We present new three-phase capillary pressure correlations that could be employed to model the dynamics of three-phase transition zones in mixed-wet reservoirs. The capillary pressures are expressed as a sum of two terms. One term is a function of a decreasing saturation and the other term a function of an increasing saturation. Thus the correlations depend on the type of displacement process, i.e., the direction of saturation change. The two-saturation dependency, together with the inclusion of adjustable parameters, ensures that the correlations account for different wettability conditions, saturation histories, and different relationships between the three capillary pressures.
The correlations are compatible with a smooth transition between two- and three-phase flow if one of the phases appears or disappears. In particular, if the gas saturation becomes zero, it is shown that the correlations are reduced to a previously published two-phase correlation validated for oil/water systems in mixed-wet rock.
Capillary pressure curves for various conditions, computed using a previously developed bundle-of-triangular-tubesmodel, are compared with the correlations, and the match is excellent in all cases. Finally, the correlations are validated experimentally by centrifuge measurements performed on water-wet cores.
Three-phase capillary pressure curves are needed to model the dynamics of gas-oil and oil-water transition zone movements in the reservoir. Production from an oil zone causes an upward movement of the oil-water contact and a downward movement of the gas-oil contact. Water may displace oil and gas and gas may displace water and oil. Other scenarios are possible as well. The transition zone dynamics is dominated by capillary-gravity forces and the relationships between the capillary pressures and saturations are required in the entire saturation space.
When solving the equations governing fluid flow in reservoir simulation, the capillary pressure vs. saturation relationship is most conveniently formulated as a simple correlation with adjustable parameters. In the reservoir, situations may occur where one of the phases appears or disappears, e.g., during phase transitions between gas and oil, or when a zero residual oil saturation is approached by drainage through continuous spreading layers in the crevices of the pore space. To implement these scenarios in a numerical reservoir simulator without creating convergence problems, a smooth transition is required between two- and three-phase flow.
In the oil industry three-phase capillary pressure curves have traditionally been predicted from corresponding two-phase measurements. However, experimental work has shown that this practice may not be valid.1 Moreover, micromodel studies of three-phase flow have revealed that the fluid distribution and the displacement mechanisms at the pore scale may be more complex than for two phases.2,3 These findings emphasize the need for direct measurements of three-phase capillary pressure curves for various conditions. To our knowledge, measurements with three varying saturations have only been reported by Kalaydjian4 and, more recently, Virnovsky et al.5 The capillary pressures were measured in water-wet sandstone core samples only. Bradford and Leij1,6,7 measured three-phase capillary pressures in sandpacks for several wetting conditions achieved by mixing different fractions of water-wet and oil-wet sands. In these experiments, however, one saturation was kept fixed.