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

Abstract

© 2018 Elsevier Ltd 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” (α) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors “radius-resolved saturations” (ψw(F),ψn(F)) to characterize the distribution of fluid phases within. Small accessivity (α→0) implies serial connections between different sized pores, while large accessivity (α→1) 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 ψnF that naturally capture capillary pressure hysteresis, with α 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.