Wettability effects on two- and three-fluid relative permeabilities

Specification of relative permeability (kr)-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 kr-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 kr-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 kr 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 kr for water or organic. The wettability of the porous medium is used to determine the contributions of the pore classes to kr. 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 kr and a decrease in the organic kr. In three-fluid media, kr 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 kr. Model predictions are shown to be consistent with available experimental data.