Improving multiscale mixed finite element method for flow simulation in highly heterogeneous reservoir using adaptivity

We present an adaptive Multiscale Mixed Finite Element Method (MsMFEM) for modeling multiphase flow in highly heterogeneous reservoir. In this framework, fractional flow model is used to approximate pressure and velocity solution on coarse scale, while resolution in fine scale is honored by the basis functions, which are calculated by local problems on fine scale. The adaptive computation in the flow problem is permitted by two different basis functions. In the numerical examples, our adaptive MsMFEM is applied to solve two dimensional and three dimensional reservoir simulation problems with highly heterogeneous porosity and permeability fields. The preliminary numerical simulation results presented show a significant speedup in comparison with the reference numerical method, which encourage and is beneficial for further investigation of the proposed method for reservoir numerical simulation.