## 3 Results and Discussion
### Multi-Objective Optimization with Well Allocations
The simulation results are in agreement with a typical feature of supercritical CO\({}_{2}\) plume movement; supercritical CO\({}_{2}\) is much more mobile than the formation water and, thereby, moves faster to the aquifer top than brine flows downward ([PERSON] et al., 2016). Figure 6 depicts the height of the CO\({}_{2}\) column over time. At 30 years, the column is highest near I1 well where most of the CO\({}_{2}\) is injected. As time passes, many of the mobile CO\({}_{2}\) plumes move upward and spread horizontally when they reach the impermeable cap rock. Eventually, most of the CO\({}_{2}\) is present near the top of the aquifer. The column near I1 well gradually decreases and the distributed area expands below the  
Figure 5: Pareto solutions with non-domination: (**a**) \(L\) aquifer model; (**b**) \(H\) aquifer model. For each aquifer model, two cases are selected such as L-1 and L-2 for \(L\) aquifer model, and H-1 and H-2 for \(H\) aquifer model. L-1 satisfies the lowest pressure while L-2 is located the opposite side (the highest injection pressure) of \(L\) aquifer model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **L-1** & **L-2** & **H-1** & **H-2** \\ \hline \multirow{4}{*}{Well allocation (m\({}^{3}\)/day)} & I1 well & 14,874 & 14,068 & 14,925 & 14,831 \\  & I2 well & 371 & 360 & 302 & 300 \\  & I3 well & 389 & 463 & 108 & 108 \\  & I4 well & 366 & 1109 & 665 & 761 \\ \hline \multirow{4}{*}{Maximum BHP 1 (bar)} & I1 well & 132.55 & 132.13 & 134.35 & 134.29 \\  & I2 well & 125.88 & 125.90 & 125.72 & 125.72 \\ \cline{1-1}  & I3 well & 123.06 & 123.15 & 122.81 & 122.82 \\ \cline{1-1}  & I4 well & 123.51 & 124.18 & 123.61 & 123.68 \\ \cline{1-1}  & Subtotal & 505.00 & 505.37 & 506.49 & 506.50 \\ \hline \multicolumn{5}{l}{Trapping CO\({}_{2}\) volume 2 (m\({}^{3}\))} & 754,304 & 759,058 & 581,682 & 582,005 \\ \hline \hline \end{tabular}  
* BHP means the bottom hole pressure; 2 the trapping volume is the volume of combined structural and residual trapping during 200 years from the first CO\({}_{2}\) injection.  
\end{table} 
Table 3: Summary of multi-objective optimization for CO\({}_{2}\) sequestration with well allocation. cap rock. Figures 7 and 8 show the spatial distributions of CO2 saturation at the cross sections (A and B line in the \(x\)-\(y\) plane) for L-1 (Figure 7) and H-1 (Figure 8). CO2 saturation is observed at 200 years. CO2 saturation near the injection wells increases similar to the cone shape, but the area where CO2 is occupied is limited at the upper zones of the aquifer (Figure 7b). The high mobility of supercritical CO2 generates an upward flow mainly, even though the vertical permeability is 0.1 of the horizontal permeability. The horizontal spreading phenomenon is possible when CO2 accumulates below the impermeable cap rock. Notwithstanding that this result explains the characteristics of high-mobile CO2 flow, it requires the detailed description of heterogeneity along a vertical direction. Figure 8: Distribution of CO\({}_{2}\) saturation of the H-1 case after 200 years. The distribution of the H-2 case is similar to this distribution: (**a**) \(x\)-\(y\) plane at the top of the aquifer (\(z\) = 840 m depth); (**b**) cross sections (A line and B line). Figure 7: Distribution of CO\({}_{2}\) saturation of the L-1 case after 200 years. The distribution of the L-2 case is similar to this distribution: (**a**) \(x\)-\(y\) plane at the top of the aquifer (\(z\) = 840 m depth); (**b**) cross sections (A line and B line). A notable result related to the heterogeneity is found at the decrement trend of the movable CO2 plume (Figure 9); the percentage of movable plume means the volume ratio of movable plume to total injection. It accounts for most of the CO2 sequestration, e.g., 73% for \(L\) aquifer (estimated at 30 years). The plume has possibilities to turn into the trap, to maintain itself, or to leak out of the boundaries. Thus, the large amount of movable plume is negative on sequestration.