mediacharge wear predictor

Moly-Cop Tools / document.xls 04/17/2023 / 19:20:06

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

Scope :

The Media Charge_Wear_Predictor spreadsheet was designed to predict grinding media consumption rates in any given Conventional or SAG milling operation, taking into account both normal wear and impact breakage mechanisms.

Theoretical Framework :

Grinding Media Wear Kinetics.

The most widely accepted approach to characterize the slow, sustained consumption (wear) kinetics of grinding bodies in rotary tumbling mills is known as the Linear Wear Theory; according to which - at every instant ‘t’ after the grinding body was thrown into the mill charge - its rate of weight loss will be directly proportional to its surface area exposed to gradual abrasion and/or corrosion wear mechanisms :

t = ∂(m)/∂(t) = - km Ab (1)

where :

t = media consumption rate, kg/hr m = ball weight, kg; after t hours in the mill Ab = surface area of the ball exposed to wear, m2

km = mass wear rate constant, kg/hr/m2.

Equivalently, taking into account the geometry of the grinding body (sphere or cylinder), Equation 1 converts to :

∂(d)/∂(t) = - 2 km / b = - kd (2)

where :

d = size (diameter) of the grinding body, after t hours in the mill charge, mm b = density of the grinding body, gr/cm3 or ton/m3

kd = linear wear rate constant, mm/hr.

For full scale, continuous mills, in order to maintain a constant inventory (hold-up) of grinding media in the mill - normally measured by the ratio Jb of the apparent volume of balls (i. e., including interstitial spaces in between the balls) to the total effective internal mill volume – operators must continuously compensate for the steel being consumed by periodically recharging new balls, preferentially of a single size dR. Given that the wear rate of each grinding body is proportional to its own exposed surface area, the integration of Equation 1 – over the whole range of possible ball sizes – demonstrates that the overall grinding media consumption rate t (kg steel/operating hour), corresponding to the ensemble of balls ('string') in the mill charge, is consequently proportional to the total area A (m2) exposed by such ‘string’ :

t = - km A = - b kd A / 2 (3)


Scope :

The Media Charge_Wear_Predictor spreadsheet was designed to predict grinding media consumption rates in any given Conventional or SAG milling operation, taking into account both normal wear and impact breakage mechanisms.

Theoretical Framework :

Grinding Media Wear Kinetics.

The most widely accepted approach to characterize the slow, sustained consumption (wear) kinetics of grinding bodies in rotary tumbling mills is known as the Linear Wear Theory; according to which - at every instant ‘t’ after the grinding body was thrown into the mill charge - its rate of weight loss will be directly proportional to its surface area exposed to gradual abrasion and/or corrosion wear mechanisms :

t = ∂(m)/∂(t) = - km Ab (1)

where :

t = media consumption rate, kg/hr m = ball weight, kg; after t hours in the mill Ab = surface area of the ball exposed to wear, m2

km = mass wear rate constant, kg/hr/m2.

Equivalently, taking into account the geometry of the grinding body (sphere or cylinder), Equation 1 converts to :

∂(d)/∂(t) = - 2 km / b = - kd (2)

where :

d = size (diameter) of the grinding body, after t hours in the mill charge, mm b = density of the grinding body, gr/cm3 or ton/m3

kd = linear wear rate constant, mm/hr.

For full scale, continuous mills, in order to maintain a constant inventory (hold-up) of grinding media in the mill - normally measured by the ratio Jb of the apparent volume of balls (i. e., including interstitial spaces in between the balls) to the total effective internal mill volume – operators must continuously compensate for the steel being consumed by periodically recharging new balls, preferentially of a single size dR. Given that the wear rate of each grinding body is proportional to its own exposed surface area, the integration of Equation 1 – over the whole range of possible ball sizes – demonstrates that the overall grinding media consumption rate t (kg steel/operating hour), corresponding to the ensemble of balls ('string') in the mill charge, is consequently proportional to the total area A (m2) exposed by such ‘string’ :

t = - km A = - b kd A / 2 (3)


Moly-Cop Tools, Version 2.0About the Media Charge_Wear & Impact_SAG Mills Spreadsheet ...

