## 5 Discussion
### Differences between Single- and Multi-Component Diffusion Approach  
Based on the migration lengths of uranium, differences between the SC and MC diffusion approach were quantified on the metre-scale. For the MC\({}_{4 Clay}\) concept, uranium migrated less far into the model for all facies using the MC approach except for the sandy facies, where it migrated farther (MC\({}_{4 Clay}\), Figure 3). We presume that not only sorption processes of uranium are facies-dependent in the Opalinus Clay [11], but also the diffusive transport. The difference is the DDL enveloping the clay mineral surfaces in the calculation with the MC approach. The effect of anion exclusion reduces uranium migration in the MC diffusion approach. In our simulations, the anionic complex \(CaUO_{2}(CO_{3})_{3}^{2-}\) is the predominant species in the porewater of the Opalinus Clay because of the geochemical system [11]. Due to the negatively charged surfaces of the clay minerals mainly cations are enriched in the respective DDL decreasing the accessible pore space for anionic species and thus reducing their diffusive transport [41; 46; 5]. For the MC\({}_{4 Clay}\) simulations, anion exclusion decreased uranium diffusion by about 0.02 m in the shaly and 0.07 m in the carbonate-rich facies corresponding to about 14% and 30% reduction compared to SC, respectively (Figure 3). Thus, for the shaly facies, our results contradict the estimate of [PERSON] et al. [11] that diffusion lengths are reduced by 30% due to anion exclusion. However, the estimate applies for the carbonate-rich facies. The accessible pore space directly depends on the ionic strength of the porewater with a decreasing thickness of the DDL with increasing ionic strength [36; 41]. Therefore, anion exclusion and with it the deviation in migration lengths between the SC and MC approach are different in the shaly and carbonate-rich facies (Figure 3a-c). Due to the lower ionic strength in the carbonate-rich compared to the shaly facies, the DDL is about 0.1 nm thicker (Shaly-76 and Carb-rich, Table 1) and thus anion exclusion is stronger. Accordingly, the deviation between both approaches should be the greatest in the sandy facies with the thickest DDL (Table 1). However, in the case of the sandy facies, uranium migrates farther instead of less into the model for the MC\({}_{4 Clay}\) simulation compared to the SC (Figure 3d). Only for the MC\({}_{2 Clay}\) scenario the sandy facies compares with the others as uranium migration is also reduced by 0.08 m, equivalent to about 30%. Therefore, anion exclusion is only one of the effects that explains the deviation in migration lengths between the two approaches. For the shaly as well as carbonate-rich facies, uranium migration is overestimated using the SC approach due to anion exclusion. A general estimate, how strong anion exclusion reduces the diffusion lengths cannot be made because of the dependence on the porewater chemistry. However, the reduced diffusion length due to anion exclusion determined here is an estimate for other clay formations with similar geochemistry and mineralogy. Uranium mainly sorbs on illite and montmorillonite. The investigated model concepts, MC\({}_{4 Clay}\) and MC\({}_{2 Clay}\), differ in their composition of clay minerals selected (Section 2.2). MC\({}_{4 Clay}\) is considered with the four clay minerals chlorite, kaolinite, illite and montmorillonite, whereas in the MC\({}_{2 Clay}\) model only the minerals illite and montmorillonite are taken into account for sorption. The \(K_{d}\) values calculated in PHREEQC and thus the sorption capacity of the individual facies (Table 3) decrease with the amount of illite and montmorillonite and hence the clay content in general (Table 1). Accordingly, the sample Shaly-76 has the highest sorption capacity followed by Shaly-61, sandy and carbonate-rich with the lowest (MC\({}_{4 Clay}\), Table 3).