Difference between revisions of "Austin SAG model"
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| + | ==History== |
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| − | ==Austin SAG model== |
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| − | The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models|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 |
+ | The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models|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. |
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| + | ==Model Form== |
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| + | The power draw model for a SAG mill cylinder of the following form: |
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<math>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)</math> |
<math>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)</math> |
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Revision as of 01:13, 5 December 2013
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)](/images/math/5/1/2/5122ae16b1e0f4a4bf3eaa0815716fd8.png)
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
- Jtotal is the mill total volumetric filling as a fraction (eg. 0.30 for 30%)
- εB is the rosity of the rock and ball load (use 0.3)
- wC is the charge %solids, fraction by weight (use 0.80 Doll, 2013)
- Jballs is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%)
- ρX is the density of component X, t/m3
- φC 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.
