Laplace Transformed Analytical Solution of Aqueous Radionuclide Transport via Heterogeneous Geological Formations for Arbitrary Length Decay Chain

We present the analytical solution to the one-dimensional radionuclide transport equation in Laplace transform space. Our model accommodates an arbitrary-length decay chain, an arbitrary combination of host rocks (i.e., an arbitrary combination of multiply fractured and porous transport segments), and a flexible source term (i.e., an arbitrary time-dependent release mode at the entrance point to the series of transport segments). The Laplace transformed analytical solution can be numerically inverted to obtain the time-dependent concentration of the radionuclides of interest at an arbitrary down gradient location. This represents an extension of the previously1 developed model to include the feature of hydrodynamic longitudinal dispersion. This additional feature is important because hydrodynamic dispersion is known to reduce the time of first arrival in radionuclide transport models. Increased fidelity in transport pathway calculations is important for reliable performance assessment for the geological disposal of spent nuclear fuels.