Transient-pressure modelling in fractured porous media with a new embedded finite element approach

This paper presents a unified, embedded finite element formulation for simulating transient fluid flow in fractured porous media while accounting for transverse and longitudinal directions. The transverse flow arises due to pressure variations on both sides of fractures, as these typically exhibit lower permeability in the perpendicular direction. A simple coupling framework is introduced to connect independent sets of finite element meshes, one for the bulk porous media and the other for natural discontinuities. Importantly, the proposed coupling technique does not introduce additional degrees of freedom, and discontinuities can arbitrarily intersect the background elements of the continuum domain. Additionally, standard quadrature rules for integration can be used without modifications, thus avoiding additional remediation steps found with nodal enrichment strategies. These advantageous features make our method a robust technique capable of modelling transient fluid flow as an integral part of a coupled hydro-mechanical formulation. The performance is assessed using several numerical examples. These encompass various cases of fracture orientation relative to the background elements. The results demonstrate a good agreement with reference solutions. The effects of the coupling parameter, as well as the transverse and longitudinal permeabilities, in the temporal domain, are also investigated. The results demonstrated that the proposed method is capable of handling any values of transverse or longitudinal permeability compared to the surrounding porous domain. Moreover, the findings confirmed that, as a rule of thumb, a coupling parameter should be selected 10 times larger than the highest permeability used in the model.