Minerals Engineering 55 (2014) 42–51

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Minerals Engineering

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The SAG grindability index test

0892-6875/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.mineng.2013.08.012

⇑ Corresponding author.E-mail address: peter@aminpro.com (P. Amelunxen).

Peter Amelunxen a,⇑, Patricio Berrios b, Esteban Rodriguez b

a AME Ltda, Cerros de Camacho 440, Dep F-17, Santiago de Surco, Lima, Perub Aminpro Chile SpA, Cerro San Cristobal 95111, Quilicura, Santiago, Chile

a r t i c l e i n f o

Article history:Received 13 June 2013Accepted 31 August 2013Available online 5 October 2013

Keywords:Semi-autogenous grindingSAG millingSGI testGrinding

a b s t r a c t

In this paper, the authors undertake a critical review of the Starkey test and the publicly available infor-mation related to the test equipment, procedures, and scale-up methodology. The following recommen-dations are proposed to improve the test method:

1. The test should be conducted for a fixed grinding time of 120 min, regardless of the time required toreach 80% passing Tyler #10 mesh.

2. The test should be conducted with constant time intervals of 15, 30, 60, and 120 min (cumulative) inorder to facilitate the application of geostatistics to the resulting index values. This would also allowfor multiple tests to be conducted in parallel (through the use of multiple mill rollers).

3. The feed size should be prepared using a more rigorous procedure to ensure constant mass in each ofthe course screen fractions.

4. The curve of finished product versus time should be modeled and the resulting index calculated fromthe model for a standard feed size distribution, so that errors attributable to the sample preparationstep are minimized.

The improved feed preparation steps and the use of constant grinding intervals enables the develop-ment of a faster alternative to the standard test that is more cost effective for high volume geometallur-gical programs.

In addition to the updated procedures, a new calibration equation is proposed, with calibration factorsfor pebble crushing, fine feed and autogenous grinding, based on information in the public literature.Detailed descriptions of the test equipment, procedures, and calibration are provided, and it is proposedthat this become an open standard procedure for SAG mill hardness testing, particularly for soft to med-ium-hard ores, over which range the test is most effective.

� 2013 Elsevier Ltd. All rights reserved.

1. Background

Since the Starkey mill was introduced more than 15 years ago,the world has seen many changes in the approach used for SAGcircuit design (in this manuscript, the term SAG will be used torefer to both SAG and FAG milling). While it is no longer the onlyavailable point hardness test method, it is the only one availablebased on a purely empirical tumbling mill test. Originally devel-oped, calibrated, and marketed by Minnovex Technologies underthe name SAG Power Index� (SPI�), the technology was acquiredby SGS in 2005. The technology and scale-up calculations arebelieved by many to be confidential and proprietary, but duringthe mid-1990s the mill and test equipment specifications werepublished openly and sold to various mining corporations (Baeza

and Villanueva, 1994; Gonzalez, 2000), and the primary scale-upequation has also found its way into the public domain throughvarious publications and presentations. Today, any individual ororganization may freely build and market a test system, and thereare now at least six laboratories offering the test, not including SGSand the various mining companies who purchased the equipmentin the mid-1990s. The authors believe that one of the main imped-iments to the widespread adoption of the test has been a generallack of awareness of the information available that is required forconstructing the equipment. This knowledge has been dissemi-nated in various languages throughout conference proceedings,journal papers, websites, and university research theses; indeed,one of the aims of this paper is to rationalize these disparate tech-nical sources into one coherent document.

A second objective of this research program is to provide a crit-ical review of the test method, equipment specifications, datainterpretation, and calibration equation, insofar as permitted bythe information available in the public domain.

Fig. 1. (a and b) The Starkey laboratory mill at El Teniente metallurgical lab (Baezaand Domingo, 2000).

P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51 43

1.1. Nomenclature

The Starkey laboratory mill has been used since 1994 to predictthe autogenous mill specific energy (Starkey and Dobby, 1996). Thetest was originally termed the Starkey SAG test (Starkey et al., 1994)and the laboratory SAG mill was called the Starkey laboratory SAGmill (Starkey and Dobby, 1996), or just the Starkey SAG Mill(Starkey et al., 1994). The test and equipment were commercializedby Minnovex Technologies, a Canadian company that is now part ofSGS Lakefield Minerals, under the name SAG Power Index�, or SPI�

test (Starkey et al., 1994), terms which were later trademarked inCanada (CIPO, 2012). During the 1990s the test equipment,procedures and calibration information were purchased by severalinstitutions (Baeza and Villanueva, 1994), and the test continues tobe used in its original public form (Asmin Industrial, 2013; AminproChile, 2013), which is essentially the same as that of the SPI� (Verretet al., 2011; Baeza and Villanueva, 1994).

