## 1 Introduction
Their approach was different in that they utilized an objective function that measures the ratio of the volume of mobile CO\({}_{2}\) phase (plume) over the volume of CO\({}_{2}\) injected after 10 years of injection and 80 years of monitoring. Their goal was to minimize this ratio, since by minimizing the plume, leakage risk is also reduced. In essence, they tried to find configurations that maximized the residual and solubility trapping of CO\({}_{2}\). In their work, PSO was able to find the optimal value of 12.5% in 500 simulation runs, while GA needed more than 850. Similarly, [PERSON] and [PERSON] (2013) ([PERSON] et al., 2019) utilized a similar objective function by using a global sampling method known as Latin Hypercube Sampling (LHS) ([PERSON] et al., 2019). Notably, in their work, they enhanced the definition of immobile CO\({}_{2}\) by taking into account the irreducibility of relative permeability curves. Besides the mentioned landmark works, there have been dozens more published on this optimization problem. [PERSON] et al. (2020) ([PERSON] et al., 2020) provided a detailed review of research conducted on the well placement optimization problem, focusing mostly on derivative-free and machine learning regression methods. Bayesian Optimization (BO) ([PERSON] et al., 2019) is a global optimization method that efficiently constructs and updates surrogate models representing black-box objective functions, rendering it suitable for addressing the well placement optimization problem. In this work, our goal is to apply this method to optimize the carbon sequestration capabilities of a saline aquifer. BO represents a cutting-edge methodology that dynamically balances the exploration of the solution space with the exploitation of promising regions to efficiently discover well placement that can lead to the global optimum configuration. BO relies on constructing a probabilistic surrogate model, often a Gaussian Process (GP), to approximate the underlying objective function, which, in this context, measures total carbon storage. This surrogate model not only captures the observed data but also quantifies the uncertainty associated with predictions, allowing for the incorporation of prior knowledge and continuous refinement as new information becomes available through successive simulation runs. By iteratively selecting well locations based on the surrogate model's predictions and subsequently updating the model with the actual reservoir response, BO intelligently adapts its search strategy. This adaptive nature makes it particularly well suited for navigating the high-dimensional and uncertain parameter space, providing a systematic and data-driven means of identifying optimal well configurations for enhanced carbon sequestration. BO for well placement optimization was implemented in the work of [PERSON] et al. (2020) ([PERSON] et al., 2020). In their work, the researchers attempted to optimize well locations by maximizing the cumulative drainage area of wells by using various derivative-free methods, with BO being one of them. In another work, [PERSON] et al. (2020) ([PERSON] et al., 2020) utilized a BO framework for field development planning while quantifying the effect of geological uncertainty. They generated a surrogate model that was able to identify well placement positions that maximized NPV while accounting for uncertainty. [PERSON] ([PERSON], 2019, 2020) also presented works on novel BO realizations, such as trust region BO ([PERSON] et al., 2020) and sparse-axis-aligned subspaces BO (SAASBO) ([PERSON] et al., 2020). BO has additionally been investigated for optimizing various decision variables crucial in reservoir exploitation besides well placement. [PERSON] et al. (2022) [47] utilized BO to optimize the time cycle of gas/surfactant injection in Water Alternating Gas (WAG) schemes. Their study conducted at the Cranfield reservoir site resulted in a 16% increase in gas storage volume and a 56% reduction in water/surfactant usage compared with the baseline WAG schedule.