Discrete fracture-matrix simulations using cell-centered nonlinear finite volume methods

Control-volume based Discrete Fracture-Matrix (DFM) models have been increasingly used to simulate flow and transport in fractured porous media. The star-delta transformation is often used to eliminate the intermediate control volumes at fracture intersections. The star-delta transformation, however, assumes that the permeability at fracture intersections is very high. Therefore, it cannot accurately model the blocking effect at fracture intersections for example when a blocking fracture intersects a permeable one. In this work, we improve the stardelta transformation by making modifications to the calculation of transmissibility at fracture intersections so that the blocking effect at fracture intersections can be captured. To account for the permeability anisotropy in the matrix and the grid non-orthogonality resulting from unstructured meshing, the nonlinear finite volume methods are used to compute transmissibility for matrix-matrix connections. The linear two-point flux approximation (TPFA) is then used to couple the fracture and matrix together. Results of numerical experiments demonstrate that the improved star-delta transformation performs very well compared to the reference solution. When permeability of the matrix is anisotropic, the linear TPFA is not consistent in general and significant errors can be incurred. The nonlinear methods, on the other hand, captures the tonsorial effect in the matrix domain more accurately for all simulations.