ballbal direct

Moly-Cop Tools / document.xls 04/22/2023 / 09:13:48

About the Ballbal_Direct Spreadsheet ...

Scope :

The Ballbal_Direct spreadsheet was designed to compute the Size-by-Size Mass Balance around the Hydrocyclone Classifiers of any given Conventional Ball Mill circuit, operating under the Direct configuration (see Flowsheet), on the basis of actual plant measurements.

Theoretical Framework :

Whenever actual grinding data are collected in a plant environment, they will invariably be affected by natural experimental and measurement errors, in such a way that the basic mass balance equation around the hydrocyclones, for particles of size di :

fiCF CF = fiU U + fiO O ??? , for i = 1,n

will never be satisfied. In the above expression CF, U and O represent the mass flowrate of solids in the cyclones feed, underflow and overflow streams, respectively. Similarly, fi

CF, fiU and fi

O represent the fraction of those total respective streams corresponding to particles of size di.

The Ballbal_Direct routine allows for the calculation of a whole new set of corresponding adjusted or fitted values fiCF, fi

U and fi

O, such that the objective functions :

fi = [ wCF (fiCF - fiCF)2 + wU (fiU - fiU)2 + wO(fiO - fi

O)2 ] ,for every particle size di

are minimized and the adjusted values so generated strictly satisfy the mass balance restrictions :

fiCF CF = fiU U + fi

O O , for i = 1,n

where wCF, wU and wO are user defined weighting factors included to represent the relative quality and reliability of the samples from each of the 3 streams and the mass flowrates CF, U and O are calculated as :

CF = F (1 + CL) U = F (CL) O = F

where F is the dry Fresh Feedrate of solids to the grinding section and the Circulating Load (CL) is estimated by :

CL = { usd S [(fiO - fiCF) / (fiCF - fiU)] + ufs (1/fSO - 1/fSCF) / (1/fSCF -1/fSU) } / (usd + ufs) all i

where fsCF, fsU and fsO are the weight fractions of total solids in the cyclones feed, underflow and overflow streams, respectively, and also usd and ufs are user defined weighting factors included to represent the relative quality and reliability of the size distribution measurements vs. the percent solids measurements in all 3 streams. In general, a high relative value of a weighting factor is indicative of a more reliable measurement with respect to the other measurements participating in the same equations. A statistically sound weighting factor may be calculated as 100/(% error)2;


Scope :






CF, fiU and fi


The Ballbal_Direct routine allows for the calculation of a whole new set of corresponding adjusted or fitted values fiCF, fi

U and fi

O, such that the objective functions :

fi = [ wCF (fiCF - fiCF)2 + wU (fiU - fiU)2 + wO(fiO - fi

O)2 ] ,for every particle size di


fiCF CF = fiU U + fi

O O , for i = 1,n


CF = F (1 + CL) U = F (CL) O = F


CL = { usd S [(fiO - fi

CF) / (fiCF - fi

U)] + ufs (1/fSO - 1/fS

CF) / (1/fSCF -1/fS

U) } / (usd + ufs) all i

where fsCF, fs

U and fsO are the weight fractions of total solids in the cyclones feed, underflow and overflow streams,

respectively, and also usd and ufs are user defined weighting factors included to represent the relative quality and reliability of the size distribution measurements vs. the percent solids measurements in all 3 streams. In general, a high relative value of a weighting factor is indicative of a more reliable measurement with respect to the other measurements participating in the same equations. A statistically sound weighting factor may be calculated as 100/(% error)2;


where (% error) corresponds to the combined sampling and measuring error percentage.

The least-square minimization problem stated above may be linearized and solved through the Lagrange Multipliers Method (see About ... in Cyclobal_Single).

Further refinement of the adjusted values so computed is achieved by imposing the condition that these values must conform to the Plitt's Classification Efficiency curve : (see About ... in Cyclosim_Single)

Ei = Bpf + (1 - Bpf ) (1 - exp [ - 0.693 (di/d50c)m ])

with the aid of the Excel Subroutine Solver to minimize a least-square objective function with respect to parameters Bpf, d50

c and m.

Finally, the size distributions for the remaining streams of the circuit (fresh feed, mill feed and mill discharge) are calculated on the basis of the adjusted values so obtained.

