Global Stability Analysis and Calculation of Liquid−Liquid Equilibrium in Multicomponent Mixtures

Abstract

A global algorithm for implementing the Gibbs tangent plane stability test in multicomponent, multiphase liquid mixtures is described. The algorithm is self-starting and significantly improves the reliability and robustness of multiphase equilibrium calculations. The main improvement is a result of a new approach for locating the stationary points of the tangent plane distance function. This relies on the geometric properties of the tangent plane distance function but is independent of the specific fluid model. For ternary mixtures, it is shown that stationary points in the tangent plane distance function satisfy a global topological constraint Nmax + Nmin − Nsad = 1 where Nmax is the number of maxima, Nmin is the number of minima, and Nsad is the number of saddles. This provides a global consistency check on the numerical results that is independent of the specific model or parameters used to describe the mixture. The method has been implemented and tested on a variety of problems with three and four com...