mediacharge_mbwt_ballmills

7/28/2019 mediacharge_mbwt_ballmills

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Moly-Cop Tools, Version 2.0About the Media Charge_MBWT_Ball Mills Spreadsheet ...

Scope :

The Media Charge_MBWT_Ball Mills spreadsheet provides specific guidelines for the design, execution and datainterpretation of a Marked Ball Wear Test (MBWT), as a standard procedure for the evaluation of alternative varieties ofgrinding media to be utilized in conventional and semiautogenous mineral grinding tumbling mills.

Theoretical Framework :

The most widely accepted mathematical description of the gradual consumption process experienced by a grinding ballinside a tumbling mill is known as the Linear Wear Theory, by which the mass rate of consumption of a grinding ball isdescribed as directly proportional to the surface area exposed by such ball to the various wear mechanisms (abrasionand/or corrosion) active in the mill charge environment :

Wt = d(mb)/d(t) = - km Abwhere :

Wt = mass wear rate, kg/hrmb = ball weight, kg; after t hours of being charged into the mill.Ab = exposed ball area, m

2km = mass wear rate constant, kg/hr/m

2.

Equivalently, taking into account the geometry of the grinding body (sphere or cylinder), one obtains :

d(d)/d(t) = - 2 km / rb = - kdwhere :

d = size (diameter) of the grinding ball, mm; after t hours of being charged into the mill.

rb = grinding ball density, ton/m3

kd = wear rate constant, mm/hr.

If kd is to remain unaffected by the extent of wear; that is, kd is not a function of the current ball size d - a conditionsatisfied by most grinding media varieties and normally referred to as Linear Wear Kinetics - the above expression maybe simply integrated to obtain :

d = dR - kd t

where dR represents the initial size of the balls.

For any given grinding media variety, the constant kd becomes an indicator of its relative quality, as compared to otheralternative products.

Moly-Cop Tools / 138325796.xls.ms_office 4/6/2013 / 12:41 PM


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Moly-Cop Tools, Version 2.0About the Media Charge_MBWT_Ball Mills Spreadsheet ...

By direct analogy to mineral particle breakage kinetics, it is postulated that an even more representative and scaleable

quality indicator is the Energy Specific Wear Rate Constant [kdE, mm/(kWh/ton)], defined through the expression :

kd = kdE (Pb/Wb) / 1000

where the ratio (Pb/Wb) corresponds to the contribution (Pb) of every ton of balls in the charge (W b) to the total power draw(Pnet) of the mill. The underlying theoretical claim is that grinding balls will wear faster in a more energy intensiveenvironment. Therefore, kd

E is expected to be more insensitive than kd to variations in mill operating conditions (that mayaffect Pb and/or Wb). As a practical evaluation criterion, it should be then accepted that the top quality grindingmedia, in any given application, will be the one that exhibits the lowest value of the wear rate constant kd

E.

The above expression creates the need for a theoretical representation of the Mill Power Draw and how each componentof the mill charge (balls, rocks and slurry) contribute to this power demand. The simple Hogg and Fuerstenau modelserves such purpose well (see Spreadsheet Mill Power_Ball Mills).

In the above theoretical framework, a MBWT consists of weighing and tagging a limited number of balls (Test Group) ofthe type (or types) under consideration charging them into the selected industrial test mill and recovering as many ofthem as possible, after a predetermined number of operating hours (ttest). The weight loss experienced by each marked

ball may then be extrapolated to its expected performance - in terms of wear resistance (durability) - in an eventual plantapplication.

After recovery, the Linear Wear Rate Constant kd for each ball may be computed from the simple expression :

kd = (dR - dF)/ttest

where dF represents the final diameter of the ball upon recovery.

Data Input :

All data required for the calculation must be defined in each corresponding unprotected white background cell of the

here attached Wear Rate_Host Charge, Test_Design orData_Analysis worksheets. Gray background cells containthe results of the corresponding formulas there defined and are protected to avoid any accidental editing.

When using the Data_Analyis worksheet, different Test Groups of balls must be analyzed in separate copies of thismaster worksheet.

As a guide to new users, every relevant cell in the worksheets has brief inserted comments that render the wholecomputation process self-explanatory.



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Moly-Cop Tools TM (Version 2.0)

Remarks

Power, kW

Mill Dimensions and Operating Conditions 3,348 Balls

Eff. Diameter Eff. Length Mill Speed Charge Balls Interstitial Lift 0 Overfilling

ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, () 536 Slurry

18.50 22.00 72.00 38.00 38.00 100.00 35.0 3,885 Net Total

rpm 12.82 10.00 % Losses

% Utilization hr/month 4,316 Gross Total

% Solids in the Mill 72.00 97.00 698 3,014 MWh/month

Ore Density, ton/m3 2.80

Slurry Density, ton/m3 1.86 Charge Apparent

Balls Density, ton/m3 7.75 Volume, Ball Density

m3 Charge Interstitial above Balls ton/m3

Ore Feedrate, ton/hr 400.0 63.76 296.48 47.48 0.00 5.395

ton/day 9,312

Energy, kWh/ton (ore) 10.79

Make-up Ball Size, mm 75.0 gr/ton gr/kWh (gross) gr/kWh (balls) Kg/hr tons/month

Scrap Size, mm 12.0 450.0 41.70 53.76 180.0 126

Spec. Area, m2/m3

(app) 63.78 Wear Rate Constants,

Total Charge Area, m2 4067 mm/[kWh(balls)/ton(balls)] 1.007mm/hr 0.0114

Purge Time, hrs 5,538

DETERMINATION OF WEAR RATE CONSTANTS

Ball Recharge Rate

Base Case Example

Special Case : BALL MILLS

Mill Charge Weight, tons

Slurry



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Remarks

Mill

Power, kW

Mill Dimensions and Operating Conditions 3,348 Balls

Eff. Diameter Eff. Length Mill Speed Charge Balls Interstitial Lift 0 Rocks


18.50 22.00 72.00 38.00 38.00 100.00 35.00 3,885 Net Total

rpm 12.82 10.00 % Losses

4,316 Gross Total

% Solids in the Mill 72.00 Charge Apparent

Ore Density, ton/m3 2.80 Volume, Ball Density

Slurry Density, ton/m3 1.86 m3 Charge Interstitial above Balls ton/m3

Balls Density, ton/m3 7.75 63.76 296.48 0.00 47.48 5.395

Initial Ball Size, mm 75.0

Final Ball Size, mm 60.0 Free Kidney

Weight Loss, % 48.8 Height Above Angle,

Wear Rate Estimates, Charge, ft Degrees

mm/[KWH(balls)/ton(balls)] 1.007 11.01 158.04

mm/hr 0.01138

TEST DURATION, hrs 1319

Recovery Available

Rate, Recovery

SAMPLE SIZE, NTOT (Minimum Number of Marked Balls per Group) m-hours/m2

Hours

0.25 8.0

Option 1. Ball Picking over Exposed Mill Charge Surface

Recovery Recovery Exposed Exposed Marked Balls Sample

Target, Area, Marked Balls, Ball Layers, Concentration, Size,

# Balls m2 # Balls/m2 # # Balls/m3 NTOT Man-hrs Inspectors

5 37.17 0.13 1.0 1.79 114 9 2

Option 2. Same as Option 1, with one full-turn inching of the mill

Recovery Recovery Exposed Exposed Marked Balls Sample

Target, Area, Marked Balls, Ball Layers, Concentration, Size,

# Balls m2 # Balls/m2 # # Balls/m3 NTOT Man-hrs Inspectors

5 89.38 0.06 1.0 0.75 48 22 4

Practical Guidelines for

Labor

Required

Labor

Required

Base Case Example


MARKED BALL WEAR TEST DESIGN

Slurry



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Remarks

Mill

Power, kW

Mill Dimensions and Operating Conditions (Actual Average for the MBWT) 3,013 Balls

Eff. Diameter Eff. Length Mill Speed Charge Balls Interstitial Lift 0 Rocks


18.50 22.00 72.00 38.00 38.00 100.00 31.1 3,496 Net Total

rpm 12.82 10.00 % Losses

3,885 Gross Total

% Solids in the Mill 72.00 Charge Apparent

Ore Density, ton/m3 2.80 Volume, Ball Osize Interstitial Density

Slurry Density, ton/m3 1.86 m3 Charge Rocks Slurry ton/m3

Balls Density, ton/m3 63.76 296.48 0.00 47.48 5.395

- Host Charge 7.75

- Test Group 7.75 Host Test

COMPARATIVE Charge Media

Operational Records during MBWT : PERFORMANCE (Actual) (Projected)

Test Duration, hrs 1365 Sp. Energy, kWh/ton (net) 9.38 9.38

Ore Processed, ktons 565 Ball Consumption, gr/ton 453.1 548.7

Energy Cons., MWh (net) 5302 , gr/kWh (net) 48.3 58.5

Balls Charged, tons 256 , kg/hr 187.5 204.4 %

Make-up Ball Size, mm 75 0.0119 0.0130 Better

Scrap Size, mm 12 mm/(kWh/ton) 1.166 1.276 (9.44)

Ball Group Identification :

TAG Initial Initial Final Final

# Weight, gr Size, mm Weight, gr Size, mm mm/hr mm/(KWH/ton)

B03 1811.0 76.4 821.0 58.7 0.0130 1.277

B10 1753.0 75.6 782.0 57.8 0.0131 1.285

B16 1702.0 74.9 764.0 57.3 0.0129 1.264

B23 1744.0 75.5 777.0 57.6 0.0131 1.285

B34 1659.0 74.2 731.0 56.5 0.0130 1.279

B38 1732.0 75.3 780.0 57.7 0.0129 1.267

Average 75.3 0.0130 1.276

Std. Dev. 0.74 0.0001 0.009

Coeff. of Variation, % 0.98 0.70 0.70

Wear Rate Constant

MARKED BALL WEAR TEST RESULTS

Group B : Alternative Product

WR Constant, mm/hr

Base Case Example



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mediacharge_mbwt_ballmills