The test should not be confused with the SAGDesign test devel-oped by Starkey & Associates, which is of similar genesis but em-ploys a different analytical approach (Starkey et al., 2006).Because Starkey no longer bears any affiliation with the test(Starkey, 2013), the authors suggest that a new name be adoptedto reflect the public nature of the test procedures. With this inmind, we propose the terms ‘‘SAG Grindability Index (SGI)’’ and‘‘SAG Grindability Index Test (SGI test)’’ for the index value andtest, respectively. These terms are used for the remainder of thismanuscript when referring to the public test and methods. Usageof the terms SPI� and SAG Power Index� will continue in the contextof the proprietary test system of the current trademark owners.

1.2. Test equipment

The Starkey laboratory mill dimensions and operating condi-tions are described in great detail in the references listed at theend of this paper. The important characteristics are described be-low, and scaled drawings are included in Appendix B. The authors’test system, which was used for the work described in this paper,was constructed to the specifications described below.

The mill has a 304.8 mm diameter by 101.6 mm length (Verretet al., 2011). The mill is equipped with six one inch by one inchcharge lifters located at 60� intervals, as can be observed in thepublished photographs shown in Fig. 1a and b (Baeza and Villanu-eva, 1994; Baeza and Domingo, 2000). A 5 kg ball charge of 1 1=4 in.balls is used (Verret et al., 2011; Gonzalez, 2000).

The mill reportedly rotates at 70% of critical velocity (Verretet al., 2011), or 54 rpm (Gonzalez, 2000). There is controversy sur-rounding the mill rotational speed. The calculation of mill criticalvelocity (Vc) is derived from the balance of gravitational forceand the centrifugal force acting on a ball, and is given by Eq. (1),after Austin and Concha (1994)

Vc ¼42:2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðD� dÞ

p ð1Þ

where D is the weighted average inside liner diameter and d is theball diameter. Using this equation, the resulting mill rotationalspeed should be 57 rpm, i.e. higher than the published value of54 rpm.

For large mills the ball diameter is negligible relative to the milldiameter, and the equation is often simplified to (Napier-Munn,1996)

Vc ¼42:2ffiffiffiffiffiffiffiffiðDÞ

p ð2Þ

This equation yields the published mill rotational speed of54 rpm; hence, it is assumed that the test designers used the sim-plified equation for computing the rotational velocity.

Back-calculating the fraction of critical speed using the correctequation indicates that the test actually operates at a rotationalspeed of approximately 66% of critical, contrary to the publishedvalue of 70%.

1.2.1. Mill rotational speedTo investigate the impact energy imparted to the ore particles

as a function of the mill rotational speed, the mill was outfittedwith a transparent acrylic lid and rotated with a ball charge at var-ious fractions of critical speed (no ore charge was used to avoid vis-ibility loss because of dust). High definition video was used tomeasure the release angle (a) and toe angle (b), where 12 o’clockis 0� (Fig. 2). Two distinct zones were observed in the video, anabrasion zone and an impact zone where the cascading ballimpacts the toe of the charge. These can be seen in Fig. 2 and inVideo 1.

The impact energy (Ei), in joules, of a single ball-on-liner colli-sion was calculated using equation (3):

Ei ¼12

mv2 ð3Þ

where m is the mass of a ball (approximately 130 g) and v is thevelocity of the ball at impact, calculated from the horizontal (vi)and vertical (vj) components of the velocity vector. Letting r equalthe mill radius (m) and vs be the circumferential speed of the millshell (m/s), the velocity components are given by

v i ¼ v s cos a ð4aÞ

Fig. 2. Image capture from SGI mill at 54 rpm showing two breakage zones.

SPI Test Result

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Time (minutes)

Rel

ativ

e Pe

rcen

t Plu

s Ty

ler

stan

dard

#10

mes

h (1

.7 m

m) SPI Definition

Test IterationsModel

Fig. 3. SPI� test grinding curve showing completion point, from (Amelunxen, 2003,p. 21).

