Solute transport in periodical heterogeneous porous media: Importance of observation scale and experimental sampling

- Tracer dispersion in a strongly heterogenous porous medium is studied.
- No significant scaling trend is identified for the dispersion coefficient.
- The advection-dispersion model is invalid for small spatial scales.
- There exists a valid transport model with scale-independent coefficients.

SummaryThis paper focuses on the effects of the observation scale and sampling on the dispersion of tracers in periodical heterogeneous porous media. A Model Heterogeneous Porous Medium (MHPM) with a high degree of heterogeneity was built. It consists of a preferential flow path surrounded by glass beads. 44 tracer experiments were carried out on several series of periodic MHPM to investigate the effect of the observation scale on solute dispersion. Each series was replicated several times, allowing for a statistical description of the unit transfer function of the MHPM. No significant trend was found for the dispersion coefficient as a function of the size of the MHPM. However, given the variability of the breakthrough curves from one experiment replicate to another, under-sampling might easily lead to conclude that the dispersion coefficient is variable with distance. Depending on the samples used, it would be as easy to (wrongly) detect an increasing trend as to detect a decreasing one. A confidence interval analysis of the experimental breakthrough curves in the Laplace space shows that (i) there exists a model with scale independent parameters that can describe the experimental breakthrough curves within the limits of experimental uncertainty, (ii) this model is not the advection-dispersion (AD) model, (iii) the modelling error of the AD model decreases with the number of periods, (iv) the size of the Reference Elementary Volume for the dispersion coefficient is between 10 and 20 periods. The effects of sampling prove to override those of scaling. This, with the invalidity of the AD model, leads to question attempts to calibrate and/or identify trends in the dispersion coefficient at intermediate scales from a limited number of experiment replicates.