General algorithm for multiphase equilibria calculation at given volume, temperature, and moles

We have developed a fast and robust algorithm for the general Π-phase equilibrium calculation at constant volume, temperature and moles, which is based on the direct minimization of the total Helmholtz energy of the mixture with respect to the mole- and volume-balance constraints. The algorithm uses the Newton–Raphson method with line-search and modified Cholesky decomposition of the Hessian matrix to produce a sequence of states with decreasing values of the total Helmholtz energy. To initialize the algorithm, an initial guess is constructed using the results of constant-volume stability testing. As the number of phases is not known a priori, the proposed strategy is based on repeated constant-volume stability testing and constant-volume phase-split calculation until a stable Π-phase state is found. The performance of the algorithm is shown on several examples of two-, three- and even four-phase equilibrium calculations of multicomponent mixtures under various conditions.