modelo de desgaste modificado

UPDATED BENAVENTE CORRELATION FOR ESTIMATING GRINDING MEDIA

CONSUMPTION RATES

Levi Guzmn R.Moly-Cop Adesur S.A

Content

Introduction Theoretical Background Linear Wear Theory The grinding process Environment Model Structure Model Application Conclusions

Introduccin

The concern regarding grinding mediaconsumption rates is as old as the inventionof the tumbling mill. This is due grindingmedia is one of the more important cost atthe concentrator (+/- 30%).

Is well accepted that grinding mediaconsumption is a function of ore propertiesas well as the grinding media quality andoperational conditions.

There have been several approaches toestimate the wear of the grinding media, allof them based on limited empiricalevidence. (Bond, et al)

Introduction

The mining industry still utilizes theBond Abrasion test that was developedin the 1960s. As shown later in thispublication, this approach shows errorgreater than 60%.

More recently, in 2007, Radziszewskifrom Mc Gill University has proposed adifferent total grinding media wearmodel; this model is based ondecoupling the effects of the abrasion,corrosion and impact wearmechanisms. This new model improvesthe error until < 20%

Introduction

Also in 2007, Benavente, at the time with Moly-Cop Peru, presented anempirical model relating both ore properties and operational conditionsthat would affect the wear performance of the grinding media. Benaventesmodel shows an average error of 12% which represents a higher degreeof improvement in comparison with previous approaches.

How we can improve the grindingmedia wear prediction .?

Theoretical BackgroundLinear Wear Theory


Wear has been defined as the interaction between the exposed area of anybody and the environment, having as a result the weight loss of the materialbeing exposed. [Chattopadhyay, 1990].

In tumbling mill, is very well know that the main wear mechanism are :

Abrasion Impact Corrosion

Being the abrasion mechanism the more important in almost all operatingconcentrators

t m bd md t k A = = ( )( )

Ab

d


at every instant t, its rate of weight losswill be directly proportional to its surfacearea exposed to wear mechanisms that existin the mill

Equivalente a:

d dd t

k kmb

d( )( )

= = 2

By direct analogy to mineral particle breakage kinetics, it appearsreasonable to postulate that a more representative and scalable qualityindicator than kd is the Energy Specific Wear Rate Constant, ,[m/(kWh/ton)], defined through the expression (Seplveda, 2004):


Donde :

kd = lineal wear rate , mm/h

kdE= Specific wear rate constant, m/[kWh/ton]bPb = Net Power /ton grinding media , Kw

Wb= Grinding media, tm

Donde :

kd = lineal wear rate , mm/h

kdE= Specific wear rate constant, m/[kWh/ton]bPb = Net Power /ton grinding media , Kw

Wb= Grinding media, tm

kdE = kd / (Pb/Wb) x 1000

The kdE rate constant is considered to be the best indicator of ballquality for the particular application being analyzed. This is due is afunction of grinding media quality and grinding process environment

kdE f [ grinding media, environment]


Slurry, pHMill speed

% Slids

F80Mill FillingCharge Exposed Area

P80

Ore Abrasivity

Ball Size

Viscosity

The grinding process Environment

kdE f (e)kdE f (e)Mill

Diameter

The abrasion is the most known wear mechanism in the industry. There aremany definitions. Generally we could define as the removal of material froma body by another of greater strength.


Abrasion Index measurements wereperformed in MolyCop Adesur MineralProcessing laboratory.


Moly-Cop Industrial Database

Based in Benaventes work ,more operational informationwas obtained from 46 differentindustrial mills (located mainlyin Per)

For the data presented in Table 1, the actual grinding media consumption rates in g/kWh were compared with those predicted by Bond

The results show an average error of 61% with a standard deviation of 32%, which undoubtedly does not satisfy the accuracy requirements.

Bonds Empirical Correlation

Using the same database so collected, it was decided to update the originalBenaventes Correlation by recalculating all the coefficients in the originalequation. The new updated correlation was as follows:

Updated Benaventes correlation, KdE

The wear rate results obtained with the updated Benavente correlation show anaverage error of 9%, with a standard deviation of 5.5%, which may be consideredmuch more reliable for the intended purposes

Updated Benaventes correlation, KdE

Application of New Wear Model

Simulation of Grinding media consumption

Moly-Cop Tools TM (Version 3.0)

Remarks

Eff. Mill Diameter, ft 27.50 Liner Design : DefaultEff. Mill Length, ft 43.50 Number of Lifter Bars 28.00 28Intersticial Filling, % 100.00 Lifters Spacing, L0 37.03 inchesPower Losses, % 7.00 , L1 30.77 inches

