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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.
q Micro - Wear : Abrasion / Corrosion.
q Macro - Wear : Spalling.q Impact Breakage.
Mechanisms forGRINDING MEDIA CONSUMPTION
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
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
Grinding Media AlgebraTHE LINEAR WEAR THEORY
Grinding Media AlgebraTHE LINEAR WEAR THEORY
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
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
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 +
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"
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 '02 755,228 632.0 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
Unit : SAG 2 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 '02 755,228 632.0 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
Fair Mining CompanyOPERATIONAL RECORDS
Fair Mining CompanyOPERATIONAL RECORDS
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SEQUENTIAL EVALUATIONSAG 2, Pre vs Post Purge Period
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
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 )
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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
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
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Moly-Cop Tools TM
Remarks
Power, kW
Mill Dimensions and Operating Conditions 7,211 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 2,233 Rocks
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1,428 Slurry
35.50 17.00 76.00 26.00 14.00 65.00 41.56 10,873 Net Total
rpm 9.77 7.00 % Losses
% Utilization hr/month 11,691 Gross Total
% Solids in the Mill 74.00 92.60 667 7,795 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 1409.7 124.13 310.80 96.25 61.56 3.775
ton/day 31,331
Energy, kWh/ton (ore) 8.29
Make-up Ball Size, mm 127.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month
Scrap Size, mm 12.7 500.9 60.40 97.92 706.1 471
Spec. Area, m2/m3 (app) 37.76 Wear Rate Constants,
Total Charge Area, m2 2524 m/[kWh(balls)/ton(balls)] 3.109
mm/hr 0.0721
Purge Time, hrs 1,585
DETERMINATION OF WEAR RATE CONSTANTS
Ball Recharge Rate
SAG 2, Post Purge Period.
Fair Mining Co.
Special Case : SAG MILLS
Mill Charge Weight, tons
Moly-Cop Tools TM
Remarks
Power, kW
Mill Dimensions and Operating Conditions 7,211 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 2,233 Rocks
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1,428 Slurry
35.50 17.00 76.00 26.00 14.00 65.00 41.56 10,873 Net Total
rpm 9.77 7.00 % Losses% Utilization hr/month 11,691 Gross Total
% Solids in the Mill 74.00 92.60 667 7,795 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 1409.7 124.13 310.80 96.25 61.56 3.775
ton/day 31,331
Energy, kWh/ton (ore) 8.29
Make-up Ball Size, mm 127.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month
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,
Total Charge Area, m2 2524 m/[kWh(balls)/ton(balls)] 3.109
mm/hr 0.0721
Purge Time, hrs 1,585
DETERMINATION OF WEAR RATE CONSTANTS
Ball Recharge Rate
SAG 2, Post Purge Period.
Fair Mining Co.
Special Case : SAG MILLS
Mill Charge Weight, tons
5 Forge+55 ForgeForge++Media Charge_Linear Wear_SAG Mills ...Media Charge_Linear Wear_SAG Mills ...
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SAG 2 SAG 2 Variat ion
Pre Purge Post Purge %
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
SAG 2 SAG 2 Variat ion
Pre Purge Post Purge %
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
SEQUENTIAL EVALUATIONSAG 2, Pre vs Post Purge Period
SEQUENTIAL EVALUATIONSAG 2, Pre vs Post Purge Period
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5 Forge+5 Forge+
Moly-Cop Tools TM
Remarks
Power, kW
Mill Dimensions and Operating Conditions 7,273 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 2,252 Rocks
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1,440 Slurry
35.50 17.00 76.00 26.00 14.00 65.00 42.00 10,966 Net Total
rpm 9.77 7.00 % Losses
% Utilization hr/month 11,791 Gross Total
% Solids in the Mill 74.00 89.82 647 7,625 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 1298.5 124.13 310.80 96.25 61.56 3.775
ton/day 27,993
Energy, kWh/ton (ore) 9.08
Make-up Ball Size, mm 127.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month
Scrap Size, mm 12.7 478.5 52.70 85.44 621.4 402
Spec. Area, m2/m3 (app) 37.76 Wear Rate Constants,
Total Charge Area, m2 2524 m/[kWh(balls)/ton(balls)] 2.712
mm/hr 0.0635
Purge Time, hrs 1,801
DETERMINATION OF WEAR RATE CONSTANTS
Ball Recharge Rate
SAG 1, Post Purge Period.
Fair Mining Co.
Special Case : SAG MILLS
Mill Charge Weight, tons
Moly-Cop Tools TM
Remarks
Power, kW
Mill Dimensions and Operating Conditions 7,273 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 2,252 Rocks
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 1,440 Slurry
35.50 17.00 76.00 26.00 14.00 65.00 42.00 10,966 Net Total
rpm 9.77 7.00 % Losses% Utilization hr/month 11,791 Gross Total
% Solids in the Mill 74.00 89.82 647 7,625 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 1298.5 124.13 310.80 96.25 61.56 3.775
ton/day 27,993
Energy, kWh/ton (ore) 9.08
Make-up Ball Size, mm 127.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month
Scrap Size, mm 12.7 478.5 52.70 85.44 621.4 402
Spec. Area, m2/m3 (app) 37.76 Wear Rate Constants,
Total Charge Area, m2 2524 m/[kWh(balls)/ton(balls)] 2.712
mm/hr 0.0635
Purge Time, hrs 1,801
DETERMINATION OF WEAR RATE CONSTANTS
Ball Recharge Rate
SAG 1, Post Purge Period.
Fair Mining Co.
Special Case : SAG MILLS
Mill Charge Weight, tons
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
SAG 1 SAG 2 Variat ion
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
SAG 1 SAG 2 Variat ion
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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q Micro - Wear : Abrasion / Corrosion.
q Macro - Wear : Spalling.q Impact Breakage.
q Micro - Wear : Abrasion / Corrosion.
qMacro - Wear : Spalling.
q Impact Breakage.
Mechanisms forGRINDING MEDIA CONSUMPTION
Mechanisms forGRINDING MEDIA CONSUMPTION
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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
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
Mill Charge Weight, tons
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
Mill Charge Weight, tons
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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