Purity, Recovery and Extraction Yield

Introduction

Metallurgy reports several percentages that may all refer to one batch but have different denominators. Ore grade describes what the feed contains; stage recovery describes how much of that content moves into the next useful stream; product purity describes the composition of the final material. Using one number in the place of another can produce a large error.

Core explanation

Suppose 1000 kg ore assays 2.00% copper by mass. Contained copper is 20.0 kg. A concentrator recovers 90.0% of the copper into concentrate, giving 18.0 kg copper in that stream. A refinery then recovers 95.0% of the copper it receives, giving 17.1 kg copper in final product. Overall copper recovery is 17.1/20.0 = 85.5%, equal to 0.900 × 0.950 when the stages form one consistent chain. This does not imply the final product weighs 17.1 kg unless it is pure copper.

If the final product is 99.0% copper by mass, total product mass is 17.1/0.990 ≈ 17.3 kg. Product purity divides target-copper mass by total output mass. It is not a loss fraction acting on already recovered copper in this calculation; multiplying 17.1 by 0.990 would incorrectly reduce the known copper content. Conversely, if a measured impure product mass is given, multiply it by purity fraction to find actual copper mass.

Ore grade can be elemental or mineral-based. A feed described as 30.0% Fe₂O₃ contains less than 30.0% iron because oxygen contributes to hematite mass. Multiply by the formula's Fe fraction before applying iron recovery. If the grade is already stated as elemental Fe, applying the formula fraction again double counts oxygen.

Extraction yield is sometimes used like percentage yield: actual target metal divided by the theoretical amount from the limiting input. In a flowsheet, “recovery” may instead refer to one separation stage or the whole plant. Read the defined boundary. A 90% flotation recovery and 95% refinery recovery multiply only if the refinery's 95% is calculated relative to copper entering the refinery . If it is already an overall recovery from ore, multiplication repeats a loss.

Material may leave useful streams without being chemically destroyed. Copper lost from concentrate may be in tailings; metal lost in smelting may be in slag, dust or other phases. A low recovered output should lead to a stream balance, not a claim that the element vanished. Mass conservation helps diagnose missing denominators.

An apparent metal yield above 100% can result from product moisture or impurities if total mass is mistaken for pure metal mass, or from a grade or assay error. It cannot represent more pure target atoms than the feed contained in a closed accounting without another metal source. Check recycled feed or added metal before judging an apparent excess.

Precision should match assay and weighing quality. A grade rounded to 2.0% does not justify many digits in a tonnage prediction. State assumptions that grade represents the whole batch and that each recovery fraction is independently applicable at its designated stage.

Step-by-step reasoning

1. Label each percentage with its numerator and denominator. 2. Convert ore mass to contained metal, including mineral formula fraction if needed. 3. Apply stage recoveries in material-flow order when their bases align. 4. Convert target-metal mass to impure product mass only if purity is specified. 5. Verify metal conservation across useful and rejected streams.

Visual explanation

Draw 1000 kg ore → 20.0 kg contained Cu → 18.0 kg Cu in concentrate → 17.1 kg Cu in refined output. Under the last box write “99.0% purity gives 17.3 kg total product.” Put 2.00%, 90.0%, 95.0% and 99.0% beside different arrows or boxes to show their distinct meanings.

Real-world analogy

A crate is 20% apples, sorting captures 90% of those apples, and the final basket is 99% apples. The first percentage describes starting composition, the second describes capture and the third describes basket composition. Treating all three as identical “efficiency” figures confuses different questions.

Real-world example

A mine report may quote copper grade in ore, copper recovery to concentrate and cathode purity. Investors, engineers and environmental managers use different numbers: contained resource, metal produced and impurities or losses. A clear calculation specifies which output is being predicted.

Why?

Why can overall recovery be the product of step recoveries? The second stage acts only on material surviving the first. For an aligned chain, recovered metal = contained metal × r₁ × r₂. This does not apply if the second percentage was already defined relative to original ore.

Common misconception

“A product that is 99% pure means 99% of the ore's metal was recovered.” Purity is target mass divided by total product mass; recovery is captured target mass divided by target initially available. A highly pure product can come from a low-recovery process.

Worked example

A 500 kg ore contains 40.0% pure ZnS by mass. ZnS mass is 200 kg, and its zinc fraction is about 0.671, so contained Zn is 134 kg. Concentration captures 85.0% of contained Zn, leaving about 114 kg in concentrate. Downstream recovery of that zinc is 90.0%, yielding about 103 kg pure Zn content. If final metal product assays 98.0% Zn, its total mass is 103/0.980 ≈ 105 kg. Each percentage has been applied once to its own basis.

Quick check

1. If 20.0 kg Cu is contained and 18.0 kg enters concentrate, what is concentration recovery? Answer: 18.0/20.0 × 100% = 90.0%.

Exam focus

Write “grade,” “recovery” and “purity” beside their respective fractions. Decide whether grade is elemental or mineral-based. Multiply aligned stage recoveries but do not multiply an already overall yield by its component yields.

Advanced insight

Uncertainty in grade can dominate output forecasts because deposits vary spatially. Stage recoveries can also depend on feed mineralogy, so treating them as fixed independent constants is an approximation. A production forecast is strongest when it includes representative assays and a range of plausible recovery values.

Summary

Ore grade measures contained value, recovery measures how much reaches a chosen stream, and purity measures target fraction in that stream. Use clearly defined bases and stage boundaries. Element-specific mass balances reveal double counting and distinguish actual losses from changing total material masses.

Practice questions

1. How much Cu is contained in 2000 kg ore at 1.50% elemental Cu grade? Answer: 30.0 kg Cu. 2. What final Cu amount follows from aligned 80% and 90% recoveries? Answer: 30.0 × 0.80 × 0.90 = 21.6 kg Cu. 3. If that product is 98.0% Cu, what total product mass is it? Answer: 21.6/0.980 ≈ 22.0 kg total product. 4. Why is high purity not proof of high recovery? Answer: Purity compares output composition; recovery compares captured target with target originally available.