A robust finite element‐finite volume strategy for viscosity‐dominated hydraulic fracture propagation using an asymptotic tip enrichment

Abstract

AbstractFluid‐driven fracture propagation is widely observed in various geological processes and crucial to many applications of geological engineering. Developing robust and accurate numerical strategies has significance in advancing the scientific understanding and engineering applications related with fluid‐driven fracture propagation. We present a finite element‐finite volume strategy using asymptotic fracture tip enrichment to model the fluid‐driven fracture propagation in three‐dimensional Cartesian meshes under the viscosity‐dominated regime, in which the fluid viscosity‐related process is the dominant energy dissipation mechanism. We use the finite element method to discretize the balance of linear momentum equation for the deformed solid and the finite volume method to discretize the Reynolds equation that governs the fluid flow. In order to track the evolving fracture front in heterogeneous media, we extend the implicit level set approach originally proposed for the displacement discontinuity method. Through this process, a signed distance‐based fracture propagation criterion naturally emerges and is suitable for the viscosity‐dominated regime when solid toughness becomes irrelevant. Critically, we enrich the fluid volume treatment near the fracture front using the tip asymptotic solution. This enrichment strategy is crucial to overcome the mesh nonconformity caused by the arbitrary intersections between propagating fracture front and underlying Cartesian meshes. We compare the numerical results with analytical solutions of the KGD problem and the penny‐shape problem, and illustrate the mesh size and time step‐insensitivity of the numerical results due to the tip enrichment technique. Also, we demonstrate the capabilities of the proposed method to model fluid‐driven fracture propagation in various heterogeneous media.