A phase field based discrete fracture model (PFDFM) for fluid flow in fractured porous media

In this study we propose a novel phase field based discrete fracture model (PFDFM) to simulate fluid flow in fractured porous media. The common discrete fracture models represent fractures by sharp topology in an explicit way, regardless of using conforming or non-conforming mesh. Inspired by the definition of crack phase field, the sharp fracture topology is treated as a diffusive one in the solution of fluid flow problems, and the integration of fluid flow equation over fractures can be transformed to the one over the matrix. The algorithm to determine the fracture phase field and finite element discretization have been described in detail. The performance of the proposed method is validated against the classic discrete fracture model on several numerical cases in both two and three dimensions. We further investigate the convergency behavior of the proposed method through sensitivity analysis to mesh resolution and fracture parameters. Numerical results are obtained, which demonstrates that the proposed method is accurate, convergent and quite promising for simulating fluid flow in fractured porous media.