## 2 Methodology
### Model Setup
The cap rock brine is composed of a 0.5 M Na\({}^{+}\)/Cl\({}^{-}\)-dominated solution equilibrated with the mineral phases of the cap rock under cap rock pressure and temperature conditions. The temperature and pressure conditions change along the diffusive pathway of the aqueous species through the cap rock, starting with 40 \({}^{\circ}\)C and 40 atm at the reservoir depth (data from [PERSON] et al. [46]). A gradient of decreasing temperature and pressure conditions according to the geothermal gradient (33.3 \({}^{\circ}\)C km\({}^{-1}\) depth) and a pressure gradient of 100 atm km\({}^{-1}\) depth under hydrostatic conditions is assumed. Therefore, each cell is defined by a specific temperature and pressure condition (e.g., cell 182: 39.967 \({}^{\circ}\)C and 39.9 atm; cell 181: 39.934 \({}^{\circ}\)C and 39.8 atm; and so on). The initial reservoir rock brine composition is a 0.5 M Na\({}^{+}\)/Cl\({}^{-}\)-dominated solution, which is in equilibrium with the reservoir rock and the initial gas composition at 40 atm and 40 \({}^{\circ}\)C. The underlying rock is dominated by a 6.7 M Na\({}^{+}\)/Cl\({}^{-}\)-dominated solution equilibrated with the underlying rock and gas composition under underlying rock pressure and temperature conditions (106.7 atm and 60 \({}^{\circ}\)C). To simulate the million-years-long interaction, molecular diffusion of all aqueous species through the cap rock brine, reservoir rock brine, and underlying rock brine is simulated over one million years. The brine compositions are summarized in Table 3.  
The high Na\({}^{+}\) and Cl\({}^{-}\) concentrations and high ionic strength in the brines require the use of the Pitzer database. However, the Pitzer database does not include Al\({}^{3+}\), which is important \begin{table}
\begin{tabular}{c c c} \hline \hline
**Primary Minerals** & **Weight Percent (wt. \%)** & **Amount (mol kgw\({}^{-1}\))** \\ \hline
**Cap rock** & & \\ Halite & 5.0 & 76.74 \\ Quartz & 50.0 & 746.42 \\ Illite & 20.0 & 46.73 \\ Dolomite & 5.0 & 24.32 \\ Anhydrite & 15.0 & 131.77 \\ \hline
**Reservoir rock** & & \\ K-feldspar & 30.0 & 103.90 \\ Kaolinite & 1.0 & 3.73 \\ Quartz & 55.0 & 882.43 \\ Calcite & 0.5 & 4.82 \\ Dolomite & 0.5 & 0.03 \\ Anhydrite & 0.5 & 0.132  \\ Illite & 11.5 & 28.88 \\ Barite & 0.5 & 0.0009 \\ Goethite & 0.5 & 0.002 \\ \hline
**Underlying rock** & & \\ Halite & 50.0 & 758.46 \\ Quartz & 8.0 & 118.04 \\ Calcite & 6.0 & 53.14 \\ Dolomite & 10.0 & 0.03 \\ Pyrite & 1.0 & 7.39 \\ Anhydrite & 25.0 & 66.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mineralogical composition of the reservoir rock, cap rock, and underlying rock. Dawsonite, nahcolite, mackinawite, sulfur, albite (and pyrite) are potential secondary phases. when modeling hydrogen storage in depleted gas fields. Therefore, the database phreeqc.dat is used. The validation that PHREEQC using phreeqc.dat simulates correct results with high Na\({}^{+}\) and Cl\({}^{-}\) concentrations and high ionic strength is shown by [PERSON] and [PERSON] [47]. Furthermore, [PERSON] and [PERSON] [48] stated that models are reliable at higher ionic strength if the system is sodium chloride dominated. Molecular diffusion of all aqueous species is the only mass transport accounted for by the model. Multicomponent diffusion is calculated where each \"solute can be given its own diffusion coefficient, allowing it to diffuse at its own rate, but with the constraint that overall charge balance is maintained\" [38; 49; 50]. Fluid flow is not considered in the model due to the lack of total hydraulic head differences in depleted gas reservoirs. A homogeneous distribution of the relevant parameters in the reservoir and cap rock such as mineralogical composition is assumed. Furthermore, no fractures or natural faults are considered. Because of the lack of data, the storage time of hydrogen in depleted oil and gas fields is based on the equipment lifetime of 30 years [51], but is varied in an additional scenario (Section 3.4.1).