VT-Based Phase Envelope and Flash Calculations in the Presence of Capillary Pressure

Phase-envelope construction and isothermal flash are two widely used phase-equilibrium calculations. Because of the increasing importance of oil and gas production from shale, there is a need to perform these calculations in the presence of capillary pressure. Such calculations are also important for other processes inside porous media. Classical phase-equilibrium calculations usually use pressure and temperature based (PT-based) thermodynamics that requires the solution of the equation of state for the molar volume or density to calculate the desired thermodynamic properties. An alternative to this formulation is volume and temperature based (VT-based) thermodynamics, in which repeated molar volume or density solutions are avoided by co-solving the equality of phase pressures in the equilibrium calculation. The formulation is particularly advantageous for equilibrium calculation with capillary pressure. It can naturally handle the negative pressures in the wetting phase (usually the liquid) caused by the capillary pressure. Furthermore, the capillary pressure function usually has a high level of implicitness for the pressure variable, which can be circumvented in the VT formulation. We present the VT-based formulations for phase-envelope construction and isothermal flash with capillary pressure. The incorporation of capillary pressure actually does not increase the number of equations because the pressure-equality equation is included in the VT-based formulations without capillary pressure. Using volume as an independent variable results in simpler derivatives for the interfacial tension models, which are more suitable for cases with large capillary pressures or with saturation-dependent capillary pressures that account for pore size distribution. The developed algorithms are tested for multicomponent reservoir fluid examples, including natural gas, gas condensate, and black oil, down to extremely small pore sizes. The algorithms converge with only a few Newton iterations, even for the extreme cases. For the cases in which pore size distribution is considered and the capillary pressure is treated as saturation-dependent, the same convergence behavior is kept. This feature is especially attractive for reservoir simulation cases in which saturation-dependent capillary pressure curves are used.