Traveling wave solutions for a realistic non-Newtonian foam flow model

Due to several environmental and petroleum engineering applications, there is a renewed interest in studying foam flow in porous media, commonly described as shear-thinning non-Newtonian flow. Based on experiments reporting saturation profiles with an unchanging shape displacing through the medium, we investigate the solution of the model describing foam displacement as a traveling wave. For that, we consider a realistic non-Newtonian foam flow model, which successfully described several experimental studies found in the literature. The aimed traveling wave solution is equivalent to the existence of the solution of the corresponding ordinary differential equations connecting initial and injection conditions. We address this problem by proposing a semi-analytical technique for finding such a connection in the phase space using the explicit foam's apparent viscosity. Our semi-analytical solution is validated with direct numerical simulations and also by comparing it to experimental data from the literature.

Automated summary

This paper investigates the traveling wave solution of foam flow in porous media, using a semi-analytical technique and a non-Newtonian foam flow model. The solution connecting the initial and injection conditions is found through the explicit foam's apparent viscosity. The results of this study are validated through comparison with experimental data and direct numerical simulations.