1-D modeling of radionuclide transport via heterogeneous geological formations for arbitrary length decay chains using numerical inversion of Laplace transforms

We present the Laplace-transformed analytical solution (LTAS) to the one-dimensional radionuclide transport equation for an arbitrary length decay-chain through an arbitrary combination of multiply fractured and porous transport segments subject to an arbitrary time-dependent release mode at the entrance point to the series of transport segments. The LTAS may be numerically inverted to obtain the time-dependent concentration of the radionuclides of interest at an arbitrary down gradient location. For a special case, where the source function is defined as the band release with a single radionuclide without precursors, the Laplace inverse transformation could be performed analytically, yielding a closed-form analytical solution. A computer code, TTBX, has been developed by implementing the LTAS, and benchmarked against the closed-form analytical solution. Numerical examples are presented to demonstrate the utility of these solutions and the importance of increased fidelity in the transport pathway for reliable performance assessment for the geological disposal of spent nuclear fuels.