Phase stability testing and phase equilibrium calculation at specified internal energy, volume, and moles

We have developed a fast and robust algorithm for the general multi-phase equilibrium calculation at constant internal energy, volume, and moles (specification UVN). The algorithm is based on the direct maximization of the total entropy of the system subject to the internal energy-, volume-, and mole-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 increasing values of the total entropy of the system. Unlike the previously published formulations, our method uses results of the UVN-phase stability testing for initialization of the UVN-flash calculation. As the number of phases is not known a-priori, the proposed strategy is based on repeated UVN-stability testing and UVN phase-split calculation until a stable phase split is found. The performance of the algorithm is demonstrated on many examples of different complexity.