Foam propagation with flow reversal

With a view towards modelling the foam improved oil recovery process, fractional flow theory is used to study the dynamics of a foam as it propagates in a porous medium that is initially filled with liquid. In particular, a case is studied whereby, at a certain time, the net pressure driving the foam is decreased below the hydrostatic pressure at depth, leading to a local change in the flow direction. This is known as flow reversal. In both forward and reverse flow, the boundary between foamed gas and liquid is found as a discontinuous jump in liquid saturation. Over a certain thickness in the neighbourhood of this discontinuity, foam is finely textured, and the mobility of foamed gas drops by orders of magnitude relative to either pure gas or pure liquid. In reverse flow, however, the foam mobility itself and also the thickness over which low mobilities apply might differ from the forward flow case. Fractional flow theory reveals that the thickness of the low mobility region, and hence the resistance to motion that it presents, increases directly proportional to the distance travelled. Previous studies recognised this, but assumed the thickness of this region to be just a small fraction of the distance travelled by the discontinuity. Here, however, we demonstrate that the extent of the low mobility region, in both forward and reverse flow, accounts for a considerable fraction of the distance travelled by the foam, despite what was assumed in previous works.