We present a new technique for computing the effective permeability in heterogeneous reservoirs on a coarse scale. The method is based on the assumption 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 such approaches often lead to non-unique solutions. The new global method is applicable whenever these local methods fail to produce an acceptable permeability field, eg, for upscaling of blocks close to wells and in cases involving heterogeneities on the coarse grid block scale. In such cases it is impossible to compute an effective permeability based on local observations of the pressure and velocity fields. The properties of the coarse reservoir model simply depend heavily on the global flow pattern.

The basic idea behind the new method is to minimize the global errors introduced in the pressure and velocity fields by the upscaling process. In this approach the total mass flux over each coarse grid block interface will be preserved on the coarse mesh. This leads to very accurate production and injection rates in the wells for the coarse model. Moreover, the associated minimization problem can be solved very efficiently. The solution of the fine scale pressure equation is, however, required. It turns out that, in view of modern numerical methods for elliptic differential equations, the efficiency of the new global scheme is comparable to the performance of the traditional local methods.