44 P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51

v j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ðv s sinaÞ2 þ 2gh

qð4bÞ

where

h ¼ r½cos aþ cosð2p� bÞ� ð4cÞ

Knowing the impact energy per collision, the energy per unittime (Et in joules per second) is calculated assuming each ballundergoes a single cycle per mill revolution. Since there are 38balls in the standard SGI charge, of which approximately sevenpertain to the abrasion zone and are, therefore, not used to gener-ate impact breakage, Et is given by

Et ¼31v rpm

60Ei ð5Þ

Table 1 shows the results of the energy calculations for variousmill speeds. Also shown is the estimated specific energy input pertonne of ore (Es in kWh/t), calculated for an assumed SGI of 60 min.The data indicate that the highest impact energy per collisionoccurs at a rotational speed of 50 rpm, but the highest energy inputper unit time occurs near 56 rpm. Because there is only minimaldifference between the total energy input at 54 rpm and 56 rpm,the publicly reported speed of 54 rpm is likely appropriate despitethe fact that it is not 70% of critical. Ongoing work is aimed at test-ing different ores with different speeds to validate this conclusion.

1.3. Original test procedures

The original procedures for the test consist of stage crushing thesample to two control points—100% minus 3=4 in. and 80% passing½ in. (Verret et al., 2011). The sample is screened and then placedin the mill with the ball charge. The test is a dry batch grinding testin which the mill is rotated and the sample ground until it reaches80% passing Tyler #10 mesh, or 1.7 mm (Starkey et al., 1994). Be-cause the time required to achieve 80% passing 1.7 mm is notknown before starting the test, an initial grinding time is selected,the sample is ground then removed from the mill and screened on

Table 1SGI mill energy vs. rotational speed.

Speed (rpm) Releaseangle (�)

Toe angle (�) Ei (j/ball) Et (j/s) Es (kWh/t)

48 28 137 0.35 8.84 4.4250 21 133 0.36 9.30 4.6552 20 128 0.35 9.45 4.7254 13 126 0.35 9.95 4.9756 10 120 0.34 9.98 4.9958 2 105 0.30 9.12 4.5660 0 90 0.26 7.98 3.99

a large Tyler #10 mesh screen. The mass of minus 10 meshmaterial produced per revolution is then used to approximatethe time required for the subsequent grinding interval. The entirecharge is then returned to the mill and ground for the next timeperiod. The sequence is repeated until the test achieves completion(Amelunxen, 2003, pp. 19–21). Fig. 3 shows the results of a typicaltest.

1.4. Revised test procedures

The above procedures were reviewed in a previous publicationby one of the authors (Amelunxen, 2003, pp. 19–21, 55–57, 62–65)and several recommendations were made to improve the test(Amelunxen, 2003 p. 108). These are summarized as follows:

� The curve of mass retained on Tyler #10 mesh (1.7 mm) versuscumulative grinding time should be mathematically modeledand the resulting index be interpolated or extrapolated. Severalalternative model forms were suggested, depending on the orehardness.� The practice of performing several iterations near the end of the

test (the three points above 120 min on the x-axis in Fig. 3) isnot necessary given that the curve can be modeled and theend result interpolated or extrapolated.� The test should be conducted for constant grinding time inter-

vals, as this facilitates the mathematical or geostatistical han-dling of the data (it generates additive parameters, ratherthan a non-additive index values).

These recommendations have been adopted in the presentwork. The times selected for the fixed grinding periods are 15,30, 60 and 120 min (cumulative). Beyond 120 min, the slope ofthe curve starts to approach zero. As a result, for ores with SGI val-ues over approximately 150 min, relatively small errors in the feedsize or competency can lead to very large differences in the result-ing SGI—in other words, the test begins to break down. This ismostly likely a result of the fact that the impact energies requiredto fracture the coarsest particles in the feed are higher than thoseattainable with such a small mill.

This problem has been mitigated, in part, by introducing a smallchange to the feed preparation procedures. The new proceduresrequire the feed to be prepared to a controlled size distribution.The new size distribution was selected to reflect the averagesize distribution from the authors’ database of SGI tests conductedfor commercial projects before the new procedures wereimplemented. It is shown in Table 2.

The proposed standard test procedures are appended.

Table 3Cost estimate for short and standard SGI tests.

