## 6 Conclusions  
In this study, the well placement optimization problem was handled as a Bayesian Optimization one. To our knowledge, this was the first attempt of applying BO in a well placement CCS setting. The analysis focused on several key modifications and comparisons to enhance the efficiency and effectiveness of the optimization process. Firstly, the issue of the input space's infeasible area was addressed by introducing a mapping to a modified input space. This adjustment allowed the algorithm not to be concerned with exploring  
Figure 15: Injection rates: optimal case (blue line) vs. sub-optimal case (red line). the infeasible regions by itself, a process which would require hundreds of thousands of iterations. Furthermore, a novel kernel modification was proposed, aiming at achieving invariance under permutations of the input vectors. This adaptation not only enhanced the robustness of the optimization process but also ensured that the model's performance remained consistent across different permutations, a crucial consideration in real-world well optimization. Subsequently, comprehensive analyses were conducted by using various acquisition functions, including expected improvement (EI), upper confidence bound (UCB), and probability of improvement (POI). Through comparative graphs, the performance differences among these functions was illustrated, providing valuable insights into their respective strengths and limitations in the context of CCS well placement optimization. One of the primary contributions of this study was the comparative evaluation of the developed modified kernel against its unmodified counterpart and a random function. The obtained findings unequivocally demonstrated the substantial impact of the modified kernel on optimization efficacy. After extensive testing, we successfully optimized the sequestration of CO\({}_{2}\) in a saline aquifer. The resulting scenario reflects both intuitive engineering principles and computational efficiency. Our efforts culminated in a comprehensive case study outlining the optimal sequestration of 115 million tons of CO\({}_{2}\) over a four-decade period. This achievement represents 80% of the theoretically maximum value of 142 million tons, signifying exceptional efficiency within a closed system. Typically, breakthrough and pressure buildup pose significant challenges in such processes, often limiting their duration and effectiveness. In conclusion, this study significantly enriches the ongoing discourse surrounding Bayesian Optimization and its practical implementation in complex domains like CCS. Through the introduction of bespoke modifications and comprehensive comparative analyses, a solid foundation for future progress in optimization methodologies has been established, tailored specifically to the nuanced challenges of real-world scenarios. Our efforts pave the way for further refinement and expansion of these techniques, bringing us ever closer to harnessing the complete capabilities of Bayesian Optimization in addressing the intricate well placement problem. Moving forward, the exploration of advanced exotic Bayesian Optimization procedures and frameworks becomes a priority, thereby pushing the boundaries of optimization capabilities in CCS and related fields. This includes extending our methodology to accommodate various types of wells, such as horizontal, inclined, and multi-segment wells, which pose unique challenges due to their non-traditional geometries and flow characteristics. Additionally, the importance of addressing geological uncertainty and the complexities of diverse formations is recognized; thus, future research endeavors will focus on incorporating these factors into the optimization framework. Furthermore, to enhance the industry relevance and real-life applicability of this research, the integration of a net present value (NPV) objective function into the optimization model is intended to be incorporated.