In this work we present a higher-order numerical model for two-phase compositional flow in fractured media in 2D and in 3D unstructured gridding. Both planar and non-planar fractures are accommodated. All commonly used types of finite elements are covered in our model; in particular, quadrangular and triangular elements in 2D, and hexahedra, prisms and tetrahedra elements in 3D.
The fracture cross-flow equilibrium (FCFE) concept is adopted to model flow in the fractures. The hybridized mixed finite element (MFE) and the higher-order discontinuous Galerkin (DG) method are used to solve for the flow and the transport equations respectively. We have developed a computer-aided-design (CAD) interface connected to the mesh generator. Using this interface with the unstructured tetrahedra we can generate the most complicated fracture shapes. The complexity of fractures that we generate/simulate is not reported in the past to the best of our knowledge. Our model can simulate all range of fracture permeability values as opposed to other models where low permeable fractures affect the accuracy of the results. Efficiency and accuracy of our model are demonstrated in different examples in 2D and in 3D.