## 2 Background
However, the complex nature and inherent variability of mineral processing systems demand ongoing research and development efforts to fully realize the potential of these modeling methodologies. The extraction of Cu and Co is a complex process that requires the application of various modeling methods to optimize efficiency and yield. These methodologies are crucial for addressing the challenges posed by the unique chemical properties of copper and cobaltores, as well as the diverse mineralogical composition of the feed material. The sections below explore different modeling approaches and techniques employed in the extraction of these metals. * Redox Chemistry in Ore Processing: A dual-benefit strategy harnesses the redox properties of Cu and Co ones, enabling simultaneous extraction without the need for additional oxidizing or reducing agents. This approach achieves high recovery efficiencies of 99.67% for copper and 98.20% for cobalt by capitalizing on the oxidizing properties of Co3+ in oxide ores and the reducibility of sulfide ores [34]. * Neural Networks and Response Surface Methodology: This approach has been implemented to forecast and improve the leaching characteristics of Cu-Co ores. The ANN employs a backpropagation algorithm to model the process, while RSM utilizes the Box-Behnken design for optimization. The method achieves leaching yields of 93.46% for Cu and 89.43% for Co, with a strong correlation between predicted and experimental values [20]. * Ammonium Sulfate Roasting: An innovative method involves ammonium sulphate roasting for the selective extraction of metals from oceanic Co-rich crusts. This process converts metal oxides into sulphates, achieving high leaching efficiencies for Co, Ni, and Cu, while minimizing Fe leaching. The method is efficient, environmentally friendly, and economically advantageous compared to traditional techniques [35; 36]. * Metal Melt Extraction: A method involving metal melting entails heating a Cu-Co alloy with a metal extraction medium under an inert atmosphere, effectively separating Cu from the alloy. The extracted Cu can then be utilized as a high-quality raw material, while the remaining alloy is suitable for further processing, such as acid leaching [37]. * Pressure Leaching and Electrodeposition: The extraction of cathode Cu from Co concentrate involves pressure leaching, followed by Cu recovery and electrodeposition. This process incorporates steps for the removal and recycling of extractants, improving the efficiency of the extraction process and enhancing the quality of the final Cu product [38; 39]. * Continuous Fluid Separation: A production method for extracting Co from Cu extraction tail liquid utilizes a continuous fluid separation system with chelate resin. This approach streamlines the process, reduces costs, and enhances cobalt purification efficiency by eliminating the need for traditional precipitation steps [40]. * Taguchi Method and ANOVA: The Taguchi method and analysis of variance (ANOVA) are employed to optimize heap leaching conditions for Cu and Co recovery from tailings. This statistical approach identifies optimal leaching parameters, including particle size, acidity, and flow rate, leading to significant metal recovery rates [41]. * Microfluidic Extraction: A procedure is employed to separate Cu and Co ions in a microchannel by optimizing parameters such as pH, flow rate, and extractant concentration. This method achieves a high Cu extraction rate while minimizing Co co-extraction, providing a more efficient and effective separation process [42]. The formulation of extraction processes for Cu and Co through the application of response surface methodology (RSM) and design of experiments (DOE) necessitates the optimization of numerous process parameters to enhance the efficiency and yield of extraction methods. RSM is a statistical approach used for modeling and analyzing problems where multiple variables influence the response of interest, with the goal of optimizing this response.