06 Jaime Sepulveda

7/27/2019 06 Jaime Sepulveda

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Methodologies for theEVALUATION OF GRINDING MEDIA

CONSUMPTION RATESat Full Plant Scale

Methodologies for theEVALUATION OF GRINDING MEDIA

CONSUMPTION RATESat Full Plant Scale

Procemin 2004Santiago, ChileAugust 19 - 20, 2004

Procemin 2004Santiago, ChileAugust 19 - 20, 2004

Dr. Jaime E. SeplvedaMoly-Cop Grinding SystemsDr. Jaime E. Seplveda

Moly-Cop Grinding Systems


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BACKGROUNDBACKGROUND

qAfter energy, grinding media consumption is typicallyidentified as the second most significant cost item in anyfine grinding operation.

q In the selection of the best grinding media type orsupplier, there is a well accepted evaluation criterion that

accounts for both product price and quality, referred to asCost Effectiveness :

Cost of Grinding = Balls Price x Balls Consumption($ /ton ground) ($/ton balls) (ton balls/ton ground)

q Therefore, for the proper application of the aboveequation, it is essential to maintain continuously updatedand representative indicators of the performance of anyparticular grinding media type being utilized.

q

After energy, grinding media consumption is typicallyidentified as the second most significant cost item in anyfine grinding operation.

q In the selection of the best grinding media type orsupplier, there is a well accepted evaluation criterion that

accounts for both product price and quality, referred to asCost Effectiveness :

Cost of Grinding = Balls Price x Balls Consumption($ /ton ground) ($/ton balls) (ton balls/ton ground)

q Therefore, for the proper application of the aboveequation, it is essential to maintain continuously updatedand representative indicators of the performance of anyparticular grinding media type being utilized.


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q Micro - Wear : Abrasion / Corrosion.

q Macro - Wear : Spalling.q Impact Breakage.



Mechanisms forGRINDING MEDIA CONSUMPTION



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Ab

dd

Grinding Media AlgebraWEAR KINETICS CHARACTERIZATION

Grinding Media AlgebraWEAR KINETICS CHARACTERIZATION

q At every instant, the weight loss ofthe grinding body is directlyproportional to the exposed surface

area :

q At every instant, the weight loss ofthe grinding body is directlyproportional to the exposed surface

area :

which is equivalent to :which is equivalent to :

t = (m)/(t) = - kmAb

t = (m)/(t) = - kmAb

(d)/(t) = - 2km/b = - kd

(d)/(t) = - 2km/b = - kd


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q Therefore, if kd remains constantover time - t hat is, i t is not af unct ion of t he inst ant aneous ball

diamet er- the rate of ball

diameter loss will also be constant :

q Therefore, if kd remains constantover time - t hat is, i t is not a f unct ion of t he inst ant aneous ball

diamet er- the rate of ball

diameter loss will also be constant :

d = dR - kd t

d = dR - kd t

Grinding Media AlgebraTHE LINEAR WEAR THEORY


(d)/(t) = - kd

(d)/(t) = - kd

q Then, upon simple integration, thefollowing linear relationship will apply :q

Then, upon simple integration, thefollowing linear relationship will apply :

Ab

dd


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dRdR

Equilibrium ConditionGENERATION OF THE STRING

Equilibrium ConditionGENERATION OF THE STRING

q The continuous recharging with balls of a singlesize dR generates, at equilibrium, a uniform sizedistribution of balls inside the mill :

q The continuous recharging with balls of a singlesize dR generates,

at equilibrium, a uniform sizedistribution of balls inside the mill :

dR-kdtdR-kdt dR-2kdtd

R-2kdt dR-nkdtdR-nkdt

ll ll ll

Therefore, there will exist an equal numberof every possible ball size in the charge.Therefore, there will exist an equal numberof every possible ball size in the charge.


