## 3 Results and Discussion
### Parametric Analysis with Proxy Models for Calcite Dissolution  
Calcite dissolution is the primary mineral reaction observed in this case. Consequently, the \"Mineralization_1000 yr\" and \"Calcite_1000 yr\" outcomes from Table 6 are practically identical. In order to better assess the impact of the volumetric percentage of calcite (%vol) on mineral dissolution, an additional parameter was introduced into the experimental design to account for different proportions of calcite, ranging from 29% to 69%. The porosity was maintained at 30%, and as the amount of calcite decreased, the amount of quartz increased at the same rate. This was conducted to simulate a transition from a carbonate-rich to a siliciclastic-rich rock, where calcite essentially acts as the rock cementation. Figure 4 provides a summary of the sensitivity analysis using a Tornado Plot, showcasing the most influential parameter on calcite dissolution. This includes the percentage of calcite in the original rock matrix, in addition to the kinetic parameters presented in Table 3. The rate constant (\(k_{25}\)) emerges as the most crucial parameter as it controls the reaction velocity and exhibits an explicit dependence on the energy of activation (\(E_{a}\)), as expressed in Equation (13) and illustrated in the interaction effect bar in Figure 4. The reactive area (\(A\)) follows as the second most influential parameter. The wide ranges of uncertainty associated with the parameters \(k_{25}\) and \(A\) not only exert significant control over calcite dissolution but also interact with other parameters, thereby enhancing their overall impact. The broad range of \(A\) can be attributed to its dependence on the grain size diameter of the reactive minerals present in the rock, further contributing to the variability observed. In essence, the impact of an individual parameter on the overall objective function (OF) is known as the main effect. However, interaction effects take into account combinations of model parameters that cannot be described solely by the first-order effects. This finding aligns with the results drawn by [PERSON] (2018) in her history-matching study involving lab experiments on carbonate cores. In order to fit the data with numerical simulations, a tuning procedure was required for the rate constant and reactive area, as demonstrated in our results, which highlight these parameters as the most influential. This type of sensitivity analysis can support history-matching studies by identifying the parameters that need to be adjusted in numerical simulations. Figure 3: Proxy model prediction versus simulation results for the training (blue dots) and verification experiments (green dots). In this particular analysis, the percentage of calcite exhibited a minimal effect. However, as will be discussed later, the limited amount of injected CO\({}_{2}\) is more influential in limiting the dissolution than the amount of calcite present. It explains why the difference between the P10 and P90 estimates is small for the calcite molar change. The proxy model effectively replicates the temporal evolution of calcite dissolution. The comparison between the simulation results (in red) of a representative model for the P50 estimate and the predictions generated by the proxy model (in blue) is shown in Figure 5. In the context of reservoir simulation or modeling, representative models refer to a collection of models created to encompass the range of potential conditions or scenarios within the reservoir. These models are designed to capture various uncertainties and factors that may influence subsurface behavior, such as parameter variations or geological properties. In this particular case, the representative models correspond to the P10, P50, and P90 estimates, with the P50 estimate typically considered for project evaluation and approval. Figure 4: Tornado plot for the objective function “Calcite_1000 yr” generated with MCS calibrated with 600 runs.