Procemin2013-AlexDoll-SAGPowerModels.pdf

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A comparison of SAG mill power modelsAlex Doll *

Alex G. Doll Consulting Ltd., Canada

ABSTRACT

SAG Mill power draw models are used in mill design and grinding circuit modelling to predicthow much power will be consumed by a particular mill geometry and operating configuration.

This paper will compare SAG mill models by Morrell, Loveday (using !ower "umbers publishedby #arratt$ and Austin against several published mill surveys. The purpose of the comparison is toidentify the fitting factors used by each model and to identify which mill configurations seem tobetter suit each model.

The importance of conducting surveys suited to model calibration will be highlighted because thereview of literature shows that survey information important to modelling is often omitted.

A recommendation for the collection of data during a mill survey is presented, along with someassumptions used by the Author in the absence of certain data. The benefit to mining companies ofpublishing their survey data, and thereby allowing modellers to improve their model calibration, isdiscussed.

The comparison of models re%uires a discussion of the measurement of power in a mill drivesystem as the models use slightly different bases for where power is measured. Thebenchmar&ing of models against plant operations re%uires a similar discussion of powermeasurement.

'orresponding author) Ale* G +oll onsulting Ltd. ! #o* -/0, Logan La&e, # 123-42anada. !hone) 5- 6678/778999. :mail) ale*.doll;sagmilling.com


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INTRODUCTION

Si


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Austin proposed a geometric factor be applied to the formula for use in cone8ended mills. Theauthors e*perience from fitting this model to published surveys suggests that Austins factor adds

too much power, and proposes that FC e*tra power should be added instead (based on #arratt,#rodie !feifer, -???$.

An unusual feature of Austins model is the pulp Csolids appearing in the denominator of two ofthe terms, meaning that the power draw drops as the pulp density increases. This is the opposite ofwhat the other models predict H higher pulp Csolids gives higher power draw in both the Lovedayand Morrell models. Austins paper recommends using a fi*ed value of 2.72 for this term and notvarying it as the mill water addition rate changes.

Loveday/Barratt Model

#rian Loveday published a simple SAG mill model (Loveday, -?67$ of the form in :%uation . The

e%uation uses mill dimensions (inside the liners$, the density of the mill charge and an empirical=power number> that encapsulates the mill speed and volumetric filling.

0.%(234 ($

4here)

Dis the mill diameter inside the liners, m

Lis the mill effective grinding length, m

Pis the power evolved at the mill shell, &4

PNis an empirical =power number> which varies with mill filling and speed, unitless Chargeis the density of the mill charge as given in :%uation /, tDmE

#all charge is not e*plicitly used in the power formula, but is considered in the mill charge densityformula)

%(234 5675887 %#$ 59:5887 %24& ;1 $ $%?@? (/$

4here)

Jxis the volumetric proportion of a component x(e.g. 2. for 2C$ xis the density of a component x, tDmE

A chart of power numbers was published by #arratt Sherman (22$. 1alues were manuallye*tracted from this chart and smoothed by curve fitting. A subset of the power number database isshown in Bigure -.


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The power measurement of the Loveday model is relative to the =mill shell>, also referred to aspower =at the pinion>. The power numbers by #arratt Sherman are fitted to =normal> cone8ended (trunnion supported$ mills. Bor flat8ended (shell supported$ mills, deduct FC from thepower draw.

Morrell C-Model

The 8model was developed by Steve Morrell at the Iniversity of Jueensland as part of his !h+thesis. The Morrell 8Model is a generalised tumbling mill model and is not specific to SAG mills.The model was adopted for use in the K3 SimMet software pac&age and this paper is based on thedescription in a K3 Mineral esearch entre publication ("apier8Munn et al, -??0$.

The model contains too many e%uations and sub8e%uations to replicate here. Nn summary, themodel consists of a friction balance between concentric layers within the rising part of the mill load.The model contains a great deal of physics and geometry, and uses some parameters that have beenfit to laboratory or industrial scale mills. The mathematics develops the power draw of a chargegeometry and motion, and then applies a fitting factor k to convert the power draw of the mill

charge into the observed gross motor power (the motor input$. The highly8simplified formula isgiven in :%uation 9)

Gross power = no-load power + k (Charge motion power) (9$

The Morrell 8model provides a power draw relative to a motor input, and it must be converted tothe same basis as the other models (mill shell basis$ to perform meaningful comparisons. Thedatabase of mills that the published k factor was fit against consisted largely of Australian andAfrican mills that typically have pinions (2.?7F efficiency$, gearbo*es (2.?7F efficiency$ and

#i$%re &'!ower "umbers from #arratt Sherman (22$

10 15 20 25 30 35 40 45

1.0

1.2

1.4

1.6

1.8

2.0

Jtotal, %volume

PowerNumber

60% of critical 65% of critical 70% of critical

75% of critical 80% of critical


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induction motors (2.?02 efficiency$. Multiplying these efficiency values together suggests aconversion factor of 2.?/- between motor input (8model result$ and mill shell (+oll, 2-$.

