A Meshless Numerical Modeling Method for Fractured Reservoirs Based on Extended Finite Volume Method

Summary In this paper, a meshless numerical modeling method named mesh-free discrete fracture model (MFDFM) of fractured reservoirs based on the newly developed extended finite volume method (EFVM) is proposed. First, matching and nonmatching point cloud generation algorithms are developed to discretize the reservoir domain with fracture networks, which avoid the gridding challenges of the reservoir domain in traditional mesh-based methods. Then, taking oil/water two-phase flow in fractured reservoirs as an example, MFDFM derives the EFVM discrete scheme of the governing equations, constructs various types of connections between matrix nodes and fracture nodes, and calculates the corresponding transmissibilities. Finally, the EFVM discrete scheme of the governing equations and the generalized finite difference discrete scheme of various boundary conditions form the global nonlinear equations, which do not increase the degree of nonlinearity compared with those in the traditional finite volume method (FVM)-based numerical simulator. The global equations can be solved by the existing nonlinear solver in the FVM-based reservoir numerical simulator by only adding the linear discrete equations of boundary conditions, which reduce the difficulty of forming a general purpose MFDFM-based fractured reservoir numerical simulator. Several numerical test cases are implemented to illustrate that the proposed MFDFM can achieve good computational performance under matching and nonmatching point clouds, and for heterogeneous reservoirs, complex fracture networks, complex boundary geometry, and complex boundary conditions, by comparing the computational results of MFDFM with embedded discrete fracture model (EDFM). Thus, MFDFM retains the computational performances of the traditional mesh-based methods and can avoid the difficulties of handling complex geometry and complex boundary conditions of the computational domain, which is the first meshless numerical framework to model fractured reservoirs in parallel with the mesh-based discrete fracture model (DFM) and EDFM.