The Linear Wear Theory referred above allows for the calculation of the total area A, for the simpler case of mono-size recharging policies with balls of diameter dR, from the expression :

A = 8000 Vap (1 - fv) [(dR)3 – (dS)3]/[(dR)4 – (dS)4] (4)

where :

Vap = apparent mill volume occupied by the charge (including interstitial spaces), m3, calculated as Wb/b/(1-fv) Wb = total weight of balls in the charge, tons fv = volumetric fraction of interstitial voids; customarily accepted to be 40%. dS = scrap or final rejection size of the worn balls, mm.

Substitution in Equation 3 above yields :

t = - 4000 kd Wb [(dR)3 – (dS)3]/[(dR)4 – (dS)4] (5)

By direct analogy to mineral particle breakage kinetics, it appears reasonable to postulate that an even more representative and scaleable quality indicator than kd is the Energy Specific Wear Rate Constant, kd

E, [m/(kWh/ton)], defined through the expression :

kd = kdE (Pb/Wb) / 1000 (6)

where the power intensity ratio (Pb/Wb) corresponds to the contribution to mill net power draw Pb (kW) of every ton of balls in the charge (Wb) to the total net power draw Pnet (kW) of the mill. The underlying theoretical claim is that grinding balls will wear faster in a more power intensive environment. In other words, kd

E is equivalent to kd, but proportionally corrected by how much power is being absorbed by each ton of balls in the charge. Therefore, it is to be expected that kd

E should be more insensitive than kd to variations in mill operating conditions (that may affect Pb and/or Wb) that may, in turn, produce higher or lower media consumption rates (kg/hr), not caused by variations in grinding media quality. As a practical evaluation criterion, it should then be accepted that the top quality grinding media, in any given application, will be the one that exhibits the lowest value of the Energy Specific Wear Rate Constant kd

E, regardless of the mill operating conditions.

Due application of Equation 6 creates the need for a mathematical representation of the total Net Power Draw of the mill in terms of its main dimensions and basic operating conditions. And also, how each component of the mill charge (balls, rocks and slurry) contributes to this total net power demand. An expanded version of the simple Hogg and Fuerstenau model serves such purpose well: (see Mill Power_SAG Mills)

Pnet = Pgross = 0.238 D3.5 (L/D) Nc ap (J - 1.065 J2) sin (7)where :

Pgross = gross power draw of the mill (kW) = Pnet / = overall mechanical and electrical transmission efficiency, °/1


The Linear Wear Theory referred above allows for the calculation of the total area A, for the simpler case of mono-size recharging policies with balls of diameter dR, from the expression :

A = 8000 Vap (1 - fv) [(dR)3 – (dS)3]/[(dR)4 – (dS)4] (4)

where :

Vap = apparent mill volume occupied by the charge (including interstitial spaces), m3, calculated as Wb/b/(1-fv) Wb = total weight of balls in the charge, tons fv = volumetric fraction of interstitial voids; customarily accepted to be 40%. dS = scrap or final rejection size of the worn balls, mm.

Substitution in Equation 3 above yields :

t = - 4000 kd Wb [(dR)3 – (dS)3]/[(dR)4 – (dS)4] (5)

By direct analogy to mineral particle breakage kinetics, it appears reasonable to postulate that an even more representative and scaleable quality indicator than kd is the Energy Specific Wear Rate Constant, kd

E, [m/(kWh/ton)], defined through the expression :

kd = kdE (Pb/Wb) / 1000 (6)

where the power intensity ratio (Pb/Wb) corresponds to the contribution to mill net power draw Pb (kW) of every ton of balls in the charge (Wb) to the total net power draw Pnet (kW) of the mill. The underlying theoretical claim is that grinding balls will wear faster in a more power intensive environment. In other words, kd

E is equivalent to kd, but proportionally corrected by how much power is being absorbed by each ton of balls in the charge. Therefore, it is to be expected that kd

E should be more insensitive than kd to variations in mill operating conditions (that may affect Pb and/or Wb) that may, in turn, produce higher or lower media consumption rates (kg/hr), not caused by variations in grinding media quality. As a practical evaluation criterion, it should then be accepted that the top quality grinding media, in any given application, will be the one that exhibits the lowest value of the Energy Specific Wear Rate Constant kd

E, regardless of the mill operating conditions.

