Metallurgical Recovery Formulas Explained

Definition

Metallurgical recovery formulas are the mass-balance relationships that turn measured plant assays into the accounting metrics of a concentrator: recovery, mass yield (mass pull), ratio of concentration, and enrichment ratio. Their defining feature is that they reconcile grades you have already measured — the feed, concentrate, and tailings assays of a metal — rather than predicting how a circuit will behave. For a single-concentrate (two-product) circuit, the whole family follows from one mass balance on a feed basis F = 1: the mass yield to concentrate is Y = (f − t)/(c − t); the metal recovery is R = Y·(c/f); the ratio of concentration is K = 1/Y = (c − t)/(f − t); and the enrichment ratio is simply c/f. A two-concentrate circuit uses the three-product formula, which solves a two-metal balance across four streams for the mass fraction of feed reporting to each concentrate. Every one of these is an accounting identity — an exact consequence of conservation of mass and metal across measured streams.

Why it matters

The single sharpest distinction in this whole topic is accounting versus prediction. These formulas account for what a circuit did over a sampled period; they do not forecast what recovery it will achieve, model flotation or leaching, optimise a plant, or replace testwork. That matters because the same word — 'recovery' — is used for two very different things: the metallurgical recovery you compute from this period's assays (accounting) and the recovery a metallurgist hopes a circuit will reach (prediction). The formulas here only do the first. Getting the accounting right matters because recovery and yield are routinely confused (a high-grade, low-mass-pull concentrate can still carry most of the metal), because the ratio of concentration and enrichment ratio describe upgrade and not recovery, and because the inputs must be physically ordered (c > f > t) or the balance returns nonsense. It also matters to know what the balance assumes — representative, reconciled samples of the same metal in the same units — because garbage assays give garbage metrics no matter how exact the algebra.

Formula

Units involved

• •f, c, t — feed, concentrate, tailings assays of one metal, same units (% or g/t)
• •Y — mass yield / mass pull, a fraction (×100 for %)
• •R — metal recovery, a fraction (×100 for %)
• •K — ratio of concentration, tonnes of feed per tonne of concentrate
• •ER — enrichment ratio, dimensionless (c/f)
• •f′, c₁′, c₂′, t′ — assays of a second metal across the four streams (three-product)

Concept diagram

Worked example

Common mistakes

• •Treating computed recovery as a prediction or guarantee of future plant performance.
• •Confusing mass yield (mass pull) with recovery — they are different fractions.
• •Mixing assay units or metals between the feed, concentrate, and tailings streams.
• •Using inputs that violate c > f > t and getting negative or >100% results.
• •Reading a high ratio of concentration or enrichment ratio as high recovery — they describe upgrade, not recovery.
• •Using non-representative or un-reconciled samples and trusting the metrics anyway.

When to use the calculator

Use the two-product formula calculator for a single-concentrate circuit to get recovery, yield, ratio of concentration, and enrichment ratio together. Use the ratio of concentration calculator when you specifically want the tonnes-of-feed-per-tonne-of-concentrate ratio. Use the three-product formula calculator when the circuit makes two concentrates plus a tailings and you have two metals assayed across all four streams. All three reconcile measured assays — for the recovery a circuit will actually achieve, use metallurgical testwork and qualified review.

FAQ