The Modeling of Flow in Heterogeneous Reservoirs with Voronoi Grid

Abstract

Abstract The flow rate at each interface between gridblocks is a function of an "effective" permeability of the connection. The upscaling procedure consists of evaluating average connection permeabilities based on a smaller scale description of the reservoir. While several procedures have been reported in the literature to scale up permeability values for Cartesian grids, these procedures have not been extended to flexible grids. The Voronoi grid allows the specification of each gridpoint independently; therefore, it provides flexibility to represent wells and reservoir heterogeneities. This paper describes an upscaling procedure of permeability values at the interface of Voronoi gridblocks. The description of the heterogeneity, e.g., a stochastic image, is independent of the grid geometry. The power law average of the permeability values at each connection is computed automatically by the computer code. The optimum value of the power law coefficient is determined by comparing fine and coarse grid results for selected images and well configurations. Several well configurations were investigated with different grid geometries (Cartesian, hexagonal and locally refined hexagonal) using the same description of the reservoir. The optimum value of the power law coefficient was almost the same for all combinations of grid geometries and well configurations (between -0.5 and 0). Also several stochastically generated images of the reservoir, all honoring the same data, were analyzed. Again the optimum value of the power law coefficient was almost the same for all images. The hexagonal grid yields more robust results because each gridblock has more neighbors than the Cartesian grid. The use of local grid refinement around wells reduces the overall error.