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q The Mass Size Distribution F3(d), corresponding to the

fraction of the total weight of balls in the string ofsize smaller than d :

q The Mass Size Distribution F3(d), corresponding to the

fraction of the total weight of balls in the string ofsize smaller than d :

F3(d) = (d/dR)4F3(d) = (d/dR)4



On the basis of the previous considerations, the followingcalculations can be made :On the basis of the previous considerations, the followingcalculations can be made :

q The Specific Area, a (m2/m3), exposed by the balls inthe string :

q The Specific Area, a (m2/m3), exposed by the balls inthe string :

a = 8000 (1-fv)/dRa = 8000 (1-fv)/dR


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Industrial Scale EvaluationsMEDIA CONSUMPTION INDICATORS

Industrial Scale EvaluationsMEDIA CONSUMPTION INDICATORS

q Consumption per Unit of Time,t (kg/hr)

q Consumption per Unit of Energy,E (gr/kWh)

q Consumption per Unit of Ore Ground,M (gr/ton)

q Consumption per Unit of Time,t (kg/hr)

q Consumption per Unit of Energy,E (gr/kWh)

q Consumption per Unit of Ore Ground,M (gr/ton)


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MEDIA CONSUMPTION RATE, kg/hrMEDIA CONSUMPTION RATE, kg/hr

q Grinding media consumption rate is directly proportionalto the total area exposed by the string :

q Grinding media consumption rate is directly proportionalto the total area exposed by the string :

and, from the Linear Wear Theory :and, from the Linear Wear Theory :

when d

R

is expressed in mm.when dR is expressed in mm.

t = - km A = - b kd A /2t = - km A = - b kd A /2

A = 8000 (1-fv) Vap /dRA = 8000 (1-fv) Vap /dR

then :then :

t = - 4000 kd [b (1-fv) Vap] /dR

= - 4000 kd Wb /dR

t = - 4000 kd [b (1-fv) Vap] /dR

= - 4000 kd Wb /dR


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q By analogy to ore grinding processes, the media wear rateis postulated to be proportionally affected by the powerintensity of the process :

q By analogy to ore grinding processes, the media wear rateis postulated to be proportionally affected by the powerintensity of the process :

and since :and since :

kd = kdE (P/Wb) /1000kd = kdE (P/Wb) /1000

MEDIA CONSUMPTION RATE, gr/kWhMEDIA CONSUMPTION RATE, gr/kWh

E

= 1000 t

/PE = 1000 t /PExper t s say . . .

The kdE rate constant,expressed in m/(kWh/ton),is considered to be the bestindicator of ball quality forthe particular applicationbeing analyzed.

Exper t s say . . .

The kdE

rate constant,expressed in m/(kWh/ton),is considered to be the bestindicator of ball quality forthe particular applicationbeing analyzed.

finally :finally :

E = - 4000 kdE /dRE = - 4000 kdE /dR


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q Sequential : comparison of historicalconsumption rates of the same mill,

before and after the purge period.q Concurrent : comparison of consumption

rates of a test mill against a standard

mill, both operating in parallel, forexactly the same time period.

q Sequential : comparison of historicalconsumption rates of the same mill,

before and after the purge period.q Concurrent : comparison of consumption

rates of a test mill against a standard

mill, both operating in parallel, forexactly the same time period.

Plant Scale Data AnalysisCOMPARATIVE EVALUATIONS

Plant Scale Data AnalysisCOMPARATIVE EVALUATIONS


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Fair Mining CompanyOPERATIONAL RECORDS


Unit : SAG 1 Make-u Balls : 5.0"

