The flow of a foam in a two-dimensional porous medium

Foams have been used for decades as displacing fluids for enhanced oil recovery and aquifer remediation, and more recently, for remediation of the vadose zone, in which case foams carry chemical amendments. Foams are better injection fluids than aqueous solutions due to their low sensitivity to gravity and because they are less sensitive to permeability heterogeneities, thus allowing a more uniform sweep. The latter aspect results from their peculiar rheology, whose understanding motivates the present study. We investigate foam flow through a two-dimensional porous medium consisting of circular obstacles positioned randomly in a horizontal transparent Hele-Shaw cell. The local foam structure is recorded in situ, which provides a measure of the spatial distribution of bubble velocities and sizes at regular time intervals. The flow exhibits a rich phenomenology including preferential flow paths and local flow nonstationarity (intermittency) despite the imposed permanent global flow rate. Moreover, the medium selects the bubble size distribution through lamella division-triggered bubble fragmentation. Varying the mean bubble size of the injected foam, its water content, and mean velocity, we characterize those processes systematically. In particular, we measure the spatial evolution of the distribution of bubble areas, and infer the efficiency of bubble fragmentation depending on the various control parameters. We furthermore show that the distributions of bubble sizes and velocities are correlated. This study sheds new light on the local rheology of foams in porous media and opens the way toward quantitative characterization of the relationship between medium geometry and foam flow properties. It also suggests that large-scale models of foam flows in the subsurface should account for the correlation between bubble sizes and velocities.