A mathematical analysis of the diffusion of the 241Am → 237Np decay chain in the artificial barrier of a high-level radioactive waste repository is presented. First, analytical solutions obtained are for the space- and time-dependent concentration of 241 Am in the artificial barrier and the time-dependent amount of americium precipitated at the surface of the waste glass, based on the assumption of the congruency of the radionuclides with solubility-limited dissolution of the glass matrix. The effects of solubility sharing with coexisting 243Am are considered. Transport and precipitation of 237Np in the artificial barrier are analyzed by dividing the time domain into a small time domain, where the 241Am concentration is so large that 237Np precipitation is dominant, and a large time domain, where the 241Am becomes negligible and the precipitation region shrinks by diffusion from the precipitation front. The equation for the movement of the precipitation front is obtained. As the overpack lifetime increases, the effect of neptunium precipitation becomes less significant. With a lifetime longer than ∼6000 yr, an earlier model, where neptunium is treated as a mother nuclide and the precipitation occurs only at the glass surface, can be used. With the solubility for Np(OH)4, the effect of neptunium precipitation is as small as a factor of 2 in terms of the maximum mass release rate at the outer boundary of the artificial barrier, and the earlier model can be used for safety assessment. With the solubility for NpO2, the current model gives a maximum mass release rate at the outer boundary that is one order of magnitude greater than the previous one.