Mill Diam. 36 ft % Balls (Nominal) 14

Mill Lenght 17 ft % Charge (Nominal) 26

% Critical 76 % % Solids (Nominal) 74

Ore Density 2.8 ton/m3

Ore Operating Grinding Energy Mill

Throughput hours Capacity Consumption Power

ton/month hr/month ton/hr MWh/month kW ton/month gr/ton kg/hr gr/kWh Supplier

Jul '02 1,017,541 721.0 1,411 8,533 11,836 499.21 491 692 58.5 Forge +

Aug 915,593 644.0 1,422 7,639 11,862 375.07 410 582 49.1 Forge +

Sep 908,071 715.0 1,270 8,576 11,994 480.04 529 671 56.0 Forge +

Oct 718,227 643.0 1,117 7,506 11,674 425.99 593 663 56.8 Forge +

Nov 703,180 627.0 1,121 6,960 11,100 358.08 509 571 51.5 Forge +

Dec 852,259 695.0 1,226 7,712 11,096 444.01 521 639 57.6 Forge +

Jan '03 995,836 718.0 1,387 7,872 10,964 513.25 515 715 65.2 Forge +

Feb1,014,800 691.0 1,469 7,814 11,308 464.15 457 672 59.4 Forge +

Mar 864,302 639.0 1,353 7,606 11,903 400.83 464 627 52.7 Forge +

Apr 935,336 699.0 1,338 8,231 11,775 400.84 429 573 48.7 Forge +

May 867,843 661.0 1,313 8,071 12,210 436.64 503 661 54.1 Forge +

Jun 747,636 631.0 1,185 7,103 11,256 396.00 530 628 55.8 Forge +

Average 878,385 673.7 1,304 7,802 11,581 432.84 493 643 55.5

Balls Consumption









Jul '02 1,017,541 721.0 1,411 8,533 11,836 499.21 491 692 58.5 Forge +

Aug 915,593 644.0 1,422 7,639 11,862 375.07 410 582 49.1 Forge +

Sep 908,071 715.0 1,270 8,576 11,994 480.04 529 671 56.0 Forge +

Oct 718,227 643.0 1,117 7,506 11,674 425.99 593 663 56.8 Forge +

Nov 703,180 627.0 1,121 6,960 11,100 358.08 509 571 51.5 Forge +

Dec 852,259 695.0 1,226 7,712 11,096 444.01 521 639 57.6 Forge +

Jan '03 995,836 718.0 1,387 7,872 10,964 513.25 515 715 65.2 Forge +

Feb 1,014,800 691.0 1,469 7,814 11,308 464.15 457 672 59.4 Forge +

Mar 864,302 639.0 1,353 7,606 11,903 400.83 464 627 52.7 Forge +

Apr 935,336 699.0 1,338 8,231 11,775 400.84 429 573 48.7 Forge +

May 867,843 661.0 1,313 8,071 12,210 436.64 503 661 54.1 Forge +

Jun 747,636 631.0 1,185 7,103 11,256 396.00 530 628 55.8 Forge +

Average 878,385 673.7 1,304 7,802 11,581 432.84 493 643 55.5

Balls Consumption


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Unit : SAG 2 Make-up Balls : 5.0"








Jul '02 755,228 632.0 1,195 7,401 11,711 401.29 531 635 54.2 Forge +

Aug 866,067 715.0 1,211 8,314 11,628 483.39 558 676 58.1 Forge +

Sep 845,614 691.0 1,224 8,879 12,849 494.29 585 715 55.7 Forge +

Oct 951,123 688.0 1,382 8,275 12,027 507.00 533 737 61.3 Forge +

Nov 985,943 710.9 1,387 8,629 12,140 370.84 376 522 43.0 NKOB

Dec 701,282 549.0 1,277 6,208 11,308 470.29 671 857 75.8 NKOB

Jan '03 877,346 723.2 1,213 8,459 11,697 431.54 492 597 51.0 NKOB

Feb 916,566 661.1 1,386 7,719 11,675 443.47 484 671 57.5 NKOBMar 915,974 678.0 1,351 7,904 11,657 412.35 450 608 52.2 NKOB

