# Optimization of Offshore Saline Aquifer CO2 Storage in Smeaheia Using Surrogate Reservoir Models
## 1 Introduction  
The main target of the Paris Agreement in December 2015 was to concentrate efforts on limiting temperature increases (above pre-industrial levels) below 1.5 \({}^{\circ}\)C [1]. Based on research findings [2], if there is not a significant reduction in greenhouse gas emissions before 2030, global warming will exceed 1.5 \({}^{\circ}\)C; consequently, the permanent demise of delicate ecosystems is inevitable. Carbon capture and storage (CCS) is an efficient method that targets CO2 emissions at their origin and has the potential to lead to a 15% reduction in overall emissions by 2050 [3]. CCS is a promising strategy for addressing climate change that involves trapping and purifying CO2 emissions from industrial and energy sources, rather than emitting them into the atmosphere. The captured CO2 is then transported and stored permanently in the underground, either onshore or offshore [4, 5]. Different techniques for storage and utilization of CO2 underground have been developed, including storing it in saline aquifers, utilizing it to enhance oil and gas recovery, recovering methane from coal beds, using it in geothermal systems, storing it in compressed air energy storage systems, and converting it into carbonate minerals in situ [6]. The geological storage of CO2 presents five possible risks: CO2 and CH4 leakage, seismicity, ground movement, and brine migration [7, 8]. Prior to injection, the primary objective is to ensure that CO2 does not flow through pre-existing fractures and faultsor newly created fractures in the caprock due to pressures exceeding the fracture pressure. Additionally, it is important to maintain the effectiveness of the caprock seal, as measured by breakthrough capillary pressure values [9; 10] and legacy wells [11; 12]. Hence, optimizing the storage process can prevent such risks by defining proper objectives and constraints [13; 14; 15]. Traditionally, the optimization of storage activities has been faced via multi-physical 3D numerical simulation approaches, which allow a holistic vision of the phenomena involving geological, fluid-flow, geochemical and geomechanical aspects. However, the high degree of accuracy in the phenomena simulation could be counteracted by time-consuming computational efforts [16; 17]. A promising alternative, Proxy Modeling, reproducing simulation outputs from input features through mathematical or statistical functions, has been used to substitute physics-based reservoir simulations [18; 19] and enhance computational time by orders of magnitude [20; 21]. There are several types of proxy models including reduced-physics, the reduced-order modeling (ROM) approach, statistics-based techniques, and artificial intelligence (AI)-based methods [22; 23]. The Smart Proxy Model (SPM) or Surrogate Reservoir Model (SRM) is a data-driven model that uses machine learning to replace/aid computationally intensive numerical models. It can accurately reproduce the pressure and saturation distribution, for instance, across the grid cells at each time step [24]. Computationally expensive optimization tasks (injection or production) can be performed by SRMs to reduce the computational time. [PERSON], et al. [25] developed a field-based SRM and later optimized the reservoir production through the Genetic Algorithm (GA). [PERSON] et al. [26] used adaptive moment estimation (Adam) to build an SPM for a fractured reservoir and optimize production [27]. Based on ten realizations of the Egg Model, [PERSON] et al. [28] showed how multilayer perceptron may be used to create data-driven models. To perform waterflooding optimization, these models were then combined with two nature-inspired algorithms, namely particle swarm optimization and the gray wolf optimizer. In parallel, they compared the optimizers' performance, which resulted in good prediction accuracy. [PERSON] et al. [29] enhanced proxy modeling applications for waterflooding optimization by utilizing a sophisticated machine learning algorithm, Long Short-Term Memory (LSTM).