New publication: Modelling solute dispersion in periodic heterogeneous porous media: model benchmarking against intermediate scale experiments

Highlights
•Solute transport experiments in heterogeneous porous media, with high quality breakthrough curves accounting for statistical variations.
•Intermediate scale behaviour of dispersion is shown to be non-Fickian.
•A Fickian asymptotic behaviour is identified for large time and space scales.
•A purely advective model with scale-independent coefficient reproduces both non-Fickian and Fickian behaviours at all scales.
Abstract
This paper is devoted to theoretical and experimental investigations of solute dispersion in heterogeneous porous media. Dispersion in heterogenous porous media has been reported to be scale-dependent, a likely indication that the proposed dispersion models are incompletely formulated. A high quality experimental data set of breakthrough curves in periodic model heterogeneous porous media is presented. In contrast with most previously published experiments, the present experiments involve numerous replicates. This allows the statistical variability of experimental data to be accounted for. Several models are benchmarked against the data set: the Fickian-based advection-dispersion, mobile-immobile, multirate, multiple region advection dispersion models, and a newly proposed dispersion model based on pure advection. A salient property of the latter model is that its solutions exhibit a ballistic behaviour for small times, while tending to the Fickian behaviour for large time scales. Model performance is assessed using a novel objective function accounting for the statistical variability of the experimental data set, while putting equal emphasis on both small ad large time scale behaivours. Besides being as accurate as the other models, the new purely advective model has the advantages that (i) it does not exhibit the undesirable effects associated with the usual Fickian operator (namely the infinite solute front propagation speed), and (ii) it allows dispersive transport to be simulated on every heterogeneity scale using scale-independent parameters.