Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings

Dissolved-phase contaminants experiencing enhanced diffusion (Le., super-diffusion) with a pronounced leading plume edge can pose risk for groundwater quality. The drivers for complex super-diffusion in geological media, however, are not fully understood. This study investigates the impacts of hydrofacies' mean lengths and the initial source geometry, motivated by a hydrofacies model built recently for the well-known MADE aquifer, on the spatial pattern of super-diffusion for two-dimensional alluvial aquifer systems. Monte Carlo simulations show that the bimodal velocity distribution, whose pattern is affected by the hydrofacies' mean lengths, leads to super-diffusion of solutes with a bi-peak plume snapshot in alluvial settings where advection dominates transport. A larger longitudinal mean length (i.e., width) for hydrofacies with high hydraulic conductivity (K) enhances the connectivity of preferential pathways, resulting in higher values in the bimodal velocity distribution and an enhanced leading front for the bi-peak plume snapshot, while the opposite impact is identified for the hydrofacies' vertical mean length (i.e., thickness) on the bi-peak super-diffusion. A multi-domain non-local transport model is then proposed, extending upon the concept of the distributed-order fractional derivative, to quantify the evolution of bi-peak super-diffusion due to differential advection and mobile-mobile mass exchange for solute particles moving in hydrofacies with distinct K. Results show that the bi-peak super-diffusion identified for the MADE site and perhaps the other similar aquifers, which is affected by the initial source geometry at an early stage and the thickness and width of high-K hydrofacies during all stages, can be quantified by the mobile-mobile fractional-derivative model. Porous medium dimensionality and stochastic model comparison are also discussed to further explore the nature of bi-peak super-diffusion in alluvial systems.