Global Upscaling of Permeability in Heterogeneous Reservoirs; the Output Least Squares (ols) Method

This paper presents a new technique for computing the eeective permeability on a coarse scale. It is assumed that the permeability is given at a ne scale and that it is necessary to reduce the number of blocks in the reservoir model. Traditional upscaling methods depend on local boundary conditions. It is well known that this approach often leads to ill-posed problems. We propose to compute a coarse scale permeability eld that minimise the error, measured in a global norm, in the velocity and pressure elds. This leads to a well posed problem for a large number of reservoirs. We present several algorithms for nding the eeective permeability values. It turns out that these algorithms are not signiicantly more computational expensive than traditional local methods. Finally, the method is illustrated by several numerical experiments.