On the Use of a Mixed Multiscale Finite Element Method for GreaterFlexibility and Increased Speed or Improved Accuracy in Reservoir Simulation

Abstract

In this paper we propose a modified mixed multiscale finite element method for solving elliptic problems with rough coefficients arising in, e.g., porous media flow. The method is based on the construction of special base functions which adapt to the local property of the differential operator. In particular, the method incorporates the effect of small-scale heterogeneous structures in the elliptic coefficients into the base functions and produces a detailed velocity field that can be used to solve phase transport equations at a subgrid scale. The method is mass conservative and accounts for radial flow in the near-well region without resorting to complicated well models or near-well upscaling procedures. As such, the method provides a step toward a more accurate and rigorous treatment of advanced well architectures in reservoir simulation. The accuracy of the method is demonstrated through a series of three-dimensional incompressible two-phase flow simulations.