A new approach to model hysteresis and its impact on CO2-EOR processes with mobility control strategies

Mobility control methods have the potential to improve coupled enhanced oil recovery and CO2 storage (CO2-EOR). There is a need for improved three-phase relative permeability models with hysteresis including especially the effects of cycle dependency so that more accurate predictions of these methods can be made. We propose a new three-phase relative permeability model with hysteresis applicable to different fluid configurations in porous medium under different wettability conditions. The model also includes compositional effects. Three-phase parameters are estimated based on saturationweighted interpolation of two-phase parameters. The proposed hysteresis model is an extension of the Land trapping model but with a dynamic Land coefficient introduced. The trapping model estimates a constantly increasing trapped saturation for intermediateand non-wetting phases. The model overcomes some of the limitations of existing three-phase hysteresis models for non-water wet rocks and mitigates the complexity associated with commonly applied models in numerical simulators. The model is validated using multi-cyclic three-phase water-alternating-gas experimental data for non-water wet rocks. Numerical simulations of a carbonate reservoir with and without hysteresis were used to assess the impact of the saturation direction and saturation path on gas entrapment and oil recovery. Background and Literature Review Unlike water-wet rocks, mixed-wet reservoirs show a continuous oil phase in three-phase flow resulting in small, yet nonzero, values of the oil relative permeability (Salathiel, 1973). The dependence of oil isoperms on one or two phase saturations in the saturation space is complex and difficult to predict a priori (van Dijke et al., 2001). Moreover, by studying three-phase displacement processes and pore-scale mechanisms in etched micromodels, it was revealed that fluid configurations can be categorized based on the phase spreading coefficient   13 2 12 23 S C       (1) The necessary condition for a spreading oil layer between aqueous and gas phases is non-negative ; otherwise, a three-phase contact line exists. In the non-spreading case, oil is wetting relative to gas and water or gas could be the wetting phase in non-water wet media depending on the gas-water contact angle. The contact angle plays a crucial role in fluid configurations in porous media. The difference between oil-water and gas-oil interfacial tension could result in either the aqueous or gas phase as the intermediate-wetting phase in oil-wet rocks. This complex fluid configuration and flow in porous media delineates regions in saturation space where commonly used models fail to replicate the physical behavior. There are commonly used correlations based on an assumed fluid configuration that are not easy to generalize to other fluid configurations. Three-Phase Relative Permeability Models Based on an extension of Marle’s (1981) description, there are numerous parameters that impact relative permeability: saturations, wettability, pore shape and size, trapping number (interaction of viscous, gravitational, and capillary forces (Pope et al. (2000)), saturation direction and saturation path, and composition. In three-phase flow, except for certain special conditions, relative permeability measurements are incomplete. More precisely, for a specified phase with a fixed saturation, there are an infinite number of combinations of the saturations for three-phase flow. A conventional approach is to estimate three-phase flow relative permeability based on measured two-phase relative permeabilities. Table 1 provides a