AUTHOR=Qiao Chuantaidou , Xu Yi , Zhao Weidong , Qian Jiazhong , Wu Yongting , Sun HongGuang TITLE=Fractional Derivative Modeling on Solute Non-Fickian Transport in a Single Vertical Fracture JOURNAL=Frontiers in Physics VOLUME=8 YEAR=2020 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00378 DOI=10.3389/fphy.2020.00378 ISSN=2296-424X ABSTRACT=

Solute transport in a single vertical fracture (SVF) cannot be reliably described by the classical advection-dispersion equation (ADE) model, due to the heterogeneity nature of fracture. This study conducted a group of experiments to investigate chloride ion transport in the SVFs under different rough-walled conditions, and then applied a time fractional advection-dispersion equation (F-ADE) model to offer an accurate description. A comparison between F-ADE model and a classical ADE model in describing experimental data, was also carried out. Results show that the FADE model is better than the ADE model in describing the breakthrough curve and heavy-tail phenomenon of solute transport in the fracture. Especially in the experiments with lower flow rate and higher roughness fracture, the FADE model can offer a better description for non-Fickian transport, indicating that it is a promising tool for characterizing solute transport heterogeneous vertical fracture.