Simplified Oil-Water Relative Permeability Expressions Accounting for Hysteresis in the Imbibition Cycle
A method which permits the calculation of wetting phase relative permeability with knowledge only of the pore size distribution index (λ) and of a trapping constant (C) has been formulated. The non-wetting phase, relative permeability correlations are derived in a manner similar to that of Land in his original work. The proposed method makes it possible to account for spatial variations in rock type since relative permeabilities for individual lithologies vary as λ and C vary.
Hysteresis in oil-water relative permeabilities is of major concern in many multi-phase flow scenarios. The early work done by Land addressed this problem, but the complicated equations introduced have been of little help for the practicing engineer. Further attempts to describe this phenomenon with simplified expressions did not fundamentally address the behavior of the wetting phase relative permeabilities.
The practical method proposed in this paper has been adapted for use in numerical studies of the Prudhoe Bay Field. The correlations have adequately described reservoir behavior in areal studies and in matching displacement efficiencies inferred from a fiberglass cased observation well where repeat dual induction logs to determine changing water saturations can be measured. The correlations also compare favorably with laboratory results.
The improved correlations have made it possible to make relative permeabilities lithology dependent without invoking heuristic relative permeability averaging techniques. This improved reservoir description has increased our confidence in simulation results.