Data Input and Program Execution :

Most of the data required by the model must be defined in each corresponding unprotected white background cell - inside the red double-lined border - 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.

The remaining information required to run the program is entered in the Control_Panel worksheet, where the user is requested to provide initial guesses of the Bpf, d50

c and m parameters (see About ... in Cyclosim_Single). The Bpc parameter is rarely used and was incorporated to take into account the possible short-circuit of coarse particles to the overflow (as could be the case in highly pressurised cyclones). Finally, the user must specify the relative weighting factors for the various feed, underflow and overflow streams plus the relative weighting factors for the size distribution and percent solids measurements.

To run the program, select the objective function Cell E22 in Control_Panel and then, from the Tools Menu, select Solver ..., then Min and then By Changing any combination of Cells C20:F20. Clicking on the Solve button will execute the desired calculations.Important Notice : Solver ... must be run every time any element of input data gets to be modified. Otherwise, the current outputs are not valid.

Calculation results are summarized in the Reports worksheet.

An interesting feature of this routine is that the user has the option to save for later reference every analyzed data set by copying the Data_File worksheet into as many as required Sample 1, Sample 2, etc. worksheets. For reprocessing these data, simply copy the information back to the Data_File and re-run the Solver routine.

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


Scope :






CF, fiU and fi


The Ballbal_Direct routine allows for the calculation of a whole new set of corresponding adjusted or fitted values fiCF, fiU

and fiO, such that the objective functions :

fi = [ wCF (fiCF - fiCF)2 + wU (fiU - fi

U)2 + wO(fiO - fiO)2 ] ,for every particle size di


fiCF CF = fi

U U + fiO O , for i = 1,n


CF = F (1 + CL) U = F (CL) O = F


CL = { usd S [(fiO - fiCF) / (fiCF - fiU)] + ufs (1/fSO - 1/fSCF) / (1/fSCF -1/fSU) } / (usd + ufs) all i

where fsCF, fsU and fsO are the weight fractions of total solids in the cyclones feed, underflow and overflow streams, respectively, and also usd and ufs are user defined weighting factors included to represent the relative quality and reliability of the size distribution measurements vs. the percent solids measurements in all 3 streams. In general, a high relative value of a weighting factor is indicative of a more reliable measurement with respect to the other measurements participating in the same equations. A statistically sound weighting factor may be calculated as 100/(% error)2;


Scope :






CF, fiU and fi


The Ballbal_Direct routine allows for the calculation of a whole new set of corresponding adjusted or fitted values fiCF, fiU

and fiO, such that the objective functions :

fi = [ wCF (fiCF - fiCF)2 + wU (fiU - fi

U)2 + wO(fiO - fiO)2 ] ,for every particle size di


fiCF CF = fi

U U + fiO O , for i = 1,n


CF = F (1 + CL) U = F (CL) O = F


CL = { usd S [(fiO - fi

CF) / (fiCF - fi

U)] + ufs (1/fSO - 1/fS

CF) / (1/fSCF -1/fS

U) } / (usd + ufs) all i

where fsCF, fs

U and fsO are the weight fractions of total solids in the cyclones feed, underflow and overflow streams,

respectively, and also usd and ufs are user defined weighting factors included to represent the relative quality and reliability of the size distribution measurements vs. the percent solids measurements in all 3 streams. In general, a high relative value of a weighting factor is indicative of a more reliable measurement with respect to the other measurements participating in the same equations. A statistically sound weighting factor may be calculated as 100/(% error)2;


where (% error) corresponds to the combined sampling and measuring error percentage.

The least-square minimization problem stated above may be linearized and solved through the Lagrange Multipliers Method (see About ... in Cyclobal_Single).

Further refinement of the adjusted values so computed is achieved by imposing the condition that these values must conform to the Plitt's Classification Efficiency curve : (see About ... in Cyclosim_Single)

Ei = Bpf + (1 - Bpf ) (1 - exp [ - 0.693 (di/d50c)m ])

with the aid of the Excel Subroutine Solver to minimize a least-square objective function with respect to parameters Bpf, d50

c and m.

Finally, the size distributions for the remaining streams of the circuit (fresh feed, mill feed and mill discharge) are calculated on the basis of the adjusted values so obtained.

