Detailed reservoir models routinely contain hundred of thousands to several million grid blocks. These models often cannot be used directly in a reservoir simulation because of the time and memory required for solving the pressure grid on the fine grid. We propose a nested gridding technique that efficiently obtains an approximate solution for the pressure field. The domain is divided into a series of coarse blocks, each containing many fine cells, for which effective mobilities are computed. The pressure is then found on the coarse scale. The pressure field within each coarse block is computed using constant flux boundary conditions obtained from the coarse pressure solution. In this way, a continuous but approximate velocity field is computed on the fine grid. The method is similar to the first step in a multigrid pressure solution. Streamline-based simulation is used to move saturations forward in time. The pressure field is periodically recomputed, taking account of the fine scale permeability and saturation distributions. We test the method for a series of example waterflood problems and demonstrate that the method can give accurate estimates of oil production for large 3D models up to 8.5 times faster than direct simulation using streamlines on the fine grid, making the method overall approximately up to 1,000 times faster than direct conventional simulation. The method is thus able to handle multi-million grid blocks problems easily, enabling simulation to be performed directly on detailed geological models. It is a robust alternative to traditional upscaling, since the effects of changing boundary conditions are automatically accommodated.

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