A successive substitution approach with embedded phase stability for simultaneous chemical and phase equilibrium calculations

We propose a nested Gibbs energy minimization method for simultaneous chemical and phase equilibrium calculations, relying on a new formulation of the Lagrange multiplier based inner sub-problem with fixed activity coefficients. Using a sufficient condition for global optimality with fixed activity coefficients equivalent in this case to the tangent plane distance criterion, we describe two equivalent algorithms, a combinatorial and a complementarity based one, allowing to robustly solve this new sub-problem always incorporating all phases. The outer-loop of the global successive substitution reactive flash then only consists in updating the values of the activity coefficients from the non necessarily normalized species fractions for all phases calculated by the inner sub-problem. Numerical experiments from the literature illustrate the correct behavior of the proposed approach.

Automated summary

We propose a nested Gibbs energy minimization method for simultaneous chemical and phase equilibrium calculations. This method relies on a new formulation of the Lagrange multiplier based inner sub-problem with fixed activity coefficients. By using a sufficient condition for global optimality with fixed activity coefficients equivalent to the tangent plane distance criterion, we describe two equivalent algorithms, a combinatorial and a complementarity based one, to solve this new sub-problem robustly while always incorporating all phases.