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 fine-scale 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.