## 3 Results and Discussion
### Multi-Objective Optimization with Well Allocations
Injecting more CO\({}_{2}\) requires the higher BHP at the facilities and negatively affects the trapping efficiency, \(f_{2}(X)\), because the injection amount (\(V_{\text{Inj}}\)) is located at the denominator. Thus, the two objective functions are dependent. \[F(X)\ =\text{argmin}\left[ \begin{array}{cc}f_{1}(X)\ =\ \sum\text{argmax}(P_{w})\\ f_{2}(X)\ =\ -\frac{V_{\text{Trap}}}{V_{\text{Inj}}}\end{array} \right. \tag{5}\]  
In Equation (5), \(P_{w}\) means BHPs observed at a well, \(w\) (\(\forall w\) = II, I2, I3, I4), which has been monitored for 200 years. \(\text{argmax}(P_{w})\) means the maximum \(P_{w}\) that should be kept smaller than the formation fracture pressure ( = 150 bar assumed at the reference depth, 840 m). If \(\text{argmax}(P_{w})\) is greater than the fracture pressure, this scenario is excluded at the optimization process. \(X\) consists of daily CO\({}_{2}\) injection rate assigned at each injector; \(x_{w}\in X\), \(x_{w}\) is the CO\({}_{2}\) injection rate (m\({}^{3}\)/day) at \(w\)-th well. The parameters in the genetic algorithm are as follows; crossover is 0.7, mutation rate is 0.02, and the maximum iteration is 50. The daily CO\({}_{2}\) injection rate is fixed as 16,000 m\({}^{3}\)/day and four vertical wells (II, I2, I3, and I4) split this value; the injection rates, less than 4000 m\({}^{3}\)/day for each well, are assigned randomly to three wells (I2, I3, and I4) and the remaining value is set at II. This study sets the constraint that the rate allocated at the well should be kept until 30 years. The total volume of CO\({}_{2}\) injected over 30 years (\(V_{\text{Inj}}\); total volume of CO\({}_{2}\) injection) is 175.2 million cubic meters (= 16,000 m\({}^{3}\)/day \(\times\) 365 days \(\times\) 30 years). Figure 5 depicts the Pareto solutions with the lowest rank and non-domination: Figure 5a presents Pareto solutions for \(L\) aquifer and Figure 5b for \(H\) aquifer. In terms of \(f_{1}\), two cases are chosen for each aquifer: L-1 means the lowest \(f_{1}\) and L-2 is located at the opposite side. H-1 and H-2 are selected at the boundaries of \(f_{1}\) for \(H\) aquifer in the same way. The distribution of Pareto solutions show that the \(L\) aquifer model can store more CO\({}_{2}\) with smaller BHP compared to the highly heterogeneous \(H\) aquifer. The maximum trappable volume of \(L\) aquifer (the mechanism of combined structural and residual trapping) is 754,304 m\({}^{3}\), while \(H\) aquifer remains at 582,005 m\({}^{3}\). The sum of maximum BHPs of \(L\) aquifer is 505.37 bar, but that of \(H\) aquifer is 506.5 bar (Table 3). The maximum BHP is assigned at II well: 132.55 bar for \(L\) aquifer and 134.35 bar for \(H\) aquifer. To sum up, these results show that a less heterogeneous aquifer with large pore volume would be positive for the trapping and cost-effective operation. Table 3 summarizes the results of the optimal well allocations, the maximum BHP at an injection well across 200 years, and the trapping volume. The optimal well allocations suggest the large amount of CO\({}_{2}\) injection through I1 well with a high BHP. CO\({}_{2}\) plumes can move from the I1 well area to the others. As the injection progresses, the pore pressure increases from 120 bar (assigned before the sequestrating operation). The small difference between the BHP and the pore pressure is able to obstruct CO\({}_{2}\) injection at the late period. Severe inter-well interference might occur, disturbing the facility operation. Under the constraint of maintaining the allocated rate, this strategy of well allocation reasonably supports the maximization of the permanent trapping but also the minimization of the sum of the operating pressures. The CO\({}_{2}\) volume injected into the aquifer is divided in the order of movable plume, residual trapping with plume, residual trapping, structural trapping, and the combined structural and residual trapping in a row. The form of movable plume accounts for 60 to 70% of the total injection.