Fractional lagrangian modeling of non-Fickian radionuclide transport in heterogeneous geological media for Nuclear waste repository safety

The ability to accurately predict long-term radionuclide migration represents a key challenge for the safety assessment of the geological disposal of nuclear waste. The conventional transport models have successfully reproduced radionuclide migration in many repository studies. These models used the processes such as matrix diffusion, sorption, and fracture – matrix interactions. Anomalous transport behavior observed in some heterogeneous geological systems has motivated the exploration of alternative modeling frameworks. This study develops a fractional-order Lagrangian framework to examine the potential influence of sub-diffusion and super-diffusion on radionuclide plume evolution. The framework combines fractional advection-dispersion theory and particle-tracking modeling to yield mechanistic insights into Anomalous Transport. Example results show that memory effects lead to longer breakthrough curves, earlier arrivals than previously anticipated, and longer plumes tailing. Similarly, risk analysis showed that fractional dynamics also led to increased probabilities of exposure within the environment on longer time frames than classical models. Overall, the results indicate that memory effects in fractional dynamics lead to earlier radionuclide arrival times and longer tailing effects compared to classical behavior. As a result, environmental exposure is more probable over longer timescales. This study highlights that the safety assessment of deep geological repositories should account for memory effects. Adopting this approach is essential for creating a rational, defensible, and scientifically credible protection strategy to protect human health and the environment over the millennia following the disposal of nuclear waste. The presented approach offers a complementary framework for investigating anomalous transport behavior and memory effects that may not be explicitly represented in conventional formulations.