Copper Flotation Circuit – Cumulative Grade and Recovery: 24-MMP-B5 Mineral Processing Design and Operations, May 2013, Q5

Question 5: Copper Flotation Circuit – Cumulative Grade and Recovery (20%)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. All stream %mass/%Cu/%S values above, expressed on a 100-units- of-fresh-feed basis (see table).

Find. Cumulative Cu grade and recovery after each stage of (i) the rougher-scavenger train and (ii) the cleaning train, and the overall final-concentrate grade and recovery.

Approach. Work entirely in "Cu units" = %mass×%Cu/100 (i.e. Cu mass on the 100-units-feed basis), which add directly across streams; close the mass balance at each node first as a check, then accumulate concentrate mass and Cu content stage-by-stage through both the rougher-scavenger train and the cleaner train.

Stream	%mass	%Cu	%S
Feed	100.0	1.43	3.18
Pri. Rougher conc.	5.1	11.71	14.46
Sec. Rougher conc.	9.2	6.05	7.78
Scavenger conc.	12.3	1.44	2.53
Scavenger tail (→Final Tails)	73.4	0.11	1.89
Cleaner-1 conc. (Stream 9)	2.6	29.53	31.93
Cleaner-2 conc. (Stream 11)	1.3	30.90	32.08
Cleaner-3 conc. (Stream 13)	0.4	30.66	32.03

Close the rougher-scavenger mass balance (check). $$100-5.1=94.9\ (\to\text{Sec.Ro feed}),\quad94.9-9.2=85.7\ (\to\text{Scav feed}),\quad 85.7-12.3=\boxed{73.4}$$ matching the given scavenger tail exactly – confirms the rougher-scavenger topology (cascading tails, each stage skimming its own concentrate).
Combined rougher-scavenger concentrate feeding the cleaner train (Stream 8). $$m_8=5.1+9.2+12.3=26.6,\qquad Cu_8=5.1(11.71)/100+9.2(6.05)/100+12.3(1.44)/100=1.331\ \text{Cu units}$$ $$\text{grade}_8=\frac{1.331}{26.6}\times100=\boxed{5.00\%\ \text{Cu}}$$
Cleaner train, stage by stage (feed 26.6 mass / 1.331 Cu units). Cleaner 1: conc(9)=2.6 mass, Cu=2.6(29.53)/100=0.768; tail forward=26.6−2.6=24.0 mass, Cu=1.331−0.768=0.563 (grade 2.35% Cu).
Cleaner 2: conc(11)=1.3 mass, Cu=1.3(30.90)/100=0.402; tail forward=24.0−1.3=22.7 mass, Cu=0.563−0.402=0.161 (grade 0.71% Cu).
Cleaner 3: conc(13)=0.4 mass, Cu=0.4(30.66)/100=0.123; tail forward (Stream 14)= 22.7−0.4=22.3 mass, Cu=0.161−0.123=0.0388 (grade 0.17% Cu) – this residual tail joins the scavenger tail as the overall Final Tails.
Final concentrate and final tails. $$m_{FC}=2.6+1.3+0.4=4.3,\quad Cu_{FC}=0.768+0.402+0.123=\boxed{1.292\ \text{Cu units}}$$ $$\text{grade}_{FC}=\frac{1.292}{4.3}\times100=\boxed{30.0\%\ \text{Cu}}$$ $$m_{FT}=73.4+22.3=95.7,\quad Cu_{FT}=73.4(0.11)/100+0.0388=0.1195$$ $$\text{grade}_{FT}=\frac{0.1195}{95.7}\times100=0.125\%\ \text{Cu}$$ Mass check: 4.3+95.7=100.0 ✓. Cu check: 1.292+0.1195=1.412 vs. feed Cu=1.430 (≈1.3% low, attributable to the 2–4-significant-figure rounding of the printed stream assays – see check note).
Overall Cu recovery to final concentrate. $$R=\frac{Cu_{FC}}{Cu_{feed}}\times100=\frac{1.292}{1.430}\times100=\boxed{90.4\%}$$

Copper flotation flowsheet mass balance (all figures on a 100-units-fresh-feed basis): rougher-scavenger train at top, regrind/cleaner train below, closing to Final Concentrate and Final Tails.

Stage (cumulative)	Mass (% feed)	Cu grade (%)	Cu recovery (%)
Rougher – Scavenger train
After Primary Rougher	5.1	11.71	41.8
After Pri.+Sec. Rougher	14.3	8.07	80.7
After Pri.+Sec.+Scavenger	26.6	5.00	93.1
Cleaning train
After Cleaner 1	2.6	29.53	53.7
After Cleaner 1+2	3.9	29.99	81.8
After Cleaner 1+2+3 (Final Conc.)	4.3	30.0	90.4

Check: the ≈1.3% shortfall between total Cu accounted for (final conc. + final tails = 1.412 Cu units) and the feed assay (1.430 Cu units) is a normal closure gap from the source's rounded 2–4-significant-figure stream assays, not a modelling error – the rougher-scavenger tail check in Step 1 closes exactly on the mass basis, confirming the flowsheet topology used is correct.

Topic: Two-product formula and cumulative metallurgical accounting through a multi-stage rougher-scavenger-cleaner circuit.

Key relations: Cu units = %mass×%Cu/100 (additive across streams); cumulative grade = ΣCu units/Σmass; cumulative recovery = ΣCu units/feed Cu units ×100.

Why this works: expressing every stream as a percentage of the SAME original feed (rather than of its own local feed) lets every stream's Cu content be summed or differenced directly without unit conversion, which is exactly what a plant-wide metal balance needs; a simple two-product recovery formula generalises node-by-node to any network topology as long as each node's own mass and metal balance is closed first.

Common pitfall: confusing this circuit's stream numbering – the HIGH-grade streams (9, 11, 13, all ≈30% Cu) are successive CLEANER CONCENTRATES converging on the final concentrate, not tailings, even though they are drawn flowing "downward" in the source figure; the low-grade Stream 14 is the true cleaner-train reject.

Source: Taggart, Handbook of Mineral Dressing, Section 19 (metallurgical balances); Wills & Finch, Mineral Processing Technology, Ch. 3.

Question 5 of 7: Copper Flotation Circuit – Cumulative Grade and Recovery

Question 5: Copper Flotation Circuit – Cumulative Grade and Recovery (20%)