One‐dimensional analytical solutions for the migration of a three‐member radionuclide decay chain in a multilayered geologic medium

Abstract

Analytical solutions are presented for the one‐dimensional convective‐dispersive and nondispersive equilibrium transport equations of a three‐member radionuclide decay chain in a multilayered porous media. The solution for the nondispersive case is exact. The solution for the general case, although analytic in the first layer, takes a semianalytical form in the subsequent layers by virtue of its numerical integration requirements. The solutions are based on the Laplace transformation technique. Two types of boundary conditions are considered at the source, i.e., a continuous and a band release mode. The accuracy of the solutions was satisfactorily tested on a selected number of problems for which experimental and analytical solutions were available. The practical use of the solutions in a two‐dimensional domain is illustrated by a scenario of radionuclide migration from a high‐level waste repository located in a saturated multilayered aquifer.