Contaminant transport in soil with depth-dependent reaction coefficients and time-dependent boundary conditions

Predicting the fate and movement of contaminant in soils and groundwater is essential to assess and reduce the risk of soil contamination and groundwater pollution. Reaction processes of contaminant often decreased monotonously with depth. Time-dependent input sources usually occurred at the inlet of natural or human-made system such as radioactive waste disposal site. This study presented a one-dimensional convection-dispersion equation (CDE) for contaminant transport in soils with depth-dependent reaction coefficients and time-dependent inlet boundary conditions, and derived its analytical solution. The adsorption coefficient and degradation rate were represented as sigmoidal functions of soil depth. Solute breakthrough curves (BTCs) and concentration profiles obtained from CDE with depth-dependent and constant reaction coefficients were compared, and a constant effective reaction coefficient, which was calculated by arithmetically averaging the depth-dependent reaction coefficient, was proposed to reflect the lumped depth-dependent reaction effect. With the effective adsorption coefficient and degradation rate, CDE could produce similar BTCs and concentration profiles as those from CDE with depth-dependent reactions in soils with moderate chemical heterogeneity. In contrast, the predicted concentrations of CDE with fitted reaction coefficients at a certain depth departed significantly from those of CDE with depth-dependent reactions. Parametric analysis was performed to illustrate the effects of sinusoidally and exponentially decaying input functions on solute BTCs. The BTCs and concentration profiles obtained from the solutions for finite and semi-infinite domain were compared to investigate the effects of effluent boundary condition. The finite solution produced higher concentrations at the increasing limb of the BTCs and possessed a higher peak concentration than the semi-infinite solution which had a slightly long tail. Furthermore, the finite solution gave a higher concentration in the immediate vicinity of the exit boundary than the semi-infinite solution. The applicability of the proposed model was tested with a field herbicide and tracer leaching experiment in an agricultural area of northeastern Greece. The simulation results indicated that the proposed CDE with depth-dependent reaction coefficients was able to capture the evolution of metolachlor concentration at the upper soil depths. However, the simulation results at deep depths were not satisfactory as the proposed model did not account for preferential flow observed in the field.