A modified multiscale finite element method for nonlinear flow in reservoirs

In this paper we propose a modified multiscale finite element method for nonlinear flow simulations in heterogeneous porous media. The main idea of the method is to use the global fine scale solution to determine the boundary conditions of the multiscale basis functions. When solving the time-dependent problems, the equations of standard MsFEM need to be solved many times for different pressure profiles. Then, we propose an adaptive criterion to determine if the basis functions need to be updated. The accuracy and the robustness of the modified MsFEM are shown through several examples. In the first two examples, we consider single phase flow in consideration of pressure sensitivity and unsaturated flow, and then compare the results solved by the finite element method. The results show that the multiscale method is accurate and robust, while using significantly less CPU time than finite element method. Then, we use the modified MsFEM to compute two phase flow in low permeability reservoirs. The results show that the greater the staring pressure gradient is, the greater the pressure drop is, and the greater the staring pressure gradient is, the smaller the swept area is. All the results indicate that modified the MsFEM offers a promising path towards direct simulation of nonl-linear flows in porous media.