Nonhysteretic Capillary Pressure in Two-Fluid Porous Medium Systems: Definition, Evaluation, Validation, and Dynamics

Abstract

A closure relation for capillary pressure plays an important role in the formulation of both traditional and evolving models of two-fluid-phase flow in porous medium systems. We review the traditional approaches to define capillary pressure, to describe it mathematically, to determine parameters for this relation, and to constrain the domain of applicability of this relation. In contrast to the traditional approach, we provide a rigorous, multiscale definition of capillary pressure, define the state domain of interest in practice, summarize computational and experimental approaches to investigate the system state, and apply the methods for two-fluid states in a model ink bottle system, the classical Finney pack of spheres, and a synthetic sphere pack system. The results of these applications show that a state equation exists that describes capillary pressure without hysteresis. This state equation parameterizes a function that describes the nonwetting phase volume fraction in terms of the capillary pressure, the interfacial area, and the specific Euler characteristic of the nonwetting phase. Furthermore, this state equation applies over the complete range of conditions encountered in practice, and it applies under both equilibrium and dynamic conditions. This state equation involving capillary pressure forms an important foundation for the development of the next generation of macroscale two-fluid-phase flow models in porous medium systems.