Global Upscaling of Permeability in Heterogeneous Reservoirs; The Output Least Squares (OLS) Method

This paper presents a new technique for computing the effective permeability on a coarse scale. It is assumed that the permeability is given at a fine 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 the permeability may depend heavily on the local boundary condition chosen. Hence the estimate is not stable. We propose to compute a coarse scale permeability field that minimises the error, measured in a global norm, in the velocity and pressure fields. This leads to stable problems for a large number of reservoirs. We present several algorithms for finding the effective permeability values. It turns out that these algorithms are not significantly more computational expensive than traditional local methods. Finally, the method is illustrated by several numerical experiments.