New insights from three-phase fractional-flow modeling of foam-oil displacements in porous media

For the first time, we apply three-phase fractional-flow theory combined with the wave-curve method to better understand the mechanisms of foam displacements with oil in porous media, employing a widely used foam model. Fractional-flow theory demonstrates that oil saturation in foam-created oil banks never exceeds the upper limit for stable foam, fmoil (i.e. an oil saturation above which foam is killed); see (Tang et al., 2019c) and section 3.4 below. This constraint suggests a criterion for creating significant oil banks: for the surfactant formulation, fmoil must be far above the initial oil saturation. We identify key factors controlling foam and oil-bank propagation: fmoil, foam quality, the regime in which foam is injected and foam strength at both injection and initial states. The mechanisms of these factors are revealed through a material balance on gas: any factor increasing gas volume injected while maintaining adequate foam strength, or reducing gas saturation in the foam region, accelerates foam propagation, and vice versa. Also, an optimal foam injection strategy is identified: inject foam in the low-quality regime near the transition foam quality (Tang et al., 2019a, 2019b), at which mobility reduction is at its maximum. This rule's universality needs to be further verified. Fractional-flow solutions, free of numerical artifacts, can be used to benchmark numerical simulators and machine-learning approaches for foam processes.