Effective properties of reservoir simulator grid blocks

Computational costs limit large scale reservoir simulations to coarse grid systems. Determination of an effective permeability for a simulation grid block requires a proper scale-up of small scale permeability heterogeneities within that grid block. Conventional scale-up techniques are limited to a diagonal tensor representation of effective permeability. Therefore, such techniques cannot handle general permeability anisotropy (full tensor) exemplified by cross-bedded permeability structures that may be present on a smaller scale.;An analytical method is developed to calculate an effective permeability tensor for a grid block by accounting for small scale heterogeneities within the grid block. The method honors both the location and the orientation of the small scale heterogeneities.;Most commercially available reservoir simulators are not equipped to handle general permeability anisotropy. This work shows in detail how transmissibility coefficients for cases of general permeability anisotropy are developed. These transmissibilities can be readily inserted into point-centered finite difference simulators which accommodate 9-point differencing.;Effective permeability tensors calculated using the analytical method and a numerical method show excellent agreement. Fluid flow simulations, both miscible displacements and waterfloods, show that the effective permeability tensor method outperforms conventional scale-up techniques when compared to the use of fine scale permeability distribution in cases of general permeability anisotropy.