Calculation Short SGItest

Standard SGItest

Units

Tests per hour 3 1 tests/hHours per shift 8 8 hNo. of technicians 4 4 techsProductivity factor 1 1Cost of labor, gross $60 $60 $/h

tech.Cost per test, labor $80 $240 $/test

Overheads and other costsAdministration (20%) $16 $48 $/testEngineering and supervision

(15%)$12 $36 $/test

Quality assurance and control(10%)

$8 $24 $/test

Financing and depreciation (7%) $6 $17 $/testMaintenance (6%) $5 $14 $/testOperating supplies (5%) $4 $12 $/testContingency (5%) $4 $12 $/testProfit (20%) $16 $48 $/test

Total overheads $70 $211 $/test

Total cost per test $150 $451 $/test

Fig. 4. Comparison of modified (short) SGI test and standard SGI test.

P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51 45

1.5. Revised test interpretation

Several equation forms were investigated for modeling the SGItest, including those described previously by Amelunxen (2003, p.55). It was found that the best performance is given by a variant ofthe Swebrec� equation (Ouchterlony, 2005) often used for model-ing cumulative size distributions. The form of the equation is

PðtÞ ¼ f ðxÞ1þ f ðxÞ ð6Þ

where P(t) is the percent retained on a Tyler #10 mesh screen at agrinding time of t (minutes) and

f ðxÞ ¼ mlnð0:25Þlnðm20 Þ

� �x ; ð7aÞ

mx ¼ln t0

tx

� �

ln t0t50

� � ð7bÞ

and

m20 ¼ln t0

t20

� �

ln t0t50

� � ð7cÞ

where tx is the indeterminate time and t0, t20, and t50 are fittedparameters that represent the cumulative grinding times at whichP(t) is equal to 0%, 20%, and 50%, respectively. Hence, by definitionthe SGI is equal to t20.

2. Lower cost, lower precision test procedures

Analysis of a data set of approximately 150 tests conductedusing the SGI mill indicate that it is possible to produce a lowercost, lower precision version of the SGI test by performing a singlegrinding iteration with the standard feed charge for a constanttime interval of 60 min. The resulting product is then screenedon a Tyler #10 mesh screen (1.7 mm) and an empirical equationis used to determine the SGI from the screen analysis results. Thenew test only requires a single grinding iteration of 60 min, soone technician can operate three or maybe four individual SGImills in parallel. This allows for a team of four technicians to pro-duce approximately three tests per hour, or 24 tests in an eighthour shift (two technicians for sample preparation, one to operatethe SGI mills and sieve shakers, and one for miscellaneous tasksincluding sample logging, data logging, quality control, and clean-up). We can estimate the unit sales cost under such a scenario byassuming a gross labor cost of US$60/h and generous allowancesfor fixed overheads and other costs. The estimates, shown inTable 3, yield a unit price of US$150 per test, compared to approx-imately US$450 for the standard test procedures detailed above.Because anybody can build and operate the test equipment, noadditional fees are assumed.

By adopting the short test procedures, only minor loss of fidelityis incurred, as the empirical correlation shows a coefficient of

Table 2Standard SGI feed size distribution.

Tyler screen Opening (lm) Mass (g)

3/400 19,050 01/200 12,700 4003/800 9525 4004-Jan 6350 400#6 3350 400#10 1700 150pan 0 250

determination of almost 0.98 (Fig. 4). This is equivalent to approx-imately 0.16 kWh/t at one sigma level of confidence—i.e. a stan-dard error of only 2% for the data set used in this study.

Notwithstanding the marginally lower precision, the modifiedtest procedures have a superior value proposition. For example(see Table 4), with a hypothetical budget of US$25,000, one couldelect to perform either 56 standard tests or 167 modified tests.The modified tests would yield mean mill power requirements ormean throughput estimates that have approximately half thetest-related error of those derived from the standard tests. In addi-tion to the cost benefits, the modified test delivers an index value(the mass retained after 60 min) that is naturally additive andtherefore is more conducive to geostatistical handling (for a discus-sion on the mathematical additivity of the SGI, see Amelunxen,2003, pp. 54–65).

Table 4Error estimates for a hypothetical characterization program, showing superior resultsfrom the modified test.

