Global Optimization for the Chemical and Phase Equilibrium Problem using Interval Analysis

Abstract

This paper addresses the problem of minimizing the Gibbs free energy in the n _c -component, multi-phase chemical and phase equilibrium problem involving different thermodynamic models. The algorithmic approach used is based on the tangent-plane criterion of Gibbs: the global optimization problem considered, which involves a search space of n(n + 1) dimensions, is reduced to a finite sequence of global optimization steps in n-space, and local optimization steps in nK-space, K ≤ n + 1.

We describe an algorithm performing the global optimization step involved in this lower-dimensional search space using techniques from interval analysis. We report good numerical results on instances of the Gibbs free energy minimization problem.