Flow and transport in the vadose zone: On the impact of partial saturation and Peclet number on non-Fickian, pre-asymptotic dispersion

Transport phenomena in unsaturated porous media still present an important research topic. In particular, in the context of recent environmental concerns, further understanding of contaminant transport in the partially saturated vadose zone is necessary. However, there is currently a lack of understanding of the relationship between water saturation, in particular the two-phase distribution, and dispersion. This is due to the intricate interactions between the two-phase flow and the porous structure, as well as the complexity of the experimental techniques, which prevents a significant number of configurations from being analysed.

We explore passive tracer transport in two-dimensional unsaturated porous media via experimental and numerical methods. To this goal, we conduct co-injection experiments to produce two-phase distributions (air/water) at different saturations in a transparent micromodel that mimics the topology of the Bentheimer sandstone. From these experiments, we generate images using multi-scale multiple-point statistics modelling (MPS). Employing the Lattice Boltzmann method, we calculate velocity and concentration fields for both experimental and generated images under saturated and unsaturated conditions. Our results show strong similarities in velocity distributions, good agreement in concentration profiles, and a matching of dispersion characteristics between experimental and MPS-generated images. MPS enables us to create a variety of unsaturated porous media structures with different topologies but similar transport properties. From these images, we analyse transport over a large range of saturations and Peclet numbers. We observe pre-asymptotic non-Fickian transport regimes characterized by a variance increasing with time according to a power law with exponent $\alpha >1$. We find that $\alpha$ increases as saturation decreases, due to enhanced flow heterogeneity, and with higher Peclet numbers. This behaviour is confirmed through large-scale simulations.