## 3 Results and Discussion
### Multi-Objective Optimization with Well Allocations
From 30 years to 200 years, the percentage at \(L\) aquifer decreases from 73% to 64%, while that of \(H\) aquifer is reduced from 68% to 61%. Thus estimates that the heterogeneity degree (Dykstra-Parsons coefficient) contributes to make these differences; the highly heterogeneous \(H\) aquifer has more obstruction for plume movement so that the shale beds would be positive in reducing the leakage risk. Figure 10 plots the trends of the combined structural and residual trapping of both aquifers. The less heterogeneous \(L\) aquifer increases the combined trapping until 200 years, while the increment in trapping volume of the highly heterogeneous \(H\) aquifer stops at around 80 years. This result recommends that if a decision maker wants to sequestrate a small volume within a relatively short time, the high heterogeneous aquifer would be favorable with a large amount of shale layers in the sandstone. However, an increment in the operating cost would be needed to maintain the high injection pressure. Figure 10: CO2 trapping trends with time: (**a**) \(L\) aquifer model with L-1 and L-2 cases (less heterogeneous); (**b**) \(H\) aquifer model with H-1 and H-2 cases (highly heterogeneous). Figure 9: Comparison of movable plume (the ratio of CO2 volumes that are movable as the plume forms to the total injection amount) between the \(L\) and \(H\) aquifer models. The total CO2 amount injected is 1.752 million cubic meter for each aquifer. The difference made by the optimal conditions at the given aquifer model, e.g., L-1 and L-2 or H-1 and H-2, is negligible. The results can be used to identify the properties significantly influencing both operation condition and trapping efficiency. Pareto optimality is obtained with non-domination among the solutions, and it provides a well allocation strategy that satisfies the aforementioned multi-objectives. This method is limited in its ability to search for non-dominated solutions; this study does not assume any tolerance or constraints of objective functions, so, while the small differences in objective values can be used to distinguish between the solutions, the differences are not significant. One solution to this limitation would involve the use of constraint scenarios, e.g., setting the two values as the same value if the difference in BHPs is negligible from the operator's view. The simulation results confirm the typical characteristics of a highly mobile CO\({}_{2}\) plume in a brine-saturated system; it moves upward in the early period, reaches the impermeable cap rock, and then spreads horizontally. Thus, the geological features of the upper part of heterogeneous aquifers govern the plume flow. The trapping amounts are mainly influenced by the pore volume, while CO\({}_{2}\) movement is significantly affected by the aquifer heterogeneity. Assessing uncertainty is an important step in elucidating the characteristics of CO\({}_{2}\) sequestration in heterogeneous media. To achieve more realistic applications, detailed descriptions of the geological as well as fluid properties--e.g., capillary trapping and hysteresis--are essential [30]. The challenges associated with this work are as follows. An individual well has been constrained to an allocated fixed rate during the entire period of the CO\({}_{2}\) injecting process. While this does reduce the enormous number of potential cases, this constraint limits this method to making rational decisions based on continuously updating dynamic data. The objective functions in the optimization problems must be appropriately relevant to result in trade-offs that satisfy the decision makers. The conflicting goals that may arise represent a problem in the proper decision-making process. This paper focuses on the sensitivity of spatial properties related to geological uncertainty. Further sensitivity analyses that include the operating conditions would be able to evaluate whether or not the objective functions have been reliably defined.