Two-phase flash for tight porous media by minimization of the Helmholtz free energy

Thermodynamic modeling of phase behavior is one of the most fundamental components in the study of enhanced oil recovery by gas injection. Robust algorithms exist for multiphase equilibrium problems with no capillary pressure as commonly used in compositional reservoir simulation. However, various convergence problems have been reported even for simple two-phase split problems in the presence of capillary pressure by using the traditional algorithm based on minimization of the Gibbs free energy. In this research, the phase-split problem with capillary pressure is formulated by using the Helmholtz free energy for a given temperature and total volume. The algorithm is based on the successive substitution (SS) for updating K values, which is coupled with the volume update by using the pressure constraint equation. The robustness of the SS algorithm is improved by using the convexity information of the Helmholtz free energy and using an under-relaxation method. Case studies present phase-split problems with capillary pressure by using the developed algorithm and highlight several advantages of using the Helmholtz free energy over the Gibbs free energy. The improved robustness comes mainly from the involvement of a single energy surface regardless of the number of phases. The pressure variability that occurs during the phase-split calculation with capillary pressure is inherent in the Helmholtz free energy in volume space. (C) 2021 Elsevier B.V. All rights reserved.