Non-Fickian transport of sodium chloride in inter-river land: experiment validation and fractional derivative modeling

River-groundwater interactions, accompanied by solute transport, are one of the most important contemporary challenges. Non-Fickian diffusion behavior has been extensively documented for solute transport in groundwater or river, but less in river-groundwater system. This paper confirms the existence of anomalous diffusion in the river-groundwater system by experiments and then accurately describes the solute transport process by fractional derivative model, especially for the long-time power law tailing characteristic. Laboratory experiment in inter-river land sample shows that the time fractional advection-dispersion equation, which has a parameter (time index a) defining memory function and other basic transport parameters (velocity v and dispersion coefficient D) with the different hydrogeologic significances, provides a prominent improvement in simulating non-Fickian diffusion behavior compared with the classical advection-dispersion equation. Analysis results indicate that low flow rates reduce mass exchange between the mobile and immobile domains, resulting in late-time heavy tailing phenomenon. In a word, this study provides a new approach to improve our understanding on solute transport in the interfluve with river-groundwater interactions.

Automated summary

This paper confirms the existence of anomalous diffusion in the river-groundwater system and accurately describes the solute transport process using a fractional derivative model.