GLOBAL OPTIMIZATION AND ANALYSIS FOR THE GIBBS FREE-ENERGY FUNCTION USING THE UNIFAC, WILSON, AND ASOG EQUATIONS

The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomp onent mixtures with only binary parameters but was incapable of predic ting more than one liquid phase. The UNIFAC and ASOG group contributio n 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 calculat ion of phase equilibria involves two important problems: (i) the minim ization of the Gibbs free energy and (ii) the tangent plane stability criterion. Problem ii, which can be implemented as the minimization of the tangent plane distance function, has found wide application in ai ding the search for the global minimum of the Gibbs free energy. Howev er, a drawback of all previous approaches is that they could not provi de theoretical guarantees that the true equilibrium solution will be o btained. The goal of this work is to find the equilibrium solution cor responding to the global minimum of the Gibbs free energy. A proof tha t the Wilson equation leads to a convex formulation for the minimizati on of the Gibbs energy is provided so that a local optimization techni que will always converge to a global minimum. In addition, new express ions are derived for the molar Gibbs free energy function when the UNI FAC, ASOG, and modified Wilson equations are employed. These expressio ns are then transformed so that application of a branch and bound base d global optimization algorithm originally due to Falk and Soland (196 9) is possible. This allows global solutions to be obtained for both t he minimization of the Gibbs free energy and the minimization of the t angent plane distance function. The algorithm is implemented in C as p art of the package GLOPEQ, global optimization for the phase equilibri um problem (McDonald and Floudas, 1994d). Results for several examples are presented.