Wettability effects on two- and three-fluid relative permeabilities

Abstract

Specification of relative permeability ( k r)-saturation ( S) relations for all fluid phases is required for the simulation of multiphase flow and transport in porous media. Indirect methods are frequently employed to estimate these k r- S relations owing to the time, expense, and difficulty associated with direct measurements. A common indirect approach uses capillary pressure data in conjunction with a selected pore-size distribution model to estimate k r- S relations. Such methods typically assume perfect wettability of the solid. Natural porous media, however, are composed of a variety of mineral constituents with different adsorptive properties, which can exhibit non-zero contact angles and/or fractional wettability. Consequently, fluid distributions in natural media may be more complex than those predicted by simple pore-size distribution models and, under such conditions, current estimation approaches for k r may be inadequate. In this work, the pore-size distribution model of N.T. Burdine (1953, Relative permeability calculations from pore-size distribution data. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers 198, 71–77) is extended to incorporate wettability variations. In this model, wetting and less wetting (non-wetting or intermediate) fluid pore classes are used to calculate k r for water or organic. The wettability of the porous medium is used to determine the contributions of the pore classes to k r. For both two- and three-fluid systems, the model predicts that an increase in the contact angle (measured through water) or organic-wet fraction of a medium will be accompanied by an increase in the water k r and a decrease in the organic k r. In three-fluid media, k r values for water and organic depend on both liquid saturations when the solid is imperfectly wetted. The model assumes that wettability variation has no influence on the air k r. Model predictions are shown to be consistent with available experimental data.