Mathematical and computational analysis of mechanistic models for foam flow in porous media

Abstract

There has been a renewed interest in studying foam flow in porous media, particularly in environmental and petroleum engineering applications. Several experimental observations reported saturation profiles maintaining a consistent shape during displacement through the medium, motivating the investigation of solutions for foam models in the form of traveling waves. In this work, we analyze three foam flow models with distinct approaches to rheology and bubble balance, including a non-Newtonian model for which we demonstrate the existence of traveling wave solutions. We validated our semi-analytical solution with numerical simulations, and both agreed well with the experimental data. We show that, for homogeneous media under the strong foam regime, all models yield the same solution when fitted to typical experimental conditions. We explored model differences through two-dimensional simulations in heterogeneous permeability fields, revealing a significant divergence in describing bubble distribution. The model featuring a permeability-dependent foam destruction rate exhibits higher bubble density in more permeable regions, consistent with observations reported in the literature. Despite these differences, all models accurately predict breakthrough time, production curves, and the shape of the foamed gas front. Our findings confirm the applicability of the traveling wave approach in obtaining semi-analytical solutions for Newtonian and non-Newtonian foam models and provide a tool to aid in selecting appropriate models for specific applications.