Apr 976,000 692.2 1,410 8,329 12,033 457.80 469 661 55.0 NKOB

May 856,863 640.9 1,337 7,296 11,385 511.82 597 799 70.1 NKOB

Jun 1,073,551 700.4 1,533 8,170 11,666 534.28 498 763 65.4 NKOB

Average 893,463 673.5 1,327 7,965 11,828 459.86 515 683 57.7

Balls Consumption









Jul '02 755,228 632.0 1,195 7,401 11,711 401.29 531 635 54.2 Forge +

Aug 866,067 715.0 1,211 8,314 11,628 483.39 558 676 58.1 Forge +

Sep 845,614 691.0 1,224 8,879 12,849 494.29 585 715 55.7 Forge +

Oct 951,123 688.0 1,382 8,275 12,027 507.00 533 737 61.3 Forge +

Nov 985,943 710.9 1,387 8,629 12,140 370.84 376 522 43.0 NKOB

Dec 701,282 549.0 1,277 6,208 11,308 470.29 671 857 75.8 NKOB

Jan '03 877,346 723.2 1,213 8,459 11,697 431.54 492 597 51.0 NKOB

Feb 916,566 661.1 1,386 7,719 11,675 443.47 484 671 57.5 NKOBMar 915,974 678.0 1,351 7,904 11,657 412.35 450 608 52.2 NKOB

Apr 976,000 692.2 1,410 8,329 12,033 457.80 469 661 55.0 NKOB

May 856,863 640.9 1,337 7,296 11,385 511.82 597 799 70.1 NKOB

Jun 1,073,551 700.4 1,533 8,170 11,666 534.28 498 763 65.4 NKOB

Average 893,463 673.5 1,327 7,965 11,828 459.86 515 683 57.7

Balls Consumption




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SEQUENTIAL EVALUATIONSAG 2, Pre vs Post Purge Period


SAG 2 SAG 2 Var iat ion

Pre Purge Post Purge %

ORE THROUGHPUTton/hr 1 ,254 1 ,410 12 .4

ENERGY CONSUMPTION

kW (net) 12 ,058 11,691 (3 .0 )

kWh/ton 9 .62 8 .29 (13 .8 )

BALLS CONSUMPTION

gr/ton 552 501 (9 .2 )

SAG 2 SAG 2 Variat ion


ORE THROUGHPUTton/hr 1 ,254 1 ,410 12 .4

ENERGY CONSUMPTION

kW (net) 12 ,058 11 ,691 (3 .0 )

kWh/ton 9 .62 8 .29 (13 .8 )

BALLS CONSUMPTION

gr/ton 552 501 (9 .2 )


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How do we estimateWear Rate Constants ?

How do we estimateWear Rate Constants ?

Software for

Grinding ProcessOptimization

Software for

Grinding ProcessOptimization


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Should be

552 gr/ton


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Media Charge_Linear Wear_SAG Mills ...Media Charge_Linear Wear_SAG Mills ... 5 Forge+55 ForgeForge++

Moly-Cop Tools TM

Remarks

Power, kW

Mill Dimensions and Operating Conditions 7,438 Balls

Diameter Length Mill Speed Charge Balls Interstitial Lift 2,303 Rocks

ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1,473 Slurry

35.50 17.00 76.00 26.00 14.00 65.00 43.18 11,214 Net Total

rpm 9.77 7.00 % Losses

% Utilization hr/month 12,058 Gross Total

% Solids in the Mill 74.00 92.34 665 8,017 MWh/month

Ore Density, ton/m3 2.80

Slurry Density, ton/m3 1.91 Charge Apparent

Balls Density, ton/m3 7.75 Volume, Ball Osize Interstitial Density

m3 Charge Rocks Slurry ton/m3

Ore Feedrate, ton/hr 1253.9 124.13 310.80 96.25 61.56 3.775

ton/day 27,789

Energy, kWh/ton (ore) 9.62

Make-up Ball Size, mm 127.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month

Scrap Size, mm 12.7 552.0 57.40 93.06 692.1 460

Spec. Area, m2/m3 (app) 37.76 Wear Rate Constants,

Total Charge Area, m2 2524 m/[kWh(balls)/ton(balls)] 2.954

mm/hr 0.0707

Purge Time, hrs 1,617

DETERMINATION OF WEAR RATE CONSTANTS

Ball Recharge Rate

SAG 2, Pre Purge Period.

Fair Mining Co.

