Foam improved oil recovery: Foam front displacement in the presence of slumping

• Shape of foam front during foam improved oil recovery is modelled.
• Foam more mobile at top as dense surfactant solution slumps downwards.
• Foam front develops transient concavity but this migrates toward bottom of the front.
• At long times, foam front actually develops convex kink.
• Apparent horizontal propagation velocity is uniform across convex kink.

Foam is often used in improved oil recovery processes to displace oil from an underground reservoir. During the process, the reservoir is flooded with surfactant, and then gas is injected to produce foam in situ, with the foam front advancing through the reservoir. Here the effect of surfactant slumping (downward movement of surfactant in relation to a lighter phase) upon the advance of a foam front is presented. Slumping which can be associated with foam drainage, coarsening and collapse, causes a rise in mobility of the foam front specifically near the top of the front. The description of a foam front displacement for an initially homogeneous foam mobility is therefore modified to account for slumping-induced inhomogeneities. Numerical solution for the front shape shows that, although slumping transiently produces a localised concave region on the otherwise convex front, this concavity has little effect on the long term front evolution. In fact in the long-time limit, a convex kink develops on the front: an analytical solution describing the convex kink agrees very well with the numerics.

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