Due application of Equation 6 creates the need for a mathematical representation of the total Net Power Draw of the mill in terms of its main dimensions and basic operating conditions. And also, how each component of the mill charge (balls, rocks and slurry) contributes to this total net power demand. An expanded version of the simple Hogg and Fuerstenau model serves such purpose well: (see Mill Power_SAG Mills)

Pnet = Pgross = 0.238 D3.5 (L/D) Nc ap (J - 1.065 J2) sin (7)where :

Pgross = gross power draw of the mill (kW) = Pnet / = overall mechanical and electrical transmission efficiency, °/1



D = effective internal diameter of the mill, ft L = effective internal length of the mill, ft Nc = rotational mill speed; expressed as a fraction (°/1) of its critical centrifugation speed : Ncrit = 76.6/D0.5

J = apparent mill filling, °/1 (including balls, rocks, slurry and the interstitial spaces, with respect to the total effective mill volume) = charge lifting angle (defines the dynamic positioning of the center of gravity of the mill load (the ‘kidney’) with respect to the vertical direction, typically with values in the range of 30° to 40°.

and where ap denotes the apparent density of the charge (ton/m3), which may be evaluated on the basis of the indicated charge components (balls, rocks and interstitial slurry):

ap = { (1-fv) b Jb + (1-fv) m (J – Jb) + p Jp fv J } / J (8) with :

Jb = apparent ball filling (°/1) (including balls and the interstitial voids in between such balls). Jp = interstitial slurry filling (°/1), corresponding to the fraction of the available interstitial voids (in between the balls and rocks in the charge) actually occupied by the slurry of finer particles. m = mineral particle density, ton/m3. p = slurry density (ton/m3), directly related to the weight % solids of the slurry (fs) by : 1/[(fs/m) + (1 - fs)].

Substitution of Equation 8 into Equation 7 allows for the decomposition of the total net power draw of the mill, in terms of the charge components (see Mill Power_SAG Mills). In particular, the contribution by the balls in the charge becomes:

Pb = [(1-fv) b Jb / ap J] • Pnet (9)

Referring back to Equations 5 and 6, an additional formula for the Energy Specific Media Consumption Rate, E (grs of steel/kWh drawn), may be derived : E = 1000 t / Pb (10)equivalent to :

E = 4000 kdE [(dR)3 – (dS)3]/[(dR)4 – (dS)4] (11)

On this basis, kdE may be easily back-calculated from actual operating records or estimates of E, dR and dS, recalling

that the top quality grinding media - in any given application - will be the one that exhibits the lowest value of the Energy Specific Wear Rate Constant kd

E, regardless of most mill(s) operating conditions.

Recently, H. Benavente (Moly-Cop 2006 : X Simposio sobre Procesamiento de Minerales, Termas de Chillán, Chile) proposed an empirical correlation for the calculation of kd

E, as a function of the Bond's Abrasion Index (54th Annual Meeting of AICHE, 1963) of the ore, the F80 feed size and the slurry pH :

kdE = kd

B [(AI - 0.02)/0.2]0.331 (F80/5000)0.13 (pH/10)-0.677 (12)

where kdB is known as the Benavente Constant.



Impact Breakage Kinetics:

In operations where noticeable ball breakage is to be expected – like in high-impact, SAG applications – an expanded, conceptual model, based on pilot Drop Ball Testing (DBT) results has been proposed to incorporate breakage as a potentially significant grinding media consumption mechanism.

The DBT is a standard, pilot scale testing procedure, originally designed by the U. S. Bureau of Mines and later adapted by the Moly-Cop Grinding Systems organization to assess the resistance of any given sample or lot of balls to repeated severe ball-to-ball impacts. Briefly, the DBT facility consists of a 10 m-high, J-shaped tube of slightly larger internal diameter than the size of the balls being tested. The curved, bottom part of the tube is filled with a constant number of balls (for instance, 24 when testing 5" balls). When another ball is dropped through the tube from a height of 10 m above, the top ball retained below in the tube suffers the direct impact of the falling ball, which is replicated through the whole line of balls retained in the curve at the bottom of the J-tube, originating the removal (through the lower tip of the J-tube) of the first ball in the line, which is so replaced by the last ball dropped. The balls removed from the tube are continuously lifted - via a bucket elevator - back to the top of the tube to be dropped down once again. The DBT is run until a certain maximum number of balls are broken (say, 10 broken balls) or a reasonable number of total cycles have been completed (say, 20,000 drops). The main outcome of a DBT test is the Average Breakage Probability, DBTstd, simply calculated as:

