Effects of wettability on three-phase flow in porous media

We study the effects of rock wettability on the flow of oil, water, and gas in hydrocarbon reservoirs. We describe the three-phase fluid configuration s and displacement processes in a pore of polygonal cross section. Initiall y water-filled, water-wet pores are invaded by oil, representing primary oi l migration. Where oil directly contacts the solid surface, the surface wil l change its wettability. We then consider water injection followed by gas injection for any possible combination of oil/water, gas/water, and gas/oil contact angles. We find the capillary pressures for the different displace ment processes and determine the circumstances under which the various flui d configurations are stable. Using empirical expressions for the phase cond uctances, we find three-phase relative permeabilites for a bundle of pores of different sizes with constant triangular cross sections. For gas injecti on, we show that the oil remains connected in wetting layers down to low oi l saturation with a characteristic layer drainage regime, which gives very high ultimate oil recoveries. The only exceptions are nonspreading oils in water-wet media and large gas/oil contact angles. The relative permeability of the phase of intermediate wettability depends on two saturations, while the relative permeabilities of the other phases are functions of their own saturation only. In water-wet media, oil is the intermediate-wet phase. In weakly oil-wet media, water is intermediate-wet. In strongly oil-wet media , gas is intermediate-wet. This finding contradicts the assumptions made in many empirical models that gas is always the most nonwetting phase and tha t its relative permeability depends only on the gas saturation. This work i ndicates appropriate functional dependencies for three-phase relative perme abilities,and represents a necessary first step toward the development of a predictive pore-scale model that accounts for the effects of wettability i n three-phase flow.