Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles

We develop a new algorithm for the calculation of phase splitting at constant volume, temperature, and moles. The method is based on the direct minimization of the total Helmholtz free energy of the mixture with respect to the mole- and volume-balance constraints. The algorithm uses the Newton–Raphson minimization method with line-search and modified Cholesky factorization of the Hessian to produce a sequence of states with decreasing values of the total Helmholtz free energy. The algorithm is initialized using an initial guess that is constructed using the results of the constant volume stability testing. The speed and robustness of the algorithm are demonstrated by a number of examples of two-phase equilibrium calculations.