The traveling wavefront for foam flow in multilayered porous media

Abstract

This work proposes the study of a system of partial differential equations (mass balance and foam transport) describing the phenomenon of foam transport in stratified porous media. The problem is approached in one-dimensional and two-dimensional forms. We use the linear kinetic model and a simplified version of the bubble population equilibrium model to investigate foam transport in both cases. First, we study foam flow in a two-layer system using the linear kinetic model. The mass exchange between layers is estimated from numerical and analytical results. By varying both the absolute permeability and porosity of the medium in both layers, we explore how mass exchange between the layers changes, marking the first analytical study of the crossflow phenomenon in the foam injection process. The existence of a significant problem of “viscous fingering” and preferential pathways is well-known in various applications of foam in fractured media. Specifically, due to the high permeability of the fracture, when gas is injected, it tends to move much faster through the fracture, affecting the uniform sweep of the medium. It is known that foam injection helps reduce gas mobility, thereby improving sweep uniformity. In this work, we address this issue in fractured media. To do so, we implement an n-layer model, allowing us to study traveling wave solutions in fractured media, treating it as a medium with three layers, where the fracture is identified as the intermediate layer with higher permeability and thinner thickness.