SAG mill scale-up from pilot data: 24-MMP-B5 Mineral Processing Design and Operations, Undated paper, Q6

Question 6: SAG mill scale-up from pilot data (6/6)

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. Pilot SAG: feed 2.2 t/h, power 10.56 kW, F80 = 10.0 cm = 100,000 μm, P80 = 1.0 mm = 1,000 μm. Commercial duty: 40,000 t/day, 95% availability, mechanical efficiency 89%. Appendix Doll & Barratt (2010) MW vs. $D^{2.5}\text{EGL}$ correlation chart, two trend lines for 15% and 18% ball charge, with marker legend by installed mill diameter (32-42 ft).

Find. (a) Specific power (kWh/t), operating work index, and commercial motor size (MW). (b) Commercial mill diameter and EGL (ft).

Fig. 5 — SAG mill circuit (ball-mill section excluded per the question), feed at F80 = 10.0 cm reduced to product P80 = 1.0 mm.

Approach. Compute the pilot mill's specific grinding energy directly from measured power and feed rate, back-calculate its equivalent Bond operating work index, scale the specific energy to the commercial tonnage (constant kWh/t, the standard scale-up assumption), correct for drivetrain mechanical efficiency to get motor size, then read the mill's $D^{2.5}\text{EGL}$ product off the appendix correlation at that motor size on the 15% ball-charge line (as specified).

Pilot specific power. $$W=\frac{10.56\ \text{kW}}{2.2\ \text{t/h}}=\boxed{4.80\ \text{kWh/t}}$$
Operating work index (Bond form, applied to the SAG's own F80/P80): $$W_{i,op}=\frac{W}{10\left(\dfrac{1}{\sqrt{P_{80}}}-\dfrac{1}{\sqrt{F_{80}}}\right)}=\frac{4.80}{10\left(\dfrac{1}{\sqrt{1{,}000}}-\dfrac{1}{\sqrt{100{,}000}}\right)}=\boxed{16.9\ \text{kWh/t}}$$
Commercial throughput and shaft power. At 95% availability, 40,000 t/day corresponds to: $$\dot m_{\text{comm}}=\frac{40{,}000}{24\times0.95}=1{,}754.4\ \text{t/h}\qquad P_{\text{shaft}}=1{,}754.4\times4.80=8{,}421\ \text{kW}=8.42\ \text{MW}$$
Motor size, correcting for mechanical efficiency. $$P_{\text{motor}}=\frac{8{,}421\ \text{kW}}{0.89}=9{,}462\ \text{kW}=\boxed{9.46\ \text{MW}}$$

Fig. 6 — Appendix correlation (Doll & Barratt, 2010): reading the 15%-ball-charge trend line at MW = 9.46 gives $D^{2.5}\text{EGL}\approx97{,}000\ \text{ft}^{3.5}$.

Read the appendix chart at MW = 9.46, then pick D and back-solve EGL. On the 15%-ball-charge trend line: $$D^{2.5}\text{EGL}\approx\boxed{97{,}000\ \text{ft}^{3.5}}$$ This value falls at the boundary of the chart's 32 ft/34 ft-diameter marker cluster; taking the nearest standard mill diameter $D=34\ \text{ft}$ from the legend: $$\text{EGL}=\frac{97{,}000}{34^{2.5}}=\frac{97{,}000}{6{,}741}=\boxed{14.4\ \text{ft}}$$ ($\text{EGL}/D=0.42$, a realistic SAG mill aspect ratio.)

Final Results — Question 6
Quantity	Value
Pilot specific power	4.80 kWh/t
Operating work index	16.9 kWh/t
Commercial shaft power	8.42 MW
Commercial motor size (MWe)	9.46 MW
Commercial mill diameter	≈ 34 ft
Commercial mill EGL	≈ 14.4 ft

Check: the diameter category (34 ft) and the two trend-line anchor points are read visually off the appendix scatter chart — the question specifies the 15% ball-charge line explicitly; D and EGL individually carry roughly ±10% engineering tolerance from the chart read. The pilot's own circulating loads (SAG 70%, ball mill 230%) are process-characterization context only and are not needed for this constant-specific-energy scale-up, per the question's own instruction to ignore the ball-mill portion.

Topic: SAG mill scale-up from pilot testwork using specific energy and installed-base correlations.

Key relations: Specific power $W=P/\dot m$; Bond-form operating work index $W_{i,op}=W/[10(1/\sqrt{P_{80}}-1/\sqrt{F_{80}})]$; motor sizing $P_{\text{motor}}=P_{\text{shaft}}/\eta_{\text{mech}}$; empirical $D^{2.5}\text{EGL}$ vs. installed MW correlation (Doll & Barratt, 2010).

Why this works: Scale-up from pilot to commercial SAG milling is normally done on a constant specific-energy basis (same kWh/t at the same F80/P80), since the fundamental breakage mechanics don't change with mill size; the $D^{2.5}\text{EGL}$ correlation then converts that installed power requirement into physical mill dimensions by regression against a large population of real operating mills, sidestepping first-principles mill power models that need charge/liner detail the exam doesn't supply.

Common pitfall: Using the shaft (gross grinding) power instead of the motor (electrical) power when entering the appendix chart — the chart's MW axis is built from installed/nameplate motor data, so the mechanical-efficiency correction must be applied BEFORE reading the chart, not after.

Source: Wills' Mineral Processing Technology, 8th ed., §5.4-5.6 (AG/SAG milling, power-based scale-up); Doll & Barratt (2010), SAG mill design correlations.

Question 6 of 8: SAG mill scale-up from pilot data

Question 6: SAG mill scale-up from pilot data (6/6)