Multiscale methods for reservoir simulation without upscaling

Jörg Aarnes
Applied Mathematics
SINTEF, Blindern, N-0314 Oslo, NORGE


We propose a new 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 3D incompressible two-phase flow simulations.