Difference between revisions of "Austin SAG model"
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| + | [[category:Models]] |
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| − | ==Austin SAG model== |
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| + | [[category:Mill power draw models]] |
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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 model were fit to empirical relationships measured by Austin, resulting in a model for the mill cylinder of the following form: |
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| + | ==History== |
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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 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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* ''L'' is the mill effective grinding length (also referred to as the 'belly length), m |
* ''L'' is the mill effective grinding length (also referred to as the 'belly length), m |
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* ''J<sub>total</sub>'' is the mill total volumetric filling as a fraction (eg. 0.30 for 30%) |
* ''J<sub>total</sub>'' is the mill total volumetric filling as a fraction (eg. 0.30 for 30%) |
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| − | * ''ε<sub>B</sub>'' is the |
+ | * ''ε<sub>B</sub>'' is the porosity of the rock and ball load (use 0.3) |
* ''w<sub>C</sub>'' is the charge %solids, fraction by weight (use 0.80 <sup>[[Bibliography:_Mill_power_draw_models|Doll, 2013]]</sup>) |
* ''w<sub>C</sub>'' is the charge %solids, fraction by weight (use 0.80 <sup>[[Bibliography:_Mill_power_draw_models|Doll, 2013]]</sup>) |
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* ''J<sub>balls</sub>'' is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%) |
* ''J<sub>balls</sub>'' is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%) |
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* ''ρ<sub>X</sub>'' is the density of component ''X'', t/m<sup>3</sup> |
* ''ρ<sub>X</sub>'' is the density of component ''X'', t/m<sup>3</sup> |
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* ''φ<sub>C</sub>'' is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical) |
* ''φ<sub>C</sub>'' is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical) |
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| + | |||
| + | === Mill cone angles === |
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| + | The model supports flat-ended mills (cone angle of 0°) or a cone angle of 15°. Any other value entered for the cone angle will be treated as 15°. |
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To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models|Doll, 2013]]</sup> instead of the formula proposed by Austin. |
To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models|Doll, 2013]]</sup> instead of the formula proposed by Austin. |
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| + | |||
| + | === Percent solids === |
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| + | The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids. |
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| + | |||
| + | == Model Inputs== |
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| + | |||
| + | <b>the Austin model</b> requests the following mill data: |
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| + | |||
| + | * mill nominal diameter inside shell |
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| + | * mill effective grinding length |
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| + | * ball load as vol percentage (eg. 10) |
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| + | * [[Media density|ball density]] |
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| + | * total charge load as vol percentage (eg. 30) |
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| + | * pulp percent solids |
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| + | * mill speed |
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| + | * liner effective thickness |
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| + | * cone end angle (only values 0-5 or >5 matter, minor angle changes have no effect) |
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| + | |||
| + | <b>Motor characteristics</b> are also requested: |
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| + | |||
| + | * Motor rated power (output shaft) |
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| + | * Mechanical efficiency of downstream drive (pinions, gearboxes) |
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| + | * Motor efficiency and any other efficiency factors to the DCS measurement position in the network. |
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| + | * Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios). |
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| + | * Quantity of pinions (and motors) |
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Latest revision as of 01:02, 18 June 2016
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 porosity 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)
Mill cone angles
The model supports flat-ended mills (cone angle of 0°) or a cone angle of 15°. Any other value entered for the cone angle will be treated as 15°.
To account for cone ends of mills, an allowance of 5% is used Doll, 2013 instead of the formula proposed by Austin.
Percent solids
The model is run with a fixed 80% solids by weight Doll, 2013. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids.
Model Inputs
the Austin model requests the following mill data:
- mill nominal diameter inside shell
- mill effective grinding length
- ball load as vol percentage (eg. 10)
- ball density
- total charge load as vol percentage (eg. 30)
- pulp percent solids
- mill speed
- liner effective thickness
- cone end angle (only values 0-5 or >5 matter, minor angle changes have no effect)
Motor characteristics are also requested:
- Motor rated power (output shaft)
- Mechanical efficiency of downstream drive (pinions, gearboxes)
- Motor efficiency and any other efficiency factors to the DCS measurement position in the network.
- Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).
- Quantity of pinions (and motors)
