Nonreactive solute transport in soil columns: classical and fractional-calculus modeling

Abstract

Vertical nonreactive solute transport data collected in three laboratory soil columns (made out of sediment samples from the Pampean aquifer located southeast of the Buenos Aires province) are contrasted with the explicit solutions of two model 1D linear PDEs: the classical advection–dispersion equation (ADE), and a fractional advection–dispersion equation (FADE) which has proven to be a useful modeling tool for highly inhomogeneous media exhibiting nontrivial scaling laws. Whereas two of the samples turn out to be quite homogeneous (thus requiring a fractional-derivative order γ → 2), the third one is best described by a FADE with fractional-derivative order γ = 1.68. This example illustrates the FADE’s ability to reveal self-similar geometric structures inside the sample.