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

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  • Sergei Fomin
    Department of Mathematics and Statistics, California State UniversityChico, CA 95928, USA
  • Vladimir Chugunov
    Department of Applied Mathematics, Kazan State Technical UniversityKazan 420111, Russia
  • Toshiyuki Hashida
    Fracture and Reliability Research Institute, School of EngineeringTohoku University, 6-6-11, Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

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<jats:p>Solute transport in a fractured porous confined aquifer is modelled by using an equation with a fractional-in-time derivative of order<jats:italic>γ</jats:italic>, 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<jats:italic>α</jats:italic>, leads to the introduction of an additional fractional-in-time derivative of order<jats:italic>α</jats:italic>/(1+<jats:italic>α</jats:italic>) 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.</jats:p>

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