DBTstd = (# of broken balls) / (total drops * # balls in J-tube) (13)

With reference to Figure 1, in a full scale mill, the most critical, outer trajectory of a ball is that of a ball of mass m being lifted to a position defined by the angle 1 in the upper-right quadrant of the section of a mill of diameter D (ft) and then allowed to free-fall down to impact the toe of the mill charge ‘kidney’ at a position 2, in the lower-left quadrant.

In such case, the associated impact energy may be estimated by:

Emax = 0.07581 m2Nc2D + 0.305 mg[(D/2)cos1 + (D/2)cos2] (14)

The equivalent DBT height to attain equal impact energy at both scales(pilot and industrial) is then obtained as:

hDBT, eq /D = 0.0763 Nc2 + 0.153 (cos1 + cos2) (15)

independent of ball size (!). Figure 1.

Then, for projecting the DBTstd ball breakage probability to full industrial scale mills, the standard test value should be corrected as follows, for every ball size 'd':

DBTind = DBTstd * (hDBT, eq / hDBT, std) * (d/dR)g * (Jb/J)2 (16)

In this expression, the first correction factor accounts for the difference in maximum impact energies between the standard test and the full scale conditions. The second correction factor accounts for the fact that the breakage probability of any given ball is being proven to be lower and lower as such ball wears down in the charge, simply because it has not been broken yet. Parameter g is estimated to take values around 4. Finally, the third correction

2

1

Nc


Impact Breakage Kinetics:

In operations where noticeable ball breakage is to be expected – like in high-impact, SAG applications – an expanded, conceptual model, based on pilot Drop Ball Testing (DBT) results has been proposed to incorporate breakage as a potentially significant grinding media consumption mechanism.

The DBT is a standard, pilot scale testing procedure, originally designed by the U. S. Bureau of Mines and later adapted by the Moly-Cop Grinding Systems organization to assess the resistance of any given sample or lot of balls to repeated severe ball-to-ball impacts. Briefly, the DBT facility consists of a 10 m-high, J-shaped tube of slightly larger internal diameter than the size of the balls being tested. The curved, bottom part of the tube is filled with a constant number of balls (for instance, 24 when testing 5" balls). When another ball is dropped through the tube from a height of 10 m above, the top ball retained below in the tube suffers the direct impact of the falling ball, which is replicated through the whole line of balls retained in the curve at the bottom of the J-tube, originating the removal (through the lower tip of the J-tube) of the first ball in the line, which is so replaced by the last ball dropped. The balls removed from the tube are continuously lifted - via a bucket elevator - back to the top of the tube to be dropped down once again. The DBT is run until a certain maximum number of balls are broken (say, 10 broken balls) or a reasonable number of total cycles have been completed (say, 20,000 drops). The main outcome of a DBT test is the Average Breakage Probability, DBTstd, simply calculated as:

DBTstd = (# of broken balls) / (total drops * # balls in J-tube) (13)

With reference to Figure 1, in a full scale mill, the most critical, outer trajectory of a ball is that of a ball of mass m being lifted to a position defined by the angle 1 in the upper-right quadrant of the section of a mill of diameter D (ft) and then allowed to free-fall down to impact the toe of the mill charge ‘kidney’ at a position 2, in the lower-left quadrant.

In such case, the associated impact energy may be estimated by:

Emax = 0.07581 m2Nc2D + 0.305 mg[(D/2)cos1 + (D/2)cos2] (14)

The equivalent DBT height to attain equal impact energy at both scales(pilot and industrial) is then obtained as:

hDBT, eq /D = 0.0763 Nc2 + 0.153 (cos1 + cos2) (15)

independent of ball size (!). Figure 1.

