Fluid flow through anisotropic and deformable double porosity media with ultra-low matrix permeability: A continuum framework

Abstract

Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns. This study aims to formulate a comprehensive coupled continuum framework that could adequately consider these critical characteristics. In our framework, fluid flow in the micro-fracture network is modeled with the generalized Darcy's law, in which the equivalent fracture permeability is upscaled from the detailed geological characterizations. The liquid in the much less permeable matrix follows a low-velocity non-Darcy flow characterized by threshold values and non-linearity. The fluid mass transfer is assumed to be a function of the shape factor, pressure difference, and (variable) interface permeability. The solid deformation relies on a thermodynamically consistent effective stress derived from the energy balance equation, and it is modeled following anisotropic poroelastic theory. The discussion revolves around generic double porosity media. Model applications reveal the capability of our framework to capture the crucial roles of coupling, poroelastic coefficients, anisotropy, and ultra-low matrix permeability in dictating the pressure and displacement fields.