A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media

A general method for the scale-up of highly detailed, heterogeneous, cross sectional flow models to coarser scales is developed and applied. The technique involves the nonuniform coarsening of the detailed description, with finer resolution introduced in regions of potentially high fluid velocities (typically regions of connected, high permeability) and coarse, homogenized descriptions applied to the remainder of the flow domain. The method is designed to capture both average behavior as well as some important behaviors which are due to the high extremes of the permeability field, such as the breakthrough of the displacing fluid. The method is applied to several example problems, including two actual oil field examples, and is shown to provide coarsened models (similar to 25 x 25) which give simulation results for fractional flows and saturations in close agreement with fine scale (similar to 100 x 100) results. These examples demonstrate the ability of the method to capture a wide variety of flow behavior without the need for specific knowledge of the global flow held, indicating that the coarsened description of the formation is, to a large degree, process independent. (C) 1997 Elsevier Science Ltd.