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.

相行为的热力学建模是研究通过注气提高采收率的最基本组成部分之一。对于组分储层模拟中通常使用的不存在毛细压力的多相平衡问题，存在鲁棒算法。然而，通过使用基于吉布斯自由能最小化的传统算法，即使对于存在毛细管压力的简单两相分离问题，也已经报道了各种收敛问题。在这项研究中，通过在给定的温度和总体积下使用亥姆霍兹自由能来解决毛细压力的相分离问题。该算法基于用于更新K值的连续替换（SS），并通过使用压力约束方程式与体积更新相结合。通过使用亥姆霍兹自由能的凸度信息和使用欠松弛方法，可以提高SS算法的鲁棒性。案例研究通过使用开发的算法提出了毛细管压力的相分离问题，并突出了使用亥姆霍兹自由能比吉布斯自由能的几个优点。改进的鲁棒性主要来自单个能量表面的参与，而与相数无关。在具有毛细管压力的相分离计算过程中发生的压力变化是体积空间中亥姆霍兹自由能所固有的。案例研究通过使用开发的算法提出了毛细管压力的相分离问题，并突出了使用亥姆霍兹自由能比吉布斯自由能的几个优点。改进的鲁棒性主要来自单个能量表面的参与，而不考虑相数。在具有毛细管压力的相分离计算过程中发生的压力变化是体积空间中亥姆霍兹自由能所固有的。案例研究通过使用开发的算法提出了毛细管压力的相分离问题，并强调了使用亥姆霍兹自由能比吉布斯自由能的几个优点。改进的鲁棒性主要来自单个能量表面的参与，而不考虑相数。在具有毛细管压力的相分离计算过程中发生的压力变化是体积空间中亥姆霍兹自由能所固有的。