## 5 Methodology and Results
### Sensitivity Analysis  
The forthcoming phase of this study will center on a sensitivity analysis to elucidate the effects of variations in rock mechanical properties, caprock permeability, and CO\({}_{2}\) injection rates on the geomechanical behavior associated with GCS. Detailed ranges of the parameters under consideration for the uniform distribution of properties are delineated in Table 4, and the designated points of interest within the 3D geomechanical model are highlighted in Figure 13.  
Figure 13: Monitoring points of interest for geomechanical sensitivity analysis. The figure displays points A–F, indicating areas of interest against a backdrop depicting vertical displacement. Points A and B represent the wellhead and the central reservoir peak displacements in m, respectively. The orthogonal I and J grid paths intersect at the reservoir’s surface midpoint, situating these points within the model. Upon defining the range of parameters for this study, 80 realizations were executed to produce an ensemble of displacement curves, as visualized in Figure 14. Panel A corresponds to the path along J = 33, while Panel B represents I = 56. These figures are crucial, as they demonstrate a significant dispersion in the displacement outcomes, indicative of the varied responses within the model to changes in CO2 injection rates. The maximum vertical displacement reaches approximately \(-0.35\) m, while some models barely have it. It is important to note that these displacements occur after the CO2 injection after 20 years, representing the expected maximum displacement within the modeled timeframe. The spread of the displacement curves underscores the importance of considering a wide range of scenarios to adequately capture the complexities and uncertainties inherent in geochemical behavior during CO2 storage operations. In Figure 15, vertical displacements along path J = 33 are analyzed and depicted, with displacement curves distinctly color-coded to represent a spectrum of sensitivity parameters utilized in this study. The visual data suggest that rocks with higher Poisson ratios and lower Young's modulus values--attributes that contribute to a rock's ductility and stiffness--experience increased vertical displacements. Additionally, increased CO2 injection rates and reduced shale permeabilities are associated with greater displacement magnitudes. Such trends are indicative of the complex interplay between rock mechanics and the operational parameters of CO2 injection, underscoring the need for meticulous evaluation in the design and monitoring of CO2 sequestration initiatives, because not considering the uncertainty in rock properties could lead to significant errors in vertical displacement predictions. \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Min Value** & **Max Value** \\ \hline Injection rate (tons/day) & 100 & 3000 \\ Poisson’s ratio (sandstone) & 0.22 & 0.39 \\ Poisson’s ratio (shale) & 0.28 & 0.48 \\ Young’s modulus (sandstone) (GPa) & 0.7 & 34 \\ Young’s modulus (shale) (GPa) & 6.9 & 69 \\ Caprock permeability (mD) & \(10^{-9}\) & \(10^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Ranges of the uniform distribution of the parameters used in the sensitivity analysis [55,56]. Figure 14: Ensemble of vertical displacement curves post-injection. Panel (**A**) (J = 33) and Panel (**B**) (I = 56) display the range of vertical displacements resulting from 80 realizations based on varied parameter inputs. The statistical analysis aimed at understanding the variability and range of geomechanical responses at various monitoring points is presented in Figure 16, parts A and B. The box plots in part A of the figure synthesize the central tendencies and dispersions of vertical displacements observed at each monitoring point (A-F) after 20 years of CO\({}_{2}\) injection. They illustrate a distinct pattern. Monitoring point B, situated at the reservoir's projected center, consistently experiences the largest vertical displacements.