Test type: Modified Standard

Budget available $25,000 $25,000Cost $150 $450No. of tests 167 56Assumed mean kWh/t (metric) 7.33 7.33Standard error of mean kWh/t (metric) 0.012 0.021Relative standard error of mean 0.16% 0.28%

46 P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51

3. SAG mill specific energy calibration

3.1. Closed circuit without pebble crushing

The original calibration equation was developed during themid-1990s under sponsorship by the Mining Industry TechnologyCouncil of Canada (MITEC) and the results were published in theproceedings of the SAG ‘96 conference held in Vancouver, Canada.The relevant equation expressed the mill power draw per unitthroughput as a function of the SPI™ and T80, as follows (Starkeyand Dobby, 1996):

SAGkWh

t¼ 2:2þ 0:1SPI

T0:3380

ð8Þ

where the T80 is the 80% passing size of the SAG screen undersize. In1999 additional data points were published, then totaling 13 differ-ent plants (Kosick and Bennett, 1999) together with a new, nonlin-ear, calibration equation. In that publication, however, the valuescale of the abscissa was not shown (Fig. 5a). Nevertheless, byassuming that the four valid concentrators from the 1996 publica-tion (Starkey and Dobby, 1996) are also included in the 1999 graph(why would they not be?), the value scale can be back-calculated bysuperposing the 1996 points on the 1999 plot and fitting the valueof n to give the best match. The results (Fig. 5b) yield the scale offthe abscissa, which can then be used to derive the values of theremaining points and the constants of the new nonlinear calibrationequation.

y = 5.9x0.55

0

2

4

6

8

10

12

1416

18

20

22

0 1 2 3 4 5 6 7 8 9

Plan

t kW

h/t

SPI * T80-0.5

10

Fig. 5. SPI� Calibration equation, left (Kosick and Bennett, 1999), with superposi-tion of 1996 data points shown by blue squares (right). (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

Fig. 6. SAG specific energy calibration plots for

The equation, shown in the form given by Dobby et al., (2001), is

SAGkWh

t¼ 5:9

SGIffiffiffiffiffiffiffiT80p� �0:55

ð9Þ

The calibration equation shown above is the primary calibrationequation and is only valid for the reference circuit consisting of aSAG mill operating in closed circuit without pebble crushing andwith nominal 6 in. SAG mill feed (Kosick and Bennett, 1999). Formills operating with finer feed and/or in-circuit pebble crushing,an adjustment factor is used to account for the reduced SAG millspecific energy (Dobby et al., 2001). The adjustment factor, termedfSAG, is then used as follows (Dobby et al., 2001):

SAGkWh

t¼ 5:9

SGIffiffiffiffiffiffiffiT80p� �0:55

fSAG ð10Þ

3.2. Fine feed and pebble crushing

Fig. 6, after Amelunxen (2003, p. 24), shows the calibration scat-terplots for grinding mills operating with fine feed (left) and within-circuit pebble crushers (right). The graphs indicate that the val-ues of fSAG are:

� With fine feed, fSAG = 0.9.� With pebble crushing, fSAG = 0.85.

Presumably, fSAG values are additive for optimized circuits. SAGmills operating in closed circuit with both finer feed and in-circuitpebblecrushing would, therefore, show fSAG values approximatelyequal to product of the fine feed and pebble crushing correctionfactors, i.e. approximately 0.77. Audit data from such a circuit(Candelaria) is available (Amelunxen et al., 2011) and corroboratesthis notion (Fig. 7).

3.3. Open circuit SAG milling

More recently, data from Los Bronces’ SAG mill circuit has be-come available (Becerra and Amelunxen, 2012), in which the SAGmill was operating in both SABC-B configuration, where thecrushed pebbles report to the ball mill feed chute, and SABC-ABconfiguration, in which the pebble crusher product is split betweenboth SAG and ball mill sections. In this configuration, the apparenttransfer size is calculated as the weighted average of the SAGclassifier undersize and the pebble crusher product. The data areshown in Fig. 8. Some interesting observations can be made:

� The mill ‘‘efficiency’’ (if fSAG can be taken as a measure of effi-ciency) was very similar to that of the Candelaria mill, in spite

fine feed (left) and pebble crushing (right).

Fig. 7. SAG specific energy calibration plot for both fine feed and pebble crushing,after (Amelunxen et al., 2011).

Fig. 8. Los Bronces data set showing open circuit and partially open circuit SAGmilling.

Fig. 9. Bagdad survey data.

P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51 47

of operating in open circuit or semi-open circuit configuration.� Counterintuitively, the mill efficiency was higher (lower fSAG)

during the three surveys in which some of the crushed pebbleswere returned to the ball mill.� As expected, the apparent transfer size of the SABC-AB configu-

ration was finer than that of the SABC-B configuration, reflect-ing the reduced flow of coarse pebble crusher product to theball mills. This observation may partly explain the lower fSAG

values for the SABC-B configuration. Because these particlestend to have sharper, less rounded edges than their same-sizedcounterparts in the SAG mill discharge, they may lead to greaterproduction of fines or finished product as these edges get‘‘rounded off’’ upon their return to the SAG mill. Therefore, aslong as they are already finer than the SAG mill classifier slotsand the SAG mill throughput is limited by the size reductionof the coarse, plus-grate size material, then passing some ofthem through the SAG mill one more time before sending themto the ball mills may not be such a bad idea.

