Fluid flow through anisotropic and deformable double porosity media with ultra-low matrix permeability: A continuum framework
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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. The purpose of this study is to formulate a comprehensive coupled flow and geomechanics model of anisotropic and deformable double porosity media with ultra-low matrix permeability. Fluid in fissures is modeled with the generalized Darcy's law with an equivalent permeability upscaled from the detailed geological characterizations while the liquid in much less permeable matrix follows a low velocity non-Darcy flow characterized by threshold values and non-linearity, and fluid mass transfer is dependent on shape factor, phase pressure difference, and interface permeability. The geomechanics relies on a thermodynamically consistent effective stress derived from the energy balance equation, and it is modeled following poroelastic theory. Scaling analysis is performed to drop negligible force density terms under reasonable parameters' ranges which also guarantee no violation of entropy inequality. The discussion revolves around generic double porosity media. Numerical simulation of the initial boundary value problem reveals the capability of this framework to capture the crucial role of coupling, anisotropy and ultra-low matrix permeability in dictating the pressure and displacement fields.
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