## 2 Petrophysical Modeling for Sandstone and Shale  
This study considered two sandstone geological models: homogeneous and heterogeneous saline aquifers (Figure 1). The caprock was modeled as a water-saturated shale, assuming homogeneous properties in both cases. The homogeneous model (Figure 1A) was 1000 m in width and 1200 m in thickness, of which 1000 m was the shale caprock. The gridblock size was 10 \(\times\) 10 m\({}^{2}\) horizontally and 1 m thick.  
Figure 1: Models studied in this work: (**A**) a homogeneous sandstone aquifer; (**B**) a heterogeneous sandstone aquifer. Coordinates are in meters. Blue areas in both images represent the shale caprock.  
Figure 1B shows the heterogeneous model with 7000 m in width and 2500 m in thickness (including the thickness of the shale caprock of about 1500 m). This latter model represented part of an actual sandstone aquifer, and it was built with seismic and well data from three wells drilled in that area, located at the Campos basin, Rio de Janeiro state in Brazil. This sector model had a pore volume of about 160 million m\({}^{3}\); the gridblock size was 100 \(\times\) 100 m\({}^{2}\) horizontally and 5 m thick. A grid refinement was performed around the injector to reduce the gridblock size from 100 m to 25 m, using the workflow proposed by [PERSON] et al. [26].  
Table 1 summarizes the key petrophysical properties assigned to both models.  
The relative permeability curves for CO\({}_{2}\) and brine in sandstone and shale were obtained by [PERSON] and [PERSON] [27]. The CO\({}_{2}\)--brine capillary pressure curves were obtained from a J-function fitted to the data from [PERSON] et al. [28] for the sandstone and from [PERSON] and [PERSON] [29] for the shale. As the mean ratio k/\(\varphi\) was the same in both models, the capillary pressure curve resulting from the J-function is also the same. Figures 2 and 3 show the final drainage curves used in the simulation for the aquifer and the caprock, respectively. The imbibition curves will be generated according to the hysteresis model to be detailed in the next section.  
The capillary pressure in the shale caprock exhibited a threshold of 318 kPa, as depicted in Figure 3. This threshold represented the minimum pressure required to exceed the capillary forces and enable free super-critical CO\({}_{2}\) migration into the caprock.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Homogeneous Model**} & \multicolumn{2}{c}{**Heterogeneous Model**} \\ \hline  & **Sandstone** & **Shale** & **Sandstone** & **Shale** \\ \hline porosity (\(\varphi\)) & 0.15 & 0.10 & 0.21 (mean) & 0.10 \\ permeability (\(k\)) & 100 mD & 0.001 mD & 140 mD (mean) & 0.001 mD \\ \(k_{\mathrm{o}}/k_{\mathrm{h}}\) ratio & 0.1 & 0.1 & 0.1 & 0.1 \\ pore compressibility & 5.8 \(\times\) 10\({}^{-7}\) kPa\({}^{-1}\) & 5 \(\times\) 10\({}^{-8}\) kPa\({}^{-1}\) & 5.8 \(\times\) 10\({}^{-7}\) kPa\({}^{-1}\) & 5 \(\times\) 10\({}^{-8}\) kPa\({}^{-1}\) \\ relative permeability & Figure 2 & Figure 3 & Figure 2 & Figure 3 \\ capillary pressure & Figure 2 & Figure 3 & Figure 2 & Figure 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the main petrophysical properties used in the geological models.  
Figure 3: Drainage relative permeability (**left**) and capillary pressure (**right**) for the shale caprock.  
Figure 2: Drainage relative permeability (**left**) and capillary pressure (**right**) for the sandstone.