures
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A systematic formulation of multicomponent/multiphase phase equilibria as a linear algebra problem in the fugacities, mole fractions, partial molar volumes, and partial molar enthalpies is given. The algorithm takes advantage of the Gibbs-Duhem relationships for each phase and a modified Gaussian elimination technique to reduce the system of equations. These algorithmic steps allow current symbolic manipulation packages to generate useful partial derivative relationships in terms of measurable thermodynamic quantities. Features of the algorithm are demonstrated by applying a computer implementation of the method to a simple two-phase/two-component system and to the more complicated examples of a two-phase/three-component supercritical fluid chromatography experiment and a mass-conserving closed system.
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