Exploring the effect of flow condition on the constitutive relationships for two-phase flow

Abstract

Empirical relationships that describe two-phase flow in porous media have been largely hysteretic in nature, thereby requiring different relationships depending on whether the system is undergoing drainage or imbibition. Recent studies have suggested using interfacial area to close the well-known capillary pressure-saturation relationship, while others expand upon this by including the Euler characteristic for a geometric description of the system. With the advancement of fast x-ray microtomography at synchrotron facilities, three-dimensional experiments of two-phase quasi- and non-equilibrium flow experiments were conducted to quantify the uniqueness of constitutive relationships under different flow conditions. We find that the state functions that include the Euler characteristic provide the most unique prediction of the state of the system for both quasi- and non-equilibrium flow. Of these functions, those that infer volume fraction from the other state variables are independent of flow condition (quasi- or non-equilibrium). This enhances the applicability of new constitutive relationships allowing for more robust models of two-phase flow.