Mobilization of trapped foam in porous media

Usually, foam in a porous medium flows through a small and spatially varying fraction of available pores, while the bulk of it remains trapped. The trapped foam is under a pressure gradient corresponding to the pressure gradient imposed by the flowing foam and continuous wetting liquid fractions. The imposed pressure gradient and coalescence of the stationary foam lamellae create periodic flow channels in the trapped foam region. Each of these channels flows briefly, but it eventually plugs, while another flow channel opens elsewhere, only to be plugged again by the finer bubbles pushed into the trapped region. This results in a cycling of flow channels that open and close throughout the trapped foam. The dynamic behavior of foam trapped in porous media has been modeled here with a pore network simulator. The simulator also predicts the magnitude of the pressure drop along a trapped foam region necessary to generate a flow channel through it. The mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path. A predictive model of foam flow in porous media requires the knowledge of the foam fraction that traps under an imposed pressure gradient and for a given distribution of pore sizes. Here we present the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and the mean and standard deviation of the pore size distribution. This expression provides the final missing piece of the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles