Modelling foam improved oil recovery: towards a formulation for pressure- driven growth with flow reversal

The pressure-driven growth model that describes the 2-D propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas
improved oil recovery. The model assumes a region of low mobility, finely-textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front,must then backtrack, reversing their flow direction. Equations for 1-D fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position vs time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow
mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow’s Darcy pressure drop, the balance of the pressure drop
shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.