Model:Bond HPGR and ball mill

HPGR and ball mill circuit

The high pressure grinding roll (HPGR) and ball mill circuit can be thought of as a variation on the classical single stage ball mill (SSBM) circuit with the final stage of cone crushing replaced by an HPGR. Simulating HPGR has two differences from a classical SSBM circuit with cone crushers: first is that the crusher product tends to be finer (~4 mm versus 9 mm) and the nature of the product is different.

Testwork Required

• Bond ball mill work index
• Bond rod mill work index
• Bond crushing (low-energy impact) work index
• High pressure grinding roll lab-scale or pilot-scale testing

Formulae

See the base formulae in the Bond SSBM model.

The circuit throughput is calculated using the ball mill (the circuit is assumed to be ball-limited).

$E_{ball} = E_{ssbm} \times (1+CF) - Wi_{C} \times \left ( \tfrac {10}{\sqrt{ 9400 }} - \tfrac {10}{\sqrt{ T_{80} }} \right )$

where CF is the calibration factor for ball mill operating work index versus laboratory ball mill work index. A value of zero means use the Bond/Rowland SSBM formula to predict E_ball, a value of -0.05 means use 5% less than Bond/Rowland SSBM formula to predict E_ball. CF is a negative number if Wi_O is less than the laboratory work index.

$\frac{tonnes}{hour} = \frac{\sum{\text{ball mill kW drawn}} }{E_{ball}}$

The crusher specific power consumption is calculated from the sum of the power drawn in all crushers (which is manually set in the crusher settings) divided by the circuit throughput (which is set by the ball mill circuit).

$E_{crushers} = \frac{\sum{\text{crusher kW drawn}} }{tonnes/hour}$

Discussion

The particle size curve of HPGR product is "non-standard" according to Bond's root-2 rule, meaning the transfer size for Bond calculations is "synthetic" (same as for SAG mills). The "microcracking" reported in HPGR product has the same effect as the non-standard particle size distribution, and both of these are simulated together by this two-step procedure:

1. Adjust the overall circuit Essbm calibration factor in the circuit settings to give you the reduction in the ball mill operating work index (Wi_O) observed in the HPGR testing.
2. Adjust the mechanical efficiency in the HPGR crusher settings to give you the E_crush observed in the HPGR testing. Allow for the specific power consumption of the secondary crushing stage in the E_crush, i.e. E_crush = E_HPGR + E_{sec crush}

Recommended Usage

This is a highly simplified HPGR model that does not consider the volumetric throughput constraints of the crushers. It is suitable for high level comparisons of the likely difference in "energy efficiency" versus SAG milling circuits. It is not intended as a HPGR circuit sizing calculation; factors such as m·dot, pressing pressure and roll speed are not considered.

Default Parameter Values

It is necessary to change the SSBM circuit default parameters to simulate an HPGR circuit:

• Crushing circuit P80, µm : set to the observed HPGR screen product size (typically 3000 to 5000 µm).
• Essbm calibration factor : set to the reduction in ball mill operation work index observed in the HPGR test (typically -0.05 to -0.10 for a 5% to 10% reduction).
• HPGR crusher model mechanical efficiency : adjust until the E_crush matches the HPGR test specific energy.