Isolation of high-level radioactive nuclear wastes from the environment is to be ensured by the disposal in deep geological formations . For safety assessments in Germany, it is of particular relevance to demonstrate that the thickness of the containment providing rock zone (CPRZ) is sufficient to retain the radionuclides for time periods of up to one million years. A thickness of at least 100 m is prescribed by law for this purpose (§ 23 Article 5 StandAG

Standortauswahlgesetz (StandAG) of 5 May 2017 (Federal Law Gazette p. 1074) as last amended by Article 1 of the Act of 7 December 2020 (Federal Law Gazette p. 2760). URL: https://www.gesetze-im-internet.de/standag_2017/BJNR107410017.html (last access: 17 June 2022).

Argillaceous formations are among favoured host rocks due to their low permeability only allowing diffusive transport of radionuclides that can be retarded by sorption processes taking place on the surfaces of the inherent clay minerals. Both processes depend on pore water geochemistry and mineralogy. Reactive transport simulations numerically solved with geochemical codes, such as PHREEQC , enable a process-based quantification of diffusion lengths and sorption effects as a function of both, pore water geochemistry and mineralogy, by the application of advanced approaches like surface complexation modelling. For this, comprehensive thermodynamic databases are required including the relevant species, mineral phases, surface complexes, exchangeable species and associated stability constants necessary to describe the investigated geochemical system and radionuclide. Therefore, changes in the underlying thermodynamic data affect simulated migration lengths. A comprehensive and up-to-date thermodynamic database is essential to quantify radionuclide migration lengths by the application of advanced approaches with reactive transport simulations.

Migration of uranium, the main component of spent fuel, in the potential host rock Opalinus Clay has been quantified as a function of mineralogical heterogeneities between three litho-facies (shaly, sandy and carbonate-rich, Fig. ) and for varying partial pressures of carbon dioxide pCO2, within the hydrogeological system at Mont Terri . It has been shown that the application of the process-based multi-component diffusion approach provided no additional profit on the host rock scale. Calculated migration lengths did not differ significantly (±5 m) to simulations following Fick's law, and thus experimentally determined effective diffusion coefficients can be used instead of the computationally intensive multi-component diffusion approach. Sorption must be quantified as a function of the geochemical conditions. Further, the results showed that present-day pore water profiles can be explained by diffusive exchange with the embedding aquifers . Previous simulations were conducted using the PSI/Nagra thermodynamic database including the Nuclear Energy Agency (NEA) data for uranium published by . With this, the anionic ternary uranyl complex CaUO2(CO3)32- is the predominant species in the geochemical system. In 2020, the NEA published an update of the thermodynamic data for uranium including recent data from the literature. In particular, the values for the stability constants of the ternary complexes with calcium and carbonate were revised. As shown by , this might lead to significant changes in the speciation, and thus resulting migration lengths within the various facies of the Opalinus Clay, as uranium speciation is dominated by ternary complexes with calcium and carbonate. For instance, a difference of 1.33 log units in the value for the stability constant of the neutral complex Ca2UO2(CO3)3 changes the migration lengths by 5 to 7 m for the sandy and shaly facies, respectively. The next step, presented here, is the investigation what such a change in underlying thermodynamic data mean in metres difference on the host rock scale after one million years quantified with one-dimensional reactive transport models based on simulations of the hydrogeological system of the Opalinus Clay at Mont Terri . For this, resulting migration lengths are compared between simulations with varying thermodynamic data sets of the NEA for uranium .

One-dimensional diffusion simulations following Fick's laws were conducted with the geochemical code PHREEQC Version 3.5.0 . The thermodynamic data is based on the PSI/Nagra database version 12/07 . This database was updated with the thermodynamic data for uranium recently published by the NEA and supplemented with the sorption data for the hydroxo-complexes of uranium on the inherent clay minerals. This sorption data set is based on published K values and was compiled in the context of an uranium sorption experiment in Opalinus Clay . All surface parameters and reactions can be found in Table 1 of the Supplement of . Aqueous uranium speciation in the modelled system is dominated by ternary complexes with carbonate and calcium that are not considered for sorption . Diffusion and sorption experiments of uranium on clay minerals could be modelled without the requirement to include uranium surface complexes with carbonate as they do not sorb or only weakly . As ionic strengths in the hydrogeological system of the Opalinus Clay at Mont Terri do not exceed 0.5 mol L-1 , the Davies approach is used for the database to represent ion-ion interactions . After closing of the repository, elevated temperatures are expected due to heat generated by the waste packages. However, this does not impact the migration behaviour of uranium . Based on diffusion experiments for 25 and 60 ∘C , it has been shown that diffusion as well as sorption increase with temperature, and thus compensate each other. Furthermore, changes in pore water composition for higher temperatures (45 ∘C) are <5 % . Therefore, all simulations were conducted isothermal for a reference temperature of 25 ∘C according to the database.

