Simulating Anomalous Migration of Radionuclides in Variably Saturation Zone Based on Fractional Derivative Model

The migration of radioactive waste in geological environments often exhibits anomalies, such as tailing and early arrival. Fractional derivative models (FADE) can provide a good description of these phenomena. However, developing models for solute transport in unsaturated media using fractional derivatives remains an unexplored area. This study developed a variably saturated fractional derivative model combined with different release scenarios, to capture the abnormal increase observed in monitoring wells at a field site. The model can comprehensively simulate the migration of nuclides in the unsaturated zone (impermeable layer)—saturated zone system. This study fully analyzed the penetration of pollutants through the unsaturated zone (retardation stage), and finally the rapid lateral and rapid diffusion of pollutants along the preferential flow channels in the saturated zone. Comparative simulations indicate that the spatial nonlocalities effect of fractured weathered rock affects solute transport much more than the temporal memory effect. Therefore, a spatial fractional derivative model was selected to simulate the super-diffusive behavior in the preferential flow pathways. The overall fitness of the proposed model is good (R2 ≈ 1), but the modeling accuracy will be lower with the increased distance from the waste source. The spatial differences between simulated and observed concentrations reflect the model’s limitations in long-distance simulations. Although the model reproduced the overall temporal variation of solute migration, it does not explain all the variability and uncertainty of the specific sites. Based on the sensitivity analysis, the fractional derivative parameters of the unsaturated zone show higher sensitivity than those of the saturated zone. Finally, the advantages and limitations of the fractional derivative model in radionuclide contamination prediction and remediation are discussed. In conclusion, the proposed FADE model coupled with unsaturated and saturated flow conditions, has significant application prospects in simulating nuclide migration in complex geological and hydrological environments.