## 2 Methodology
### Modeling Geochemical Reactions  
CO\({}_{2}\) injection for CCS was numerically simulated using CMG-GEM [39], version. 2023.30, considering the following features:  
* Diffusion coefficient (\(D\)) for supercritical CO\({}_{2}\) in brine equals 3.65 \(\times\) 10\({}^{-5}\) cm\({}^{2}\)/s, according to [PERSON] et al. [40], with an average value over the pressure range considered during the simulations. * CO\({}_{2}\) solubility in brine according to the method by [PERSON] [41] based on [PERSON]'s law. This model is based on [PERSON]'s constant calculation according to Equation (1) as a function of pressure and temperature. Still, the effect of salt on the gas solubility in the aqueous phase is modeled by the salting-out coefficient [42]. \[ln(H_{i})=ln(H_{i}^{*})+\frac{\overline{v_{i}}}{RT}(p-p^{*}) \tag{1}\]  
where  
\(H_{i}\): [PERSON]'s constant at current pressure (\(p\)) and temperature (\(T\));  
\(H_{i}^{*}\): [PERSON]'s constant at reference pressure (\(p^{*}\)) and temperature (\(T\));  
\(\overline{v_{i}}\): partial molar volume at infinite dilution;  
\(R\): universal gas constant;  
\(i\): species dissolved in water (CO\({}_{2}\) in this work). The \(H_{i}^{*}\) constant was computed considering the initial conditions (prior to the commencement of CO\({}_{2}\) injection) of the models in Table 1. \begin{table}
\begin{tabular}{l c} \hline \hline
**Properties** & **Values** \\ \hline Initial pressure & 11,800 kPa @ 1200 m \\ Temperature & 80 \({}^{\circ}\)C \\ Salinity & 50,000 ppm (NaCl) \\ \(H_{i}^{*}\) & 5.66 \(\times\) 10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Solubility parameter at the initial conditions of the reservoir model. * Water acidic reactions for bicarbonate and carbonate ions generation, using kinetic parameters from the PHREQC database [5,5]: \[\rm{OH^{-}}_{(aq)}+H^{+}{{}_{(aq)}}=H_{2}O_{(aq)}\] (2) \[\rm{CO_{2(g)}+H_{2}O_{(aq)}=H^{+}{{}_{(aq)}}+HCO{{}_{3}}^{-}{{}_{(aq)}}}\] (3) \[\rm{CO_{3}}^{2-}{{}_{(aq)}+H^{+}{{}_{(aq)}}=HCO{{}_{3}}^{-}{{}_{(aq)}}}\] (4)  
The synthetic water composition (ions with non-zero initial concentration) assigned for this case is represented in Table 2.  
* Reactions with primary ((5)-(10)) and secondary minerals ((11) and (12)), using the Transition State Theory (TST)-derived rate laws [14]: \[\rm{Calcite\ [CaCO_{3\ (s)}]+H^{+}{{}_{(aq)}}=Ca^{2+}{{}_{(aq)}}+HCO{{}_{3}}^{-}{{}_{(aq)}}}\] (5) \[\rm{Quartz\ [SiO_{2\ (s)}]=SiO_{2\ (aq)}}\] (6) \[\rm{Kaolinite\ [Al_{2}Si_{2}O_{5}(OH)_{4\ (s)}]+6.0\ H^{+}{{}_{(aq)}}=5.0\ H_{2}O_{(aq)}+2\ Al^{3+}{{}_{(aq)}}+2\ SiO_{2\ (aq)}}\] (7) \[\rm{Albite\ [NaAlSi_{3}O_{8\ (s)}]+4\ H^{+}{{}_{(aq)}}=3\ SiO_{2\ (aq)}+Al^{3+}{{}_{(aq)}}+Na^{+}{{}_{(aq)}}+2\ H_{2}O_{(aq)}}\] (8) \[\rm{K\-\mbox{feldspar [KAlSi}_{3}O_{8\ (s)}]+4\ H^{+}{{}_{(aq)}}=3\ SiO_{2\ (aq)}+Al^{3+}{{}_{(aq)}}+K^{+}{{}_{(aq)}}+2\ H_{2}O_{(aq)}}\] (9) \[\rm{OH^{-}}_{(aq)}+H^{+}{{}_{(aq)}}=H_{2}O_{(aq)}\]0 (10) \[\rm{OH^{-}}_{(aq)}+H^{+}{{}_{(aq)}}=H_{2}O_{(aq)}\]1 (11) \[\rm{OH^{-}}_{(aq)}+H^{+}{{}_{(aq)}}=H_{2}O_{(aq)}\]2 (12)  
The mineral reactions are regulated by four parameters, as follows:  
* \(K_{eq}\) is the chemical equilibrium constant;
* \(A\) is the reactive surface area;
* \(E_{q}\) is the activation energy;
* \(k_{25}\) is the rate constant at \(T_{25}=298.15\) K (25 \({}^{\circ}\)C), and the rate constant (\(k\)) in different temperature conditions can be expressed as follows: \[\rm{OH^{-}}_{(aq)}+H^{+}{{}_{(aq)}}=H_{2}O_{(aq)}\]3 (13) where \(R\) is the universal gas constant. \begin{table}
\begin{tabular}{c c} \hline
**Ions** & **Concentration (mol/kgw)** \\ \hline H\({}^{+}\) & \(1.95618\times 10^{-6}\) \\ Ca\({}^{2+}\) & 0.30308 \\ Mg\({}^{2+}\) & 0.04185 \\ Na\({}^{+}\) & 0.3234 \\ Cl\({}^{-}\) & 0.551 \\ HCO\({}_{3}\)\({}^{-}\) & 0.007482 \\ \hline \end{tabular}
\end{table} 
Table 2: Ionic composition of formation brine.