A method for multiphase equilibrium calculations

Abstract

Methods for multiphase equilibrium calculations are generally based on Gibbs free energy minimization or equation-solving. Equation-solving methods, although superior to free energy minimization methods for phase equilibrium calculations without chemical reactions, often involve sequential procedures for a priori phase identification. A simultaneous equation-solving method ( τ-method), based on modifying mole fraction summations, is proposed for these calculations. It requires the solution of a minimization problem only once, and provides phases actually present at equilibrium, their quantities and compositions simultaneously; and phase identification in advance is not required. Phase characteristic variable and pseudo phase are introduced, and their significance discussed. τ-method is shown by analysis and numerical results, to be consistent with Nelson’s (1987, Comput. Chem. Engng 11, 581–591) criteria for phase existence. The method is tested on typical examples for two-phase (vapor–liquid and liquid–liquid) and three-phase (vapor–liquid–liquid) equilibrium calculations. For each example, several conditions and/or different initializations are used, and the minimization problem is solved by a version of successive linear programming method. The results show that τ-method is successful and reliable for multiphase equilibrium calculations.