## 4 Results and Discussion
### Effect of Variables  
Principal components analysis reveals that the factors of time (min) and the ferromanganese crust/Fe(res) ratio have a significant effect, as variations in their levels impact the response differently. This is evident from the main effects plots for Mn and Co extraction shown in Figures 4 and 6, respectively. The main effects analysis indicates that for both samples, S1 and S2, as well as for both Mn and Co extraction, time is directly proportional to mineral extraction, whereas the ferromanganese crust/Fe(res) ratio is inversely proportional to mineral extraction. Leaching time is directly correlated with an increase in mineral recovery percentage, as the extended duration allows for the complete progression of the chemical and physical reactions that drive mineral dissolution. This phenomenon is primarily attributed to the inherently gradual nature of chemical reactions. Specifically, as the duration increases, the molecules of the leaching agent have more opportunities to interact with the target mineral, thereby improving the extraction efficiency of the desired metal. Several additional factors contribute to this behavior: (i) Reagent diffusion: the leaching agent penetrates the mineral more effectively over time; (ii) Dissolution of less reactive minerals: certain minerals, which require more time for complete dissolution, are progressively broken down; (iii) Dilution of reaction products: prolonged leaching can dilute the concentration of reaction products, such as metal ions in the solution, enabling reactions to continue with greater efficiency; and (iv) Secondary processes: extended leaching times may activate secondary mechanisms, such as the oxidation of accompanying elements or the breakdown of passivating layers, improving mineral exposure to the leaching agent. In contrast, the recovery rates of Co and Mn decline as the scale-to-iron ratio increases, due to several factors that affect the interaction between the target mineral and the leaching agent. For example: (i) Insufficient reagent concentration: as the quantity of mineral increases without a proportional rise in the leaching agent, the reagent becomes spread too thinly across a larger number of particles, potentially leading to inadequate concentrations for complete metal dissolution; (ii) Reduced mixture uniformity: at higher mineral concentrations, the mixture may become less homogenous, hindering the leaching agent's ability to effectively interact with the mineral particles, thereby reducing process efficiency; and (iii) Solution saturation: a larger quantity of mineral may release more metal ions into the solution, increasing the concentration of dissolved constituents. This can result in solution saturation, impairing the leaching agent's capacity to further dissolve the metal. Overall, these factors highlight the delicate balance required to optimize leaching conditions for maximum recovery efficiency. Contour graphs (see Figures 5 and 7), on the other hand, show that the maximum Mn extraction is reached at higher time levels and lower to medium levels of ferromanganese crust/Fe(res) ratio (both samples S1 and S2), while the maximum Co extraction is also reached at higher time levels and lower ferromanganese crust/Fe(res) ratio levels (also both samples S1 and S2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Fe wt\%** & **Mn wt\%** & **Co ug/g** & **Ni ug/g** & **Cu ug/g** & **REE + Y ug/g** \\ \hline DRAGO 0511/DR04-15 & 19.9 & 14.5 & 4262 & 2359 & 474 & 2298 \\ SUBVENT 1/DA06-4 & 19.4 & 15.7 & 2424 & 2844 & 1342 & 2323 \\ Mean & 19.7 & 15.1 & 3343 & 2602 & 908 & 2311 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Bulk chemistry of samples in selected elements for this study. Developing the ANOVA test and the multiple regression adjustment (see Table 7), the Mn and Co extraction for samples S1 and S2 according to the predictive variables of time and ferromanganese crust/Fe(res) ratio is given by Equations (2)-(5), respectively.