Simulating Three-Dimensional Plume Migration of a Radionuclide Decay Chain through Groundwater

Abstract

In this study, we present a semi-analytical model for simulating three-dimensional radioactivity transport of a radionuclide decay chain and assessing the radiological dose impact on the general public. The mechanisms and processes considered in the model include the one-dimensional advection, hydrodynamic dispersion in longitudinal and two lateral directions, linear equilibrium sorption, and first-order radioactive decay reactions. The semi-analytical model is derived for a semi-infinite domain, and the solutions in the Laplace domain for members of the decay chain are first generalized in a compact format. The concentrations in the original domain of each nuclide are independently evaluated with the help of the efficient and robust Laplace numerical inverse algorithms. The accuracy of the derived semi-analytical model is demonstrated by comparison of our developed model with an existing analytical model described in the literature. The results of the verification exercise indicate that the derived semi-analytical model is accurate and robust. The developed semi-analytical model is applied to an illustrative example that simulates the three-dimensional plume migration of a radionuclide decay chain on both the temporal and spatial scales. Moreover, the time histories of the radiological doses at different distances from the inflow source boundary are presented to understand the potential radiological impact on the general public. The developed model facilitates rapid assessment of the radiological impact posed by the presence of radionuclides in the environment because of leakage from a nuclear waste repository or accidental discharges from nuclear facilities.

Keywords

• analytical model
• radionuclide decay chain
• advection–dispersion equation
• first-order decay reaction
• radiological dose