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 language | English |
|---|---|
| Pages (from-to) | 2923-2939 |
| Number of pages | 17 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 461 |
| Issue number | 2061 |
| DOIs | |
| Publication status | Published - 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)