An extended finite volume model for implicit cohesive zone fracture propagation in a poroelastic medium

Abstract

Models for fluid-driven fractures in a poroelastic medium involve the simultaneous simulation of multiple physical processes—diffusion of pore pressure, poroelastic stresses, fluid injection into a fractured porous medium, and fracture propagation. To simulate the above-mentioned physics, many algorithms and discretization techniques have been used in the past. The finite volume method has been gaining popularity for simulating solid mechanics problems. The discretization algorithms discussed in the past have used a segregated method for solving the poroelastic momentum balance, where iterations are necessary to obtain a converged solution for each component of the displacement vector. This segregated approach, when coupled with fluid-driven fracture propagation, can lead to excessive simulation times because of the coupled nature of the problem.In this study, an implicit formulation was designed to construct a linear system of equation for the components of the displacement vector to solve the poroelastic momentum balance equation (without iterating between components). Within this formulation, a fluid-driven fracture propagation model was implicitly incorporated using a cohesive zone approach. This methodology provided accurate solutions as shown by the validations in this paper where simulated results were compared with various well-known analytical solutions. The implicitness of the new model allowed significant improvements in computation speed when solving multi-physics problems. The simulation speed-ups were found to be 2 to 8 times when compared with the segregated method.