Nonlinear optimization of gravity separation, feed and deck angles with response surface methodology

Most minerals, their ores, and gangue require sorting in order to maximize the recovery of the primary product during concentration. Gravity separation though old, is not obsolete and is continually playing an important role in mineral processing and many other industries, especially where plant energy efficiency is of concern. Screen designs e.g. material of construction, deck angle of inclination, the feed throughput, and physical as well as chemical properties of the particles, are critical factors to consider when using gravity for solid separation. Solids loading and screen geometry are significant, and easily manipulated operational parameters that affect both the screening rate and efficiency to a large extent. In this paper we applied nonlinear least squares optimization technique, and response surface methodology first, to assess the significance of the two factors, and secondly to select the best mathematical models that optimize both capacity and efficiency of the screening process. Initial experiments and confirmation tests were conducted on a prototype screen of 846.51cm2 effective area, (2100 cm2 total area). For glass beads of sizes 0.75-3mm, with feed loads of 10g up to 160g, and inclination angles from 5-20o, a maximum efficiency of 66.7%, and a screening rate of 22g/s was achieved with a screen loading of 86.5g, and an inclination angle of 12.43o. These results were then subjected to nonlinear least squares optimization, in which afterwards an optimum theoretical efficiency of 72% and screening rate of 31.2g/s were achieved at a loading of up to 104g. There was excellent performance at angles 12.5≤θ≤17.5, but poor at the angles outside this range. The screening efficiency did not seem to respond significantly to changes in screen loading. Confirmation tests conducted at selected optimum parameters achieved an efficiency of 72.1% (at 17.5o with 88g load), and a rate of 27g/s at 16.5o with 104g.