A Novel Projection-based Embedded Discrete Fracture Model (pEDFM) for Anisotropic Two-phase Flow Simulation Using Hybrid of Two-point Flux Approximation and Mimetic Finite Difference (TPFA-MFD) Methods

This paper presents a novel projection-based embedded discrete fracture model (pEDFM) applicable to general two-phase flow simulation in anisotropic reservoirs for the first time. The novel pEDFM is developed based on hybrid two-point flux approximation and mimetic finite difference (TPFA-MFD) methods, which retains the basic features of two-point flux approximation (TPFA) based generic pEDFM workflow and incorporates new features of mimetic finite difference (MFD) to handle full-tensor permeabilities. This is achieved by introducing the concept of effective connection, formulating additional pressure degrees of freedom for effective connections, assigning effective matrix-matrix (m-m) and matrix-fracture (m-f) connections to the corresponding sides of matrix-cell interfaces, presenting methods corresponding to different types of connections to handle low-conductivity fractures, and further deriving formulas of numerical fluxes for effective connections. The resulting global equation system is solved by a Newton-Raphson nonlinear solver with the temporary discretization of the implicit backward Euler scheme. The 2D and 2.5D numerical examples show the novel pEDFM could achieve the same level of computation accuracy and convergence as the reference discrete fracture model (DFM), while avoiding the gridding difficulty of complex fracture networks. It also significantly outperforms classical EDFM based on MFD and generic pEDFM workflow in the computational accuracy for cases with anisotropic full tensor permeabilities. The novel pEDFM, to our best knowledge, is for the first time proposed and developed for general anisotropic two-phase flow simulation and maybe the numerical simulation framework for multi-phase flow in fractured reservoirs with the best comprehensive performance so far.