3.4. Fully autogenous milling

The Bagdad mill consists of five autogenous grinding lines fol-lowed by ball milling. Using the available SPI and plant survey data(Amelunxen et al., 2011), we can compare the fSAG values from Bag-dad to those of the other circuit configurations discussed above. Itcan be seen that the Bagdad ABC-A configuration averages fSAG val-ues of approximately 0.62. This is an improvement over that of theSABC-B and SABC-AB configuration of Los Bronces discussed above,

but it should be noted that this does not include the power of thepebble crushers, and Bagdad operated with a high circulating load(routinely above 50%), as can be seen from the appended data set.Fig. 9 shows the Bagdad calibration data relative to the previouslydiscussed points.

While the relationship between predicted and actual specificenergy is weaker with the Bagdad data (this is likely a result of dif-ferences in pebble crusher loads), the average fSAG value of 0.62 cannevertheless be used as a guide for those considering fully autoge-nous grinding circuits.

3.5. Discussion of error

At this point, it should be noted that there is some scatter inFig. 9. This is expected due to the difficulties of obtaining represen-tative samples and mass balance estimates for large grinding cir-cuits, particularly those involving high circulating loads andpebble crushing. Amelunxen (2003, p. 107) estimates the standarderror of the specific energy at between 20% and 26% due to error ofthe primary calibration equation and sub-models for T80 and fSAG.Furthermore, studies performed at Chino Mines and elsewhereindicate that normal drill-hole collar intervals may be outside therange of typical SGI variograms (Amelunxen, 2001; Amelunxen,2003, p. 107), and therefore, error reduction due to geostatisticalcorrelation may not be significant (at least not in the horizontaldirections). As such, the central limit theorem provides a reason-able basis for estimating error for different forecast periods; i.e.

S ¼ rffiffiffinp ð11Þ

where S is the standard error of the mean throughput estimate for agiven production period, r is the standard error of the throughputestimate for a point hardness sample (including calibration errors),and n is the number of samples that represent the ore in that pro-duction period.

Note that when modeling for design purposes, one must alsoconsider the error inherent in the estimated mill power draws;Morrell (1993) estimates this at 5.4% for one sigma.

For a complete analysis and discussion of the error, includingthe error as it relates to the forecasting time period, refer to Amel-unxen (2003, pp. 66–104).

3.6. Estimating the transfer size

One of the limitations of the scale-up methodology describedabove is that the transfer size must be known in order to estimatethe specific energy required for a given SAG mill circuit. One caneither select a transfer size, and then determine the mill power re-

48 P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51

quired to achieve it (given a throughput target), or one can selectthe installed power and tonnage and then use the resulting trans-fer size to size the ball mills (presumably on the basis that the milloperators would then select the grates, pebble ports, crushing con-figuration, and classifier opening such that the calculated transfersize can actually be achieved in practice).

The transfer size conundrum results from fact that in practicethe transfer size is not exogenous—it is itself a function of the millthroughput and ore hardness (for a fixed system). Over long timeperiods it may be reasonable to assume that the grates, pebbleports, and other system parameters will be optimized to achievethe desired mean transfer size, but for simulations targeting spe-cific process configurations or shorter timeframes (such as thoseperformed on point samples representing ore reserve blocks or‘‘snapshot’’ process audits), the energy based scale-up methodol-ogy described above should be used in conjunction with eitherphenomenological or semi-empirical models that incorporatebreakage and selection functions in some form or another. For thispurpose the authors favor an energy-based phenomenologicalbreakage model that will be presented as part of a futurepublication.

4. Conclusions

This paper has provided a comprehensive review of the publiclyavailable information related to the Starkey test and calibrationmethodology. It has also provided an analysis of test data gener-ated using the SGI test mill constructed by the authors as shown

Appendix A. Previously published calibration data

See Figs. A1.a, A1.b, A2.a and A2.b.

