An operator - based approach to upscaling thepressure

Permeability and porosity parameters of a porous medium are known only in a statistical sense. For risk assessment, one must perform multiple ow simulations of a single site, varying these input parameters. Because multiple simulations of large sites are computationally prohibitive, upscaling from ne to coarse scales is necessary. Traditional upscaling techniques determine a new eeective or upscaled permeability eld deened on a coarser scale, which is then used in a standard coarse grid discretization operator. We develop here a method of determining a new coarse grid discretization operator that provides an upscaled solution but bypasses the determination of eeective permeability and porosity elds. The method has two steps. We rst solve for ne scale ow information internal to each coarse grid cell. Because the problems are small, this step is relatively fast. Then we determine a modiied coarse grid operator for solving the upscaled problem that includes the ne scale ow information from the rst step. The method is developed for single-phase ow in the context of the mixed nite element method; therefore, the method is locally mass conservative. Unlike traditional upscaling methods (such as homogenization) we do not impose arbitrary boundary conditions on the coarse grid. We present comparisons of our method with the harmonic average permeability upscaling technique.