A Treatment for Overlapping Fractures in the Context of Mixed Finite Elements for Flow in Fractured Porous Media

Resumo

Accurately modeling flow in discrete fracture networks (DFNs) can be important for several fields of engineering such as groundwater management, petroleum engineering, and geotechnical engineering where these DFNs can play a key role in the flow patterns in a formation. These fracture networks are often complex and can have fractures in very close proximity, which, in turn, can lead to challenges in creating fitting meshes for finite element analyses. This work proposes a methodology to handle overlapping fractures in the context of simulating flow in fractured porous media using a Mixed Finite Element Method formulation. With this capability, fractures in close proximity can simply occupy the same geometric location in the mesh, which avoids the creation of elements with poor aspect ratio. In this work, the porous media flow is modeled with traditional Darcy's equations and the fractures and their interaction with the porous media are modeled using the Discrete-Fracture-Matrix (DFM) representation. A mixed finite element formulation is adopted to solve the flow problem in both porous media and fractures, which has key features such as local mass conservation and improved velocity approximation. The mesh generation is done using the DFNMesh algorithm, which is a mesh generator for DFNs that can handle overlapping fractures by using pre-defined user settings. The proposed methodology is analyzed using a set of numerical examples, which show the importance of the treatment even for very simple cases and that it can handle overlapping fractures and provide accurate results for the flow in complex fractured porous media problems.