## 4 Results
### Multi-Component Diffusion for Varying Total Amounts of Minerals on the Metre-Scale  
The migration of uranium as a function of the variability of hydro-physical parameters, e.g., porosity or dry bulk density, and the resulting amounts of minerals within a facies of the Opalinus Clay were simulated in minimum and maximum scenarios (MC_max_ and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Parameter** & **Shaly-76** & **Shaly-61** & **Sandy** & **Carb-Rich** \\ \hline MC\({}_{4 Clay}\) & \(K_{d}\) (\(10^{-3}\) m\({}^{3}\)/kg) & 4.04 & 3.09 & 1.55 & 1.43 \\  & \(D_{e}\) (\(10^{-12}\) m\({}^{2}\)/s) & 1.50 & 1.60 & 2.25 & 1.00 \\ \hline MC\({}_{max}\) & \(K_{d}\) (\(10^{-3}\) m\({}^{3}\)/kg) & 4.04 & 3.09 & 1.55 & 1.43 \\  & \(D_{e}\) (\(10^{-12}\) m\({}^{2}\)/s) & 1.00 & 1.10 & 2.00 & 1.00 \\ \hline MC\({}_{min}\) & \(K_{d}\) (\(10^{-3}\) m\({}^{3}\)/kg) & 4.04 & 3.09 & 1.55 & 1.43 \\  & \(D_{e}\) (\(10^{-12}\) m\({}^{2}\)/s) & 2.20 & 2.65 & 4.50 & 1.25 \\ \hline MC\({}_{2 Clay}\) & \(K_{d}\) (\(10^{-3}\) m\({}^{3}\)/kg) & 3.64 & 2.71 & 1.10 & 1.29 \\  & \(D_{e}\) (\(10^{-12}\) m\({}^{2}\)/s) & 1.50 & 1.40 & 0.80 & 1.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calibrated transport parameters (\(K_{d}\) and \(D_{e}\)) from the different scenarios of the MC diffusion simulations on the metre-scale and after a simulation time of 100 years for the facies of the Opalinus Clay. Figure 4: Concentrations of calcium and magnesium (**a**), sulphate and chloride (**b**,**c**) and uranium (**d**) in the DDL of the clay minerals for the sandy facies after a simulation time of 100 years and for a pCO\({}_{2}\) of \(10^{-2.2}\) bar. For better clarity, the concentration of sulphate in the DDL of chlorite is given in **c** as close-up of (**b**). MC\({}_{min}\), Table 2) using MC diffusion simulations (MC\({}_{4 CIay}\)) on the metre-scale. The effect of the total mineral amount on the diffusion lengths was quantified by comparison with the MC simulations based on the averaged data given in Table 1. From the results of the MC simulations, \(K_{d}\) was calculated and \(D_{e}\) calibrated to reproduce the MC simulations with the SC approach. Figure 5 shows the results of the MC simulations for the minimum and maximum total amount of rock for all facies as well as the SC simulations using the calibrated transport parameters. In all facies, uranium migrated farther into the formation for the MC\({}_{min}\) scenario. After a simulation time of 100 years, the maximum diffusion length of 0.35 m was determined in the sandy facies (Figure 5d). The difference in migration distance between the two scenarios for the total amount of rock per kg porewater ranged from 0.02 m in the carbonate-rich facies (Figure 5b) to 0.13 m in the sandy facies (Figure 5d). In Figure 5b,d, the diffusion lengths of the maximum scenarios are similar to the simulations using the averaged values of the hydro-physical parameters. For all scenarios and facies, MC simulations could be reproduced with the calibrated transport parameters with a deviation between 1% and 6% (average 3%) between SC and MC simulation (Figure 5). The \(K_{d}\) and \(D_{e}\) for the scenarios presented in Figure 5 are given in Table 3. The calculated \(K_{d}\) values are unaffected by the variation in total mineral amount, whereas especially the calibrated \(D_{e}\) of the MC\({}_{min}\) more than doubles in some cases compared to  
Figure 5: Concentration of uranium in the porewater of the shaly (**a**,**c**), carbonate-rich (**b**) and sandy facies (**d**) for the scenarios with minimum (MC\({}_{min}\), 12-13 kg\({}_{rock}\)/kg\({}_{pw}\), light, green line), maximum (MC\({}_{max}\), 15–18 kg\({}_{rock}\)/kg\({}_{pw}\), dark, green line) and average (MC, 14–17 kg\({}_{rock}\)/kg\({}_{pw}\), blue line) total amount of rock per kg porewater. The red, dotted lines represent the results of the simulations based on the SC approach with the \(K_{d}\) and \(D_{e}\) calibrated from the MC simulations.