Absolute permeability upscaling for super element model of petroleum reservoir

This paper presents a new method of local upscaling of absolute permeability for super element simulation of oil reservoir. Upscaling performed for each block of super element unstructured grid. To do this, the set of problems of steady state one phase flow solved on a fine computational grid with the initial scalar field of absolute permeability with various boundary conditions that reflect the specific variants of filtrational flow through the super element and take into account the presence or absence of boreholes in the coarse block. The resulting components of the effective permeability tensor in each super element found from the solution of the problem of minimizing the deviations of averaged on a detailed computational grid from approximated on a coarse super element grid normal flows through the super element faces. The results of using the method are demonstrated for reservoirs with periodic and non-periodic structure of absolute permeability field. The comparison with the traditional methods of local upscaling is performed.