## 3 Results and Discussion  
### Simulation Validation  
Common commercial simulators still employ the traditional PR-EOS or SRK-EOS, without considering the effects of nanopore constraints on phase behavior [49]. For example, the CMG-GEM simulator (Version 2022) uses a hysteretic relative permeability approximation to simulate changes in flow caused by compositional variations. Therefore, this section adopts a model degradation approach, comparing the multiscale compositional model with the ECLIPSE E300 simulator (Version 2022) to validate the accuracy of the multiscale calculations in the current model. The validation employed a one-dimensional, two-phase model (1000 \(\times\) 1 \(\times\) 0.1 m), with its 3D view depicted in Figure 2. The parameters for the validation reservoir model are presented in Table 1.  
Carbon dioxide was injected into a mixture of CO\({}_{2}\), methane, and decane (10% CO\({}_{2}\) + 30% C\({}_{1}\) + 60% C\({}_{10}\)). The model comprises 1000 grid cells, with an initial reservoir temperature of 150 \({}^{\circ}\)C and an initial pressure of 7.5 MPa. The initial component properties are summarized in Table 2. The relative permeability curves are shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Model Grid**} & \multirow{2}{*}{\begin{tabular}{c} **Grid Size** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Initial** \\ **Reservoir** \\ **Temperature** \\ **(\(\lx@sectionsign\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Density** \\ **Reservoir** \\ **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Porosity** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Permeability** \\ **(mD)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Injection** \\ **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Production** \\ **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Simulation** \\ **Time** \\ **(Year)** \\ \end{tabular} } \\ \cline{1-1}  & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Validation reservoir model parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Pc (Bar)**} & \multirow{2}{*}{**Tc (K)**} & \multirow{2}{*}{**Vc (L/mol)**} & \multirow{2}{*}{**Mol. Weight**} & \multirow{2}{*}{**Acentric Fact**} & \multicolumn{2}{c}{**Initial Total**} \\  & & & & & & **Composition Values** \\ \hline C\({}_{1}\) & 45.922 & 190.654 & 0.09863 & 16.04 & 0.01142 & 0.3 \\ C\({}_{10}\) & 21.03 & 617.7 & 0.6098 & 142.28 & 0.4884 & 0.6 \\ CO\({}_{2}\) & 73.733 & 304.128 & 0.09412 & 44 & 0.22394 & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Component properties of the fluid mixture in the one-dimensional validation model. Figure 2: Schematic diagram of the 3D model. To ensure consistent time step selection across simulators, the problem is discretized into a large number of time steps. Given the relatively low pressure, phase behavior exhibits strong pressure dependence, with all components present in both phases. Since the well operates under bottom-hole pressure control, the injected fluid volume relies on precise calculations of fluid properties and densities within the reservoir. To validate the simulator (MS)'s accuracy, the predicted cumulative oil production curve over 20 years (Figure 4) and the total molar fractions of different components at various stages were compared with results from ECLIPSE E300 (Figure 5). The minimal discrepancies between the two sets of results confirm the reliability of the proposed simulator. Additionally, due to the large number of time steps in the model calculations, the runtime logs for the first 50-time steps were extracted to compare the computational efficiency of the traditional fully implicit (FI) method with the multiscale method proposed in this study.