Austin SAG model

History

The SAG mill model by proposed by Leonard Austin (1990) was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.

Model Form

The power draw model for a SAG mill cylinder of the following form:

$P = K D^{2.5} L ( 1 - AJ_{total}) \left [ (1-\epsilon_{B}) \left( \frac{\rho_{solids}}{w_{C}} \right ) J_{total} + 0.6 J_{balls} \left( \rho_{balls} - \frac{\rho_{solids}}{w_C} \right) \right ] \phi_{C} \left( 1 - \frac{0.1}{2^{9-10\phi_C}} \right)$

Where:

• P is the power evolved at the mill shell, kW
• K and A are empirical fitting factors (use 10.6 and 1.03, respectively)
• D is the mill effective diameter (inside the effective liner thickness), m
• L is the mill effective grinding length (also referred to as the 'belly length), m
• J_total is the mill total volumetric filling as a fraction (eg. 0.30 for 30%)
• ε_B is the rosity of the rock and ball load (use 0.3)
• w_C is the charge %solids, fraction by weight (use 0.80 ^{Doll, 2013})
• J_balls is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%)
• ρ_X is the density of component X, t/m³
• φ_C is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical)

To account for cone ends of mills, an allowance of 5% is used ^{Doll, 2013} instead of the formula proposed by Austin.