Recent Advances in Upgridding

Abstract

Upscaling is the process whereby the properties of a high resolution geologic description are approximated by a lower resolution flow simulation model. Upgridding is the process whereby we determine the spatial resolution (the 3D computational grid) of the simulation model. In our current work we explore different measures of the error introduced by the upscaling approximations. These measures are based upon local flow properties and hence are not dependent upon knowledge of global fluid flow patterns. Based upon these error measures it is possible to design a computational grid that is optimal, i.e., that introduces the minimal upscaling error for a specific number of cells. We explore three different applications of these error measures. In the first, an optimal reservoir simulation layering scheme is derived from the layering scheme of the geologic description by sequentially grouping the layers in such a way to minimize the error. The error associated with this sequence explores the trade-off between upscaling bias and variance, with the optimal scheme being determined by a balance between the two. The second application is in areal upscaling. Here we utilize two different definitions of transmissibility and the cross-terms in the upscaled full permeability tensor, to provide local measures of error. The final application examines other constraints or considerations that we may place upon the reservoir simulation grid design. In terms of reservoir characterization, these constraints are associated with preserving reservoir structure, stratigraphy and layering, or locally, facies continuity. Simulation and process representation will also have an impact on the optimal grid design, i.e., the optimal simulation grid design will differ between a waterflood and a gas displacement process. The resulting simulation grid will be a composite of corner point cells, with many of the computational advantages of an unstructured PEBI grid, without the requirement to revise our modeling technology to utilize such grids.