The hydrogeological system at Mont Terri is characterised by diffusive exchange over millions of years between the embedding aquifers in the Dogger and Lias and the 210 m thick CPRZ consisting of Opalinus Clay and Liassic shales . The Mont Terri anticline was uplifted during the Jura folding about 10 Ma ago and subsequent erosion enabled freshwater infiltration into both aquifers, and thus activated the current hydrogeological boundaries. Only after erosion of the overlying stratigraphic layers, the footwall aquifer was activated leading to a substantial time lag in freshwater infiltration, and thus to an asymmetric shape of present-day pore water profiles . Based on purely diffusion-driven simulations , modelled profiles match with pore water data measured at the underground laboratory Mont Terri .

The conceptual model applied here is equal to the one presented in despite the application of the updated thermodynamic data for uranium published by the NEA . Therefore, the simulations of the hydrogeological system at Mont Terri presented by were used to represent the initial geochemical conditions in the investigated system as the NEA update only affects the speciation of uranium. Calcium, magnesium, pH and pCO2 are the governing parameters for uranium speciation , and therefore only these modelled profiles are shown as an example for the other pore water components (Fig. ). With differences <15 %, all modelled profiles match with the measured data. Within the CPRZ, pH and pCO2 are coupled via the calcite-carbonate-ion system . The scattering of measured values can be explained by the high sensitivity of both parameters, and thus associated uncertainties with measurements . Therefore, the profiles modelled by with differences <12 % to the measured values were considered as sufficient to represent the initial conditions within the system. The model boundaries were defined by the water composition of the aquifers as Dirichlet-conditions at the model outlets. Numerical stability is ensured by the Neumann criteria. The uranium source term to represent the failed high-level waste canisters is integrated via a mineral equilibrium with uraninite (UO2(am,hyd)) as well as pyrite and siderite to control the redox conditions. The saturation index of uraninite is chosen so that a concentration of 1 µmolL-1 is applied in the centre of the model according to and . For further details on the conceptual model as well as initial and boundary conditions for the simulation of the hydrogeological system, we refer to .

Sorption is integrated via a bottom-up approach using surface complexation models based on the two-layer model of as well as cation exchange . An average clay mineral composition of 66 wt. % is used for the entire CPRZ as the geochemistry of the pore water is more decisive for uranium sorption processes than the amount of clay minerals . The individual clay mineral quantities of illite, montmorillonite and kaolinite as well as the values for the hydro-physical parameters are equal to . The distribution coefficient Kd (m3 kg-1) is calculated from the PHREEQC results and used to evaluate the differences in the sorption capacity. The Kd is defined as ratio between the species concentration adsorbed on the solid phase and present in the liquid phase. Diffusion processes are quantified following Fick's law using the De with a value of 1.9×10-12 m2 s-1 as determined by in an uranium diffusion experiment with Opalinus Clay. In previous studies , the present conceptual model was calibrated against this experiment. The neutral ternary complex was identified as predominant species in the diffusion experiment based on speciation calculations using stability constants similar to the NEA data of . The De of was used for all simulations. Accordingly, anion exclusion effects that would be reflected by a reduction of Dp are not considered. In the literature, no data on the anion-accessible porosity ratios for the different ternary uranyl complexes are available. Therefore, the reduction of Dp can only be estimated based on the porosity ratio for other species, like chloride. Furthermore, process-based simulations using the multi-component diffusion approach, which takes the interaction of charged species with the diffuse double layer into account , showed for the hydrogeological system at Mont Terri that anion exclusion effects only have a minor impact on the resulting migration lengths of uranium .

The impact of the second NEA update for the thermodynamic data for uranium on the migration behaviour is quantified for the example of the geochemically heterogeneous Opalinus Clay system at Mont Terri. This is done by comparing resulting migration lengths with equal simulations except for the application of the first NEA update .

