## 3 Modeling CO2 Entrapment for Sandstone and Shale Formations  
The sandstone saline aquifer and its shale caprock in the aforementioned models were numerically simulated using CMG-GEM [30]. CMG-GEM is known for its versatility and robustness in predicting and analyzing various thermodynamic properties and fluid behavior for CCS projects [2; 3; 11; 22; 26]. It is based on the discretization of component conservation and energy balance equations in space and time using finite volume and finite difference methods [31; 32]. One of the key strengths of the CMG-GEM model lies in its accurate prediction of CO2 phase behavior for wide ranges of pressure and temperature. It can effectively capture the transition of CO2 from gaseous to liquid states, as well as its behavior in supercritical conditions, which is crucial for understanding and studying CO2 storage. Overall, the CMG-GEM simulation model enables accurate prediction and analysis of CO2 behavior and the following trapping mechanisms:  
* CO2 solubility in brine according to the method by [PERSON] and [PERSON] [33] based on Henry's law. This model is based on [PERSON]'s constant calculation according to Equation (1) as a function of pressure and temperature. The effect of salt on the gas solubility in the aqueous phase is modeled by the salting-out coefficient [34]. \[ln(H_{i})=ln(H_{i}^{*})+\frac{\overline{v_{i}}}{RT}(p-p^{*})\] (1) where: \(H_{i}\) is [PERSON]'s constant at current pressure (\(p\)) and temperature (\(T\)); \(H_{i}^{*}\) is [PERSON]'s constant at reference pressure (\(p^{*}\)) and temperature (\(T\)); \(\overline{v_{i}}\) is the partial molar volume at infinite dilution; \(R\) is universal gas constant; \(I\) is species dissolved in water (CO2(aq) in this work). The \(H_{i}^{*}\) constant was computed considering the initial conditions of the models in Table 2.
* Solubility trapping in brine can be enhanced by diffusion. To model this effect, the diffusion coefficient (\(D\)) for super-critical CO2 in brine is applied to compute the effective CO2 diffusion (\(D_{\textit{eff}}\)) considering tortuosity \(\tau\)[35]: \[D_{\textit{eff}}=\frac{D}{\tau}\] (2) In shales, where diffusion is a relevant mechanism due to lower permeability, the tortuosity value ranges approximately from 40 to 70 [36]. An effective diffusion equal to 2.8 \(\times\) 10\({}^{-7}\) cm\({}^{2}\)/s [37] was used in the simulations. * Chemical trapping by adsorption of CO2 in the gas phase was modeled using a Langmuir model [38], which is a widely accepted isotherm adsorption equation [39; 40]. With data for shales [41; 42] and sandstone [43], two isotherms were matched to model the adsorption. Table 3 summarizes Langmuir parameters (\({}^{B}CO_{2}\) and \({}^{\omega}CO_{2,max}\)  
\begin{table} \begin{tabular}{l c c} \hline \hline  & **Homogeneous Saline Aquifer** & **Heterogeneous Saline Aquifer** \\ \hline Initial pressure & 11,800 kPa at 1000 m & 7159 kPa at 730 m \\ Temperature & 80 \({}^{\circ}\)C & 70 \({}^{\circ}\)C \\ Salinity & 50,000 ppm & 70,000 ppm \\ \(H_{i}^{*}\) & \(5.66\times 10^{5}\) & \(6.44\times 10^{5}\) \\ \hline \hline \end{tabular}   
* Solubility trapping in brine can be enhanced by diffusion. To model this effect, the diffusion coefficient (\(D\)) for super-critical CO2 in brine is applied to compute the effective CO2 diffusion (\(D_{\textit{eff}}\)) considering tortuosity \(\tau\)[35]: \[D_{\textit{eff}}=\frac{D}{\tau}\] (2) In shales, where diffusion is a relevant mechanism due to lower permeability, the tortuosity value ranges approximately from 40 to 70 [36]. An effective diffusion equal to 2.8 \(\times\) 10\({}^{-7}\) cm\({}^{2}\)/s [37] was used in the simulations. * Chemical trapping by adsorption of CO2 in the gas phase was modeled using a Langmuir model [38], which is a widely accepted isotherm adsorption equation [39; 40]. With data for shales [41; 42] and sandstone [43], two isotherms were matched to model the adsorption. Table 3 summarizes Langmuir parameters (\({}^{B}CO_{2}\) and \({}^{\omega}CO_{2,max}\))