Network models are often used to predict oil, gas and water relative permeabilities and residual saturations. It was recently shown that most previous network model calculations involving significant numbers of double-displacement events were invalid because of material balance errors1.

The current study used a model that conserved oil, gas and water volumes. The model accounted for heterogeneity and the snap-off displacement mechanism. Gas injection followed waterflooding to displace the remaining oil saturation. The remaining saturations were a function of the level of snap-off events that occurred during waterflood imbibition. The model was used to study the effect of the fluid saturation profiles at the end of waterflooding on three-phase oil relative permeabilities and oil recovery from a subsequent gas flood.

The level of snap-off events during waterflood imbibition displacement significantly affected the remaining oil and water saturations before gas flooding. This, in turn, affected three-phase oil relative permeabilities and recoveries. Residual oil saturation to gas flood increased with increased remaining oil saturation following waterflood. Introducing spatial and local correlations significantly increased oil, water and gas relative permeabilities and reduced remaining oil and water saturations.

Oil relative permeability was found to be a function of both oil saturation and the oil remaining after waterflood. Gas and water relative permeabilities were only functions of their respective saturations.


Three-phase flow in porous media is an active research area in a number of engineering and scientific disciplines, particularly the study of three-phase flow of oil, water and gas in hydrocarbon reservoirs. Accurate estimates of three-phase relative permeabilities are required in order to predict the relative movement of each phase2. Kantzas et al.3 and Oren and Pinczewski4 among others5–7 showed that additional oil may be recovered by injecting gas into a reservoir that was previously waterflooded. In enhanced oil recovery operations, gas may be injected into a reservoir in which the three phases may have different saturations. Oak's8 three-phase experimental work and the three-phase network model study of Lerdahl et al.2 showed the importance of initial conditions on three-phase relative permeabilities and residual saturations. Although direct experimental measurements of three-phase properties such as residual saturations and relative permeabilities are sometimes made in the laboratory on cores from reservoirs, these measurements are expensive, time consuming and somewhat difficult to conduct with precision. For expedience, empirical or semi-empirical models were used to estimate three-phase relative permeabilities from two-phase data9,10. There is no substitute for direct measurement and to date, 6the models do not adequately predict three-phase relative permeabilities nor phenomena such as spreading11–13.

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