## 2 Methodology
### Modeling Geochemical Reactions
These parameters compose the TST dissolution and precipitation reaction rate (\(r\)), as follows [43]:  
\[r=sgn\left[1-\left(\frac{Q}{K_{eq}}\right)\right]AS_{w}\left[k+\sum_{i=1}^{nct}k_{ i}a_{i}^{vi}\right]\left|1-\left(\frac{Q}{K_{eq}}\right)^{\xi}\right|^{\xi} \tag{14}\]  
where  
_sgn_: mathematical operator to return the sign of the expression;  
_Q_: ion activity product (IAP);  
_S_\(w\): aqueous phase saturation;  
_nct_: number of reactant components;  
_a_\(i\): activity of component \(i\) computed with [PERSON]'s model [44; 45];  
_wi_: activity power;  
_\(\xi\), \(\zeta\)_: TST model parameters. The ratio \(\log(Q/K_{eq})\) is called the saturation index of the reaction. In this study, the numerical geochemistry model used assumes that if \(\log(Q/K_{eq})>1\), mineral precipitation occurs, and if \(\log(Q/K_{eq})<1\), mineral dissolution occurs. In the model used, the convention adopted is as follows: rate \(r\) is negative for dissolution and positive for precipitation. The rate is zero when \(\log(Q/K_{eq})=1\). \(Q\) and \(K_{eq}\) were assumed to be known from models [44; 45] and open-source databases [46; 47], respectively. However, \(A\), \(k_{25}\), and \(E_{a}\) were further investigated. The published values of the reactive surface area, for example, vary considerably among different authors due to the dependence on the grain size diameter of the rock minerals [17; 48]. Table 3 provides a concise overview of the kinetic values derived from an extensive literature survey. This uncertainty analysis will be specifically focused on the most representative and highly reactive minerals, namely quartz, calcite, and dolomite. For these minerals, ranges of values considered in the stochastic simulations are included in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline
**Mineral** & **Parameter** & **Value/Range** & **Source** \\ \hline \multirow{4}{*}{Calcite} & \(\log_{10}(K_{eq})\) & \(-8.38\) & \\  & \(A\) & \(88\) to \(23,000\) m\({}^{2}\)/m\({}^{3}\) & \\  & \(\log_{10}(k_{25})\) & \(-8.8\) to \(-0.3\) mol/m\({}^{2}\)s & [5; 8; 46; 47; 48; 49] \\  & \(E_{a}\) & \(14,400\) to \(41,870\) J/mol & \\ \hline \multirow{4}{*}{Quartz} & \(\log_{10}(K_{eq})\) & \(-4.38\) & \\  & \(A\) & \(2650\) to \(7128\) m\({}^{2}\)/m\({}^{3}\) & \\  & \(\log_{10}(k_{25})\) & \(-15\) to \(-10\) mol/m\({}^{2}\)s & [5; 8; 46; 47; 49] \\  & \(E_{a}\) & \(68,175\) to \(113,625\) J/mol & \\ \hline \multirow{4}{*}{Kaolinite} & \(\log_{10}(K_{eq})\) & \(9.80\) & \\  & \(A\) & \(1760\) m\({}^{2}\)/m\({}^{3}\) & \\  & \(\log_{10}(k_{25})\) & \(-13\) mol/m\({}^{2}\)s & [5; 8; 46; 47; 50] \\  & \(E_{a}\) & \(62,760\) J/mol & \\ \hline \multirow{4}{*}{Albite} & \(\log_{10}(K_{eq})\) & \(-19.7\) & \\  & \(A\) & \(2563.38\) m\({}^{2}\)/m\({}^{3}\) & \\ \cline{1-1}  & \(\log_{10}(k_{25})\) & \(-10.16\) mol/m\({}^{2}\)s & [5; 8; 16; 47] \\ \cline{1-1}  & \(E_{a}\) & \(65,000\) J/mol & \\ \hline \end{tabular}
\end{table} 
Table 3: Kinetic parameters of TST model for mineral reactions. * Permeability alteration due to mineral precipitation or dissolution was computed by applying the Kozeny-Carman equation with an exponent value of 3, as [PERSON] et al. (2016) recommended: \[k_{k}=k_{n}/rf\] (15) where \[rf=rf_{n}\bigg{(}\frac{\varphi_{n}}{\varphi_{k}}\bigg{)}^{3}\bigg{(}\frac{1- \varphi_{k}}{1-\varphi_{n}}\bigg{)}^{2}\] (16) where the resistance factor \(rf\) is modeled by the Kozeny-Carman equation or the power-law relationship, \(k_{n}\) and \(k_{k}\) refer to permeability at previous (\(n\)) and current (\(k\)) timesteps, respectively.