A Novel Edge-Based Green Element Method for Simulating Fluid Flow in Unconventional Reservoirs with Discrete Fractures
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Copyright 2019, Society of Petroleum Engineers 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 (eGEM) for this problem, and two significant modifications are made to the classical GEM. An edge-based discretization scheme is proposed to improve the GEM's accuracy. 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 multi-porosity models because the boundary integral equation form 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 could 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 like BEM. The finite difference method is used to handle the fracture-fracture flow. In this paper, we tested the numerical accuracy and computational efficiency of eGEM based on 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 eGEM's ability to handle discrete fractures was validated with the several models for transient flow problems. Comparing to the commercial numerical simulator in handling flow in orthogonal fractures, the eGEM is shown to be less grid-sensitive and maintain relative high precision even with coarse grids near the discrete fractures. A detailed grid sensitivity analysis on grids was performed. It is recommended that fracture grids be refined to capture the early time flow behavior in pressure transient analysis. On the other hand, relatively coarse grids meet the accuracy requirements for production performance simulation. This is the first time to present an efficient edge-based discretization scheme for GEM to enhance accuracy in handling unknown flux while at the same time utilizing 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 eGEM's high precision with coarse grids, the technique can be readily used in larger field applications.
author list (cited authors)
Wu, Y., Cheng, L., Fang, S., Killough, J. E., Huang, S., & Jia, P.