Impact of Chaotic Advection on Solute Transport in Porous Media

Chaotic advection can enhance mixing processes in porous media by increasing the solution-solvent interface available for diffusion. While the pore structure can generate chaotic advection at the pore scale, transient flow fields can lead to chaotic advection at the Darcy scale. This concept can be applied to groundwater remediation, as the flow field can be engineered using injection-extraction systems. This study investigates two injection-extraction systems known to exhibit chaotic structures: a source-sink dipole and a rotated potential mixing. Using Lagrangian particle tracking combined with random walk we solve the stochastic differential equation to simulate solute transport. The pulsed source-sink system is parametrized by the pumping rate, while for the rotated potential mixing system, we use the rotation angle and the rotation frequency to change the flow properties. Using a grid search over the parameter spaces of both systems, we test different configurations. We quantify the temporal increase in dilution and the mixing enhancement with the dilution index by using a novel approach of selecting the optimal grid size with minimal approximation error for each particle density estimation. Furthermore, we analyze the corresponding flow structure to identify Kolmogorov-Arnol'd-Moser (KAM) islands, non-mixing regions that arise around elliptic points of the flow. We find that the parameters of the system control the occurrence and size of KAM islands, which consequently affect the increase in dilution by limiting the chaotic area in the domain. Overall, our results show that not all chaotic systems lead to the same maximum mixing enhancement. Therefore, it is important to properly assess the uncertainty in the design parameters of injection-extraction systems to effectively engineer chaotic advection.