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Simple steady-state solutions of radionuclide migration of a decay chain through a porous medium by focusing on the similarities with the sequential radioactive decay formulas

Takahashi, Yuta*; Oe, Toshiaki*; Wakasugi, Keiichiro

Simple equations of radionuclide chain migration in semi-infinite porous medium are presented. The exact mathematical expressions on the non-steady migration of nuclides in radioactive decay chains have complex structures and are impractical for quick check of the hazardous impacts driven by the chain migration. The maximum hazard is, actually, a main interest and that maxima can be given by a steady concentration. For this interest, rather simple equations which indicate the maximum concentrations of parent, daughter and grand-daughter nuclides are given for the three different constant boundary conditions; Dirichlet, Neumann, and Robin conditions. The equations are quite similar to the sequential radioactive decay formulas and applicable to overview the effect of the parameter variations such as groundwater flow, sorption characteristics, hydrodynamic dispersion, etc.

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