A Novel Edge-Based Green Element Method for Simulating Fluid Flow in Unconventional Reservoirs with Discrete Fractures

Summary The boundary-element method (BEM) is widely used in modeling fluid flow in fractured reservoirs. However, the computation is extremely expensive when real heterogeneity and large numbers of fractures are modeled. This paper presents a novel edge-based Green element method (GEM) (eGEM) for this problem, and two significant modifications are made to the classical GEM. An edge-based discretization scheme is proposed to improve accuracy of the GEM. The eGEM technique is further enriched for simulating discrete fractures. The mathematical model is transformed into the Laplace domain, which makes it convenient to incorporate multiporosity models because the form of the boundary integral equation is the same. The matrix is meshed using Cartesian grids, and discrete fractures are handled flexibly by embedding into the matrix grids. In eGEM, the matrix/matrix flow is coupled at the common edge, so the unknown flux can be eliminated by using the edge-based scheme. In each matrix block, the matrix/fracture flow is modeled by treating the fracture elements as sources or sinks, as with BEM. The finite-difference method (FDM) is used to handle the fracture/fracture flow. In this paper, we tested the numerical accuracy and computational efficiency of the eGEM using several cases. First, the technique was shown to have higher accuracy than the classical corner-based GEM for transient problems in the petroleum industry. This shows the advantage of the edge-based discretization approach in handling the unknown flux of each solution point. The ability of the eGEM to handle discrete fractures was validated with the several models for transient-flow problems. The computation of the proposed eGEM is much less expensive than that for BEM in modeling the transient behavior of fractured media. Compared with the commercial numerical simulator in handling discrete fractures, the eGEM is shown to be less grid sensitive and to maintain a relatively high precision even with coarse grids near the discrete fractures. A detailed grid-sensitivity analysis was performed. The fracture grids are recommended to be refined to capture the early-time-flow behavior in pressure-transient analysis, especially in modeling low-conductivity fractures. For the first time, an efficient edge-based discretization scheme for GEM is presented, which handles the unknown flux of each solution point and at the same time uses eGEM to enrich simulation of discrete-fracture networks. This method serves as a new efficient approach for reservoir simulation and numerical well testing. Because of the high precision of eGEM with coarse grids, it would be efficient in larger field applications.