, L2 36.03 inchesMill Volume, m3 787.78 Lifter Height, inches 5.91Ore Density, ton/m3 2.95 Lifter Width, wL 1.00 inchesBalls Density, ton/m3 7.75 Lifter Face Angle, ()

Forward, 1F 24.00 ()Mill Throughput, ton/hr 2000 Backward, 1B 24.00 ()Mill Filling, % 34.67 Load Angle, 2 45.00 ()Mill Speed, %Vc 72.00 hx 24.93 inches% Solids 73.14Mill Power, Kw 20020 Lifting Cavity Filling, m3/lifter 0.0828Ball Size, mm 76 Lifting Cavity Filling, % 4.9

Voids Fraction in Lifting Cavity, % 0.0

DYNAMIC EVOLUTION OF BALL CHARGE COMPOSITIONAS A RESULT OF VARIABLE BALL RECHARGES AND OPERATING CONDITIONS.

Evolucion de carga dinamica - Ball Mill #1

Moly-Cop Tools TM (Version 3.0)

Remarks

Eff. Mill Diameter, ft 27.50 Liner Design : DefaultEff. Mill Length, ft 43.50 Number of Lifter Bars 28.00 28Intersticial Filling, % 100.00 Lifters Spacing, L0 37.03 inchesPower Losses, % 7.00 , L1 30.77 inches

, L2 36.03 inchesMill Volume, m3 787.78 Lifter Height, inches 5.91Ore Density, ton/m3 2.95 Lifter Width, wL 1.00 inchesBalls Density, ton/m3 7.75 Lifter Face Angle, ()

Forward, 1F 24.00 ()Mill Throughput, ton/hr 2000 Backward, 1B 24.00 ()Mill Filling, % 34.67 Load Angle, 2 45.00 ()Mill Speed, %Vc 72.00 hx 24.93 inches% Solids 73.14Mill Power, Kw 20020 Lifting Cavity Filling, m3/lifter 0.0828Ball Size, mm 76 Lifting Cavity Filling, % 4.9

Voids Fraction in Lifting Cavity, % 0.0

DYNAMIC EVOLUTION OF BALL CHARGE COMPOSITIONAS A RESULT OF VARIABLE BALL RECHARGES AND OPERATING CONDITIONS.

Evolucion de carga dinamica - Ball Mill #1



Energy Specific Make-up ScrapkWh kWh/ton Medido Gross Total Net Total Balls Rocks Slurry Angle, () mm mm tons gr/ton gr/kWh(gross) Kg/hr

