## 5 Discussion
### Implications for the Host Rock Scale  
We developed a workflow to set-up surrogate models on the metre-scale for efficient application on the host rock scale. As the previously investigated MC scenarios could be reproduced on the metre-scale with the SC approach using the calibrated \(K_{d}\) and \(D_{e}\) (Figures 3 and 5), the application to the host rock scale was evaluated by comparison with a representative MC simulation for each facies and for a simulation time of one million years (Figure 6). The MC\({}_{4 Clay}\) simulations could be reproduced on the host rock scale with the transport parameters calibrated on the small scale with a deviation between 2% and 4% (Figure 6). Scale invariance enables the application of the calibrated \(K_{d}\) and \(D_{e}\) from the metre-scale to the host rock scale. The properties of a state and chemical processes remain largely or exactly the same and universality is given. Based on our presented modeling workflow, transport parameters for varying mineralogy and chemistry can therefore be determined. Since SC simulations using the calibrated transport parameters only required a few seconds (<10 s) of computing time, this represents time saving on the order of \(10^{4}\) for the host rock scale compared to full complexity MC simulations, which require up to 6 h (=21,600 s). This improvement enables performing 'MC' diffusion simulations on the host rock scale, for instance for a sequence of facies or in 2D models, with acceptable computing times and without numerous previous experiments otherwise required. Uranium migration in Opalinus Clay is facies-dependent and its diffusion length is constrained by the rock type itself (shaly, sandy, carbonate-rich), as well as by the respective internal heterogeneity of varying mineral amounts and compositions. On the host rock scale, this results in an offset of up to 25 m between the shaly facies with a maximum amount of clays and the sandy facies with a minimum amount of clays (Figure 6a,d). Within the sandy facies for instance, variations in porosity and bulk densities led to a deviation between the diffusion lengths of up to 13 m (Figure 6d). In contrast, the diffusion lengths in the shaly facies varied by 5 m (Figure 6a) and in the carbonate-rich one even only by 2 m (Figure 6b). Due to the high amount of clay minerals in the shaly facies, heterogeneities are buffered, whereas in the carbonate-rich variations in the hydro-physical parameters are less effective because of the low clay content in combination with the porewater composition. In the case of the sandy facies, the heterogeneity within the individual facies causes a higher uncertainty regarding the diffusion lengths compared to the shaly and carbonate-rich. Our simulation results demonstrate the effect of hydro-physical parameters and the amount of clay minerals on migration, especially on the transport properties. This influence of heterogeneity on transport properties does not only apply to the Opalinus Clay, but it is likely that this is also the case for any other clay formation. In any case, detailed measurements are required because facies or clay formations in general can vary immensely in their properties on the dm-scale, e.g., for the Opalinus Clay through clay layers within the sandy facies and vice versa [51]. It is shown for the sandy facies, compared the shaly and carbonate-rich ones, that, with decreasing clay content within the rock, the variation in mineral composition and its effect on the porewater chemistry and with that on the transport behaviour of uranium increases. On the host rock scale, it becomes obvious that the shaly facies is best suited for the storage of nuclear waste followed by the carbonate-rich and sandy ones due to the shorter diffusion lengths. The high amount of clay minerals in the shaly facies (\(>\)50%) dominates diffusion and sorption processes and hence better compensates chemical and mineralogical heterogeneities compared to the other facies, which is apparent from the shorter diffusion lengths and their smaller span.