Comparison of theory and experiment for solute transport in weakly heterogeneous bimodal porous media

In this work, the influence of non-equilibrium effects on solute transport in a weakly heterogeneous medium is discussed. Three macro-scale models (upscaled via the volume averaging technique) are investigated: (i) the two-equation non-equilibrium model, (ii) the one-equation asymptotic model and (iii) the one-equation local equilibrium model. The relevance of each of these models to the experimental system conditions (duration of the pulse injection, dispersivity values…) is analyzed. The numerical results predicted by these macroscale models are compared directly with the experimental data (breakthrough curves). Our results suggest that the preasymptotic zone (for which a non-Fickian model is required) increases as the solute input pulse time decreases. Beyond this limit, the asymptotic regime is recovered. A comparison with the results issued from the stochastic theory for this regime is performed. Results predicted by both approaches (volume averaging method and stochastic analysis) are found to be consistent.