Upscaling of Transmissibility Applied to Corner Point Geometry

Abstract

Abstract Comer Point Geometry (CPG) is a gridding technique that is used more and more in modern numerical flow simulation because it allows a good representation of reservoir geological features. This kind of grid is tailored to conform to reservoir boundaries, wells, heterogeneities of petrophysical properties, faults and flow patterns. A CPG grid can be built from a geological model generated with stochastic simulations for instance. A crucial step in this process is the upscaling of grid block permeability. Present methods for upscaling fine scale permeability data for use in reservoir simulation produce effective permeabilities for each coarse grid block. Still, it is difficult to determine the transmissibility from the block permeability. Usually, the harmonic average of the block permeability is used for the transmissibility calculation, but it might cause a loss of precision. In this paper, we propose a method to upscale internodal permeabilities on CPG mesh. This method, called "shifted method", was first developed for Cartesian grids but it was found to be so efficient that it has been adapted to CPG. The permeability upscaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is upscaled via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A special difficulty associated to CPG is the problem encountered with five-point scheme, which yields erroneous results with distorted grids. More accurate numerical schemes are needed with the ability to handle cross derivative terms. A nine-point finite volume scheme is particularly studied here and the internodal permeability technique for this scheme is presented. The "shifted method" improves fluid flow calculation on CPG mesh. Some numerical examples based on various flow patterns are presented. The "shifted method" is compared with some published permeability upscaling procedures. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.