The enriched-embedded discrete fracture model (nEDFM) for fluid flow in fractured porous media

The embedded discrete fracture model (EDFM) is widely adopted for simulating fluid flow in fractured porous media, but it faces limitations when dealing with blocking fractures due to its assumption of symmetric and linear pressure distribution around fractures. To improve this, our work presents a novel numerical framework named the enriched-embedded discrete fracture model (nEDFM). This framework, based on a non-conforming grid and discretized using the mass-conservative finite volume method, offers significant advancements. An attractive feature of the nEDFM is its applicability to both conductive and blocking fractures, as well as isotropic and anisotropic matrix permeability, all while maintaining a low computational cost. The local shape function, which introduces two enriched degrees of freedom for every fracture cell, is developed to model the discontinuities of pressure and its gradient on two sides of the fracture. Additionally, two equations for coupling the matrix and reduced fracture are supplemented to close the system and improve the accuracy of mass exchange between the matrix and fracture. Comparative assessments between the nEDFM, classical EDFM, and projection-based EDFM (pEDFM) demonstrate the superior performance of nEDFM. Specifically, the nEDFM outperforms the EDFM for conductive fractures and can obtain better pressure distribution inside blocking fractures than the pEDFM. In scenarios involving anisotropic matrix permeability with either conductive or blocking fractures, the nEDFM can get solutions comparable to those obtained by the reference solution. Hence, the nEDFM emerges as an accurate and flexible method for simulating fluid flow in fractured porous media.