A Multi-Resolution Approach to Hydraulic Fracture Simulation

TL;DR

This paper introduces a multi-resolution simulation method for hydraulic fracturing that combines global discrete crack modeling with local phase-field fracture propagation to improve accuracy and computational efficiency.

Contribution

It presents a hybrid scheme coupling discrete crack representation with phase-field modeling for efficient, mesh-independent hydraulic fracture simulation.

Findings

Effective in benchmark hydraulic fracturing problems

Capable of simulating crack growth around inclusions

Reduces computational costs compared to traditional methods

Abstract

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.