Then, for projecting the DBTstd ball breakage probability to full industrial scale mills, the standard test value should be corrected as follows, for every ball size 'd':

DBTind = DBTstd * (hDBT, eq / hDBT, std) * (d/dR)g * (Jb/J)2 (16)

In this expression, the first correction factor accounts for the difference in maximum impact energies between the standard test and the full scale conditions. The second correction factor accounts for the fact that the breakage probability of any given ball is being proven to be lower and lower as such ball wears down in the charge, simply because it has not been broken yet. Parameter g is estimated to take values around 4. Finally, the third correction



factor may be considered a cushioning factor: the probability of a falling ball hitting directly another ball surrounded mostly by other balls (most severe impact condition).

On the other hand, based on the geometry of the mill liners, one can estimate the lifting capacity of any given lifting cavity; i. e. how many tons/hr of charge (a 'Jb/J' fraction of which would be just balls) are being lifted and allowed to impact back over the charge 'kidney'. The resulting formulas are quite cumbersome and may be explored by the interested Moly-Cop Tools user directly in each corresponding cell in the Data_File spreadsheet.

Finally, the combination of the tons of balls per hour subject to impact and the probability of these balls being broken allow for the calculation of the balls breakage rate, which added to the projected ball wear rate provides an estimate of the overall grinding media consumption rate.

Data Input :

All data required by the calculation routine must be defined in each corresponding unprotected white background cell of the here attached Data_File worksheet. Gray background cells contain the results of the corresponding formulas there defined and are protected to avoid any accidental editing.

You may tune the wear model to actual operational data - that is, find the proper value of the Benavente Constant kdB

that projects exactly the observed ball consumption rate (whenever available) in either gr/ton (Cell H50) or gr/kWh (Cell I50) or kg/hr (Cell K50) or ton/month (Cell L50) - use the Excel Goal Seek function setting the corresponding cell equal to the observed value, by changing Cell E57.

New Moly-Cop Tools users are invited to explore the brief comments inserted in each relevant cell, rendering the whole utilization of the worksheet self-explanatory. Eventually, the user may wish to remove the view of the comments by selecting Tools / Options / View / Comments / None.


MEDIA CONSUMPTION ESTIMATOR(Ball Mills)

Remarks Base Case Example

Power, kWMill Dimensions and Operating Conditions 3545 Balls

Eff. Diam. Eff. Length Mill Speed Charge Balls Interstitial Lift 0 Rocksft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, (°) 568 Slurry

18.50 25.00 72.00 36.00 36.00 100.00 33.00 4113 Net TotalL/D 1.35 12.82 rpm 5.00 % Losses

% Utilization hr/month 4329 Gross Total92.00 662.4 2,868 MWh/month

% Solids in the Mill 72.00

Ore Density, ton/m3 2.80

Slurry Density, ton/m3 1.862 Charge Mill Charge Weight, tons ApparentOre Feedrate, ton/hr 400.0 ton/hr Volume, Ball O´size Interstitial Density ton/day 8,832 ton/day m3 Charge Rocks Slurry ton/m3Energy, kWh/ton (ore) 10.82 kWh/ton (ore) 68.64 319.17 0.00 51.11 5.395

Balls Density, ton/m3 7.75 Eq. # of Balls 172,266Ball Size, mm 77.00 mmScrap Size, mm 12.00 mm

Liner Design : Default Lifting Cavity Filling, m3/lifter 0.045Number of Lifter Bars 38 36 Voids Fraction in Lifting Cavity, % 35.0Mill Speed, lifters/min 487 lifters/minLifters Spacing, inches 18.35 inches Lifting Capacity :Lifter Height, inches 4.00 inches Total Balls & Rocks, m3(ap)/hr 1,328

Rocks Lifting Rate, m3(ap)/hr 0Lifter Width (at base), in 4.62 inches Balls Lifting Rate, m3(ap)/hr 1,328Lifter Face Angle, (°) 30.0 (°) , ton/hr 6,689

, balls/hr 3,610,705Load Angle of Repose, (°) 60.0 (°)Angle at Balls Release, (°) 45.0 (°) Critical Ball on Ball Impacts per hour 3,610,705Angle at Balls Impact, (°) 45.0 (°) Corr. Breakage Probability, events/impact 0.000E+00Equiv. DBT Height, m 4.73 m Cushioning Factor 1.000

