In the present work it is proposed a conditional and iterative approach of upscaling of permeability based on the formulation of mass balance equations and Darcy's Law. In the classic approaches, the effective permeability in a particular set of blocks derives from the application of a pressure gradient between two opposite boundaries and imposing a no flow condition in the others. Based on the solver pressure techniques, the idea is to improve the quality of upscaling by including, in the calculation of the equivalent permeability of each large scale block (macroblock) the influence of the permeability values in the set of neighbouring small scale blocks (microblocks) as well as the interdependence between the scale up values of macroblocks previously transformed. These outlines have conduced to the proposed interactive method: in each iteration corresponding to the upscaling of one macroblock, the solutions are ranked according a criterion based on a flow test and expressed on one objective function. In a second step, the macroblock corresponding to the minimum value of the objective function is selected. The process continue until all blocks are scale up. This method guarantee that the solutions are successively conditioned both to initial permeability values and/or scale up values obtained in previous iterations.
The performance of this method is illustrated in opposition with the classic approach by comparing the amount of flow in a local grid (each local grid include the set of blocks to come up with one value) using the small scale blocks and the large scale blocks. A second test is the comparison of the waterflood shape in a flow test using two opposite wells located in the small scale blocks and the large scale blocks using the flow simulator ECLIPSE 100.