Modeling Hydraulically Fractured Shale Wells Using the Fast-Marching Method With Local Grid Refinements and an Embedded Discrete Fracture Model
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SummaryRecently, fastmarchingmethod (FMM) based flow simulation has shown great promise for rapid modeling of unconventional oil and gas reservoirs. Currently, the application of FMMbased simulation has been limited to using tartan grids to model the hydraulic fractures (HFs). The use of tartan grids adversely impacts the computational efficiency, particularly for fieldscale applications with hundreds of HFs. Our purpose in this paper is to extend FMMbased simulation to incorporate local grid refinements (LGRs) and an embedded discrete fracture model (EDFM) to simulate HFs with natural fractures, and to validate the accuracy and efficiency of the methodologies.The FMMbased simulation is extended to LGRs and EDFM. This requires novel gridding through the introduction of triangles (2D) and tetrahedrons (2.5D) to link the local and global domain and solution of the Eikonal equation in unstructured grids to compute the diffusive time of flight (DTOF). The FMMbased flow simulation reduces a 3D simulation to an equivalent 1D simulation using the DTOF as a spatial coordinate. The 1D simulation can be carried out using a standard finitedifference method, thus leading to orders of magnitude of savings in computation time compared with full 3D simulation for highresolution models.First, we validate the accuracy and computational efficiency of the FMMbased simulation with LGRs by comparing them with tartan grids. The results show good agreement and the FMMbased simulation with LGRs shows significant improvement in computational efficiency. Then, we apply the FMMbased simulation with LGRs to the case of a multistagehydraulicfractured horizontal well with multiphase flow, to demonstrate the practical feasibility of our proposed approach. After that, we investigate various discretization schemes for the transition between the local and global domain in the FMMbased flow simulation. The results are used to identify optimal gridding schemes to maintain accuracy while improving computational efficiency. Finally, we demonstrate the workflow of the FMMbased simulation with EDFM, including grid generation; comparison with FMM with unstructured grid; and validation of the results. The FMM with EDFM can simulate arbitrary fracture patterns without simplification and shows good accuracy and efficiency.This is the first study to apply the FMMbased flow simulation with LGRs and EDFM. The three main contributions of the proposed methodology are (i) unique meshgeneration schemes to link fracture and matrix flow domains, (ii) DTOF calculations in locally refined grids, and (iii) sensitivity studies to identify optimal discretization schemes for the FMMbased simulation.
