## 4 Potential Changes in the Caprock Integrity with a Vertical Injector
Figure 6B shows that almost 11% of CO2 was adsorbed in the shale and that most of the CO2 in the caprock penetrated it by diffusion since CO2 dissolved in the brine was the highest amount (41.8%). Since there was no invasion of CO2 to caprock for the case with the horizontal well, the adsorbed quantity was expected to be lower, as shown in Figure 5.  
Figure 5: CO2 inventory after 3000 years through a vertical well (**A**) and a horizontal well with \(L_{w}=800\) m (**B**). The mass of mineralized CO\({}_{2}\) was omitted from the previous graphs, because it was only 0.0005% of the total injected after 3000 years. It was mainly related to the calcite (83% in moles), dolomite (8% in moles), and pyrite (9% in moles) precipitation in the caprock with the vertical injector where CO\({}_{2}\) contacted the caprock. There was no evidence of mineralization inside the aquifer since mainly non-reactive minerals constitute the sandstone matrix. Thus, those reactions are more relevant for modeling the caprock. To compute how horizontal wells can make the CO\({}_{2}\) flow less gravity-driven compared to vertical wells, the concept of the gravity number introduced by [PERSON] et al. [56] was applied, specified by Equation (20):  
\[\frac{MN_{gv}}{1+M} \tag{20}\]  
where  
\(N_{gv}=\frac{\Delta\rho KL_{v}}{H\mu_{brine}}\), which is the characteristic time ratio for fluid to flow in the transverse direction due to gravity;  
\(M\) is the mobility ratio;  
\(\Delta\rho\) is the density difference between the brine and CO\({}_{2}\);  
\(g\) is the acceleration due to gravity;  
\(L\) is the length of the aquifer;  
\(H\) is the aquifer thickness;  
\(k_{v}\) is the average vertical permeability;  
\(u\) is the Darcy velocity (=interstitial velocity \(\times\)\(\varphi\));  
\(\mu_{brine}\) is the brine viscosity. The higher the gravity number (Equation (20)) is, the more gravity-dominant the flow becomes. In our comparison, a value of 200 was calculated for a vertical well, whereas it was 100 for a horizontal well with 800 m of length, reinforcing the buoyancy observation in Figure 4.  
The invasion depth in caprock due to diffusion reached over 26 m after 3000 years using a vertical well (based on the values of CO\({}_{2}\) in the aqueous phase (CO\({}_{2(aq)}\)). The CO\({}_{2}\) gas saturation plume (CO\({}_{2(g)}\)) in Figure 7 was only 17 m thick, highlighting that the diffusive flow was more relevant than Darcy flow in the caprock, as concluded by [PERSON] et al. [57] during the numerical investigation of CO\({}_{2}\) leakage scenarios in shale caprock. Higher capillary pressure, critical water saturation typical of the shale (Figure 3), and lower permeability all inhibited the CO\({}_{2}\) convective flow through the caprock. This computed upward CO\({}_{2}\) velocity of 26 m/3000 years had the same magnitude compared with other numerical studies, such as 3 m/100,000 years [36], 8 m/ 100,000 years [58], and 1 to 77 m/1000 years [57]. The numbers are unequal due to differences in the models' properties and grid resolution and should be used only for qualitative comparison. In our case, a vertical refinement by a factor of 10 times was tested 50 m under and above the interface between sandstone and shale rocks using gridblocks of a 0.1 m thickness. With the finer gridblocks, the penetration was reduced by only 15% from the estimated penetration (22 m). Figure 6: CO\({}_{2}\) inventory after 3000 years in the sandstone aquifer (**A**) and in the shale caprock (**B**) with a vertical injector. Those results show that CO\({}_{2}\) penetration in the caprock is possible (mainly by diffusion) and can generate leakage to the surface or other non-target zones when the migration is associated with flow through fault/fracture potentially activated by the pressure buildup [57]. Figure 8 compares the CO\({}_{2}\) propagation in terms of saturation and aqueous mole fraction when an open fracture with 10 mD of intrinsic permeability and an aperture of 0.00014 m was placed inside the caprock [57].