# Optimization of Offshore Saline Aquifer CO2 Storage in Smeaheia Using Surrogate Reservoir Models
## 3 Methodology
### Proxy Modeling  
As previously mentioned, there are three distinct categories of SRMs: field-based, well-based, and grid-based. The choice of a single or coupled-type SRM depends on the specific SRM application. Due to the need to control and monitor CO\({}_{2}\) saturation and pressure at different sites both horizontally and vertically in order to optimize storage, a grid-based SRM (SRM\({}_{\text{G}}\)) will be constructed for each parameter. Figure 9 demonstrates the proxy modeling workflow. An ANN requires a wide range of input data in order to effectively learn the behavior of a phenomena and accurately predict outputs under different conditions. If there is a lack of or insufficient actual data, synthetic data are generated using analytical or numerical models. Since the Smeaheia project has not yet started, we will use numerical simulation to generate the necessary data. The optimization variables are injection rate and injection time; so, an adequate number of scenarios were investigated to define the model response as a function of injection rates and times. This dataset represents the training data. To develop SRM\({}_{\text{G}}\), [PERSON] [44] used three simulation cases with a fixed injection period and different injection rates and added two more cases to enhance the precision at the periphery of the CO\({}_{2}\) accumulation area. According to the workflow (Figure 9), the quantity of numerical simulation cases that impact the ANN's accuracy and ability to generalize to diverse inputs was tuned while training. Accordingly, in this study, the proxy development began by presenting the outcomes of three simulated scenarios and continued with seven cases until the acceptance of the model's accuracy. Due to the superior performance of proxy models in interpolation compared to extrapolation, the injection rate range for numerical simulations should be limited to the minimum and maximum admissible rates. The maximum possible rate, without exceeding the bottom-hole pressure constraint, is 5.5 Mt/year. Therefore, seven rates between 1.3 Mt/year and 5.5 Mt/year will be chosen, as shown in Figure 10.  
Sensitivity analyses were developed considering time steps in the range from 1 month up to 5 years within the fixed simulation time frame of 50 years of CO\({}_{2}\) storage. On the basis of the results, a 6-month time step was selected, balancing accuracy and generated data volume, splitting the simulation time into 100 steps. Further sensitivity analysis on the cascading and non-cascading SRM method was performed. The cascading approach showed numerous drawbacks in terms of error accumulation, complexity, and time-consuming step-by-step predictions. Therefore, the non-cascading approach was adopted and the input features for training the ANN were selected and listed in Table 1.  
The qualities and conditions of neighboring cells surrounding a grid block must be considered as a boundary condition, because they impact the movement of fluids. During the process of injecting and storing CO\({}_{2}\), the CO\({}_{2}\) moves upwards due to gravitational forces and changes the level of CO\({}_{2}\) saturation in the grids, depending on the properties of the layers above and below. A tier model was developed to determine the average pressure, saturation, permeability, and porosity of neighboring grid blocks for each cell in the current layer (the cell layer), as well as the layers directly above and below it. These average properties are referred to as tier-1, tier-2, and tier-3, respectively. Indeed, the average property of cells, which are connected to the main grid block through a surface, line, and point, is computed in three sequential layers. Apart from permeability, which uses a harmonic averaging method shown by this Equation (5), the average of all the other parameters is computed by the arithmetic method.