Dynamics of foam mobility in porous media
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Foam reduces gas mobility in porous media by trapping substantial amount of gas and applying a viscous resistance of flowing lamellas to gas flow. In mechanistic foam modeling, gas relative permeability is significantly modified by gas trapping, while an effective gas viscosity, which is a function of flowing lamella density, is assigned to flowing gas. A complete understanding of foam mobility in porous media requires being able to predict the effects of pressure gradient, foam texture, rock and fluid properties on gas trapping, and therefore gas relative permeability, and effective gas viscosity. In the foam literature, separating the contributions of gas trapping and effective gas viscosity on foam mobility has not been achieved because the dynamics of gas trapping and its effects on the effective gas viscosity have been neglected. In this study, dynamics of foam mobility in porous media is investigated with a special focus on gas trapping and its effects on gas relative permeability and effective gas viscosity. Three-dimensional pore-network models representative of real porous media coupled with fluid models characterizing a lamella flow through a pore throat are used to predict flow paths, threshold pressure gradient and Darcy velocity of foam. It is found that the threshold path and the pore volume open above the threshold pressure are independent of the fluid model used in this study. Furthermore, analytical correlations of flowing gas fraction as functions of pressure gradient, lamella density, rock and fluid properties are obtained. At a constant pressure gradient, flowing gas fraction increases as overall lamella density decreases. In the discontinuous-gas foam flow regime, there exists a threshold pressure gradient, which increases with overall lamella density. One of the important findings of this study is that gas relative permeability is a strong non-linear function of flowing gas fraction, opposing most of the existing theoretical models. However, the shape of the relative gas permeability curve is poorly sensitive to overall lamella density. Flowing and trapped lamella densities change with pressure gradient. Moreover, analytical correlations of effective gas viscosity as functions of capillary number, lamella density and rock properties are obtained by up-scaling a commonly used pore-scale apparent gas (lamella) viscosity model. Effective gas viscosity increases nonlinearly with flowing lamella density, which opposes to the existing linear foam viscosity models. In addition, the individual contributions of gas trapping and effective gas viscosity on foam mobility are quantified for the first time. The functional relationship between effective gas viscosity and flowing lamella density in the presence of dynamic trapped gas is verified. A mechanistic foam model is developed by using the analytical correlations of flowing gas fraction and effective gas viscosity generated from the pore-network study and a modified population balance model. The developed model is successful in simulating unsteady-state and steady state flow of foam through porous media. Moreover, the flow behaviors in high- and low-quality flow regimes are verified by the experimental studies in the literature. Finally, the simulation results are successfully history matched with two different core-flood data.