473095.46 9.86 13990.1 19712.3 18332 15929.8 0.0 2402.6 32.0 76.2 25.0 20.000 416.7 42.3 833.3472419.38 9.84 13656.4 19684.1 18306 15907.1 0.0 2399.2 32.0 76.2 25.0 20.000 416.7 42.3 833.3471742.47 9.83 13859.0 19655.9 18280 15884.3 0.0 2395.7 32.0 76.2 25.0 20.000 416.7 42.4 833.3471064.87 9.81 13944.1 19627.7 18254 15861.5 0.0 2392.3 32.0 76.2 25.0 20.000 416.7 42.5 833.3470386.73 9.80 13278.7 19599.4 18227 15838.6 0.0 2388.9 32.0 76.2 25.0 20.000 416.7 42.5 833.3477721.47 9.95 15314.4 19905.1 18512 15815.8 0.0 2695.9 32.0 76.2 25.0 20.000 416.7 41.9 833.3471770.34 9.83 14612.5 19657.1 18281 15792.9 0.0 2488.2 32.0 76.2 25.0 20.000 416.7 42.4 833.3471087.51 9.81 11828.1 19628.6 18255 15770.1 0.0 2484.6 32.0 76.2 25.0 20.000 416.7 42.5 833.3470404.73 9.80 13828.1 19600.2 18228 15747.2 0.0 2481.0 32.0 76.2 25.0 20.000 416.7 42.5 833.3469722.14 9.79 13828.1 19571.8 18202 15724.4 0.0 2477.4 32.0 76.2 25.0 20.000 416.7 42.6 833.3469039.86 9.77 13828.1 19543.3 18175 15701.5 0.0 2473.8 32.0 76.2 25.0 20.000 416.7 42.6 833.3459492.43 9.57 13828.1 19145.5 17805 15678.7 0.0 2126.6 32.0 76.2 25.0 20.000 416.7 43.5 833.3458824.10 9.56 13828.1 19117.7 17779 15655.9 0.0 2123.5 32.0 76.2 25.0 20.000 416.7 43.6 833.3458156.47 9.54 13828.1 19089.9 17754 15633.1 0.0 2120.5 32.0 76.2 25.0 20.000 416.7 43.7 833.3463775.97 9.66 12828.1 19324.0 17971 15610.4 0.0 2361.0 32.0 76.2 25.0 20.000 416.7 43.1 833.3466091.56 9.71 12346.3 19420.5 18061 15587.6 0.0 2473.4 32.0 76.2 25.0 20.000 416.7 42.9 833.3482604.41 10.05 12075.2 20108.5 18701 15564.9 0.0 3136.0 32.0 76.2 25.0 20.000 416.7 41.4 833.3481830.39 10.04 11832.6 20076.3 18671 15542.3 0.0 3128.6 32.0 76.2 25.0 20.000 416.7 41.5 833.3476817.62 9.93 12196.8 19867.4 18477 15519.7 0.0 2957.0 32.0 76.2 25.0 20.000 416.7 41.9 833.3481163.24 10.02 12998.2 20048.5 18645 15497.2 0.0 3147.9 32.0 76.2 25.0 20.000 416.7 41.6 833.3462713.50 9.64 12112.9 19279.7 17930 15474.7 0.0 2455.5 32.0 76.2 25.0 20.000 416.7 43.2 833.3461229.69 9.61 10612.1 19217.9 17873 15452.2 0.0 2420.4 32.0 76.2 25.0 20.000 416.7 43.4 833.3472346.79 9.84 9872.8 19681.1 18303 15429.8 0.0 2873.6 32.0 76.2 25.0 20.000 416.7 42.3 833.3475067.87 9.90 10089.4 19794.5 18409 15407.5 0.0 3001.4 32.0 76.2 25.0 20.000 416.7 42.1 833.3399065.95 8.31 8650.2 16627.7 15464 15385.3 0.0 78.5 32.0 76.2 25.0 20.000 416.7 50.1 833.3465277.63 9.69 9227.0 19386.6 18030 15363.1 0.0 2666.4 32.0 76.2 25.0 20.000 416.7 43.0 833.3462517.50 9.64 11539.8 19271.6 17923 15341.0 0.0 2581.6 32.0 76.2 25.0 20.000 416.7 43.2 833.3469172.15 9.77 11482.1 19548.8 18180 15318.9 0.0 2861.5 32.0 76.2 25.0 20.000 416.7 42.6 833.3468863.61 9.77 9594.4 19536.0 18168 15297.0 0.0 2871.5 32.0 76.2 25.0 20.000 416.7 42.7 833.3460764.38 9.60 9493.2 19198.5 17855 15275.1 0.0 2579.5 32.0 76.2 25.0 20.000 416.7 43.4 833.3465025.33 9.69 10014.1 19376.1 18020 15253.3 0.0 2766.4 32.0 76.2 25.0 20.000 416.7 43.0 833.3458530.93 9.55 12939.4 19105.5 17768 15231.6 0.0 2536.5 32.0 76.2 25.0 20.000 416.7 43.6 833.3457031.98 9.52 10513.6 19043.0 17710 15210.0 0.0 2500.0 32.0 76.2 25.0 20.000 416.7 43.8 833.3452833.56 9.43 10695.20 18868.1 17547 15188.5 0.0 2358.8 32.0 76.2 25.0 23.000 479.2 50.8 958.3451801.11 9.41 10688.56 18825.0 17507 15187.1 0.0 2320.2 32.0 76.2 25.0 23.000 479.2 50.9 958.3449005.33 9.35 10250.76 18708.6 17399 15185.7 0.0 2213.3 32.0 76.2 25.0 23.000 479.2 51.2 958.3452672.30 9.43 9014.32 18861.3 17541 15184.2 0.0 2356.8 32.0 76.2 25.0 23.000 479.2 50.8 958.3447330.32 9.32 5524.99 18638.8 17334 15182.9 0.0 2151.2 32.0 76.2 25.0 23.000 479.2 51.4 958.3447289.58 9.32 5524.99 18637.1 17332 15181.5 0.0 2151.0 32.0 76.2 25.0 23.000 479.2 51.4 958.3447249.12 9.32 5524.99 18635.4 17331 15180.1 0.0 2150.8 32.0 76.2 25.0 23.000 479.2 51.4 958.3447208.94 9.32 5524.99 18633.7 17329 15178.7 0.0 2150.6 32.0 76.2 25.0 23.000 479.2 51.4 958.3

