# Optimization of Offshore Saline Aquifer CO2 Storage in Smeaheia Using Surrogate Reservoir Models
## 1 Introduction
Furthermore, SRMs were exploited for injection optimization in CO\({}_{2}\) Storage and CO\({}_{2}\)-EOR by [PERSON] et al. [30], [PERSON] et al. [31], [PERSON] et al. [32], [PERSON] et al. [33]. Various optimization algorithms were used such as GA [30; 32; 34; 35], Ant Colony [31], Hooke-Jeeves Direct Search [36], SIMPLEX (a simple optimization technique by linear programming), and Generalized Reduced Gradient [13]. The main aim of these works was optimizing the CO\({}_{2}\) injection rate, Water Alternating Gas (WAG) cycle, slug size, and well location to maximize Field Oil Production Total and CO\({}_{2}\) storage capacity based on operational goal and CO\({}_{2}\) storage type (in saline aquifer or CO\({}_{2}\)-EOR). Various machine learning algorithms, such as Artificial Neural Network (ANN), Support Vector Machine, and Random Forest, can be employed for proxy modeling [37]. Due to the strong performance in highly non-linear problems and precise predictive capabilities of Artificial Neural Networks (ANNs) [38; 39; 40], much research has utilized this method or its advanced variations, such as Deep Neural Networks (DNNs), Convolutional Neural Networks (CNNs), or Recurrent Neural Networks (RNNs), for surrogate reservoir modeling [41; 42]. [PERSON] [43] integrated a grid-based and a well-based SRM to optimize CO\({}_{2}\)-EOR by utilizing ANN. They used a cascading (sequential) grid-based approach to simulate the distribution of CO\({}_{2}\) mole fraction, pressure, water saturation, and oil saturation in a compositional model. A cascading approach produces distinct SRMs for each time step and parameter. The model output at the preceding time step, \(t-1\), becomes the model input at time step \(t\). In addition, the robust SRM accurately simulated the production rate and the total amount of oil produced. [PERSON] [44] employed ANN to build grid-based SRMs for coarse and fine grid models using cascading and non-cascading approaches. Unlike cascading, the non-cascading method involves creating a single model for the entire simulation time for each parameter. Only the original state of dynamic features at time step zero is provided to the model. As a result, the cascading grid-based SRM (SRM\({}_{\text{G}}\)) led to the accumulation of errors from each time step with prior time steps, resulting in lower accuracy compared to the non-cascading approach. In addition, the non-cascading SRM\({}_{\text{G}}\), which was constructed using the fine-grid model, led to greater precision in predicting pressure but a bigger margin of error in predicting saturation when compared to the coarse-grid model. [PERSON], et al. [45] employed DNNs to develop field-based proxy models and address a multi-objective optimization problem through the utilization of NSGA-II (Non-dominated Sorting Genetic Algorithm II) in two reservoir models. The research was conducted to investigate the application of CO\({}_{2}\)-WAG (Water Alternating Gas) in order to optimize oil recovery and CO\({}_{2}\) storage in the reservoir. The study focused on optimizing the injection rates of gas and water, as well as the duration of half-cycles. [PERSON] et al. [46] proposed an economical optimization framework that combines machine learning models and several optimization techniques to determine the ideal setting for injecting flue gas-WAG into the \"Gullfaks\" reservoir. Proxy models such as DNN, Cascade Forward Neural Network (CFNN), Radial Basis Function, and Generalized Regression Neural Network were used in this study to develop robust machine learning models. The CFNN and DNN models exhibited the most accurate predictions for recovery factor and CO\({}_{2}\) storage. A limitation of the current SRM studies (presented briefly in this section) lies in their applicability to real-world field development planning, which requires long-term simulation and optimization of numerous temporal and spatial factors. The majority of the aforementioned works have a brief and restricted time span.