The effect of non-Fickian diffusion into surrounding rocks on contaminant transport in a fractured porous aquifer

Sergei Fomin, Vladimir Chugunov, Toshiyuki Hashida

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

Solute transport in a fractured porous confined aquifer is modelled by using an equation with a fractional-in-time derivative of order γ, which may vary from 0 to 1. Accounting for non-Fickian diffusion into the surrounding rock mass, which is modelled by a fractional spatial derivative of order α, leads to the introduction of an additional fractional-in-time derivative of order α/(1+α) in the equation for solute transport. Closed-form solutions for solute concentrations in the aquifer and surrounding rocks are obtained for an arbitrary time-dependent source of contamination located at the inlet of the aquifer. Based on these solutions, different regimes of contaminant transport in aquifers with various physical properties are modelled and analysed.

Original languageEnglish
Pages (from-to)2923-2939
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2061
DOIs
Publication statusPublished - 2005 Aug 9

Keywords

  • Contamination
  • Fractional derivative
  • Fractured aquifer
  • Non-Fickian diffusion
  • Porous blocks
  • Solute transport

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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