Balls Recharge

Bolas

RelativeAI m pH Wear Factor kdB Resistance tons gr/ton gr/kWh(gross) Kg/hr

0.150 5700 11.0 1.195 1.360 1.000 24.356 507.4 51.5 1014.80.150 5700 11.0 1.195 1.360 1.000 24.320 506.7 51.5 1013.30.150 5700 11.0 1.195 1.360 1.000 24.284 505.9 51.5 1011.80.150 5700 11.0 1.195 1.360 1.000 24.248 505.2 51.5 1010.30.150 5700 11.0 1.195 1.360 1.000 24.212 504.4 51.5 1008.80.150 5700 11.0 1.195 1.360 1.000 24.176 503.7 50.6 1007.30.150 5700 11.0 1.195 1.360 1.000 24.140 502.9 51.2 1005.80.150 5700 11.0 1.195 1.360 1.000 24.105 502.2 51.2 1004.40.150 5700 11.0 1.195 1.360 1.000 24.069 501.4 51.2 1002.90.150 5700 11.0 1.195 1.360 1.000 24.033 500.7 51.2 1001.40.150 5700 11.0 1.195 1.360 1.000 23.998 500.0 51.2 999.90.150 5700 11.0 1.195 1.360 1.000 23.963 499.2 52.2 998.40.150 5700 11.0 1.195 1.360 1.000 23.927 498.5 52.1 997.00.150 5700 11.0 1.195 1.360 1.000 23.892 497.8 52.1 995.50.150 5700 11.0 1.195 1.360 1.000 23.857 497.0 51.4 994.00.150 5700 11.0 1.195 1.360 1.000 23.822 496.3 51.1 992.60.150 5700 11.0 1.195 1.360 1.000 23.787 495.6 49.3 991.10.150 5700 11.0 1.195 1.360 1.000 23.752 494.8 49.3 989.70.150 5700 11.0 1.195 1.360 1.000 23.718 494.1 49.7 988.20.150 5700 11.0 1.195 1.360 1.000 23.683 493.4 49.2 986.80.150 5700 11.0 1.195 1.360 1.000 23.649 492.7 51.1 985.40.150 5700 11.0 1.195 1.360 1.000 23.614 492.0 51.2 983.90.150 5700 11.0 1.195 1.360 1.000 23.580 491.3 49.9 982.50.150 5700 11.0 1.195 1.360 1.000 23.546 490.5 49.6 981.10.150 5700 11.0 1.195 1.360 1.000 23.512 489.8 58.9 979.70.150 5700 11.0 1.195 1.360 1.000 23.478 489.1 50.5 978.30.150 5700 11.0 1.195 1.360 1.000 23.445 488.4 50.7 976.90.150 5700 11.0 1.195 1.360 1.000 23.411 487.7 49.9 975.50.150 5700 11.0 1.195 1.360 1.000 23.378 487.0 49.9 974.10.150 5700 11.0 1.195 1.360 1.000 23.345 486.3 50.7 972.70.150 5700 11.0 1.195 1.360 1.000 23.311 485.7 50.1 971.30.150 5700 11.0 1.195 1.360 1.000 23.279 485.0 50.8 969.90.150 5700 11.0 1.195 1.360 1.000 23.246 484.3 50.9 968.60.150 5700 11.0 1.195 1.360 1.000 23.214 483.6 51.3 967.20.150 5700 11.0 1.195 1.360 1.000 23.212 483.6 51.4 967.20.150 5700 11.0 1.195 1.360 1.000 23.211 483.6 51.7 967.10.150 5700 11.0 1.195 1.360 1.000 23.209 483.5 51.3 967.10.150 5700 11.0 1.195 1.360 1.000 23.208 483.5 51.9 967.00.150 5700 11.0 1.195 1.360 1.000 23.206 483.5 51.9 966.90.150 5700 11.0 1.195 1.360 1.000 23.205 483.4 51.9 966.90.150 5700 11.0 1.195 1.360 1.000 23.203 483.4 51.9 966.80.150 5700 11.0 1.195 1.360 1.000 23.202 483.4 51.2 966.7

Wear Rate Constants Balls Consumption

Abrasion IndexChange from0.15 to 0.35

F80 decreasefrom 5700 to3000 microns

Ph Reduces from 11 to 9

Abrasion Indexreduces from0.35 to 0.15


Conclusions

Based on the model originally developed by Benavente, updated by these authors, a projection of grinding media consumption results in an error of about 9%, which is considered satisfactory.

The Updated Benavente Model is powerful tool for cost estimation in the case of greenfield or brownfield projects, as well as for the analysis of grinding media consumption rates in existing concentrators.

Pending work is to develop a grinding media wear model for SAG Mills, were impact conditions must be consider.

modelo de desgaste modificado

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