Present continuum models for large scale averaging rely on volume averaging and homogenization methods, typically under the premise of capillary control. However, such methods are intrinsically unable to provide the local saturation distribution, which is needed for the computation of effective flow properties. In this paper, paralleling porelevel approaches, a percolation method is proposed for the derivation of large scale properties in a drainage process at low flow rates. Percolation is applied to a macroscopically heterogeneous region with a random, uncorrelated permeability distribution. We show that at conditions of local capillary control, when a local description is possible, the large scale capillary pressure curve is a non-trivial average of the individual curves. Large scale capillary trapping is predicted and a corresponding large scale trapped saturation is calculated. Large scale phase premeabilities are also derived. It is found that capillary heterogeneity renders a system more strongly wet in a macroscopic sense.

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