Modeling the orientation- and stress-dependent permeability of anisotropic rock with particle-based discrete element method

Abstract

A novel physics-based numerical model is proposed to simulate the orientation and effective confining pressure dependent permeability of anisotropic rock. In the two-dimensional discrete element model, presence of anisotropy is explicitly represented by inserting a set of smooth joints. Based on the experimentally obtained effective stress law at sample scale, a physics-based relation is deduced to describe the reduction of pipe aperture upon the normal contact force at grain scale. Darcy test is conducted to validate the model by comparing the flow rate and pressure distributions with analytical solutions. Different parameters are assigned to represent the difference in flow capacity of rock matrix and beddings. Fluid flow tests performed on the isotropic model and anisotropic models with horizontal and vertical beddings reveal that the macro permeability decreases with increasing effective stress, following the same effective stress law. The initial aperture dominates the intrinsic permeability while the reduction of permeability is due to the closure of pipe aperture. Permeability anisotropy is caused by the different apertures assigned to the rock matrix and the bedding while the force sensitivity factors determine the stress-dependence of the permeability anisotropy. Simulations of the stress concentration and fluid dissipation around borehole confirm the capacity of the model in capturing the hydro-mechanical coupled responses of anisotropic rock formation. This study provides a fluid flow model for the exploration of mechanisms underlying the orientation and stress dependent permeability of anisotropic rocks and for the simulation of their engineering responses subjected to hydro-mechanical coupling.