This work presents a fractional flow theory analysis of gravity-dominated, immiscible displacement in porous media. This effort represents the first to extend Buckley-Leverett theory to account for the effects of countercurrent flow while fluid injection and production is ongoing. The driving force for countercurrent flow is gravity, phase density differences, and a non-horizontal flow dimension. Our analysis is limited by the usual fractional flow theory assumptions, most importantly one-dimensional flow. Countercurrent flows are possible if the ratio of gravity to viscous forces forces is sufficiently large. Our analysis characterizes the gravity to viscous force ratio by a dimensionless Gravity Number. Our effort yields a more general and unified theory of immiscible displacement. We present new graphical solution methods to predict displacement performance for arbitrary initial and injected conditions.

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