Dispersivity-Saturation relationship for various porous media; Experiments and modelling

Abstract

Dispersion of solutes has been studied widely in saturated porous media. However, unsaturated porous media lacks substantial experimental data to provide correlation on the saturation-dependency of hydrodynamic dispersion. This study aims to provide experimental data through CaCl$_2$ injections in unit hydraulic gradient unsaturated sandy porous media at lab-scale columns (z = 37 cm). Dispersivity ($\alpha$) as a function of wetting phase saturation (S$_w$) are extracted from measured electrical conductivity at equidistant depths along the column. Results show a clear non-monotonic $\alpha-S_w$ relation, with a maximum dispersivity of 1.32 cm at a saturation (S$_w$) of 0.43 [-] for a porous medium with D$_{50}$ of 500 $\mu$m. For both S$_w$ \textless 0.39 and S$_w$ \textgreater 0.43, $\alpha$ decreases. For higher saturations, $\alpha$ decreases until a saturated $\alpha$ of 0.05 cm. For lower saturation, $\alpha$ decreases until only diffusion is the dominant process of solute displacement. Tailing is observed in all unsaturated experiments, indicating stagnant zones in the flow domain. Comparison with literature shows a resemblance for dispersivity values corresponding to S$_w$ \textgreater 0.43. For S$_w$ \textless 0.43, experimental results by this study confirm numerical porenetwork results by \citet{Raoof2013Saturation-dependentProcesses} and experimental results by \citet{Toride2003HydrodynamicSand}. The accuracy of dispersivity over the entire range of saturation resulted in a general equation describing the phenomenon. Dispersivity is calculated as a function of wetting phase saturation for a specific set of constants a,b, and c by $ \alpha = ae^{(-(\frac{S_w - b}{c})^2)} $. An approach for scaling the results of this study through intrinsic soil parameters is proposed. Hopefully, results from this study help improve accuracy of contaminant, virus, and colloids fate and transport in the unsaturated zone.