## 5 Methodology and Results
### Sensitivity Analysis
This pattern is indicative of the pressure distribution and stress diffusion within the reservoir, highlighting the central region as the primary locus of geomechanical impact due to CO\({}_{2}\) injection. Part B of Figure 16 assesses the impact of geomechanical properties on these vertical displacements, demonstrating that the mechanical properties, as characterized by [PERSON]'s modulus for both sandstone and shale, have effects on displacement comparable to those of the CO\({}_{2}\) injection rate. This emphasizes the significance of obtaining precise geomechanical properties to effectively characterize the rock and its caprock in GCS projects. Figure 16: Integrated analysis of geomechanical responses’ and properties’ impacts on vertical displacement. Panel (**A**) presents box plots of vertical displacements at monitoring points A–F. Panel (**B**) quantifies the correlation between geomechanical properties and vertical displacement. Figure 15: Sensitivity analysis of vertical displacement curves along path J = 33. Displacement curves are stratified by parameters used in the sensitivity analyses. The negative correlation coefficients signify that an increase in these mechanical properties correlates with more significant upward displacement, emphasizing that the mechanical constitution of the reservoir plays a critical role in the deformation observed, alongside the operational parameters of the injection. This parallel in impact underscores the dual importance of understanding both the inherent mechanical behavior of the geological formation and the operational dynamics of CO\({}_{2}\) injection in managing geomechanical risks in GCS projects. Figure 17 presents the correlations between geomechanical properties and vertical displacements at individual monitoring points within the reservoir after twenty years of CO\({}_{2}\) injection. Subplots A through F denote these points, indicating localized responses. The correlation coefficients, derived from variables including Young's modulus, Poisson's ratio for sandstone and shale, and CO\({}_{2}\) injection rates, reveal a multifaceted relationship that aligns with the overall behavior patterns identified across the reservoir. This suggests that the geomechanical behavior at single monitoring points reflects the broader, systematic influences of the injection process. Building on the comprehensive analyses detailed earlier, this study progresses to evaluate the influence of shale permeability on the dissipation of reservoir pressure over time in Figure 18. It depicts the interplay between shale permeability, CO\({}_{2}\) injection rates, and their combined effects on reservoir pressure over time. Panel A shows the influence of shale permeability on reservoir pressure, and it is observed that except for very low permeability scenarios (10\({}^{-6}\) mD to 10\({}^{-9}\) mD), reservoir pressure decreases significantly after the cessation of CO\({}_{2}\) injection. This trend suggests that while shale  
Figure 17: Correlation coefficients by monitoring point for geomechanical properties impacting vertical displacement. This figure demonstrates the correlation between geomechanical properties and vertical displacement, disaggregated by monitoring points (A–F). acts as a semi-permeable barrier, its permeability is crucial in regulating the rate at which pressure normalizes post-injection. For reservoir management, this implies that higher shale permeability can potentially be harnessed to mitigate risks associated with overpressure, provided that the permeability does not compromise the seal's integrity. Conversely, very low permeability could pose challenges in pressure management, possibly leading to an increased risk of induced seismicity or caprock failure. Panel B further elaborates on the effect of injection rates on reservoir pressure. It demonstrates that under typical conditions [86; 87], increased injection rates are associated with a proportional rise in average reservoir pressure.