Nonlinear finite volume method for 3D discrete fracture-matrix simulations

Wenjuan Zhang, Mohammed Al Kobaisi

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    4 Scopus citations


    We present a lower dimensional discrete fracture-matrix (DFM) model for general nonorthogonal meshes populated by anisotropic permeability tensors in 3D spatial dimension. The discrete fractures are represented as 2D planes embedded in a 3D matrix domain and serve as internal boundaries for conforming meshing of the entire computational domain. The nonlinear finite volume method (FVM) is used to derive flux for both matrix-matrix connections and fracture-fracture connections to account for permeability anisotropy in the matrix and inside the fracture planes, whereas the linear two-point flux approximation (TPFA) is used to couple the matrix and fracture together. The nonlinear method proceeds by first constructing two one-sided fluxes for a connection, and then a unique flux is obtained by a convex combination of the two one-sided fluxes. Construction of one-sided fluxes requires introducing the so-called harmonic averaging points as auxiliary points. While the nonlinear FVM can be applied to derive the flux for matrix-matrix connections in a straightforward way, difficulties arise for fracture-fracture connections because of the presence of fracture intersections. Therefore, to construct the one-sided fluxes for fracture-fracture connections, we first present a novel generalization of the concept of harmonic averaging point so that auxiliary points can be calculated at fracture intersections. Unique nonlinear fluxes are then derived for fracture-fracture connections and fracture intersections. Results of the numerical examples demonstrate that the linear TPFA coupling of matrix and fracture seems to be adequate even for relatively strong anisotropy on a non-K-orthogonal grid, and the new DFM model can accurately capture the permeability anisotropy effect inside the fracture planes as well as the permeability anisotropy in the matrix domain compared with the equidimensional models in which the fractures are gridded explicitly. Finally, the DFM model is applied successfully to deal with complex fracture networks embedded in a heterogeneous matrix domain or fracture network with challenging geometric features.

    Original languageBritish English
    Pages (from-to)2079-2097
    Number of pages19
    JournalSPE Journal
    Issue number4
    StatePublished - 2020


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