## 2 Materials and Methods
### Numerical Model
For the analysis of the porewater chemical composition (concentrations of dissolved species and activities), the thermodynamic database ThermoChimie v11a [31] was used. The ThermoChimie database was first developed in 1995 by Andra (the French National Radioactive Waste Management Agency). Now, it is being developed jointly with Radioactive Waste Management (RWM) (Didcot, UK) and ONDRAF/NIRAS (Bruxelles, Belgium). As stated in [32], the thermodynamic database ThermoChimie provides an accurate and consistent set of data specifically chosen for use in modelling the behaviour of radionuclides in waste packages, engineered barriers, and both the near surface and deep geosphere. In this study, the ion exchange reactions were modelled with the Gaines-Thomas convention [25]. Ion selectivity constants for montmorillonite and initial concentrations of exchanged ions were taken from [13]. The surface complexation was modelled using data for site capacities (Table 4) and photolysis constants for montmorillonite given in [23] (Table 5). The data on initial porewater composition, initial mineral volume fractions, initial concentrations of exchanged ions at 25 \({}^{\circ}\)C, selectivity constants, and total concentrations of surface complexation sites are summarized in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Bentonite** & **Granite** \\ \hline Initial porewater composition & & \\ pH & 7.72 & 8.35 \\ Na\({}^{+}\) (mol/L) & \(1.3\times 10^{-1}\) & \(3.83\times 10^{-4}\) \\ K\({}^{+}\) (mol/L) & \(1.73\times 10^{-3}\) & \(7.83\times 10^{-6}\) \\ Ca\({}^{2+}\) (mol/L) & \(2.23\times 10^{-2}\) & \(1.83\times 10^{-4}\) \\ Mg\({}^{2+}\) (mol/L) & \(2.33\times 10^{-2}\) & \(1.33\times 10^{-6}\) \\ HCO\({}_{3}\)\({}^{-}\) (mol/L) & \(4.13\times 10^{-4}\) & \(3.93\times 10^{-6}\) \\ SO\({}_{4}\)\({}^{2-}\) (mol/L) & \(3.23\times 10^{-2}\) & \(7.93\times 10^{-5}\) \\ Cl\({}^{-}\) (mol/L) & \(1.63\times 10^{-1}\) & \(1.33\times 10^{-5}\) \\ SiO\({}_{2(\text{aq})}\) (mol/L) & \(1.13\times 10^{-6}\) & \(1.43\times 10^{-4}\) \\ \hline \hline Initial volume fraction of the minerals (\%) & & \\ Calcite & 1 & 5 \\ Quartz & 4.5 & 20 \\ Anhydrite & 0 & 0 \\ Gypsum & 0.016 & 0 \\ Halite & 0 & 0 \\ \hline \hline Initial ion exchange concentration meq/100 g & & \\ bentonite & & \\ Na\({}^{+}\) & 21.10 & - \\ K\({}^{+}\) & 1.94 & - \\ Ca\({}^{2+}\) & 31.31 & - \\ Mg\({}^{2+}\) & 41.41 & - \\ \hline \hline Total concentration of surface complexation sites & & \\ (mol/kg) & & \\ \(\equiv S^{\text{s}}OH\) & \(2\times 10^{-3}\) & - \\ \(\equiv S^{\text{s}}\
u 1\text{O}H\) & \(4\times 10^{-3}\) & - \\ \(\equiv S^{\text{s}}\
u 2\text{O}H\) & \(4\times 10^{-3}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial porewater composition, initial mineral volume fractions, initial concentrations of exchanged ions, selectivity constants, and total concentrations of surface complexation sites [13]. The following initial and boundary conditions were assumed (see also Figure 3):  
* With the heater temperature of 100 \({}^{\circ}\)C and the initial temperature in granite of 12 \({}^{\circ}\)C, the temperature gradient establishes quickly across the bentonite layer [12], with \(\sim\)45 \({}^{\circ}\)C on the bentonite-granite interface. Thus, fixed-temperature boundary conditions were applied on the bottom (z = 0.45 m) boundary (T = 100 \({}^{\circ}\)C), representing the heater-bentonite interface, and on the upper (z = 1.14 m) boundary (T = 45 \({}^{\circ}\)C), representing the bentonite-granite interface. * Before transport simulation, the equilibrated porewater compositions with mineral phases, cation exchange sites, and surface protonation at 45 \({}^{\circ}\)C were derived with Phreeqc. * Initial suction (\(P_{G}-P_{L}\)) of 117.8 MPa was prescribed in the bentonite. With the defined water retention curve, this suction corresponded to 60% saturation.