A graph-based algorithm for the Continuous-Projection Embedded Discrete Fracture Model (CpEDFM-U) to simulate two-phase flows in naturally fractured porous media using the MPFA-D method on general unstructured meshes

Modeling fluid flow in naturally fractured porous media is crucial for applications such as hydrocarbon production and CO2 sequestration. However, accurately simulating these flows remains challenging due to fractures with complex permeability distributions. The Embedded Discrete Fracture Model (EDFM) has been widely used but has limitations in representing fractures acting as barriers, especially in multiphase flows. To overcome these challenges, the Projection-based Embedded Discrete Fracture Model (pEDFM) was developed, offering better handling of fractures with lower permeability than the matrix. However, it can still exhibit discontinuities in fracture projections. To address these limitations, we propose the Continuous-Projection Embedded Discrete Fracture Model (CpEDFM-U), a graph-based algorithm that guarantees continuous fracture projections in both structured and unstructured 2D meshes. The CpEDFM-U uses Dijkstra’s algorithm to find the shortest path between fracture tips and applies the MPFA-D method for matrix flow and TPFA for fractures. In numerical simulations analyzed, CpEDFM-U outperforms EDFM and pEDFM, demonstrating lower errors and robust performance across different fracture types and mesh resolutions. • The proposed Graph-based CpEDFM-U handles barriers and channels in general 2D meshes. • The Non-orthodox MPFA-D solves flow in heterogeneous, anisotropic 2D fractured media. • The two graph weights tested yielded similar results, converging with refinement. • The CpEDFM-U algorithm ensures a continuous projection in general meshes.