Large scale averaging of drainage at local capillary control.

摘要

Large scale averaging is important for the description of displacement processes in heterogeneous porous media for example, in petroleum reservoirs. For immiscible displacement, key objective is the determination of effective (pseudo) capillary pressure and phase permeabilities. Present continuum models 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 pore-level approaches, a percolation method is proposed for the derivation of large scale properties in a drainage process at low flow rates. Percolation concepts are applied to a macroscopically heterogeneous region with a random and uncorrelated permeability distribution. Appropriate modifications of ordinary and invasion percolation, and percolation with trapping are developed for the determination of the large scale averages. Analytical results are also presented for certain simple cases. They 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 permeabilities are also derived. It is found that capillary heterogeneity renders a system more strongly wet in a macroscopic sense. 35 refs., 12 figs.