An examination of pore-scale capillary pressure & impact of interfacial area under dynamic conditions using volume-of-fluid (vof) method

Conventional two-phase flow equations for porous media require empirical closure relations that are nonlinear functions of saturation, S.  The capillary pressure-saturation (P_c-S) relation is one such example that is non-unique, hysteretic and material specific. Extended theories have been proposed to include additional macroscopic state variables to remove the history dependence in the P_c-S relationship. Recent computational and experimental studies have shown that under quasi-static (equilibrium) conditions the inclusion of fluid-fluid interfacial area (a^wn) as a third state variable may uniquely define P_c. We investigate the role of interfacial area using microscale direct numerical simulations (DNS) with Volume-of-Fluid (VOF) method under non-equilibrium (dynamic) conditions. Drainage and imbibition are simulated in a virtual porous medium for different capillary numbers. From the DNS data, the interfacial area is estimated, and the pore-scale capillary pressure is directly computed at the fluid-fluid invasion front. The quasi-static and dynamic P_c–S–a^wn surfaces are constructed to establish if this relationship represents a set of state variables that removes the hysteretic effect under all conditions.