The Method of Characteristics Applied to Oil Displacement by Foam

Summary Solutions obtained by the method of characteristics (MOC) provide key insights into complex foam enhanced-oil-recovery (EOR) displacements and the simulators that represent them. Most applications of the MOC to foam have excluded oil. We extend the MOC to foam flow with oil, where foam is weakened or destroyed by oil saturations above a critical oil saturation and/or weakened or destroyed at low water saturations, as seen in experiments and represented in foam simulators. Simulators account for the effects of oil and capillary pressure on foam using algorithms that bring foam strength to zero as a function of oil or water saturation, respectively. Different simulators use different algorithms to accomplish this. We examine SAG (surfactant-alternating-gas) and continuous foam-flood (coinjection of gas and surfactant solution) processes in one dimension, using both the MOC and numerical simulation. We find that the way simulators express the negative effect of oil or water saturation on foam can have a large effect on the calculated nature of the displacement. For instance, for gas injection in a SAG process, if foam collapses at the injection point because of infinite capillary pressure, foam has almost no effect on the displacement in the cases examined here. On the other hand, if foam maintains finite strength at the injection point in the gas-injection cycle of a SAG process, displacement leads to implied success in several cases. However, successful mobility control is always possible with continuous foam flood if the initial oil saturation in the reservoir is below the critical oil saturation above which foam collapses. The resulting displacements can be complex. One may observe, for instance, foam propagation predicted at residual water saturation, with zero flow of water. In other cases, the displacement jumps in a shock past the entire range of conditions in which foam forms. We examine the sensitivity of the displacement to initial oil and water saturations in the reservoir, the foam quality, the functional forms used to express foam sensitivity to oil and water saturations, and linear and nonlinear relative permeability models.