Abstract
When performing fluid-flow simulations, up-scaling techniques must be used because of the required coarse grids. For this purpose, algebraic formula, combining arithmetic and harmonic averagings, extension of Cardwell and Parsons’s results, derived from perturbation techniques are proposed taking into account the anistotropy, either natural or due to the reservoir geometry. These formula are valid for 2D or 3D problems and are very little computational time consuming compared to direct numerical methods. Moreover they integrate rigorous mimima and maxima thus showing the global uncertainty on equivalent permeability determination. They proved to work well for large permeability contrasts and anisotropy ratios either for simple log-normal or geostatiscally generated media.
In the first application case numerical calculations were carried out for the upscaling of isolated cells. In the other case well test simulations were performed either with the original fine grid or further coarser grids.
