## 4 Results  
### Multi- and Single-Component Simulations on the Metre-Scale  
The difference between MC and SC diffusion was determined depending on mineralogical and geochemical variations in the facies of the Opalinus Clay (Table 1) by quantifying and comparing the resulting migration lengths of uranium. MC diffusion simulations were performed for two model concepts (MC\({}_{4 Clay}\) and MC\({}_{2 Clay}\)), which differ in the clay minerals considered for sorption, to identify the effect of the clay mineral composition on the migration lengths. For all facies, the results of the MC simulations for the two model concepts as well as the SC simulations are shown in Figure 3.  
Differences in the migration length between the MC and SC approach are obvious in all facies. After a simulation time of 100 years, the maximum diffusion lengths determined with the MC diffusion approach ranged from 0.12 m in the shaly (MC\({}_{4 Clay}\), Figure 3a) up to 0.24 m in the sandy facies (MC\({}_{4 Clay}\), Figure 3d). Using the SC diffusion approach, the migration lengths varied between 0.14 m in the shaly (Figure 3a) and 0.23 m in the carbonate-rich facies (Figure 3b). In the shaly and carbonate-rich facies, uranium migrated less far into the Opalinus Clay in the MC simulations compared to SC, whereas, in the sandy facies, it was opposite. The difference in migration length in a facies between the two approaches varied from around 0.07 m less (Figure 3b) up to 0.02 m farther (Figure 3d) into the formation using the MC approach with four clay minerals (MC\({}_{4 CLay}\)). Consideration of only two (MC\({}_{2 Clay}\)) instead of four clay minerals (MC\({}_{4 Clay}\)) for sorption in the MC simulations led to a farther migration of uranium into the model and thus reduced the difference between MC and SC in the shaly (Shaly-76) as well as carbonate-rich facies (Figure 3a,c). However, uranium still migrated less far into the Opalinus Clay compared to the SC approach. For the second mineral composition representing the shaly facies (Shaly-61), uranium migration was roughly 0.01 m less far into the formation, when using only two clay minerals (MC\({}_{2 Clay}\), Figure 3c). In the sandy facies, the migration  
Figure 2: For the model concept considering all clay minerals (kaolinite, illite, montmorillonite and chlorite) for sorption (MC\({}_{4 Clay}\), green line), the modeled results match with the experimental data (dots) of the diffusion experiment with U(VI) and Opalinus Clay of the sandy facies for an exponent n of 2.6. For the model taking into account only the two clay minerals illite and montmorillonite (MC\({}_{2 Clay}\), blue line), n is 2.1.  
lengths changed from 0.02 m farther to 0.08 m less into the formation in the MC simulations compared to the SC (Figure 3d). The results of the MC simulations could be reproduced with the SC approach using the calculated \(K_{d}\) and calibrated \(D_{e}\) given in Table 3 with a deviation between 1% and 6% (average 2%) between the calibrated SC and the MC simulations. In the experiment, a \(K_{d}\) of 0.025 m\({}^{3}\)/kg was identified [17]. All of our calculated \(K_{d}\) values are an order of magnitude smaller and decrease with the clay mineral content, with only a minimal difference in sorption between the sandy and carbonate-rich facies despite the fact that 20 wt.% more clay minerals are in the sandy facies (Table 3). It is to be highlighted that the \(K_{d}\) values (Table 3) of the shaly facies are more than twice as large compared to the sandy and carbonate-rich facies. For all facies, the \(K_{d}\) values and hence sorption were slightly reduced using the MC\({}_{2 Clay}\) scenario. The calibrated \(D_{e}\) range from 1 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s to 2.25 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s (Table 3) for the MC\({}_{4 Clay}\) scenario and thus the experimentally determined value of 1.9 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s from the diffusion experiment of [PERSON] et al. [17] is within our range.