Reservoir simulation models multiphase flow in reservoirs. Since geological models usually are heterogeneous and may contain millions of cells, upscaling is often a necessary step to reduce the model size to make them suitable for simulation. When grid coarsening is done to obtain fast simulation results, simulation grid cells can be quite large and may also contain localized geological features. Obviously, the upscaled model, though easier to simulate, is only an approximation of the original model. Errors introduced in the upscaling process generally may be small when flow field is relatively smooth but could be large otherwise. A critical technical challenge in upscaling is to be able to coarsen the reservoir model for fast computational performance while maintaining a high degree of accuracy for the results.

In this paper we propose a new Dirichlet Neumann representation method, DNR for short, for upscaling and simulating flow in reservoirs. With DNR, expressions are derived for flow rates as linear functions of multiple discrete pressure values along the boundary of each coarse block and pressure value at the center of the block. The number of pressure values at the boundary is flexible and may be chosen so that those pressure points provide an adequate representation of the possible pressure profiles and flow distributions during the simulation. Because of this, the error induced by artificial boundary conditions in traditional upscaling methods is greatly reduced. Test results show that DNR produces substantially more accurate results when compared to existing approaches using similar number of unknown variables, especially for reservoirs which contain high permeability streaks or are highly channelized. This method makes it possible to coarsen reservoir models while preserving a high degree of reliability for simulation results. DNR also allows straightforward reconstruction of fine-scale flow solutions and so can be used as part of a multiscale computational procedure.

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