Numerical Simulation of Foam Flow In Porous Media
Authors: Islam M.R. , Ali S.M. Farouq 
Published: March 2010

Abstract
This paper presents a new mathematical formulation that provides one possible 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 view efforts have been made toward 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 to incorporate 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 formulation 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.

Introduction
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 injection(1). The initial work with foam indicated that it could improve the conformance of gasdrive oil recovery processes because it selectively reduces the relative permeability to gas in a reservoir rock(2). Bernard et al. (3) showed that foam flooding recovered more oil mainly because it created a higher trapped-gas saturation which indirectly yielded a lower relative permeability to water. Marsden and Khan(4) 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 Holm(6) was observed. Radke and Ransohof(7) 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: