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

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.

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