Closed-circuit crushing and grinding, with the size distribution carried

180 t/h of quartz ore at a 60 mm median goes through a cone crusher in closed circuit with a 16 mm screen, then a ball mill in closed circuit with a 150 micron screen. Every solid stream carries its full particle-size distribution, class by class, so each unit acts on the distribution rather than on a median and a spread. The crusher is Whiten's model: everything finer than its 12 mm closed-side setting passes, everything coarser than its 30 mm open-side setting is broken, and between them a classification function decides. It reduces the circuit feed from an F80 of 90 mm to 13.4 mm for 165 kW, and the screen returns 19% of what it receives to it. The mill is a breakage/selection-function size-mass balance in three mixed stages, not a target size: its product is whatever the breakage of each class produces, fines tail included. The 150 micron screen sends 72% of the mill discharge back, a circulating load of 258% that nobody specified — it is where the recycle settles given the breakage rate and the screen's sharpness. The circuit product leaves at a P80 of 158 microns, and the screen recovers 81% of the true undersize, because a screen with a sharpness of 3 is not a perfect cut. Bounded, and stated. The mill's power is Bond's law applied to the mill's own throughput and its own F80 and P80; Bond's work index is defined on the circuit's fresh feed, so read it as a screening number. The breakage function is Broadbent-Callcott and the selection exponent 1.0 — an ore's own breakage and selection parameters come from its laboratory tests and replace them. Dry circuit: water is not carried.