Mixing in Porous Media

The difficulty of efficient mixing in porous media flows stems from the fact that the Reynolds number is small, and therefore one cannot rely on turbulence as an agent for mixing. We have developed a new model that predicts how to improve mixing in this regime of low Reynolds numbers. It has been known for decades that the displacement of a more viscous fluid by a less viscous fluid is unstable and leads to what is known as viscous fingering, but it was not known how the instability could affect mixing. As shown in the snapshot below from one of our simulations, viscous fingering can facilitate mixing by increasing the disorder and the interfacial area between the more viscous (dark) and less viscous (light) fluids. But the instability also can cause channeling of the low-viscosity fluid, which reduces the mixing efficiency. Competition between those effects results in nontrivial and nonmonotonic mixing behavior. In the spirit of turbulence modeling, we have taken the coupled partial differential equations governing the system and reduced them to two first- order ordinary differential equations that capture and quantify the effect of viscous fingering on mixing.

We have also worked on convective mixing in porous media, that is, the flow and mixing that results from an unstable density stratification of fluids. While convective mixing has been studied extensively (recently, in the context of CO2 sequestration in saline aquifers), the fundamental behavior of the dissolution flux and its dependence on the system parameters are not yet well understood. We have shown that the dissolution flux and the rate of fluid mixing are determined by the mean scalar dissipation rate. We used this theoretical result to provide computational evidence that the classical model of convective mixing in porous media exhibits, in the regime of high Rayleigh number, a dissolution flux that is constant and independent of the Rayleigh number, thus supporting the universal character of convective mixing.