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
Year: 2026
Type: article
Abstract: Accurate and efficient modeling of fluid flow in naturally fractured porous media is essential in applications such as hydrocarbon production, CO₂ sequestration, and geothermal energy. However, the precise simulation of fluid flow in these reservoirs remains a significant challenge. The explicit modeling of fractures with wide permeability variations greatly increases the complexity of numerical simulations. The Embedded Discrete Fracture Model (EDFM) was one of the first methods to explicitly represent fractures, without mesh conformity, producing accurate results in cases of highly permeable fractures. However, its ability to adequately represent scenarios where the fracture acts as a barrier is limited. To overcome this and some other limitations, the Projection-based Embedded Discrete Fracture Model (pEDFM) was developed, capable of handling fractures with high permeability contrast. Still, pEDFM can present discontinuities in the fracture projections, which compromises the representation of low-permeability fractures when they are angled relative to the x, y, and/or z axes. In this work, we propose the CpEDFM-U, a robust graph-based algorithm that guarantees continuous projection in both structured and unstructured 2D meshes. The method maps cells to a weighted graph, applies Dijkstra’s algorithm to find the shortest path between fracture ends, and converts this path into a continuous projection configuration. A finite volume technique using the Multipoint Flux Approximation with Diamond stencil (MPFA-D) for the matrix and the Two Point Flux Approximation (TPFA) for the fractures is employed. The robustness of CpEDFM-U is verified in three scenarios: (1) single-phase flow in a diagonal sealing fracture, (2) two-phase water-oil flow considering an inclined fracture configuration, and (3) a complex scenario with 11 fractures, either conductive or sealant. In all cases, CpEDFM-U showed significantly lower errors when compared to EDFM and pEDFM, demonstrating robustness and the ability to capture fractures with diverse properties in both structured and unstructured two-dimensional meshes.
Source: Computers and Geotechnics
Institution: Universidade Federal de Pernambuco
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,640
OpenAlex ID: W7125788543