Mathematical Model of Foam Flowing Characteristics by Snap-Off Mechanisms at Steady State in Porous Media

Abstract

Flow characteristics and regeneration processes of foams were influenced by lamella properties and pore-throat structure in porous media. In this article, porous media was simplified as a bunch of constricted capillary tubes according to grain size, pore-throat radius, and immobile water saturation in porous media. Based on an analysis of forces upon liquid lamella, a mathematical model of foam migration and regeneration at steady state was established according to the mass conservation law and the momentum conservation law in porous media. The model could be used to calculate some important parameters in porous media, such as pressure distribution, shearing stress, lamella morphology, liquid-layer thickness, regeneration bubble size, etc. A series of flow experiments were carried out to investigate the influence of liquid properties and pore-throat structure on flow characteristics and resistance behavior of foams in porous media. The experimental results showed that pressure distribution monotonously decreased along porous media. The theoretical results were in good agreement with the experimental results. Foam structure, that is, foam quality was an important factor upon foam resistance behavior in porous media. The strongest resistance ability of foams was achieved at foam quality of 85% in porous media.