No Source Plant Circuit Feedsize F80

SPI TPHdry

name (in) (min) (t/hr)

1 18 Bagdad ABC-A 5.6 100 6242 18 Bagdad ABC-A 5.5 91 8543 18 Bagdad ABC-A 3.8 92 8444 18 Bagdad ABC-A 3.2 120 6555 18 Bagdad ABC-A 4.3 118 6476 18 Bagdad ABC-A 3.1 120 7217 18 Bagdad ABC-A 2.7 82 6968 18 Bagdad ABC-A 6.5 149 6919 18 Bagdad ABC-A 4.8 101 663

10 18 Bagdad ABC-A 3.5 140 64011 18 Bagdad ABC-A 4.2 114 64212 18 Bagdad ABC-A 4.6 118 69613 18 Bagdad ABC-A 7.8 112 52114 18 Bagdad ABC-A 5.1 92 67015 18 Bagdad ABC-A 6.0 121 59116 18 Bagdad ABC-A 7.7 104 67017 18 Bagdad ABC-A 3.6 132 55418 18 Bagdad ABC-A 5.1 127 58919 18 Bagdad ABC-A 3.1 112 49820 18 Bagdad ABC-A 3.0 88 59921 18 Candelaria SABC-B 3.8 87 136022 18 Candelaria SABC-B 3.7 119 109023 18 Candelaria SABC-B 3.6 93 145724 18 Candelaria SABC-B 3.7 104 1282

in the appended schematics. A case has been made for makingthe following changes to the terminology, procedures, and scale-up methods of the test:

� The terms ‘‘Starkey mill,’’ ‘‘Starkey test,’’ and ‘‘Starkey index’’ areobsolete, confusing, and should be dropped from the lexicon.The authors have proposed the terms ‘‘SAG grindability index’’or ‘‘SGI’’ mill and test.� To reduce error, the feed size distribution for the test should

be fixed for the coarse fractions above the Tyler #10 meshscreen.� The test should be conducted for fixed grinding time intervals of

15, 30, 60, and 120 min, after which the test is completed.� The grinding curve should be modeled using a variant of the

Swebrec™ equation and the SGI extrapolated or interpolatedfrom the fitted equation.� A shorter, lower cost/lower precision version of the test has

been recommended for large geometallurgical projects thatrequire very large datasets and can tolerate relatively minorreductions in test fidelity.

An updated calibration equation has been provided, togetherwith calibration factors for finer feed, pebble crushing, and fullyautogenous milling. The appendices contain detailed drawings ofthe laboratory mill, a summary of published calibration data, andthe test procedures for the standard and short versions of the SGItest. The authors suggest that these should constitute a freelyavailable, open standard SGI test.

Pebblecirc load

Power Prodsize T80

S.E. SPIshell

S.E. Plantshell

Fsag

(%) (kW) (lm) (kWh/t) (kWh/t)

58 4501 1857 8.62 7.22 0.8457 3974 4725 6.89 4.65 0.6756 4474 4843 6.89 5.30 0.7759 4477 7914 6.97 6.83 0.9855 4490 6678 7.21 6.93 0.9666 4116 1523 10.96 5.71 0.5275 4158 2173 8.04 5.97 0.7489 4434 2971 10.24 6.42 0.6342 4322 1096 10.91 6.51 0.6089 3810 990 13.41 5.95 0.4475 3915 1748 10.23 6.10 0.6078 4274 3685 8.49 6.14 0.7261 4452 963 11.92 8.54 0.7262 4382 1685 9.17 6.54 0.7133 4366 619 14.05 7.39 0.5361 4341 1092 11.08 6.47 0.5872 4300 1105 12.61 7.77 0.6238 4409 756 13.70 7.48 0.5553 4453 386 15.38 8.94 0.5877 4114 764 11.13 6.87 0.6226 9982 1573 9.09 7.34 0.8125 10907 786 13.07 10.01 0.7726 10436 1888 8.97 7.16 0.8021 10566 1764 9.71 8.24 0.85

Appendix A (continued)

No Source Plant Circuit Feedsize F80

SPI TPHdry

Pebblecirc load

Power Prodsize T80

S.E. SPIshell

S.E. Plantshell

Fsag

name (in) (min) (t/hr) (%) (kW) (lm) (kWh/t) (kWh/t)

