Upscaling of solute transport in mildly heterogeneous media. Comparison of Fickian and non-Fickian approaches

Non-Fickian solute transport models were investigated in the case of mildly heterogeneous porous media using a synthetic two-dimensional In(K) field, generated randomly. Transport was fully solved using MT3D and exhibited scale-dependence. Monte Carlo simulations were used to quantify uncertainty in the absence of a priori data. Then, inverse and direct modelling using the continuous time random walk approach and the fractional advection-dispersion equation were performed in order to assess the upscaling capacities of these models. A sensitive improvement could be observed compared to the classical advection-dispersion model.