## 5 Sensitivity Analysis with a Horizontal Injector
### Sensitivity to the Natural Water Flow  
Aquifers typically receive groundwater recharge, generating a natural flux in porous media. For the specific target represented by the heterogeneous base model, the natural water flow velocity was assumed to be 0.0015 ft/d [64]. To model this effect, two open boundary conditions were imposed on the lateral edges of the aquifer, coupled with an analytical function to calculate the water influx to the aquifer using the Carter\(-\)Tracy method [65]. The left edge was modeled as the source, and the right edge was modeled as the sink, as represented in Figure 13. Calibrating the analytical aquifer permeability, it was possible to calculate a similar velocity of 0.0015 ft/d (yellow region in Figure 13).  
Despite the low velocity, this flux affected the CO\({}_{2}\) plume propagation. Increased plume spreading makes the monitoring more challenging and impossible to prevent contact with the caprock even with a horizontal well. Table 7 shows the lateral spread of the CO\({}_{2}\)(g) plume and the thickness inside the shale from Figure 14 and the percentage of brine mass with CO\({}_{2(\text{aq})}\) inside the caprock from Figure 15.  
Figure 12: Cross-sectional views of the CO\({}_{2}\) global mole fraction (Z) after 3000 years with a vertical injector (**A**) and a horizontal injector of \(L_{w}\) = 2000 m (**B**) for different ratios of \(k_{v}/k_{h}\). The light blue zone is the caprock; the coordinates are in meters.  
Figure 13: Modeling a natural water influx into the aquifer using open lateral boundaries. The colors represent the water velocity in ft/day; positive values are the influx, and negative values are the efflux. The caprock is in yellow, because the velocity is zero.  
It is clear that the natural water flux contributed to expanding the CO\({}_{2}\) lateral extension, limiting its vertical migration, e.g., reducing the leakage risk but making it more difficult for plume monitoring with observation wells due to its spread over thousands of meters and with seismic methods due to its small thickness (the thickness of less than 10 m was challenging due to the seismic vertical resolution).  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Aquifer CO\({}_{2}\) Plume** & **Caprock CO\({}_{2}\) Plume** & **Brine in the Caprock** \\  & **Spread (m)** & **Thickness (m)** & **(\% in Mass)** \\ \hline vertical injector & 2980–5510 & 36\(-\)6 & 2.0\(-\)1.1 \\ horizontal injector with a 2000 m length & 0–1440 & 0–6 & 0.0–0.26 \\ \hline \end{tabular}
\end{table}
Table 7: Lateral CO\({}_{2}\) plume extension in the aquifer, thickness in the caprock and the diffused mass of brine mass saturated with CO\({}_{2}\).  
Figure 14: CO\({}_{2}\) saturation filtered only inside the caprock region after 3000 years considering a vertical injector (**A**), a vertical injector and water influx (**B**), and a horizontal injector with water influx (**C**).  
Figure 15: Cross-sectional views of the CO\({}_{2}\) global mole fraction after 3000 years for the base case without water influx (**A**) and with water influx (**B**). The dashed white line marks the boundary of the aquifer and caprock; the coordinates are in meters.  
However, this contact with the shale overburden using the vertical well case was still more pronounced compared to that using the horizontal well, which further increased the risk of flowing via existing or activated fractures and faults in the caprock.