## 3 Results and Discussion  
The objective functions (OF) that were evaluated are as follows:  
* _II_: the CO2 injectivity index after five years of injection, computed according to Equation (19): \[II=\frac{q_{CO2}}{\left(p_{bh}-\overline{p}_{at}\right)},\] (19) where _II_ is the CO2 injectivity index, \(q_{CO2}\) is the bottom-hole CO2 volumetric injection rate; \(p_{bh}\) is the bottom-hole pressure, and \(\overline{p}_{at}\) is the average aquifer pressure. * Mineralization_1000 yr: Mineral dissolution or precipitation after 1000 years of CO2 redistribution;
* Calcite_1000 yr: Calcite concentration change (in gmoles) after 1000 years of CO2 redistribution;
* Dolomite_1000 yr: Dolomite concentration change (in gmoles) after 1000 years of CO2 redistribution;
* Quartz_1000 yr: Quartz concentration change (in gmoles) after 1000 years of CO2 redistribution. Table 6 summarizes the simulation results (SR) from 65,000 Monte Carlo simulations (MCS) using quadratic response surfaces (in Appendix??) as proxy models to represent the SR for each objective function (OF) in terms of the three estimates: P10, P50, and P90. In this context, the P90 represents the estimate with a 90% probability that the OF will have higher values. In other words, it signifies the lower end of the range of possible values for  
Figure 2: Drainage CO2/brine relative permeability curves (on the left) and capillary pressure (on the right) for a carbonate rock, Bennion and Bachu [54]. \begin{table}
\begin{tabular}{l c} \hline \hline  & **Property** & **Value** \\ \hline Initial pressure & 11,800 kPa @ 1200 m \\ Temperature & 80 \({}^{\circ}\)C \\ Horizontal permeability & 100 mD \\ \(K_{\
u}/K_{h}\) ratio & 0.1 \\ Porosity & 30\% \\ Rock compressibility & 5.8 \(\times\) 10\({}^{-7}\) kPa\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of reservoir properties. the OF, with only a 10% chance of the OF falling below this estimate. On the other hand, the P10 represents the upper end of the range of possible values for the OF, with only a 10% chance of the OF exceeding this estimate. The two last columns in the table display the respective R-squared (\(R^{2}\)) coefficient, which measures the reduction in the variability of the response achieved by using the regressor variables in the model. The adjusted \(R^{2}\) provides an estimate of the quality of fit of a proxy model to the simulation results (600 training experiments). On the other hand, the predicted \(R^{2}\) is a measure of the model's ability to accurately predict outcomes for new, unseen data (10 verification experiments), according to the representation shown in Figure 3. Overall, the results obtained from the SR and MCS analyses, along with the \(R^{2}\) coefficients, indicate that the proxy models built using quadratic response surfaces are reliable and provide satisfactory estimates for the objectives of this study. The errors between the SR and MCS results were found to be lower than 5%, with an \(R^{2}\) higher than 80%. When considering only the P50 estimate, the prediction error decreased to less than 2%. These error levels are commonly observed in reservoir simulation applications [26; 29; 59]. Therefore, they were considered sufficiently accurate for this study, considering the numerous variables involved, and they will be considered for the following analysis.