Special Case : SAG MILLS

Mill Charge Weight, tons

Moly-Cop Tools TM

Remarks

Power, kW




35.50 17.00 76.00 26.00 14.00 65.00 43.18 11,214 Net Total

rpm 9.77 7.00 % Losses% Utilization hr/month 12,058 Gross Total







ton/day 27,789



Scrap Size, mm 12.7 552.0 57.40 93.06 692.1 460



mm/hr 0.0707



Ball Recharge Rate

SAG 2, Pre Purge Period.

Fair Mining Co.




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Moly-Cop Tools TM

Remarks

Power, kW




35.50 17.00 76.00 26.00 14.00 65.00 41.56 10,873 Net Total









ton/day 31,331



Scrap Size, mm 12.7 500.9 60.40 97.92 706.1 471



mm/hr 0.0721



Ball Recharge Rate

SAG 2, Post Purge Period.

Fair Mining Co.



Moly-Cop Tools TM

Remarks

Power, kW




35.50 17.00 76.00 26.00 14.00 65.00 41.56 10,873 Net Total








ton/day 31,331



Scrap Size, mm 12.7 500.9 60.40 97.92 706.1 471

Spec. Area, m 2/m3 (app) 37.76 Wear Rate Constants,


mm/hr 0.0721



Ball Recharge Rate


Fair Mining Co.



5 Forge+55 ForgeForge++Media Charge_Linear Wear_SAG Mills ...Media Charge_Linear Wear_SAG Mills ...


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ORE THROUGHPUT

ton/hr 1 ,254 1 ,410 12.4

ENERGY CONSUMPTION

kW (net) 12 ,058 11 ,691 (3 .0)

kWh/ton 9 .62 8 .29 (13 .8)

BALLS CONSUMPTION

gr/ton 552 501 (9 .2)

kg/hr 692 707 2.2

gr/kWh 57.4 60 .4 5.2

Sp. Wear Constant, kdE 2.95 3 .11 5 .2



ORE THROUGHPUT

ton/hr 1 ,254 1 ,410 12 .4

ENERGY CONSUMPTION

kW (net) 12 ,058 11 ,691 (3 .0)

kWh/ton 9 .62 8 .29 (13.8)

BALLS CONSUMPTION

gr/ton 552 501 (9 .2)

kg/hr 692 707 2.2

gr/kWh 57.4 60 .4 5.2

Sp. Wear Constant, k dE 2.95 3 .11 5 .2




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5 Forge+5 Forge+

Moly-Cop Tools TM

Remarks

Power, kW




35.50 17.00 76.00 26.00 14.00 65.00 42.00 10,966 Net Total









ton/day 27,993



Scrap Size, mm 12.7 478.5 52.70 85.44 621.4 402



mm/hr 0.0635



Ball Recharge Rate


Fair Mining Co.



Moly-Cop Tools TM

Remarks

Power, kW




35.50 17.00 76.00 26.00 14.00 65.00 42.00 10,966 Net Total








ton/day 27,993



Scrap Size, mm 12.7 478.5 52.70 85.44 621.4 402



mm/hr 0.0635



Ball Recharge Rate


Fair Mining Co.



Media Charge_Linear Wear_SAG Mills ...Media Charge_Linear Wear_SAG Mills ...


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CONCURRENT EVALUATIONSAG 1 vs SAG 2 in Post PurgeCONCURRENT EVALUATION

SAG 1 vs SAG 2 in Post Purge


Post Purge Post Purge %

ORE THROUGHPUT

ton/hr 1 ,299 1 ,410 8.5

ENERGY CONSUMPTION

kW (net) 11 ,791 11 ,691 (0 .8 )

kWh/ton 9 .08 8 .29 (8 .7 )

BALLS CONSUMPTIONgr/ton 4 7 9 501 4.6

kg/hr 6 2 1 707 13.8

gr/kWh 52 .7 60 .4 14 .6

Sp. Wear Constant, k dE 2 .71 3 .11 14 .6


Post Purge Post Purge %

ORE THROUGHPUT

ton/hr 1 ,299 1 ,410 8.5

ENERGY CONSUMPTION

kW (net) 11 ,791 11 ,691 (0 .8 )

kWh/ton 9 .08 8 .29 (8 .7 )

