How much grinding energy does a classifier loop save at the same product size, and does a ball-mill population balance agree with Bond's law?

research/infra-grind

Ball-mill population balance (Austin form): at the same 100 um P80 a closed circuit at 278% circulating load uses 0.47 of the open-circuit energy, 1.8 to 3.7 times better across the swept mill and classifier inputs, far above Bond's 1.2 open-circuit factor and a vendor's ~10% for cement; the model's size exponent matches Bond's only at a selection exponent near 0.5.

13 tests

What it found

A size-by-size ball-mill model (selection function S_i = S₁(x_i/1 mm)^α, Austin breakage function, three perfectly mixed tanks in series) with a Whiten classifier loop, solved by forward substitution and fixed-point iteration in the standard library. At the same 100 µm P80 from a 1500 µm feed, a closed circuit with the cut at P80 and 278 % circulating load uses 0.47 of the open-circuit energy (53 % saving); a coarser cut saves less (0.78 at cut = 2×P80, 35 % load). The saving is 1.8 to 3.7 times in energy ratio over tank number 1 to 10, classifier sharpness 2 to 8, bypass 0 to 0.3 and the breakage parameters; it does not collapse to the published figures: Bond’s open-circuit factor EF2 is 1.2 at 80 % passing and a vendor guide gives about 10 % for cement mills. That is reported as a discrepancy, with likely causes (slowing of fines, tested, does not close it; a mill flow limit of 1.5 to 2 times the open circuit’s feed, with that limit assumed rather than sourced, brings the fixed-power capacity advantage to 1.2 to 1.4; auxiliary power) rather than tuned away. The local size exponent of energy (E ∝ P80^−m, 50 to 200 µm) runs from 0.60 to 1.27 over α 0.4 to 1.2 against Bond’s 0.68, so Bond’s law corresponds to α near 0.5 in this model. Absolute kWh/t is in model units (S₁ was not fitted to a mill); every shape parameter is a typical value from memory of the Austin literature, swept, not measured.

A figure from its own output

Figure produced by research/infra-grind: circuit — infra-grind/experiments/circuit.svg, written by the project's own experiment code.

Paper, code and results

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What it found

A figure from its own output

Paper, code and results

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