Solute Trapping and the Mechanisms of Non-Fickian Transport in Partially Saturated Porous Media

We study the upscaling of pore-scale solute transport in partially saturated porous media at different saturation degrees. The interaction between structural heterogeneity, phases distribution and small-scale flow dynamics induces complex flow patterns and broad probability distributions of flow, which control key aspects of transport, such as residence and arrival times, dispersion, and spatial solute distributions, as well as chemical reactions. A continuous-time random walk (CTRW) framework that integrates the processes of advection, diffusion, and trapping in immobile zones is used to upscale and evaluate the transport of diluted solutes. Results of this model were compared to direct numerical simulations solving the advection-diffusion equation in experimental saturation patterns. The comparison between simulations results, with different Peclet numbers (Pe), and the physics-based upscaled CTRW approach allows for a quantitative analysis of the governing factors of transport in partially saturated porous media. This analysis shows that the fluid phase saturation decreases the advective tortuosity, the media's characteristic length, the fraction of the immobile region, and the mean trapping time. At the same time, for a given saturation degree, the normalized mean trapping time is proportional to the Pe. This suggests that the characteristic trapping length is proportional to the media's characteristic (correlation) length. Moreover, the trapping frequency decreases with increasing Pe.