BALLS CONSUMPTION

gr/ton 479 501 4.6

kg/hr 621 707 13.8

gr/kWh 52.7 60 .4 14.6

Sp. Wear Constant, k dE 2 .71 3 .11 14 .6

Pl l D l


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q

Cross Reference 1 : difference in the consumption rate of thetest mill (B) - bef or e and af t er t he pur ge per iod- minus thesame difference for the standard mill (A), normalized withrespect to the standard mill wear constant, before the purgeperiod :

q

Cross Reference 1 : difference in the consumption rate of thetest mill (B) - bef or e and af t er t he pur ge per iod- minus thesame difference for the standard mill (A), normalized withrespect to the standard mill wear constant, before the purgeperiod :

[ (kdE)B,after - (kdE)B,before] - [(kdE)A,after - (kdE)A,before](kdE)A,before

x 100

[ (kdE)B,after - (kdE)A,after] - [(kdE)B,before - (kdE)A,before]

(kd

E)A,before

x 100

q Cross Reference 2 : difference in the consumption rate ofboth mills (A and B) - bef or e and af t er t he pur ge per iod-normalized with respect to the standard mill wear constant,before the purge period :

q Cross Reference 2 : difference in the consumption rate ofboth mills (A and B) - bef or e and af t er t he pur ge per iod-normalized with respect to the standard mill wear constant,before the purge period :

Plant Scale Data AnalysisCROSS REFERENCES

Plant Scale Data AnalysisCROSS REFERENCES


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CROSS REFERENCESAG 1 vs SAG 2

CROSS REFERENCESAG 1 vs SAG 2

Specific Wear Rate Constant, kdESpecific Wear Rate Constant, kdE

SAG 1 SAG 2

Pre Purge 2.84 2.95

Post Purge 2.71 3.11

1 0 . 0%

SAG 1 SAG 2

Pre Purge 2.84 2.95

Post Purge 2.71 3.11

1 0 . 0%


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qMacro - Wear : Spalling.

q Impact Breakage.




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q Recognizing the need to improveon the tenacity of the grinding

media, the Drop Ball Tester(DBT) has become a very usefulexperimental tool to assess theexpected full scale breakageperformance of any type ofgrinding media, particularly inSAG applications.

q Recognizing the need to improveon the tenacity of the grinding

media, the Drop Ball Tester(DBT) has become a very usefulexperimental tool to assess theexpected full scale breakageperformance of any type ofgrinding media, particularly inSAG applications.

Impact Breakage CharacterizationTHE DROP BALL TESTER (DBT)

Impact Breakage CharacterizationTHE DROP BALL TESTER (DBT)


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A Simple Conceptual ModelLINER LIFTING CAPACITYA Simple Conceptual Model

LINER LIFTING CAPACITY

1

2


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Media Charge_Impact & Wear Data_FileMedia Charge_Impact & Wear Data_File

Moly-Cop Tools TM

Remarks SAG 2, Pre Purge Period.

Fair Mining Co.

Power, kW

Mill Dimensions and Operating Conditions 7438 Balls

Diameter Length Mill Speed Charge Balls Interstitial Lift 2303 Rocks

ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1473 Slurry

35.50 17.00 76.00 26.00 14.00 65.00 43.18 11214 Net Total


% Utilization hr/month 12058 Gross Total

92.34 664.9 8,017 MWh/month

% Solids in the Mill 74.00

Ore Density, ton/m3 2.80 ton/m3

Slurry Density, ton/m3 1.907 ton/m3 Charge Apparent

Ore Feedrate, ton/hr 1253.9 ton/hr Volume, Ball Osize Interstitial Density

ton/day 27,789 ton/day m3 Charge Rocks Slurry ton/m3

Energy, kWh/ton (ore) 9.62 kWh/ton (ore) 124.13 310.80 96.25 61.56 3.775

Balls Density, ton/m3 7.75 ton/m3 Eq. # of Balls 37,386Ball Size, mm 127.00 mm

Scrap Size, mm 12.7 mm


BALL BREAKAGE RATES IN SAG MILLS

Moly-Cop Tools TM

Remarks SAG 2, Pre Purge Period.

