Simplifying solute transport modelling of the geological multi-barrier disposal system

A simplified model was developed to represent radionuclide migration from a deep geological nuclear waste repository system to the biosphere. The modelled repository system is based on the concept of multiple nested transport barriers. The model can be used to assess migration and migration properties of single nuclides (no decay chains) through the repository system. Radionuclide transport processes included to the model are diffusion and sorption in the repository near-field and advection, matrix diffusion and sorption in the geosphere. A simplified approach to handle solubility limited release of the nuclide from the waste canister is included into the model. The model treats transport barriers as well-mixed volumes. It is also assumed that radionuclide outflow from a barrier can be calculated by neglecting radionuclide concentration in the target barrier. Radionuclide transport through the simplified system can be calculated by applying formal analogy of the model to the mathematical model of the radioactive decay chain. Simplifying the barriers as well-mixed volumes suggests that they can be characterised by simple performance measures. Radionuclide outflow from the barrier can be represented by an equivalent flow rate, which is an apparent volumetric flow rate that combined with the radionuclide concentration in the barrier gives the outflow rate of the nuclide. Temporal behaviour of the release rate can be described by two time constants: i) compartment half-life of the nuclide concentration calculated by dividing capacity of the barrier (the total pore volume multiplied by the retardation factor) with the equivalent flow rate and ii) delay time for start of the outflow from barrier after beginning of the inflow to barrier. Performance of the simplified approach to produce actual release rates for different nuclides was tested by modelling C-14, I-129 and Pu-239 using data from the RNT-2008 radionuclide migration analysis. Accuracy of the simplified approach is challenged if the nuclide’s half-life is not long compared to the time required for the development of perfectly mixed solute concentration field in the barrier. The nuclide and barrier combinations that are prone to this behaviour can be identified by comparing the estimated compartment delay time with the nuclide’s radioactive half-life. The simplified model performed well for the C-14 and I-129, as expected based on the measures above. Early transients of the concentration field in the buffer and in the geosphere are important for the transport of Pu-239 in the calculated case. The simplified model gave results for Pu-239 that were roughly of the same order of magnitude than the corresponding numerical results.