Numerical observation of traveling wave solution in a non-Newtonian foam model

Resumo

Foam injection is an oil recovery technique with great potential to be applied in the Brazillian Pre-salt
reservoirs. It consists of injecting gas and surfactant solution into the reservoir to control the gas mobility, avoid the
fingering formation, and improve sweep efficiency. Investigating the foam flow in porous media is challenging due
to foams’ non-Newtonian behavior. That is why most mathematical studies on this subject consider Newtonian
models. In the literature, there is a non-Newtonian model describing the foam displacement validated through
laboratory experiments. In the present work, we numerically verified that this model possesses a traveling wave
solution i.e., a stable-shape profile displacing in space with constant velocity. Such a solution is similar to ones
appearing in Newtonian models. We validate our results by comparing them to the experimental data found in the
literature. The numerical method is based on a finite difference Crank-Nicolson scheme with the Newton-Raphson
method for time step evolution.