How to Do a Mass Balance on a Crushing Plant
A mass balance is the plant's arithmetic conscience: everything that goes in must come out somewhere, and when the numbers won't close, the plant is telling you where it's lying. Here's the method, with the two-product formula that solves most quarry problems in one line.
01Draw the flowsheet and box it
Sketch every stream: feed, screens, crushers, products, recycle. Draw a dashed box around the unit (or whole plant) you're balancing. The law inside any box: total in = total out, and for every size fraction, fraction in = fraction out. Two equations, infinite arguments settled.
02Write the two balances
Total: F = P₁ + P₂. Component (pick a marker — % passing a control sieve works like an assay): F·f = P₁·p₁ + P₂·p₂, where f, p₁, p₂ are the marker values of each stream.
03Solve the classic split
300 tph feed carrying 40% passing 1" splits over a screen into overs (10% passing 1") and unders (95% passing 1"). P₂ = F(f − p₁)/(p₂ − p₁) = 300(40−10)/(95−10) = 300 × 30/85 = 105.9 tph unders, and overs = 194.1 tph. Two gradations and a belt scale just measured a split no one could see.
04Chase the circulating load
Closed circuits recycle: crusher discharge returns to the screen. Circulating load = recycle ÷ new feed (×100%). Healthy tertiary circuits often run 50–150%; a climbing ratio means the crusher setting opened, the screen blinded, or the feed hardened. It's the single best early-warning number in a crushing plant.
05Reconcile against the scales
Sum your computed products against the shipped/stockpiled tons for the period. Closure within ±2% is a balanced plant; worse means a lying belt scale (calibrate first — it's usually the scale), an unmetered stream (dust, spillage, fines to the pond), or sampling that grabbed the segregated edge of a stockpile.
06Turn it into money
Once balanced, the model prices decisions: what does diverting 15% of screen feed do to the salable split? What does a worn crusher liner cost in misplaced tons per shift? The balance is the sandbox where plant changes get tested for free before they get tested for real.
ShotRock builds live mass-balance workbooks for real plants — blue input cells, gradation-linked splits, and the circulating-load dashboard your shift foreman will actually use.
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