A model for foam generation in homogeneous media

Abstract

Recent laboratory research in a wide range of porous media shows that creating foam in steady flow in homogeneous media requires exceeding a minimum pressure gradient ∇pmin. Data fit trends predicted by a model in which foam generation depends on attaining sufficient ∇p to mobilize liquid lenses present before foam generation. Data show three regimes: a coarse-foam regime at low ∇p, strong foam at high ∇ p, and, in between, an unstable transient regime alternating between weaker and stronger foam. Here, for the first time, a population-balance foam model incorporates a bubble-creation function that depends on pressure gradient. The new model reproduces the three foam regimes seen in the laboratory, the abrupt occurrence of foam generation at a threshold velocity or pressure gradient, hysteresis in experimental results, the interplay between foam stability and foam generation, the effect of injected-liquid fractional flow on foam generation, and foam behavior in the high-quality and low-quality steady-state strong-foam regimes. Once strong foam is created, the details of the lamella-creation function have little further effect on its rheology, which is controlled by other mechanisms. The fractional-flow curves predicted for foam are complex. This model is a necessary step toward quantitative prediction of foam performance in the field.