Fair Mining Co.

Power, kW

Mill Dimensions and Operating Conditions 7438 Balls

Diameter Length Mill Speed Charge Balls Interstitial Lift 2303 Rocks

ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1473 Slurry

35.50 17.00 76.00 26.00 14.00 65.00 43.18 11214 Net Total

rpm 9.77 7.00 % Losses% Utilization hr/month 12058 Gross Total

92.34 664.9 8,017 MWh/month

% Solids in the Mill 74.00

Ore Density, ton/m3 2.80 ton/m3

Slurry Density, ton/m3 1.907 ton/m3 Charge Apparent

Ore Feedrate, ton/hr 1253.9 ton/hr Volume, Ball Osize Interstitial Density

ton/day 27,789 ton/day m3 Charge Rocks Slurry ton/m3

Energy, kWh/ton (ore) 9.62 kWh/ton (ore) 124.13 310.80 96.25 61.56 3.775

Balls Density, ton/m3 7.75 ton/m3

Eq. # of Balls 37,386Ball Size, mm 127.00 mm

Scrap Size, mm 12.7 mm


BALL BREAKAGE RATES IN SAG MILLS

Cont inues . . .Cont inues . . .


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Liner Design : Lifting Cavity Filling, m3/lifter 0.193

Number of Lifter Bars 36.0 Voids Fraction in Lifting Cavity, % 35.0

Mill Speed, lifters/min 352 lifters/min

Lifters Spacing, inches 37.18 inches Lifting Capacity :Lifter Height, inches 10.00 inches Total Balls & Rocks, m3(ap)/hr 4,074

Rocks Lifting Rate, m3(ap)/hr 1,880

Lifter Width (at base), in 11.55 inches Balls Lifting Rate, m3(ap)/hr 2,194

Lifter Face Angle, () 30.0 () , ton/hr 11,050

, balls/hr 1,329,439

Load Angle of Repose, () 60.0 ()

Angle at Balls Release, ( 30.0 () Critical Ball on Ball Impacts per hour 715,852

Angle at Balls Impact, () 30.0 () Corr. Breakage Probability, events/impac 1.143E-05

Equiv. DBT Height, m 10.97 m Cushioning Factor 0.538

Breakage Rate, events/hr 4.406

gr/kWh gr/kWh

Total # of Balls # of Broken Events/ gr/ton (gross) (balls) kg/hr ton/month %

# of Cycles in Tube Balls Impact

20,000 24 5 1.042E-05 29.2 3.04 4.92 36.6 24.3 5.3

522.8 54.36 88.13 655.5 436 94.7

Spec. Area, m2/m3 (app) 37.76 m2/m3 (app)Total Charge Area, m2 2524 m2 552.0 57.40 93.06 692.1 460 100.0

Purge Time, hrs 1,707 hrs

Wear Rate Constants,

kdE 2.798 m/[kWh/ton] Overall

kd 0.0670 mm/hr kg/hr % kg/hr % kg/hr

0.7 1.8 36.6 98.2 37.3

SCRAP GENERATION

Nuclei Fragments

Caused by Wear

Overall

Caused by Breakage

DBT Test Results BALL CONSUMPTION RATES

Liner Design : Lifting Cavity Filling, m3/lifter 0.193

Number of Lifter Bars 36.0 Voids Fraction in Lifting Cavity, % 35.0

Mill Speed, lifters/min 352 lifters/min

Lifters Spacing, inches 37.18 inches Lifting Capacity :

Lifter Height, inches 10.00 inches Total Balls & Rocks, m3(ap)/hr 4,074

Rocks Lifting Rate, m3(ap)/hr 1,880

Lifter Width (at base), in 11.55 inches Balls Lifting Rate, m3(ap)/hr 2,194

Lifter Face Angle, () 30.0 () , ton/hr 11,050

, balls/hr 1,329,439

Load Angle of Repose, () 60.0 ()

