Modeling Steady-State Foam Flow: Hysteresis and Backward Front Movement

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Foaming gaseous injectants is an attractive option because of the much lower gas mobility achieved in porous media. This paper reports an experimental and numerical investigation to improve our understanding of aqueous foam flow in heterogeneous sandstone. Our experimental program reveals two interesting behaviors: hysteresis in the steady-state pressure gradient and movement of a foam front opposite the direction of flow. Steady-state pressure gradient measurements across a sandstone core demonstrate the absence of a critical velocity requirement for foam generation, support the possibility of foam propagation away from the injection well, and exhibit hysteresis in the pressure gradient upon decreasing the injection gas velocity. Quasi-steady pressure drop profiles show that the pressure gradient increases against the direction of flow in what we coin the ”backward front movement”. This paper models experimental observations of steady-state pressure-drop hysteresis as well as quasi-steady backward front movement. Specifically, a steady-state population balance model that is based on pore-scale observations is developed. The model is verified against experimental data to confirm the steady-state predictions of the pressure, the flowing bubble density, and the flowing foam fraction (Tang and Kovscek, Transport in Porous Media 2006, 65, 287–307; Chen et al. SPE J. 2010, 15, 171–183). The model is then used to predict the experimental behavior. The flowing foam fraction (i.e., the fraction of the gas saturation that flows) is a key parameter in interpreting both hysteresis and backward propagation of the pressure gradient. Our findings highlight the importance of the flowing foam fraction to predicting various foam behavior.