New Insights into the Geometric State for Two-Fluid Porous Medium Systems*

Mechanistic models for two-fluid flow in porous medium systems are closed with an empirical relation usually referred to as a capillary pressure-fluid saturation relation.The ad hoc and hysteretic nature of this closure relation has been the focus of attention for the last two decades. We show that capillary pressure can be represented as a function of fluid saturation, specific interfacial area, and the Euler characteristic. The posited form of the state equation is investigated by using data generated from synchrotron-based micro-CT and simulations performed on the Titan supercomputer to explore the possible geometric states for a representative set of media. The results conclusively demonstrate that hysteresis appearing in standard closure relations can be removed and that the resultant state equation describes not only equilibrium states but also dynamic states. This work provides an important foundational component for a new generation of high fidelity multiphase porous medium models.