## 6 Horizontal Well Design  
The study identified two primary findings associated with the use of horizontal wells in CO\({}_{2}\) storage:  
* Horizontal injection wells effectively prevent or minimize CO\({}_{2}\) penetration into the caprock across various sensitivity scenarios. This finding is closely linked with the buoyancy effect, which can be modeled by the gravity number introduced in Equation (20). Consequently, the gravity number is one of the variables used to determine the optimal length of horizontal wells;
* Horizontal wells offer a safer approach to trapping CO\({}_{2}\) by increasing its entrapment as a residual phase compared to the use of vertical wells as injectors. In this context, the additional CO\({}_{2}\) trapped as a residual phase becomes a crucial variable.  
Therefore, the ideal length for a horizontal well would be one that maximizes CO\({}_{2}\) entrapment while minimizing buoyancy effects.  
To confirm our hypothesis that the wider the lateral CO\({}_{2}\) spreading, the more the residual entrapment, Figure 17 brings the evolution of the residual CO\({}_{2}\) trapped by hysteresis for the cases considered in Figure 9. Figure 17 shows that a longer \(L_{w}\) increased residual saturations as the plume contacted new permeability regions of the aquifer. However, the residual CO\({}_{2}\) mass developed a plateau after 1500 years for all these cases, which represented the optimum value. For instance, from \(L_{w}\) = 2000 m, there was no additional  
Figure 16: Cross-sectional views of the CO\({}_{2}\) global mole fraction after 20,000 years with a vertical well (**A**) and a horizontal well with \(L_{w}\) = 2000 m (**B**). The light blue zone is the caprock; the coordinates are in meters.  
entrapment for longer horizontal branches. Therefore, \(L_{w}\) = 2000 m seems to be an optimum length for the entrapment.  
Figure 18 combines two parameters plotted against the length of the horizontal well:  
* On the left: the difference between the CO2 saturation trapped as a residual phase (\(\Delta\)CO2 residual) obtained with the vertical well minus the one with the horizontal well after 1500 years, corresponding to the time of plateau in Figure 17;
* On the right: the gravity numbers according to Equation (20) for different well lengths.  
Due to the permeability heterogeneity, a well length of \(L_{w}\) = 2000 m had more access to higher permeability regions (i.e., concentrated in the middle of this model). Hence, it developed higher \(z\)-transverse velocities (\(u\) in Equation (20)), causing a lower gravity number for the well length of 2000 m (Figure 18).  
This combination allows setting an optimum horizontal well length to enhance the CO2 entrapment and to control the rise of the CO2 plume, preventing its contact with the caprock and mitigating the associated risks. In this case, the optimum considering both purposes was \(L_{w}\) = 2000 m, which is technically possible according to actual CCS field projects [18; 25].  
Figure 17: The masses of residual CO2 trapped by relative permeability and capillary pressure hysteresis for different well geometries over 3000 years.  
Figure 18: The difference between the residual trapped CO2 for vertical and horizontal wells (axis on the left) and the gravity number (axis on the right) against the well length after 1500 years.