Relative phase permeability upscaling for super element model of petroleum reservoirs

The technique of local upscaling of relative permeability functions developed. The technique minimizes the phase rates approximation error during waterflood simulation of layered oil reservoir by super element method. Local upscaling is performed for each superelement and is based on the two-dimensional two-phase problem on detailed computational grid. Special analytical form for the modified functions of relative permeability is proposed. All parameters are the solution of the problem of minimizing deviations averaged and approximated phase rates through the areas corresponding to the superelement faces. Upscaling efficiency at superelement simulation is shown in the example of the synthetic reservoir section containing the set of production and injection wells, as well as in the example of real oil reservoir sector.