Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

The capillary pressure–saturation (P c–S w) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P c–S w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P c–S w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as “hysteresis”. A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389–3904, 1993a) suggests that, by introducing a new state variable, called the specific interfacial area (a nw, defined as the ratio of fluid–fluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure–saturation relationship using a dynamic pore-network model. The simulation results imply that P c–S w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure–saturation–interfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P c–S w–a nw relationship.