## 3 Modeling CO\({}_{2}\) Entrapment for Sandstone and Shale Formations  
The sandstone saline aquifer and its shale caprock in the model in this study were numerically simulated using CMG-GEM [63]. CMG-GEM is known for its versatility and robustness in predicting and analyzing various thermodynamic properties and fluid behavior for GCS projects [2; 3; 16; 50; 64]. It is based on the discretization of component conservation and energy balance equations in space and time using finite volume and finite difference methods [65; 66].  
One of the key strengths of the CMG-GEM model lies in its accurate prediction of CO\({}_{2}\) phase behavior for wide ranges of pressure and temperature. It can effectively capture  
Figure 1: 3D view of the geological model showing porosity distribution and injector well position (**left**). A sliced view highlighting the depth of the reservoir and porosity characteristics (**right**). Coordinates are in meters.  
Figure 3: Drainage relative permeability (**left**) and capillary pressure ((**right**) in orange) for the shale caprock.  
the transition of CO\({}_{2}\) from gaseous to liquid states, as well as its behavior in supercritical conditions. Overall, the CMG-GEM simulation model enables accurate prediction and analysis of CO\({}_{2}\) behavior and the following trapping mechanisms:  
* CO\({}_{2}\) solubility in brine is modeled in this study by applying the Li and Nghiem model [67]. This model has been calibrated using published experimental data, and it calculates [PERSON]'s constant based on Equation (1), which considers the pressure and temperature variations. Additionally, the impact of brine salinity on gas solubility in the aqueous phase is accounted for through the salting-out coefficient [68]. \[ln(H_{i})=ln(H_{i}^{*})+\frac{\overline{v_{i}}}{RT}(p-p^{*})\] (1) where \(H_{i}\): [PERSON]'s constant at current pressure (\(p\)) and temperature (\(T\)); \(H_{i}^{*}\): [PERSON]'s constant at reference pressure (\(p^{*}\)) and temperature (\(T\)); \(\overline{v_{i}}\): partial molar volume at infinite dilution; \(R\): universal gas constant; \(i\): species dissolved in water (CO\({}_{2(\text{aq})}\) in this work). The \(H_{i}^{*}\) constant was computed considering the initial conditions of the models in Table 2. \(\bullet\) Solubility trapping in brine can be enhanced through physical diffusion, which is mandatory for an accurate representation of the convective mixing to obtain a grid-converged solution. To model this effect, even in a simplified way due to our model's scale, the diffusion coefficient (\(D\)) for supercritical CO\({}_{2}\) in brine is applied to compute the effective CO\({}_{2}\) diffusion (\(D_{\text{eff}}\)) considering tortuosity \(\tau\)[69]: \[D_{eff}=\frac{D}{\tau}\] (2) In shales, where diffusion is a relevant mechanism due to lower permeability, the tortuosity value ranges from approximately 40 to 70 [70]. An effective diffusion equal to 2.8 \(\times\) 10\({}^{-7}\) cm\({}^{2}\)/s [71] is used in the simulations. \(\bullet\) The residual CO\({}_{2}\) trapping due to the relative permeability and capillarity hysteresis with the saturation changes was modeled with the maximum gas trapped (\(S_{gt}\)) converted to the Land's constant I [72] in the two-phase [PERSON]'s model [73], according to Equation (3): \[S_{gt}=\frac{S_{g\ max}}{1+CS_{g\ max}}\] (3) where \(S_{g\ max}\) is the maximum gas saturation. [PERSON] and [PERSON] [74] obtained a \(S_{gt}\) distribution for sandstone, shale, and carbonates based on more than 30 published coreflood data for CO\({}_{2}\) and brine. The mean values for each lithology are presented in Table 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **Saline Aquifer** \\ \hline Reference pressure & 11,800 kPa @ 1000 m \\ Temperature & 80 \({}^{\circ}\)C \\ Salinity & 50,000 ppm \\ \(H_{i}^{*}\) & 5.66 \(\times\) 10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the reference conditions applied to the solubility calculation in the aquifer models.