25 18 Candelaria SABC-B 3.6 132 1500 26 10505 2899 9.66 7.00 0.7226 18 Candelaria SABC-B 3.4 89 1596 19 10421 3689 7.26 6.53 0.9027 18 Candelaria SABC-B 3.4 110 1358 23 10620 1905 9.81 7.82 0.8028 18 Candelaria SABC-B 4.0 131 1964 21 9978 2242 10.3329 18 Candelaria SABC-B 4.1 151 1297 21 10602 2178 11.25 8.18 0.7330 18 Candelaria SABC-B 3.3 116 1693 27 10317 3171 8.78 6.09 0.6931 18 Candelaria SABC-B 4.0 124 1693 25 10568 3311 9.00 6.24 0.6932 18 Candelaria SABC-B 3.9 171 1151 27 10734 2674 11.39 9.33 0.8233 18 Candelaria SABC-B 2.9 176 1072 36 10852 2100 12.37 10.12 0.8234 19 L. Bronces SABC-B 1.8 80.8 2488 11211 5200 6.28 4.51 0.7835 19 L. Bronces SABC-AB 2.1 72.4 3173 10755 3950 6.38 3.39 0.5836 19 L. Bronces SABC-AB 1.2 67.4 2970 10716 3300 6.44 3.61 0.6137 19 L. Bronces SABC-AB 1.7 75.9 2922 11327 2800 7.19 3.88 0.5838 19 L. Bronces SABC-B 2.2 90.1 2656 13882 5750 6.49 5.23 0.8739 19 L. Bronces SABC-B 3.1 63.0 2344 13059 4200 5.81 5.57 1.0440 19 L. Bronces SABC-B 4.0 68.4 2553 12945 5250 5.72 5.07 0.9641 19 L. Bronces SABC-B 3.5 73.4 2511 12932 3300 6.75 5.15 0.8342 19 L. Bronces SABC-B 2.8 74.4 2563 12847 5300 5.97 5.01 0.9143 3 HVC SABC-A 32.0 1659 6380 2570 4.21 3.54 0.8444 3 HVC SABC-A 43.0 1252 6786 1925 5.37 4.99 0.9345 3 HVC SABC-A 60.0 919 6722 1880 6.49 6.73 1.0446 3 Selbaie SABC-A 42.0 297 2555 323 8.66 7.91 0.9147 3 Selbaie SABC-A 54.0 306 3024 337 9.83 9.09 0.9348 3 Selbaie SABC-A 53.0 268 3200 308 9.97 10.99 1.1049 3 Q-Cartier SABC-A 8.0 1018 3655 515 3.06 3.30 1.0850 3 Q-Cartier SABC-A 9.0 1164 4514 480 3.33 3.57 1.0751 3 Q-Cartier SABC-A 12.0 1045 5005 460 3.94 4.41 1.1252 16 unknown 18.4 18.4 1.0053 16 unknown 14.5 14.3 0.9854 16 unknown 14.4 14.1 0.9855 16 unknown 11.3 11.0 0.9856 16 unknown 9.9 9.2 0.9357 16 unknown 8.8 7.8 0.8958 16 unknown 6.3 6.8 1.0959 16 unknown 4.5 3.7 0.82

Fig. A1.a. Detail SGI mill shell. Fig. A1.b. SGI mill shell Section A.

P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51 49

Fig. A2.b. Detail lid rubber liner.

Fig. A2.a. Detail SGI mill.

50 P. Amelunxen et al. / Minerals Engineering 55 (2014) 42–51

Appendix B. SGI mill drawings

The following construction drawings depict the SAG grindabili-ty test mill constructed to perform the research described in thispaper. The drawings were reconstructed from the publicly avail-able sources as described in the body of this manuscript.

Appendix C. SGI test procedures

Standard SGI test procedures:

1. Using a laboratory jaw crusher, stage crush the sample toapproximately 100% minus 3=4 in. and approximately 80% minus½ in.

2. Screen the material on the following screens, and create a con-trolled SGI feed size distribution using standard laboratorysplitting equipment and procedures:

Screen

lm Mass (g)

3/400

19,050 0 1/200 12,700 400 3/800 9525 400 1/400 6350 400 #6 3350 400 #10 1700 150 pan 0 250

1. Place the 5 kg ball charge and 2 kg mass charge in the SGI mill

and grind it for 15, 30, 60, and 120 min, measuring the sizedistribution after each cycle (with the same screens as shownabove).

2. Using least squares methods, fit Eqs. 6, 7a, 7b, and 7c to thecurve of% retained on a Tyler #10 mesh screen versus time,and using the resulting equation to calculate the time requiredto reach 80% passing Tyler #10 mesh (note that only the Tyler#10 mesh screen is required after each cycle; the entire stackis included in these procedures just to avoid blinding and to col-lect additional information in the event that it is required in thefuture).

Appendix D. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.mineng.2013.08.012.

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