Summary Natural fracture systems comprise numerous small features and relatively few large ones. At field scale, it is impractical to treat all fractures explicitly. We represent the largest fractures using an embedded discrete fracture model (EDFM) and account for smaller ones using a dual-porosity, dual-permeability (DPDK) idealized representation of the fracture network. The hybrid EDFM + DPDK approach uses consistent discretization schemes and efficiently simulates realistic field cases. Further speedup can be obtained using aggregation-based upscaling. Capabilities to visualize and post-process simulation results facilitate understanding for effective management of fractured reservoirs. The proposed approach embeds large discrete fractures as EDFM within a DPDK grid (which contains both matrix and idealized fracture continua for smaller fractures) and captures all connections among the triple media. In contrast with existing EDFM formulations, we account for discrete fracture spacing within each matrix cell via a new matrix-fracture transfer term and use consistent assumptions for classical EDFM and DPDK calculations. In addition, the workflow enables coarse EDFM representations using flow-based cell-aggregation upscaling for computational efficiency. Using a synthetic case, we show that the proposed EDFM + DPDK approach provides a close match of simulation results from a reference model that represents all fractures explicitly, while providing runtime speedup. It is also more accurate than previous standard EDFM and DPDK models. We demonstrate that the matrix-fracture transfer function agrees with flow-based upscaling of high-resolution fracture models. Next, the automated workflow is applied to a waterflooding study for a giant carbonate reservoir, with an ensemble of stochastic fracture realizations. The overall workflow provides the computational efficiency needed for performance forecasts in practical field studies, and the 3D visualization allows for the derivation of insights into recovery mechanisms. Finally, we apply a finite-volume tracer-based flux post-processing scheme on simulation results to analyze production allocation and sweep for understanding expected waterflood performance.
Grid orientation effect (GOE) is the appearance of preferential flow along grid coordinate directions in numerical reservoir simulation. GOE is most evident in simulations with strong adverse mobility ratios, such as immiscible gas injection and steamfloods. Motivated by previous work, an eleven-point finite difference formulation for multiphase flow is investigated and found to reduce errors for steamfloods using structured grids. The eleven-point formulation is implemented in a parallel, fully-implicit reservoir simulator with thermal, black-oil and compositional formulations, and the implementation supports both local grid refinement (LGR) and dual-porosity, dual-permeability (DPDK) modeling. Systematic tests are performed for compositional steamflood cases with different grid resolutions and grid coordinate angles between wells. A comparison of seven and eleven-point formulation results, using different grid scales and hybrid unstructured grids, demonstrate that the eleven-point scheme is effective in mitigating GOE and can leverage the benefits of structured LGR and DPDK options. Using grid-refinement as a means of reducing GOE is case dependent and is not always successful. Additional results suggest that using grid refinement with local application of the eleven-point scheme around only the injector does help mitigate GOE with increased computational efficiency, but GOE is not reduced as well as when the eleven-point scheme is used in the entire grid-system.
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