E(AM)!E CA!CU!ATION

A mill survey was published for the Meadowban& gold mine in northern anada (Muteb Allaire,2-/$. The following criteria were identified for the May 2- survey)

D +iameter inside liners) 6.6 m (diameter inside shell) 0 ft$

L :ffective grinding length) /./F m (-- ft$

C Mill speed) 2.6F of critical (--.99 rpm$

Jtotal 1olumetric filling) 2.0 (.0C vDv$

Jballs #all charge) 2.-/F (-/.FC vDv$

ore re density) .?/ tDmE

wC pulp density) 2.6F (6FC solids $

Grindability) AOb /7.0P 4i#M-2.? &4hDt

Length (assumed to be flange8to8flange length$) -.9 ft

Motor is low8speed synchronous with pinion (assume 2.?9F0 conversion to shell$

Motor si$C( D !."#$ B%#$%$=>$C( DE '(B1

!.1FGH*)ID


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RESU!TS AND DISCUSSION

The model inputs are given in Table - and outputs are provided in Table . All models are run withtheir published =tuning parameters>, e*cept as noted.

Austin model)

o A Q -.2/, K Q -2.0P BQ 2./

o use a fi*ed pulp Csolids wCQ 2.72P

o

use FC allowance for cone ends instead of the published formula.

LovedayD#arratt model)

o !ower numbers interpolated from Bigure -P

o deduct FC from predicted power in the case of flat8ended mills.

Morrell model)o kQ-.0 (conversion to gross power at the input of a wound8rotor induction motor$P

o JoidsQ2.92 (different from Bin the Austin e%uation$P

o use 2.?/- conversion between gross power and shell power.

Tabulation of recommended data for publication

A published mill survey would ideally provide the following information)

D, L, Jtotal, Jballs, !C, ore, wCandPDC"#

A description of the motor and drive system and a description of where in the electrical

system the +S power indication is measuredP #all metallurgy (e.g. =forged steel> or =high8chrome>$ or ballsP

Liner thic&ness estimate.

Tabulation of published surveys

The following surveys have been considered in Tables - )

(survey -$ Meadowban&) Muteb Allaire (2-/$

(surveys through 6$ adia) ad


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Tale & Summary of published survey data (model inputs$

N+ Mine D m L m !total !balls "C #ore $C )DCS, -. con/ersion )s0ell,-.

