Crusher selection (power and capacity criteria) and preliminary cost: 24-MMP-B5 Mineral Processing Design and Operations, May 2016, Q2

Question 2: Crusher selection (power and capacity criteria) and preliminary cost (2/6)

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. $W_i = 20.3\ \text{kWh/t}$; circulating load $130\%$; ore tonnage 4,500 t/day; availability 85%; reduction ratio $RR=3.5$; crusher product $P_{80}=24.4\ \text{mm}$ (crusher discharge table, cum. % passing 24.4 mm = 80.1% ≈ 80%); three candidate crusher sizes with rated kW/t-h. Cost law $\text{Cost}=aX^{1.70}$, $a=30{,}010$ at M&S = 1,400; current M&S = 1,750.

Find. Crusher size and number of units by (i) power and (ii) capacity criteria, and the preliminary current cost of the selected fleet.

Approach. Convert daily tonnage to an hourly design rate through the crusher (new feed grossed up by the circulating load), size by capacity against the manufacturer table, cross-check against the Bond-equation power demand, then escalate the purchase cost from the base M&S index to the current one.

Design throughput through the crusher. New (fresh) feed rate, corrected for availability: $$\dot m_{\text{new}} = \frac{4{,}500\ \text{t/day}}{24\ \text{h}\times0.85}=220.6\ \text{t/h}$$ The crusher itself handles new feed plus the 130% recirculating load: $$\dot m_{\text{crusher}} = 220.6\times(1+1.30) = \boxed{507.4\ \text{t/h}}$$
Capacity criterion. Dividing 507.4 t/h by each candidate's rated capacity and rounding up: 120/6-8 (100 t/h) needs 6 units; 175/8-11 (150 t/h) needs 4 units; 210/9-13 (270 t/h) needs $\lceil 507.4/270\rceil = 2$ units (540 t/h ≥ 507.4 t/h).
Power criterion (Bond equation). With $P_{80}=24.4\ \text{mm} = 24{,}400\ \mu\text{m}$ and, from the stated reduction ratio, $F_{80}=3.5\times24.4=85.4\ \text{mm}=85{,}400\ \mu\text{m}$: $$W = 10 W_i\left(\frac{1}{\sqrt{P_{80}}}-\frac{1}{\sqrt{F_{80}}}\right)=10(20.3)\left(\frac{1}{\sqrt{24{,}400}}-\frac{1}{\sqrt{85{,}400}}\right)=0.605\ \text{kWh/t}$$ Total power demand: $P_{tot}=0.605\times507.4=\boxed{306.9\ \text{kW}}$. By unit rating: 120/6-8 (110 kW) needs 3 units; 175/8-11 (150 kW) needs 3 units; 210/9-13 (220 kW) needs $\lceil306.9/220\rceil=2$ units (440 kW ≥ 307 kW).
Select the crusher. The 210/9-13 unit is the only size where the power criterion (2 units) and the capacity criterion (2 units) agree on the same fleet size, giving the smallest, most balanced installation: 2 × 210/9-13 SH cone crushers.
Preliminary cost, escalated to the current M&S index. $X = D = 210\ \text{cm} = 6.890\ \text{ft}$. $$\text{Cost}_{1400} = aX^{1.70}=30{,}010\times(6.890)^{1.70}=\$798{,}400/\text{unit}$$ $$\text{Cost}_{1750}=\text{Cost}_{1400}\times\frac{1750}{1400}=\$798{,}400\times1.25=\$998{,}000/\text{unit}$$ $$\text{Total (2 units)} = \boxed{\$1{,}996{,}000}$$

Final Results — Question 2
Quantity	Value
Design crusher throughput	507.4 t/h
Bond specific power	0.605 kWh/t
Total power demand	306.9 kW
Selected crusher & count	2 × 210/9-13 SH cone
Preliminary cost (M&S = 1,750), total	≈ USD 2.00 million

Check: the reduction ratio (3.5) is applied to the crusher's own P80 to back-calculate its F80, per the standard definition $RR = F_{80}/P_{80}$; the crusher discharge table's 24.4 mm row (80.1% cum. passing) is read as the design P80 since it lands almost exactly on 80%.

Topic: Bond comminution law and manufacturer capacity-table crusher selection.

Key relations: Bond's third theory $W=10W_i(1/\sqrt{P_{80}}-1/\sqrt{F_{80}})$; circulating-load-adjusted design tonnage $\dot m_{\text{crusher}}=\dot m_{\text{new}}(1+\text{C.L.})$; six-tenths-family cost law $\text{Cost}=aX^b$ with linear M&S index escalation.

Why this works: A closed crushing circuit's crusher never sees only the fresh ore — every particle above the screen aperture passes through it again — so equipment must be sized on the gross (new + recirculating) tonnage, not the plant's nominal daily rate. Cross-checking power and capacity independently guards against under-sizing a crusher that meets one criterion but not the other.

Common pitfall: Sizing the crusher fleet from capacity alone and ignoring the power check (or vice versa) can select a fleet that is mechanically undersized even though its rated tonnage looks adequate.

Source: Wills' Mineral Processing Technology, 8th ed., §4.3 (Bond's law) and §4.4 (cone crushers); Mular & Poulin, CIM Special Volume 47 (1998), preliminary cost estimation by the six-tenths/M&S-index method.

Question 2 of 8: Crusher selection (power and capacity criteria) and preliminary cost

Question 2: Crusher selection (power and capacity criteria) and preliminary cost (2/6)