A Gabriel-Delaunay Triangulation of Complex Fractured Media for Multiphase Flow Simulations

Fractured reservoirs are complex domains where discrete fractures are constraining boundaries. The discrete fractures are discretized into intersected edges during a grid generation process. Delaunay triangulations are often used to represent complex structures. However, a Delaunay triangulation of a fractured medium generally does not conform to the fracture boundaries. Recovering the fracture elements may violate the Delaunay empty-circle (2D) criterion. Refining the triangulation is not a practical solution in complex fractured media. This paper presents a new approach that combines both Gabriel and Delaunay triangulations. The Gabriel condition of edge-empty-circle is locally employed to quantify the quality of the fracture edges in 2D. The fracture edges violating the Gabriel criterion are released in a first stage. After that, a Delaunay triangulation quality is generated considering the rest of the fracture constraints. The released fracture edges are then approximated by the edges of the Delaunay triangles. The final representation of fractures might be slightly different, but a very accurate solution is always maintained. The method is near optimal and has the capability to generate fine grids and to offer an accurate good-quality grid. Numerical examples are presented to assess the performance and efficiency of the proposed method.