Angle at Balls Release, ( 30.0 () Critical Ball on Ball Impacts per hour 715,852

Angle at Balls Impact, () 30.0 () Corr. Breakage Probability, events/impac 1.143E-05

Equiv. DBT Height, m 10.97 m Cushioning Factor 0.538

Breakage Rate, events/hr 4.406

gr/kWh gr/kWh

Total # of Balls # of Broken Events/ gr/ton (gross) (balls) kg/hr ton/month %

# of Cycles in Tube Balls Impact

20,000 24 5 1.042E-05 29.2 3.04 4.92 36.6 24.3 5.3

522.8 54.36 88.13 655.5 436 94.7

Spec. Area, m2

/m

3

(app) 37.76 m

2

/m

3

(app)Total Charge Area, m2 2524 m2 552.0 57.40 93.06 692.1 460 100.0

Purge Time, hrs 1,707 hrs

Wear Rate Constants,

kdE 2.798 m/[kWh/ton] Overall

kd 0.0670 mm/hr kg/hr % kg/hr % kg/hr

0.7 1.8 36.6 98.2 37.3

SCRAP GENERATION

Nuclei Fragments

Caused by Wear

Overall

Caused by Breakage

DBT Test Results BALL CONSUMPTION RATES

Media Charge_Impact & Wear Data_FileMedia Charge_Impact & Wear Data_File


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Effect of the Balls / Rocks RatioEffect of the Balls / Rocks Ratio

0

20

40

60

80

100

120

9 10 11 12 13 14 15 16 17 18 19

% Balls Filling

gr/kWh

0

20

40

60

80

100

120

9 10 11 12 13 14 15 16 17 18 19

% Balls Filling

gr/kW

h Total

Wear

Breakage

J = 26 %Mill Size : 36' x17'Speed : 76 %Crit.

Lift Angle, : 43

5 Broken Balls in 20,000 Drops


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Breakage Contribution to Total Wear,as a function of Balls Impact Resistance

Breakage Contribution to Total Wear,as a function of Balls Impact Resistance

0

5

10

15

20

25

9 10 11 12 13 14 15 16 17 18 19

% Balls Filling

gr/kWh

0

5

10

15

20

25

9 10 11 12 13 14 15 16 17 18 19

% Balls Filling

gr/kWh

Index = 15

10

5

J = 26 %Mill Size : 36' x17'

Speed : 76 %Crit.Lift Angle, : 43

DBT Index = # of Broken Balls per 20,000 DropsDBT Index = # of Broken Balls per 20,000 Drops


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SUMMARYSUMMARY

q The Linear Wear Model provides a theoretical frameworkfor the most reliable estimations of comparative grindingmedia wear performance (in t he absence of br eakage)inany given application, on the basis of the Specific WearRate Constant, kdE.

q

Because of natural process fluctuations and measurementerrors, it is not possible to develop a single comparativeperformance indicator.

q In such context, evaluations should be ideally conducted inparallel lines, in order to have the option to establish

multiple cross reference comparisons.q The Drop Ball Tester (DBT) is gaining wide acceptance as

a test method to allow for the independent analysis ofwear and breakage consumption mechanisms and so be ableto learn more from actual operational data.

q The Linear Wear Model provides a theoretical framework

for the most reliable estimations of comparative grindingmedia wear performance (in t he absence of br eakage)inany given application, on the basis of the Specific WearRate Constant, kdE.

q Because of natural process fluctuations and measurementerrors, it is not possible to develop a single comparativeperformance indicator.

q In such context, evaluations should be ideally conducted inparallel lines, in order to have the option to establish

multiple cross reference comparisons.q The Drop Ball Tester (DBT) is gaining wide acceptance as

a test method to allow for the independent analysis ofwear and breakage consumption mechanisms and so be ableto learn more from actual operational data.


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06 Jaime Sepulveda

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