Breakage Rate, events/hr 0.000

DBT Test Results BALL CONSUMPTION RATESgr/kWh gr/kWh

Total # of Balls # of Broken Events/ gr/ton (gross) (balls) kg/hr ton/month %# of Drops in Tube Balls Impact Caused by Breakage

10,000 24 0 0.000E+00 0.0 0.00 0.00 0.0 0.0 0.0Caused by Wear

575.9 53.21 64.97 230.4 152.6 100.0

62.14 Overall

4265 575.9 53.21 64.97 230.4 152.6 100.0Purge Time, hrs 4,681 hrs

Default SCRAP GENERATIONWear Rate Constants, Values Nuclei Fragments Overall Bond's Abrasion Index 0.22 0.22 kg/hr % kg/hr % kg/hr

5000 5000 0.9 100.0 0.0 0.0 0.9 Slurry pH 10.5 10.5

1.29

1.250

0.0139 mm/hr

Moly-Cop Tools TM (Version 2.0)

ton/m3

ton/m3

ton/m3

Spec. Area, m2/m3 (app) m2/m3 (app)

Total Charge Area, m2 m2

Fresh Feed F80, m

Benavente Constant, kdB

kdE m/[kWh/ton]

kd

J10

Component of the Total Mill Power Draw (Cell J14) contributed by the Ball Charge.

J11

Component of the Total Mill Power Draw (Cell J14) contributed by the Rocks.

J12

Component of the Total Mill Power Draw (Cell J14) contributed by the Interstitial Slurry.

C13

Mill Diameter, inside liners.

D13

Effective Grinding Lenght.

E13

Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill.

F13

Total Apparent Volumetric Charge Filling - including balls and rocks, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners). "Rocks" are loosely defined as those particles big enough to increase the total apparent charge volume; i. e. do not fit in between the ball charge interstices.

G13

Apparent Volumetric Ball Filling Level, expressed as a percentage of the net internal mill volume (inside liners). Necessarily less or equal than the Total Charge Filling (Cell F14).

H13

This value represents the Volumetric Fractional Filling of the Voids - in between the balls and the rocks - by the retained slurry in the mill charge. In lack of actual measurements, a reasonable default value seems to be of the order of 50%.

I13

Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge ("the kidney") with respect to the horizontal. A reasonable default value for this angle is 40°, but may be easily "tuned" to specific applications against any available actual power data.

J13

See attached Worksheet About ...

J14

Mill Drive transmision losses. May vary from 3-5% for modern large mills up to 10-15% for older smaller mills.

H16

Average percentage of the total daily hours that the mill is operating normally.

L22

Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids).

E25

Default Values : With Discharge Grates = Grate Opening. Overflow Discharge Mills = 12 mm or less.

E28

Normally equal to twice the Nominal Mill Diameter, expressed in feet.

E34

Defined as the angle formed by the lifting (or attack) face of the lifter bar and a plane orthogonal to the mill shell, at the base line of the lifter bar. A larger angle indicates a "softer" lifting action.

E54

The Bond's Abrasion Index may vary in the range of 0.15 (low abrasivity) to 0.4 (high abrasivity).

E55

For primary ball mills, F80 may be as high as 10,000 microns. For secondary ball mills, F80 may be as low as 2,000 microns.

E56

For alcaline circuits, pH should be close to 10.5. If no lime is added to the mill, natural pH would be around 6.5. Acid circuit applications could run at pH as low as 4.5.


MEDIA CONSUMPTION ESTIMATOR(SAG Mills)

Remarks Base Case Example

Power, kWMill Dimensions and Operating Conditions 10824 Balls

Eff. Diam. Eff. Length Mill Speed Charge Balls Interstitial Lift 2793 Rocksft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, (°) 2081 Slurry

37.30 23.00 78.00 24.00 14.00 65.00 38.00 15699 Net TotalL/D 0.62 9.78 rpm 5.00 % Losses

% Utilization hr/month 16525 Gross Total92.00 662.4 10,946 MWh/month

% Solids in the Mill 78.00

Ore Density, ton/m3 2.80

Slurry Density, ton/m3 2.006 Charge Mill Charge Weight, tons ApparentOre Feedrate, ton/hr 1574.1 ton/hr Volume, Ball O´size Interstitial Density ton/day 34,756 ton/day m3 Charge Rocks Slurry ton/m3Energy, kWh/ton (ore) 10.50 kWh/ton (ore) 171.14 464.21 119.80 89.25 3.934

