Physics-based models of hysteresis in multiphase flow in porous media

Abstract

We propose a novel probabilistic framework based on pore-scale probabilistic events to derive a theory of hysteresis in multiphase flow in porous media. In particular, we define the pore-space accessivity to contrast the serial and parallel arrangement of different-radius pore slices, and the radius-resolved saturations to detail the pore-scale distribution of immiscible fluids. We show that accessivity can be measured by mercury cyclic porosimetry. Our microscopic theory of hysteresis produces simple formulae that are suitable for use as hysteresis-enabling constitutive laws for capillary pressure and relative permeabilities in conventional continuum simulations of multiphase flow.