Upscaling relative phase permeability for superelement modeling of petroleum reservoir engineering

Abstract

A technique for locally rescaling (upscaling) the functions of the relative phase permeability (RPP) has been developed, which minimizes the error in the approximating the phase filtration rates for the superelement modeling of waterflooding a layered heterogeneous oil reservoir. The RPP is locally upscaled for each superelement based on the solution of two-dimensional two-phase filtration problems on a refined computational grid. Modified RPP functions (MFRPPs) are represented in the parametric form; i.e., the values of the parameters are sought when solving the problem of minimizing the deviations of the averaged and approximated phase velocities at the sites corresponding to the faces of the superelement. The efficiency of applying MFRPP to superelement modeling is illustrated by an example of a model reservoir region where oil is extracted using injection and production wells and by an example of waterflooding at a real oilfield.