When can the local advection–dispersion equation simulate non-Fickian transport through rough fractures?

  • Lizhi Zheng
  • Lichun WangEmail author
  • Scott C. James
Original Paper


Non-Fickian solute transport is observed across many scales, which has motivated development of numerous non-Fickian-based models. Assuming that local fluid flow was estimable from the Modified Local Cubic Law, this study determined whether the local ADE better simulated non-Fickian transport through rough (3-D) fractures when local dispersion was described using either  the Taylor dispersion coefficient (DTaylor) or the molecular diffusion coefficient (Dm). The assessment was based on how well the local ADE compared to particle-tracking solutions for solute transport across a range of Péclét numbers (Pe) through two simulated fractures. Even though the local ADE is based on local Fickian transport processes, it was able to reproduce non-Fickian transport characteristics through these heterogeneous fractures. When supplying DTaylor to the local ADE, it extended the applicability of the local ADE to a threshold of Pe < 450; using Dm, the local ADE was only accurate when Pe < 70. No differences were observed for small Pe. Therefore, our recommendation is to always use DTaylor in the local ADE to capture non-Fickian transport so long as the Pe threshold is not exceeded.


Non-Fickian transport Local advection–dispersion equation Fracture flow Particle tracking Taylor dispersion 



This work is financially supported by National Key R&D Program of China (Grant No. 2016YFA0601002). Additional financial support is provided by the Geology Foundation of the University of Texas and by Tianjin University.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Geological SciencesUniversity of Texas at AustinAustinUSA
  2. 2.Institute of Surface-Earth System ScienceTianjin UniversityTianjinChina
  3. 3.Department of Geoscience and Mechanical EngineeringBaylor UniversityWacoUSA

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