Microscopic theory of capillary pressure hysteresis based on pore-space accessivity and radius-resolved saturation

TL;DR

This paper introduces a macroscopic property called accessivity and radius-resolved saturations to model pore connectivity and fluid distribution, providing a new statistical theory that captures capillary pressure hysteresis in porous media.

Contribution

It proposes the concepts of accessivity and radius-resolved saturations to develop a statistical theory for hysteresis in porous media, extending classical models.

Findings

Accessivity controls the extent of capillary pressure hysteresis.

Simple algebraic formulas for saturation updates capture hysteresis effects.

Framework aids interpretation of hysteretic data and upscaling pore-scale observations.

Abstract

Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" ($\alpha$) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" ($\psi_w(F),\psi_n(F)$) to characterize the distribution of fluid phases within. Small accessivity ($\alpha\to0$) implies serial connections between different sized pores, while large accessivity ($\alpha\to1$) corresponds to more parallel arrangements, as the classical capillary bundle model implicitly assumes. Based on these concepts, we develop a statistical theory for quasistatic immiscible drainage-imbibition in arbitrary cycles, and arrive at simple algebraic formulae for updating $\psi_n(F)$ that naturally capture capillary pressure hysteresis, with $\alpha$ controlling the amount of hysteresis. These concepts may be used to interpret hysteretic data, upscale pore-scale observations, and formulate new constitutive laws by providing a simple conceptual framework for quantifying connectivity effects, and may have broader utility in continuum modeling of transport, reactions, and phase transformations in porous media.