Foam front displacement in improved oil recovery in systems with anisotropic permeability

A foam front propagating through an oil reservoir is considered in the context of foam improved oil recovery. Specifically the evolution of the shape of a foam front in a strongly anisotropic reservoir (vertical permeability much smaller than horizontal permeability) is determined via the pressure-driven growth model. The shape of the foam front is demonstrated to be extremely close to that predicted in the limiting case of a reservoir with no vertical permeability whatsoever, in particular any deviations from this shape are found to be second order in the ratio of vertical to horizontal permeabilities. Material points used to represent the foam front shape are shown to exhibit a uniform downward vertical motion, with a vertical velocity component which is proportional to the ratio of vertical to horizontal permeabilities. As the material points in question migrate downwards, they are replaced by new material points arriving from higher up, representing a long-time asymptotic solution for the front shape. This long-time asymptotic shape is sensitive to the ratio of vertical to horizontal permeabilities, with the foam front sweeping the reservoir less effectively as this ratio decreases.