Speciation calculations for the pore water composition of the shaly facies, i.e. at a depth of 140 m corresponding to the highest ionic strength (Fig. ), showed that the predominant species changes from anionic to almost only the neutral ternary complex (Table ). This is in line with speciation measurements done in the frame of an uranium diffusion experiment with Opalinus Clay . The change in the predominant species (Table ) is associated with a farther migration of uranium of up to 30 m (Fig. a) due to a decrease in the sorption capacity (Fig. b). This can only be explained by the speciation, in particular the stronger complexation of uranium with calcium and carbonate (Table ) with the application of the second NEA update , as the same De was used for all simulations. Anion exclusion effects are not taken into account as the composition of the diffuse double layer is only used in the model concept to counterbalance the surface charge. With the first NEA update , about 94 % of uranium is present as ternary complexes as can be read from the percentages given in Table . However, this percentage proportion increases to almost 100 % with the second update . This, in turn, means that uranium increasingly forms ternary complexes, and thus less uranyl-ions are in total available to be retarded by sorption processes on the clay minerals (Table ). The sorption capacity or Kd value, respectively, decreases and migration lengths increase (Fig. ), because only uranyl ions are considered for sorption in the database. Consequently, the uranyl concentration in the modelled system has a huge impact on the sorption effects and ultimately on the calculated migration lengths.

Maximum migration distance of uranium is 80 m after one million years. The retention capacity of the Opalinus Clay seems to be sufficient to retain uranium, since concentrations close to the aquifers do not exceed the natural background concentration (Fig. a). However, the total thickness of the CPRZ is >200 m in the investigated scenario. In Germany, one of the minimum requirements defined by law (§ 23 Article 5 StandAG1) is a thickness of at least 100 m for the CPRZ, regardless of the host rock type: argillaceous formation, crystalline or salt rock. This does not imply that such a thickness is sufficient in any case. Assuming that a potential repository is constructed in the centre, this would mean for the investigated case that uranium reaches adjacent aquifers as the retention capacity of the CPRZ is not sufficient. In this case, the site would not be suitable, because the safety requirements are not fulfilled. Should a thickness of at least 200 m therefore be favoured to fulfill safety requirements? The underground rock laboratory Mont Terri solely serves for the investigation of the Opalinus Clay as host formation. The site was and will never be considered as a potential disposal site due to its specific geological structure. For instance, the geochemical gradients at the potential disposal sites in Switzerland are less pronounced compared to Mont Terri . Sorption would decrease less towards the aquifers leading to reduced uranium migration. Hence, the impact of the hydrogeological system at the potential disposal sites on the migration lengths is diminished compared to Mont Terri. Furthermore, our simulations have to be considered as maximum scenarios as the impact of the engineered barriers is not taken into account . They are supposed to minimize the source term concentration. Accordingly, the concentration gradient in Fick's laws is smaller and so diffusive transport. Site-specific analyses of the hydrogeological system as well as a more realistic integration of the source term concentration is required in order to calculate migration lengths of uranium at a potential disposal site. Nevertheless, our work shows how sensitive migration lengths resulting from reactive transport simulations are to the model conceptualization as well as selection of underlying thermodynamic data. Consequently, compilation and further development of comprehensive data sets is required and a site specific analyses of the hydrogeological system indispensable.

The impact of thermodynamic data on migration lengths resulting from reactive transport simulations is quantified for the example of uranium in the hydrogeological system of the Opalinus Clay at Mont Terri. In the geochemical system, speciation is controlled by the calcite-carbonate-ion system. In the pore water, uranium is mainly present as U(VI) as ternary complexes with calcium or magnesium together with carbonate. Previous simulations using the first NEA update of thermodynamic data for uranium indicated that the anionic complex CaUO2(CO3)32- is the predominant species with a maximum distance of 50 m after one million years. The NEA published an update of the thermodynamic data for uranium, what, in turn, changes the predominant species from anionic to almost only the neutral ternary complex Ca2UO2(CO3)3. With identical simulations, except for the application of the second NEA update, a maximum distance of 80 m was obtained. Consequently, the impact of the change in the underlying thermodnamic data can be quantified with +30 m.

A stronger complexation of uranium with calcium and carbonate decreases sorption capacity. Sorption is quantified for the uranyl-hydroxo complexes. Due to the stronger complexation of uranium with calcium and carbonate with the application of the second NEA update, less uranyl-ions are in total available for sorption. This, in turn, decreases the sorption capacity, as shown by calculated Kd values, and leads to a farther migration through the formation.

The presented simulations show, how sensitive migration lengths of uranium resulting from reactive transport simulations are to the model concept, underlying thermodynamic data and applied approaches. Consequently, a site specific analysis of the hydrogeological system at potential disposal sites in combination with a comprehensive and up-to-date database are required to conduct reliable and powerful process-based simulations to quantify radionuclide migration lengths.