An attainable region analysis of the effect of ball size on milling

Abstract

A theoretical investigation of the effect of ball diameter on milling kinetics using the attainable region methodology is presented. Under a predefined fineness of the grind in the product, attainable region plots are produced and results qualitatively interpreted. Initially, parameters describing the selection function, the breakage function, and the ball size effect are defined using batch experimental results obtained on a particular coal. Then, assuming a first-order kinetics law and a normalizable breakage, particle size distributions are generated for the following grinding times: 0.5–1–2–4–10–30–60 min. Several single-sized feed materials ranging from 26,500 μm down to 425 μm together with ball diameters between 10 and 50 mm are considered for simulation. Finally, the obtained data is analyzed with the attainable region technique. The targeted objective is chosen to be the amount of material less than 75 μm produced at each stage of batch milling. Results show that the attainable region plots lie nearly on top of each other irrespective of ball size. One thing though, smaller media sizes seem to exhibit a more differentiated behavior suggesting that size reduction could be more effectively controlled with smaller media. Similar trends are also observed with coarser feed materials.