The significance of coal ball milling model equations in manufacturing industries

The achievable area technique helps engineers optimize milling costs by precisely identifying optimal mill configurations, which results in lower expenses. Research advancements that utilize the achievable region strategic plan and mathematical model equations, have focused on the sustainability of mineral beneficiation by lowering milling power production costs, reducing inputs such as milling time and the number of grinding media employed, minimizing material wastage, and maximizing product yield, among other aspects. This research therefore seeks to optimize coal ball milling processes using an integrated Attainable Region (AR) and Response Surface Methodology (RSM) approach. The coal sample used in this study was obtained from a mine situated in the central region area in Botswana and the AR method was used to quantify the percentage coal mass retained across four optimal class intervals of M1 (−850 µm, +425 µm), M2 (−300 µm, +150 µm), M3 (−106 µm, +80 µm) and M4 (−63 µm). Our main objective was to investigate the application of the integrated approach in reducing the energy consumed during the comminution of this local coal that has been identified for application in the country’s upcoming coal-to-fuels industry. Practically, results obtained from this work shows that Botswana coal is also economically amenable for use in different types of industries including civil engineering, construction, cement manufacturing, pyrolysis, gasification and pharmaceuticals. Our characterization of the coal feed samples revealed that the ash components displayed phases of Quartz (ϱ), Dolomite (ς), Sphalerite (φ), and kaolinite (Δ) minerals mixed with organic maceral. These mineral components greatly influence the coal’s hardness, with strong minerals like sulfides (Sphalerite) and silicates (quartz) enhancing fracture toughness. The total percentage mass retained of all tested coal samples indicated a positive correlation indicating that factors like large mass recovery, material fragmentation, and grind-ability were significantly affected by the coal particle size. type. The response surface method charts displayed the graphical depiction of the quadratic model within 3-dimensional space and illustrate the optimal parameter interactions of a ball-mill operation for run-of-mine coal samples, with the Lack of Fit F-value of 2.99. indicating that the lack of Fit is not considerable when compared to the pure error, as the likelihood of obtaining such a significant Lack of Fit F-value due to random noise is 19.91%. A non-significant lack-of-fit is favorable since we desire the model to align well.