14-17 May 2018
New Orleans
US/Central timezone

Unified presentation and comparison of various formulations of the phase stability and phase equilibrium calculation problems

15 May 2018, 11:53
New Orleans

New Orleans

Oral 20 Minutes MS 2.16: Frontiers in understanding of gas migration processes in porous media Parallel 4-A


Tomáš Smejkal


We present general formulations of the phase-equilibrium and phase-stability problems for multicomponent mixtures and verify that these formulations generalize the problems of phase-equilibrium and phase-stability at constant volume, temperature, and mole numbers ($VTN$-flash), at constant internal energy, volume, and mole numbers ($UVN$-flash), and at constant pressure, temperature, and mole numbers ($PTN$-flash). Furthermore, we develop a numerical method for solving the general formulation of phase-equilibrium problems. This algorithm is based on the direct minimization of the objective function with respect to the constraints. The algorithm uses a modified Newton-Raphson method, along with a modified Cholesky decomposition of the Hessian matrix to generate a sequence of states with decreasing values of the objective function. The algorithm was implemented in C++ and using generic programing we have a single, portable solver for all three flash formulations. Properties of the algorithm are shown on phase-equilibria problems of multicomponent mixtures in different specifications and with different levels of difficulty. Complexities and numerical performance of the individual flash formulations are discussed.

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