Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid‐Dimensional Computational Model

We formulate the problem of fully coupled transient fluid flow and quasi-static poroelasticity in arbitrarily fractured, deformable porous media saturated with a single-phase compressible fluid. The fractures we consider are hydraulically highly conductive, allowing discontinuous fluid flux across them; mechanically they act as finite-thickness shear deformation zones prior to failure (i.e., non-slipping and non-propagating), leading to ‘apparent discontinuity’ in strain and stress across them. Local nonlinearity arising from pressure-dependent permeability of fractures is also included. Taking advantage of typically high aspect ratio of a fracture, we do not resolve transversal variations and instead assume uniform flow velocity and simple shear strain within each fracture, rendering the coupled problem numerically more tractable. Fractures are discretized as lower-dimensional zero-thickness elements tangentially conforming to unstructured matrix elements. A hybrid-dimensional, equal-low-order, two-field mixed finite element method is developed, which is free from stability issues for a drained coupled system. The fully implicit backward Euler scheme is employed for advancing the fully coupled solution in time, and the Newton-Raphson scheme is implemented for linearization. We show that the fully discretized system retains a canonical form of a fracture-free poromechanical problem; the effect of fractures is translated to the modification of some existing terms as well as the addition of several terms to the capacity, conductivity and stiffness matrices, therefore, allowing the development of independent subroutines for treating fractures within a standard computational framework. Our computational model provides more realistic inputs for some fracture-dominated poromechanical problems like fluid-induced seismicity.