Application of fractional flow theory to foams in porous media

Abstract

Mechanisms of foam displacement in porous media were investigated by the fractional flow theory in this study, incorporating fully mechanistic foam descriptions. During a change in total injection velocity by 8.15 times, the shape of fractional flow curves changed significantly, which in turn affected sweep efficiency and pressure profile markedly. The analytical solutions were in good agreement with recent mechanistic foam simulations in terms of foam texture, location of displacement front, saturation profile and pressure distribution. The fractional flow theory in this study explains many features of conventional foam-generation experiments successfully: a weak-foam state at low injection velocity and a strong-foam state at high injection velocity, the transition from weak-foam to strong-foam state with a stepwise increase in injection velocity, the hysteresis associated with foam generation, and the effect of foam quality on foam generation. It should also be noted that the catastrophic nature of foam rheology observed in recent experimental and modelling studies is fully captured, showing multiple solutions corresponding to weak-, intermediate- and strong-foam states. Construction of a three-dimensional surface of fractional flow curves enabled complicated foam mechanisms to be analysed more conveniently.