Study of Cd transport in undisturbed loamy soil with the FADE model

Accurate expression of the solute transport in porous media is critical for evaluating and remediating pollutants in soils and aquifers. An important aspect of the transport of solutes and pollutants is the use of appropriate models to describe their transport behavior. In this study, the concentration of the heavy metal cadmium in the column of undisturbed loamy soil was measured using the miscible displacement experiment. This experiment was repeated in three initial concentrations (50, 100, and 150 mg/L). Then, Cd metal transport was simulated by fractional advection-dispersion equation (FADE). The breakthrough curves obtained from the simulation of FADE and the results of the experiments were fitted and the effect of C0 on its performance was investigated. The order of fractional differentiation (α), dispersion coefficient (D) and retardation factor (R) in all three initial concentrations were estimated and compared using the inverse modeling. The results showed that the FADE model simulates cadmium transport well with r2=0.98 and RMSE=0.05. The comparison of BTSs fitted by the FADE model and the observed laboratory data also confirms this issue. The order of fractional differentiation (α) obtained by the FADE model for Cd was almost the same and equal to 1.7, which indicated the anomalous and non-Fickian transport of cadmium metal in loamy soil columns. It seems that the lack of effect of C0 on α, which is the main parameter of the FADE model, has caused the performance of FADE to have no special trend with the changes of  C0 and can be ignored. The hydrodynamic dispersion coefficient in the transport of Cd was increased by increasing C0 and its process is non-linear and unpredictable and the relationship between R and initial concentration is inverse.