Traveling waves for the newtonian foam displacement in porous media

Abstract

This thesis presents the analytical study of three systems of partial differential equations that describe foam flow in porous media. The first two models consider the surfactant concentration fixed above the critical micellar concentration: the linear kinetic model and a simplified version of the stochastic bubble population balance model. A significant difference between these models is the influence of critical water saturation in the first model. The third system generalizes the second by varying the surfactant concentration and considering gas mobility that depends on the surfactant concentration. We study the traveling wave solutions of such systems using phase portrait analysis. All obtained analytical solutions are confirmed using direct numerical simulations of the system of partial differential equations. The second model is validated with experimental data.