Traveling Wave Solutions for Non-Newtonian Foam Flow in Porous Media

The injection and in situ generation of foam in porous media successfully control gas mobility and improve the fluids' sweep efficiency inside porous media. Mathematical models describing this problem use two phases, foamed gas, and fluid, and usually have a term for foam generation and destruction. Moreover, the non-Newtonian foam behavior is frequently modeled using Hirasaki and Lawson's formula for foamed gas viscosity. In this paper, we detail how the traveling wave analysis can be used to estimate the propagation profiles and velocity for a range of non-Newtonian foam models in porous media at constant total superficial flow velocity. We reformulate Hirasaki and Lawson's formula in an explicit form allowing us to find traveling wave solutions for a foam model with non-Newtonian gas viscosity and a foam generation linearly dependent on the foam texture. Comparing the solution with the one for the Newtonian version allows us to analyze qualitatively and quantitatively the rheology of the foam flow in porous media.