Balls Density, ton/m3 7.75 Eq. # of Balls 55,840Ball Size, mm 127.00 mmScrap Size, mm 65.00 mm

Liner Design : Default Lifting Cavity Filling, m3/lifter 0.167Number of Lifter Bars 38 38 Voids Fraction in Lifting Cavity, % 35.0Mill Speed, lifters/min 372 lifters/minLifters Spacing, inches 37.00 inches Lifting Capacity :Lifter Height, inches 8.00 inches Total Balls & Rocks, m3(ap)/hr 3,728

Rocks Lifting Rate, m3(ap)/hr 1,553Lifter Width (at base), in 9.24 inches Balls Lifting Rate, m3(ap)/hr 2,175Lifter Face Angle, (°) 30.0 (°) , ton/hr 10,955

, balls/hr 1,317,987Load Angle of Repose, (°) 60.0 (°)Angle at Balls Release, (°) 45.0 (°) Critical Ball on Ball Impacts per hour 768,826Angle at Balls Impact, (°) 45.0 (°) Corr. Breakage Probability, events/impact 2.042E-05Equiv. DBT Height, m 9.80 m Cushioning Factor 0.583

Breakage Rate, events/hr 9.159

DBT Test Results BALL CONSUMPTION RATESgr/kWh gr/kWh

Total # of Balls # of Broken Events/ gr/ton (gross) (balls) kg/hr ton/month %# of Drops in Tube Balls Impact Caused by Breakage

20,000 24 10 2.083E-05 48.4 4.61 7.03 76.1 50.4 7.0Caused by Wear

643.6 61.31 93.60 1013.1 671.1 93.0

35.14 Overall

3508 692.0 65.92 100.63 1089.3 721.5 100.0Purge Time, hrs 961 hrs

Default SCRAP GENERATIONWear Rate Constants, Values Nuclei Fragments Overall Bond's Abrasion Index 0.22 0.22 kg/hr % kg/hr % kg/hr

100000 100000 135.8 64.1 76.1 35.9 212.0 Slurry pH 10.5 10.5

1.94

2.768

0.0645 mm/hr

Moly-Cop Tools TM (Version 2.0)

ton/m3

ton/m3

ton/m3

Spec. Area, m2/m3 (app) m2/m3 (app)

Total Charge Area, m2 m2

Fresh Feed F80, m

Benavente Constant, kdB

kdE m/[kWh/ton]

kd

J10

Component of the Total Mill Power Draw (Cell J14) contributed by the Ball Charge.

J11

Component of the Total Mill Power Draw (Cell J14) contributed by the Rocks.

J12

Component of the Total Mill Power Draw (Cell J14) contributed by the Interstitial Slurry.

C13

Mill Diameter, inside liners.

D13

Effective Grinding Lenght.

E13

Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill.

F13

Total Apparent Volumetric Charge Filling - including balls and rocks, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners). "Rocks" are loosely defined as those particles big enough to increase the total apparent charge volume; i. e. do not fit in between the ball charge interstices.

G13

Apparent Volumetric Ball Filling Level, expressed as a percentage of the net internal mill volume (inside liners). Necessarily less or equal than the Total Charge Filling (Cell F14).

H13

This value represents the Volumetric Fractional Filling of the Voids - in between the balls and the rocks - by the retained slurry in the mill charge. In lack of actual measurements, a reasonable default value seems to be of the order of 50%.

I13

Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge ("the kidney") with respect to the horizontal. A reasonable default value for this angle is 40°, but may be easily "tuned" to specific applications against any available actual power data.

J13

See attached Worksheet About ...

L22

Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids).

E25

Default Values : With Pebbles Removal : 65 mm. Without Pebbles Removal : 17 mm.

E28

Normally equal to the Nominal Mill Diameter, expressed in feet.

E34

Defined as the angle formed by the lifting (or attack) face of the lifter bar and a plane orthogonal to the mill shell, at the base line of the lifter bar. A larger angle indicates a "softer" lifting action.

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