Francois Katubilwa Mulenga

Application of the attainable region technique to the analysis of a full-scale mill in open circuit

Glasser and Hildebrandt (1997) propounded the attainable region (AR) as a technique for the analysis of chemical engineering reactor systems. Results have since been produced and tested on both the laboratory and pilot scales. The method results in a graphical description of chemical reactions by considering the fundamental processes taking place in the system, rather than the equipment. From the plotted graphs, the process and the reactors can be synthesized optimally into a flow sheet. The use of the AR method still has a long way to go as far as mineral processing is concerned. For instance, several articles have reported the application of the AR technique to ball milling: Khumalo et al. (2006, 2007, 2008); Khumalo (2007); Metzger et al. (2009, 2012); Metzger (2011); Katubilwa et al. (2011); Hlabangana et al. (2012). Their main shortcoming has been the exclusive use of laboratory batch grinding data. To address this deficiency, Mulenga and Chimwani (2013) proposed a way by which the technique could be extended to continuous milling. In effect, the batch milling characteristics of a platinum-bearing ore (Chimwani et al., 2013) were used and scaled up to an open milling circuit. Then, with simplifying assumptions, an attempt was made to optimize the residence time of particles inside the mill. Later, Chimwani et al. (2014a) presented some optimization examples involving various milling parameters. The sequence of published articles then paved the way for the study of industrial milling systems with the AR methodology. Admittedly, the limitation has been that the exit classification of the milling circuit was not included (Mulenga and Chimwani, 2014; Chimwani et al., 2014a, 2004b). The importance of this internal phenomenon has been discussed in detail elsewhere (Cho and Austin, 2004; Austin et al., 2007). Suffice to say that the exit classification (also referred to as post-classification or internal classification) is responsible for the preferential discharge of smaller particles and the retention of larger particles back into the mill load until sufficient milling has been achieved. In the present work, MODSIM® – a modular software package for the simulation of mineral processing units (King, 2001) – was used. The flexibility of the simulator enabled the internal classification of particles before exiting the mill to be taken into account, thereby making it possible to generate industrially sound data. From there, the effects of ball filling, ball size, mill speed, and feed flow rate on the product of an open milling circuit were simulated.A methodology for the Application of the attainable region technique to the analysis of a full-scale mill in open circuit