SAG mill scale-up from pilot data: 24-MMP-B5 Mineral Processing Design and Operations, May 2016, 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%. Doll & Barratt (2010) MW vs. $D^{2.5}\text{EGL}$ correlation chart (appendix), two trend lines for 10% and 15% ball charge, with marker legend by installed mill diameter.

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

Fig. 3 — 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 (same energy-per-tonne, 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.

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: $$\dot m_{\text{comm}}=\frac{40{,}000}{24\times0.95}=1{,}754.4\ \text{t/h} \qquad P_{\text{shaft}}=1{,}754.4\times4.80=8{,}421\ \text{kW}$$
Motor size, correcting for mechanical efficiency. $$P_{\text{motor}}=\frac{8{,}421\ \text{kW}}{0.89}=9{,}462\ \text{kW}=\boxed{9.46\ \text{MW}}$$
Read the appendix chart at MW = 9.46. On the 15%-ball-charge trend line (a reasonable mid-range assumption; the question gives no ball charge), the line runs approximately through (100,000, 9.0) and (250,000, 25.5) on the linear $D^{2.5}\text{EGL}$ vs. MW axes, giving $$D^{2.5}\text{EGL} \approx 100{,}000+\frac{9.46-9.0}{25.5-9.0}\times150{,}000\approx\boxed{104{,}500\ \text{ft}^{3.5}}$$ This value falls within the chart's 34 ft-diameter marker cluster, so taking $D=34\ \text{ft}$: $$\text{EGL}=\frac{104{,}500}{34^{2.5}}=\frac{104{,}500}{6{,}741}=\boxed{15.4\ \text{ft}}$$ ($\text{EGL}/D=0.45$, 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 motor size	9.46 MW
Commercial mill diameter	≈ 34 ft
Commercial mill EGL	≈ 15.4 ft

Check: the ball-charge trend line (15%, vs. the alternative 10% line) and the diameter category (34 ft) are read visually off the appendix scatter chart — the question does not state a ball charge, so 15% is taken as the mid-range, defensible assumption; D and EGL individually depend on this chart read and carry roughly ±10% engineering tolerance.

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)