Recently, fast–marching–method (FMM) –based flow simulation has shown great promise for rapid modeling of unconventional oil and gas reservoirs. Currently, the application of FMM–based 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 field–scale applications with hundreds of HFs. Our purpose in this paper is to extend FMM–based 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 FMM–based 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 FMM–based 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 finite–difference method, thus leading to orders of magnitude of savings in computation time compared with full 3D simulation for high–resolution models.
First, we validate the accuracy and computational efficiency of the FMM–based simulation with LGRs by comparing them with tartan grids. The results show good agreement and the FMM–based simulation with LGRs shows significant improvement in computational efficiency. Then, we apply the FMM–based simulation with LGRs to the case of a multistage–hydraulic–fractured 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 FMM–based 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 FMM–based 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 FMM–based flow simulation with LGRs and EDFM. The three main contributions of the proposed methodology are (i) unique mesh–generation 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 FMM–based simulation.