A stochastic multi-scale approach to study contaminant transport in heterogeneous alluvial sediments

Equiprobable spatial distributions of hydrofacies can be modelled by stochastic simulations, conditioned on field data. Such 3D arrays can be used as input data in numerical models of groundwater flow and contaminant transport, which can be used to assess how the fine scale heterogeneity affects contaminant transport at large scale. The most common stochastic simulation method is Sequential Indicator Simulation (SISIM). Despite being widely used, SISIM suffers some weaknesses, e.g., in integrating geological information and in reproducing structures with curved shapes. This work deals with a modification of SISIM with a hierarchical approach (HSISIM), which consists in the repeated application of SISIM to perform binary simulations at different hierarchical levels. The advantages of this approach are (1) the possibility of designing a hierarchy based on geological information and (2) the shorter simulation time than for the standard approach, because the time required by SISIM dramatically increases with the number of hydrofacies that are simultaneously simulated. We illustrate the advantages of the proposed hierarchical method over the standard SISIM using the hydrofacies mapped on the sides of three blocks of glacio-fluvial sediments that were dug in a open air quarry in the Ticino valley (Northern Italy). Each block has a volume of few cubic meters and most of their lateral sides have been analyzed and mapped from the sedimentological point of view with a resolution of 5 cm. From the three field data sets, different ensembles were obtained both with SISIM and with two different HSISIM applications: the first one based on the relative abundance of the hydrofacies; the second one based on geological arguments. Then, the results of the geostatistical simulations were used to perform numerical transport experiments that yielded the statistical distribution of average pore water velocity and effective longitudinal dispersion coefficients at a scale length of the order of 1 m. Finally, these probability distributions were used to predict the fate of toxic and radioactive contaminants over a length scale of 100 m with a 1D stochastic model of solute transport model based on the Kolmogorov-Dmitriev theory in a Montecarlo framework. The results confirm that a proper estimate of contaminant transport requires a precise reconstruction of the heterogeneity field at the fine scale.