Wavelet upscaling based on piecewise bilinear approximation of the permeability field

A method for upscaling of permeability in heterogeneous porous media is presented. The upscaled field takes the form K = e ^Y , where Y, in two dimensions, is a piecewise bilinear function. The method is tested on a number of random permeability fields, with different integral scale/correlation length and variance. The numerical results show that this method conserves much more of the heterogeneous fingering than classical block-based upscaling methods, e.g., geometric mean.