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An investigation on the fractional derivative model in characterizing sodium chloride transport in a single fracture

  • HongGuang Sun
  • Yang Wang
  • Jiazhong QianEmail author
  • Yong Zhang
  • Dongbao Zhou
Regular Article
  • 14 Downloads
Part of the following topical collections:
  1. Focus Point on Fractional Differential Equations in Physics: Recent Advantages and Future Direction

Abstract.

Contaminant transport in a single fracture cannot be reliably captured by the classical advection-dispersion equation model, due to the heterogeneity nature of the fracture. This study applied a time fractional advection-dispersion equation (ADE) model to quantify chloride ion transport in a single fracture observed in the lab. We further explored the solute transport characteristics by comparing them with the simulation results using a classical ADE model and a space-time fractional ADE model. Comparison results show that the time fractional derivative model is better than the classical ADE model in describing the blocking process of solute transport in the fracture (the tailing phenomenon of the breakthrough curve or BTC). The space-time fractional ADE model is not needed to describe the observed BTC, because only time evolution of solute concentration is considered in this case. Experimental analysis also indicates that the order of the time fractional derivative increases with the fracture aperture, and sub-diffusion is enhanced by a slower flow velocity.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • HongGuang Sun
    • 1
  • Yang Wang
    • 1
  • Jiazhong Qian
    • 2
    Email author
  • Yong Zhang
    • 3
  • Dongbao Zhou
    • 1
  1. 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and MaterialsHohai UniversityNanjingChina
  2. 2.School of Resources and Environmental EngineeringHefei University of TechnologyHefeiChina
  3. 3.Department of Geological SciencesUniversity of AlabamaTuscaloosaUSA

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