Loveday/Barratt SAG model - Revision history

Alex Doll at 13:27, 23 April 2014

2014-04-23T13:27:03Z

Alex Doll at 17:32, 5 March 2014

2014-03-05T17:32:35Z

Alex Doll at 05:00, 7 February 2014

2014-02-07T05:00:09Z

Alex Doll: /* Model Form */

2013-12-05T03:01:26Z

Model Form

Alex Doll: Created page with "==History== Brian Loveday (1978) published a scale-up procedure for autogenous pilot plant power draw to industrial sized machines tha..."

2013-12-05T02:55:02Z

Created page with "==History== Brian Loveday (1978) published a scale-up procedure for autogenous pilot plant power draw to industrial sized machines tha..."

New page

==History==
[[Bibliography:_Mill_power_draw_models|Brian Loveday (1978)]] published a scale-up procedure for autogenous pilot plant power draw to industrial sized machines that used an empirical ''power number'' to encompass all the motion effects of a mill charge. [[Bibliography:_Mill_power_draw_models|Derek Barratt (2002)]] derived a set of power numbers for industrial machines for use in Loveday's base formula, where a power number for a particular mill filling and speed are read from a chart and then charge density, including the ball load, are fed into Loveday's formula to predict SAG mill power draw.

The power numbers that Barratt published are based on mills with 'typical' cone-ends (probably 15° to 25°). A flat-ended (shell-supported) mill is expected to have 5% less power draw.

==Model Form==
Loveday's equation is:

<math>P=P_N D^{2.5} L \rho_{charge}</math>

Where:
* ''P'' is the power evolved at the mill shell, kW
* ''PN'' is the empirical power number read from the chart below
* ''D'' is the mill diameter inside the effective liner thickness, m
* ''L'' is the mill effective grinding length (or 'belly length'), m
* ''ρcharge'' is the density of the mill charge, including balls, rocks and slurry, t/m3

The formula for ρcharge is as follows:

<math>\rho_{charge} = \left[\tfrac{J_{balls}}{J_{total}} \rho_{balls} + \tfrac{J_{ore}}{J_{total}} \rho_{ore} \right] \times \left( 1- J_{voids} \right) + J_{voids} \rho_{pulp} </math>

Where:
* ''Jtotal'' is the fractional mill volumetric filling (eg. 0.30 for 30%)
* ''Jballs'' is the fractional volumetric filling of balls (eg. 0.10 for 10%)
* ''Jore'' is the fractional volumetric filling of coarse ore (eg. ''Jtotal - Jballs'')
* ''Jvoids'' is the fractional volumetric void space between rocks and balls (use 0.4)
* ''ρballs'' is the density of the grinding balls, t/m3
* ''ρore'' is the density of the ore, t/m3
* ''ρpulp'' is the density of the pulp, excluding rocks and balls, t/m3

← Older revision		Revision as of 13:27, 23 April 2014
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	source: [[Bibliography:_Mill_power_draw_models\|Barratt & Sherman (2002)]]		source: [[Bibliography:_Mill_power_draw_models\|Barratt & Sherman (2002)]]
		+
		+	==Discusion==
		+	The paper [https://www.sagmilling.com/articles/20/view/?s=1\|A comparison of SAG mill power models] published by Doll at Procemin 2013 suggests that this model predicts power draw about 10% high when the mill speed is below about 78% of critical. This model is not recommended for doing throughput or mill sizing calculations, but is a conservative (good) model to use when selecting the motor size for a mill.

← Older revision		Revision as of 17:32, 5 March 2014
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	==Power Number Nomograph==		==Power Number Nomograph==
	[[File:Barratt2002-PowerNumbers.png]]		[[File:Barratt2002-PowerNumbers.png]]
		+
		+	source: [[Bibliography:_Mill_power_draw_models\|Barratt & Sherman (2002)]]

← Older revision		Revision as of 05:00, 7 February 2014
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		+	[[category:Models]]
		+	[[category:Mill power draw models]]
	==History==		==History==
	[[Bibliography:_Mill_power_draw_models\|Brian Loveday (1978)]] published a scale-up procedure for autogenous pilot plant power draw to industrial sized machines that used an empirical ''power number'' to encompass all the motion effects of a mill charge. [[Bibliography:_Mill_power_draw_models\|Derek Barratt (2002)]] derived a set of power numbers for industrial machines for use in Loveday's base formula, where a power number for a particular mill filling and speed are read from a chart and then charge density, including the ball load, are fed into Loveday's formula to predict SAG mill power draw.		[[Bibliography:_Mill_power_draw_models\|Brian Loveday (1978)]] published a scale-up procedure for autogenous pilot plant power draw to industrial sized machines that used an empirical ''power number'' to encompass all the motion effects of a mill charge. [[Bibliography:_Mill_power_draw_models\|Derek Barratt (2002)]] derived a set of power numbers for industrial machines for use in Loveday's base formula, where a power number for a particular mill filling and speed are read from a chart and then charge density, including the ball load, are fed into Loveday's formula to predict SAG mill power draw.

← Older revision		Revision as of 03:01, 5 December 2013
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	* ''ρ<sub>ore</sub>'' is the density of the ore, t/m<sup>3</sup>		* ''ρ<sub>ore</sub>'' is the density of the ore, t/m<sup>3</sup>
	* ''ρ<sub>pulp</sub>'' is the density of the pulp, excluding rocks and balls, t/m<sup>3</sup>		* ''ρ<sub>pulp</sub>'' is the density of the pulp, excluding rocks and balls, t/m<sup>3</sup>
		+
		+	==Power Number Nomograph==
		+	[[File:Barratt2002-PowerNumbers.png]]