One important aspect in long-term safety assessments for radioactive waste disposals is related to radionuclide transport in geologic formations. To assess the influence of migration and retardation over time frames of one million years numerical models describing flow and transport are applied. In addition to solubility constraints, sorption on mineral surfaces is the most relevant process retarding radionuclide transport. On the one hand, an increased transport time might cause a decrease in radionuclide concentration by radioactive decay. On the other hand, it might increase concentrations of dose-relevant daughter nuclides in decay chains.

To treat radionuclide sorption processes in natural systems as close to reality as possible the smart Kd‑concept is implemented into the flow and transport program d3f++. The code is designed for large model areas and very long time scales as being typical in long-term safety assessment. In the first stage, this approach is developed for a representative sedimentary system covering rock salt and clay formations in Northern Germany  (System).

The smart Kd‑values are based on mechanistic surface complexation models (SCM) and ion exchange (IEx), varying in time and space and depending on actual geochemical conditions, which might change in future e. g. due to the impact of climate changes. The concept developed and introduced here is based on a feasible treatment of the most relevant geochemical parameters in the transport code as well as on a matrix of smart Kd‑values (Concept).

The current state of the concept comprises

  • the selection of relevant elements (radioactive contaminants and background components) and minerals to be considered,
  • an experimental program to fill data gaps of the thermodynamic sorption database,
  • an uncertainty and sensitivity analysis to identify the most important environmental parameters influencing sorption of long-term relevant radionuclides,
  • the creation of a matrix with Kd-values dependent on the selected environmental parameters, and
  • the development and implementation of the conceptual model for treatment of temporal and spatial changes of the geochemical conditions.

The implementation of this concept into the flow and transport code d3f++, is verified by two kinds of test cases:

  • 1D test cases are used to check the plausibility of the development in a relatively simple system, where chemical changes cause dissolution or precipitation of calcite, which in turn affect the pH-value, the DIC and Ca concentrations. In consequence the Kd-value and therewith the transport of the radionuclides are impacted. The results of the 1D calculations are plausible showing the applicability of this approach to implement the smart Kd‑concept.
  • One 2D test case is considered, too, and results show that the method is able to describe long-term chemical changes in large model areas including their impact on radionuclide sorption.


A further positive aspect is that both test case calculations are performed with acceptable computing time.