Dynamic Multilevel Multiscale Simulation of Naturally Fractured Reservoirs with Generic Fracture-Matrix Conductivity Contrasts

Abstract

An algebraic dynamic multilevel (ADM) method for multiphase flow in heterogeneous fractured porous media using the projection-based embedded discrete fracture model (pEDFM) is presented. The fine-scale discrete system is obtained independently for matrix and each lower-dimensional fracture. On the finescale high resolution computational grids, an independent dynamic multilevel gird (i.e., ADM grid) is imposed. The fully implicit discrete system is mapped completely algebraically to this ADM grid resolution using sequences of restriction and prolongation operators. Multilevel multiscale basis functions are locally computed and employed to honor the heterogeneity contrasts of the fractured domain by interpolating the solution accurately. These basis functions are computed only at the beginning of the simulation to increase the computational efficiency. Once the ADM system is solved for all unknowns (i.e., pressure and saturation), the solution at ADM resolution is prolonged back to fine-scale resolution in order to obtain an approximated fine-scale solution. This dynamic multilevel system employs the fine-scale grid cells only at the sharp gradient of the solution (e.g., at the moving front). With two fractured test-cases (homogeneous and heterogeneous), the performance of ADM is assessed by comparing it to fine-scale results as reference solution. It will be shown that ADM is able to reduce the computational costs and provide efficiency while maintaining the desired accuracy.

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

“…These geometrical strategies are well suited for permeability fields containing either channels or barriers, but not both. In this contribution, we propose a strategy to deal with the simultaneous presence of channels and barriers, since such situation is not unfrequent in reservoir simulation [26]. For this purpose, we take advantage of the Multiscale Robin Coupled Method (MRCM, [27]), which allows for the independent choice of the pressure and flux interface spaces.…”

Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

“…These geometrical strategies are well suited for permeability fields containing either channels or barriers, but not both. In this chapter, we propose a strategy to deal with the simultaneous presence of channels and barriers, since such situation is not unfrequent in reservoir simulation (HOSSEINIMEHR et al, 2019). For this purpose, we use the MRCM for the independent choice of the pressure and flux interface spaces.…”