Chemical and phase equilibria through deterministic global optimization

Abstract

Chemical and phase equilibrium calculations are commonly performed by solving a constrained optimization problem known as Gibbs energy minimization. This problem is, in general, nonconvex, which implies that it is not a trivial task to solve for its global minimum, as many local minima may exist. The global minimum is the only solution that bears physical significance. Among the various techniques found in the literature that attempt to solve this problem, the algorithm with interval analysis seems particularly interesting due to its generality and to the fact that it mathematically guarantees global optimality. However, in order to apply itdirectly to the equilibrium problem, it is necessary to circumvent somehow the fact that in its original formulation, lower bounds for mole numbers that are too close to zero may cause numerical underflow, leading the algorithm to fail. An algorithm based on the original is presented and is used to evaluate 8 benchmark equilibrium problems extracted form the literature. The algorithm, despite no longer being able to mathematically guarantee global optimality, was capable of solving all problems correctly and with relative efficiency.