## 3 Results and Discussion
### Thorough Proxy Analysis  
The Tornado plots for calcite and dolomite, depicting the influence of various parameters after 1000 years, reveal that the rate constant emerges as the most significant kinetic parameter. This parameter holds direct control over the reaction rate, especially in the context of calcite dissolution. However, it is important to note that the rate constant also exhibits a wide range of uncertainty in open databases, as [PERSON] et al. [12] highlighted in their analysis of batch simulation results. Building upon the foundational research on uncertainty assessment conducted by [PERSON] et al. [11], who suggested that geochemical reactions become more significant at higher CO2 injection rates, a new experimental design incorporated the CO2 injection rate as a variable to better understand its relevance in comparison to the rate constant. As a result, the final uncertainty analysis includes the same set of kinetic parameters for calcite, dolomite, and quartz, along with the percentage of calcite in the initial rock and the initial brine pH. Additionally, the injection rate varied over five years, ranging from 0.1 to 25 metric tonnes/day. Figure 8 presents the updated Tornado plots for the objective functions (OFs) \"Calcite_1000 yr\" and \"Dolomite_1000 yr\". The findings support the observations made by [PERSON] et al. [11], as the CO2 injection rate emerges as the most influential parameter. This parameter plays a crucial role in fueling the calcite dissolution reaction, which, in turn, is closely linked to the growth of dolomite, as evidenced by the right Tornado plot in Figure 8. Consequently, a positive relationship is expected and observed between the injection rate and both calcite dissolution (with a much greater magnitude) and dolomite precipitation. These results further underscore the significance of the CO2 injection rate in driving mineral reactions and highlight its impact on the carbonate system. The direct impact of calcite dissolution can be quantified by monitoring the evolution of injectivity, which serves as an important parameter in laboratory experiments and field-scale operations. By applying Equations (15)-(17), the rock porosity and permeability can be updated as a result of geochemical reactions, leading to an increase in the injectivity index (\(I\)I). Considering the significant uncertainty associated with calcite dissolution, injectivity uncertainty is expected to also increase proportionally to the extent of calcite dissolution, particularly at higher injection rates, as illustrated in the left Tornado plot in Figure 8 and the crosplot in Figure 9.  
Figure 8: Tornado plot for the objective function “Calcite_1000 yr” (on the left) and “Dolomite_1000 yr” (on the right) generated with MCS calibrated with 600 runs, including the brine pH and CO2 injection rate in the experiment design. Table 8 provides an assessment of the uncertainty level, measured by the ratio of \(I\!I\) in the P90 estimate to that in the P10 estimate. By comparing the first experiment (Section 4), where the CO\({}_{2}\) injection rate was fixed at 0.5 tonne/day, with the second experiment, which incorporates a broad range of CO\({}_{2}\) injection rates as a parameter, the table highlights the uncertainty increase associated with injectivity in the second experiment, where greater amounts of CO\({}_{2}\) are involved. This information can be valuable in field and laboratory tests, as it aids in calibrating the balance between the dissolution and precipitation of carbonate minerals, with injectivity serving as a monitoring parameter, in addition to the effluent composition. It is important to acknowledge that precipitation reactions of other secondary minerals, such as halite scale in the dry-out zone, can occur and partially counteract the changes in porosity and permeability resulting from calcite dissolution. Although this specific effect was not evaluated in the present study, it has been extensively studied and documented in work conducted by [PERSON] et al. [22; 61].