This paper presets a new mathematical formulation chat provides a realistic and appropriate representation of foam behaviour in a porous medium. Foams are gaining increasing importance in the petroleum industry in a number of roles, notably as mobility control and/or blocking agents in enhanced oil recovery operations. It has been shown in the past that appropriate foams can indeed improve the recovery efficiency of a given process. and foams can serve as temporary blocking agents. Even though many laboratory studies have been conducted to understand the rheology of foams and the mechanics of foam flow in porous media, relatively few efforts have been made towards the mathematical simulation of foam rheology and flow in a porous medium. Recently a few researchers have addressed the problem but often no experimental data were available to validate the numerical simulation results. Besides, no attempt was made co incroporate effects of variable absolute permeability, the presence of oil, or optimum surfactant concentration. Experimental evidence has shown that oil acts as a defoamer for most surfactants. The formulacion developed in the present work explains the blocking mechanism of foam in the presence of oil and water. The mathematical model is tested against experimental results, showing good agreement.
There have been several attempts to use foam as blocking agents. However, most of these tests were applied in enhanced oil recovery by gas or steam injection1. The initial work with foam indicated that it could improve the conformance of gas-drive oil recovery processes because it selectively reduces the gas permeability of reservoir rock2 Also, Bernard et al.3 showed that foam flooding recovered more oil mainly because it created a higher trapped- gas sacuration which indirectly yielded a lower relative permeability co water. Marsden and Khan4 observed a higher mobility reduction in higher permeability cores. A microscopic model study was carried out by owette et al.5 They used visual models saturated with surfactant solutions. They observed that when gas alone was injected only a few interfaces were formed behind the gas liquid front. However, when foam was injected the bubbles were larger. They also observed that larger channels could not be blocked by the foam and most of the gas flow took place through those larger channels. This flow mechanism was independent of surfactant concentration. Even though at low concentrations flow was similar to that in a homogeneous medium, at higher concentrations foam bubbles were actually generated and the process of "breaking and reforming" as described by Holm6 was observed Radke and Ransohoff7 also used visual observation to identify foam generation in glass bead packs. They showed the importance of pore geometry on the mechanisms of foam generation. Snap-off and lamella divisions were observed in flow across a boundary from low to high permeability but neither mechanism was seen below a critical capillary number when flowing from a high to low permeability zone.
Based on experimental studies, five major mechanisms of foam flow have been recognized. These are:
