Global Optimization and Analysis for the Gibbs Free Energy Function Using the UNIFAC, Wilson, and ASOG Equations

Abstract

The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not have this limitation and can predict the presence of multiple liquid phases. The most important area of application of all these equations is in the prediction of phase equilibria. The calculation of phase equilibria involves two important problems: (1) the minimization of the Gibbs free energy and (2) the tangent plane stability criterion. Problem (2), which can be implemented as the minimization of the tangent plane distance function, has found wide application in aiding the search for the global minimum of the Gibbs free energy. However, a drawback of all previous approaches is that they could not provide theoretical guarantees that the true equilibrium solution will be obtained. The goal of the work is to find the equilibrium solution corresponding to the global minimum of the Gibbs free energy. A proof that the Wilson equation leads to a convex formulation for the minimization of the Gibbs energy is provided so that a local optimization technique will always converge to a global minimum. In addition, new expressions are derived for the molar Gibbs free energy function when the UNIFAC, ASOG, and modified Wilson equations are employed. These expressions are then transformed so that application of a branch and bound based global optimization algorithm originally due to Falk and Soland (1969) is possible. This allows global solutions to be obtained for both the minimization of the Gibbs free energy and the minimization of the tangent plane distance function. The algorithm is implemented in C as part of the package GLOPEQ, global optimization for the phase equilibrium problem (McDonald and Floudas, 1994d). Results for several examples are presented