On the modeling of the foam dynamics in heterogeneous porous media

Foam flow in porous media is important in various engineering applications, including soil remediation, carbon dioxide sequestration, and enhanced oil recovery. This study explores the relationship between bubble density and permeability in foam flow models, focusing on how different approaches capture foam formation in highly permeable regions. We compare two mechanistic models numerically. The first one is a Newtonian model with simple foam generation mechanics, while the second is a non-Newtonian model that incorporates complex mechanisms of foam generation and destruction depending on phase velocities and capillary pressure. Our results demonstrated that the more complex model exhibited a strong correlation between bubble density and permeability, while the simpler model maintained a constant bubble density despite the heterogeneity. This observed correlation, while experimentally documented, was not analyzed from a theoretical modeling perspective. For comparing both models, we developed a workflow for fitting the corresponding parameters based on foam equilibrium. As a result, two-dimensional simulations showed good agreement in gas front location, breakthrough time, and production rates for both models.