- Meadowban& 6.62 /./F 2.0 2.-/F 2.6F2 .?/ 2.6F /,/69 2.?9F0 1,&23

adia ' -.2 0.-2 2.77 2.222 2.6?2 .02 $.%$ --,-7? 2.?022 &3,45&

/ adia ' -.2 0.-2 2.7F 2.222 2.6?2 .02 $.%$ -2,/- 2.?022 2,236

9 adia ' -.2 0.-2 2.F2 2.292 2.672 .02 $.%$ -2,79 2.?022 &3,12&

F adia ' -.2 0.-2 2.926 2.292 2.672 .02 $.%$ -9,?9F 2.?022 &5,154

0 adia ' -.2 0.-2 2./-0 2.-2 2.692 .02 $.%$ -6,F70 2.?022 &7,661

6 adia ' -.2 0.-2 2.0- 2.-2 2.672 .02 $.%$ -6,?0/ 2.?022 &4,855

7 Bimiston -2.72 9.9 2.-0 2.-/2 2.6F .?2 2.00 ?,FF 2.?9F0 6,498

? Bimiston -2.72 9.9 2.F 2.-/2 2.662 .?2 2.0/ -2,/69 2.?9F0 2,6&3

-2 Bimiston -2.72 9.9 2. 2.--F 2.722 .?2 2.02 -2,?60 2.?9F0 &3,142

-- Bimiston -2.72 9.9 2.22 2.-92 2.72 .?2 2.6F --,079 2.?9F0 &&,356

- Bimiston -2.72 9.9 2.70 2.-/2 2.672 .?2 2.6F --,0-2 2.?9F0 &3,246

-/ Bimiston -2.72 9.9 2.F7 2.-/2 2.672 .?2 2.6F --,F6- 2.?9F0 &3,258

-9 Bimiston -2.72 9.9 2.-?2 2.-2 2.722 .?2 2.6F ?,927 2.?9F0 6,627

-F !hoeni* -2.69 F.2/ 2./22 2.-/2 2.692 &.%$ $.%' -2,?0F (.$$$$ &3,279

-0 !hoeni* -2.69 F.2/ 2.62 2.-/2 2.692 &.%$ $.%' -2,/29 (.$$$$ &3,135

-6 anacocha ?.92 ?.60 2.-6? 2.-0F 2.09F .F 2.6/ -,70 (.$$$$ &8,867

-7 anacocha ?.92 ?.60 2.? 2.-?- 2.0/- .F 2.72 -/,?? (.$$$$ &1,228

-? L3A# (BAG$ 0.7 F./2 2./2F 2.222 2.6F/ 9.-2 2.6F ,722 $.)*'+ 8,756

2 !orgera 7./7 /./F 2.0/ 2.--2 2.67 .6/ $.%' 9,FF2 $.)&+% 5,8&7

- !orgera 7./7 /./F 2./29 2.-- 2.67 .6/ $.%' 9,/F2 $.)&+% 5,31&

!orgera 7./7 /./F 2.7 2.-/7 2.67 .6/ $.%' 9,0F2 $.)&+% 5,132

/ !orgera 7./7 /./F 2./92 2.-6 2.67 .6/ $.%' 9,922 $.)&+% 5,344

9 !orgera 7./7 /./F 2.0? 2.-/ 2.676 .6/ $.%' 9,/-2 $.)&+% 1,225

F !orgera 7./7 /./F 2./0 2.-6 2.676 .6/ $.%' 9,/F2 $.)&+% 5,31&

' All models run with 6.72 tDmE ball density e*cept the adia surveys use 6.7F tDmE.

Assumed values for unreported parameters are indicated by italics.


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Tale 8 esults of models under survey conditions (model outputs$

A%s:in !o/eda;


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CONC!USION

The Austin model is in good agreement with the surveys across a wide range of mill filling and millspeeds. Nt is also suitable for a typical range of ball fillings, between 7C and -7C.

+ifference between model survey) average .2CP median -.6CP standard deviation 7./C.

The LovedayD#arratt model predicts high in most conditions surveyed and only at very high millspeeds (72C of critical and beyond$ is it consistently within 7C of the surveyed power.

+ifference between model survey) average ?.CP median ?.0CP standard deviation 7.-C.

The Morrell 8Model is in good agreement with the surveys across a wide range of mill filling andmill speeds. Nt is also suitable for a typical range of ball fillings, between 6C and -7C.

+ifference between model survey) average -.9CP median 2.CP standard deviation 6.9C.!ublished survey information is fre%uently missing pulp density, a description of the electrical anddrive system and an indication of how thic& the liners are at the time of the survey. Nncluding adescription such as =gearless motor with +S indicating the motor output> or =induction motorwith gearbo*> allows model operators to choose appropriate factors for power conversions.

AC>NO.!EDGEMENTS

Than&s to the authors of the three methods described herein for publishing their mill models withsufficient detail to permit the calculations used in this paper.

Many than&s to all the operators and authors who have published the survey data used in thispaper. 4ithout the ability to perform this sort of comparison to real operating data, all thesemodels are nothing more than fancy mathematics.

NOMENC!ATURE

A empirical fitting factor for the Austin SAG model

D mill diameter inside the liner, m

Jballs ball filling level, as a fraction of the total mill volume (e.g. 2.-2 for -2C$

Jore ore filling inside a mill, as a fraction of the total mill volume (e.g. 2.2 for 2C$

Jtotal total filling inside a mill, as a fraction of the total mill volume (e.g. 2./2 for /2C$Joids interstitial void space between balls and coarse roc&s in a mill charge (e.g. 2.29 for 9C$

k empirical fitting factor in Morrell 8model to convert charge power draw to motor inputpower draw

K empirical fitting factor for the Austin SAG model

L mill effective grinding length, m

P the power evolved at the mill shell, &4

PN empirical =power number> for the Loveday model which varies with mill filling and speed


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wC charge Csolids, fraction by weight (e.g. 2.6F for 6FC$

B porosity of the roc& and ball bed, as a fraction of total bed volume (e.g. 2./ for /2C$

x density of a component x, tDmE

C mill speed, as a fraction of the mill critical speed (e.g. 2.6F for 6FC$

RE#ERENCES

#arratt, +.K. Sherman, M. (22$ Selection and Si


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"elson, M., 1alery, 4. Morrell, S. (-??0$ !erformance haracteristics and ptimisation of the Bimiston(3GM$ SAG Mill ircuit, Pro-eedings o the /nternational Coneren-e on Autogenous and "e2iautogenous

Grinding 5e-hnolog1 ())+, 1ancouver, anada, pp. //H97.ad

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