## 2 Background  
These modeling techniques provide valuable tools for enhancing extraction processes and underscore the effectiveness of employing and/or combining RSM, DOE, and ANN methods for optimizing and predicting outcomes in the hydrometallurgical extraction of Cu and Co. This approach offers improved efficiency and higher recovery rates. Finally, understanding the impact of time and the crust/Fe ratio on the leaching process of Co and Mn from ferromanganese submarine crusts is crucial to optimizing efficiency, reducing costs, and improving process sustainability. Analyzing leaching time helps determine the duration required to achieve maximum dissolution of the target metals. Insufficient time may result in incomplete recovery, while excessive durations can lead to inefficiencies and increased costs. The crust/Fe ratio, on the other hand, ensures an adequate amount of leaching agent is available to dissolve the metals without wasting chemical reagents. Striking a balance between the quantity of mineral and the leaching agent minimizes excessive reagent use, significantly reducing operating costs while avoiding issues such as solution saturation or the formation of unwanted precipitates. Examining the relationship between these parameters allows for the fine-tuning of operating conditions to maintain consistent and predictable extraction, reducing variability and enhancing process stability. In summary, a detailed analysis of these variables not only improves the technical and economic efficiency of the leaching process but also delivers operational and environmental benefits essential for modern, sustainable operations [26; 27]. Methods such as population balance modeling (PBM) are employed to predict the distribution of particle sizes in processes like grinding and flotation, supporting the design and optimization of these operations [26]. In terms of the contribution of modeling to mineral processing, models such as the MiSCOR model for the upstream supply chain play a significant role. This model addresses the dynamics of the upstream segment of the mineral supply chain, offering a standardized framework that seamlessly integrates with the downstream segment. It is specifically designed to enhance collaboration and decision-making in mineral supply chain management [28]. Another noteworthy model is model predictive static programming (MPSP), a technique applied to control problems in mineral processing, such as grinding and flotation circuits. MPSP provides computational efficiency and enhanced performance compared to traditional methods, making it a highly viable option for achieving optimal control in mineral processing plants [29]. Geochemical modeling for mineralization processes is another approach with extensive applications in mineral processing management. This method is vital for developing mineralization processes, particularly in the context of CO2 utilization. It supports feedstock selection and process engineering by predicting product speciation in complex systems [30]. Mathematical modeling of particle motion is utilized to simulate particle movement in enrichment devices, aiding in the identification of effective parameters for optimizing the enrichment process [31]. Process simulations are employed to model mineral processing operations at various levels, ranging from bulk processes to mineral-specific models. These simulations provide valuable insights into the processing of Fe ore and other minerals, aiding in their optimization and improved efficiency [32]. Algorithms and simulation models are developed to optimize the transport and unloading of mineral resources, enhancing operational efficiency and reducing costs [33]. While the primary focus of mineral process modeling is on enhancing efficiency and sustainability, challenges such as integrating various modeling techniques and the need for standardized frameworks persist. The adoption of artificial intelligence and advanced computational methods is continually evolving, presenting new opportunities for innovation in mineral processing.