Data Input and Program Execution :

Most of the data required by the model must be defined in each corresponding unprotected white background cell - inside the red double-lined border - 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.

The remaining information required to run the program is entered in the Control_Panel worksheet, where the user is requested to provide initial guesses of the Bpf, d50

c and m parameters (see About ... in Cyclosim_Single). The Bpc parameter is rarely used and was incorporated to take into account the possible short-circuit of coarse particles to the overflow (as could be the case in highly pressurised cyclones). Finally, the user must specify the relative weighting factors for the various feed, underflow and overflow streams plus the relative weighting factors for the size distribution and percent solids measurements.

To run the program, select the objective function Cell E22 in Control_Panel and then, from the Tools Menu, select Solver ..., then Min and then By Changing any combination of Cells C20:F20. Clicking on the Solve button will execute the desired calculations.Important Notice : Solver ... must be run every time any element of input data gets to be modified. Otherwise, the current outputs are not valid.

Calculation results are summarized in the Reports worksheet.

An interesting feature of this routine is that the user has the option to save for later reference every analyzed data set by copying the Data_File worksheet into as many as required Sample 1, Sample 2, etc. worksheets. For reprocessing these data, simply copy the information back to the Data_File and re-run the Solver routine.

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


Sample N° 1

Weighting Factors :Streams : Fresh Feed 0 Mill Discharge 1 Cyclone Feed 1 Cyclone U'flow 1 Cyclone O'flow 1

Size Distributions 1% Solids 1

Initial Guesses :Bpf Bpc d50c m0.372 0.000 179.8 1.619 4

Obj. Function : 0.000

Classifier Constants :a1 9.68a2 1.401a3 54.95a4 0.524l 0.950

Moly-Cop Tools TM

Ballbal_Direct : MASS BALANCE CLOSURE AROUND A BALL MILL GRINDING CIRCUIT

Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.

10 100 1000 100001

10

100

Mill Discharge

Cyclone U'flow

Cyclone O'flow

Fresh Feed

Particle Size, microns

% P

assi

ng

E10

Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1

E12


E13


E15

Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1

E16

Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1

D20

Fractional short-circuit of slurry to the cyclone overflow. Default Value : 0

E22

To minimize this value, use Tools / Solver / Min, by changing any combination of Cells C20:F20.

E25

See Cyclosim_Single spreadsheet for further reference.

E26


E27


E28


E29



Circuit Type DIRECT Sample N° 1

Remarks Base Case Example

Mill Dimensions and Operating Conditions 3348 Balls Charge Mill Charge Weight, tons ApparentDiameter Length Speed Charge Balls Interstitial Lift 0 Overfilling Volume, Ball Slurry Density

ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, (°) 536 Slurry m3 Charge Interstitial Excess ton/m318.5 22.0 72.0 38.00 38.00 100.00 35.0 3885 Net Power 63.76 296.48 47.48 0.00 5.395

rpm 12.82 10.0 % Losses4316 Gross kW Feedrate, ton/hr (dry) 400.0

Cyclone Dimensions (inches) and Operating Pressure (psi)Number Diameter Height Inlet Vortex Apex psi Ore Density, ton/m3 2.80

10 20.0 75.0 3.50 7.50 3.67 7.98 Balls Density, ton/m3 7.75

EXPERIMENTAL SIZE DISTRIBUTIONSFresh Feed Mill Discharge Cyclone Feed Cyclone U'flow Cyclone O'flow Circ.

i Mesh Opening Mid-Size ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing Load

1 1.05 25400 100.00 100.00 100.00 100.00 100.002 0.742 19050 21997 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.003 0.525 12700 15554 20.00 5.00 95.00 13.69 1.12 98.88 18.17 1.12 98.88 18.17 1.49 98.51 0.00 0.00 100.004 0.371 9500 10984 66.40 16.60 78.40 31.26 2.56 96.32 41.49 2.56 96.32 41.49 3.39 95.12 0.00 0.00 100.005 3 6700 7978 56.28 14.07 64.33 30.71 2.51 93.81 40.76 2.51 93.81 40.76 3.33 91.79 0.00 0.00 100.006 4 4750 5641 41.32 10.33 54.00 27.88 2.28 91.53 37.01 2.28 91.53 37.01 3.03 88.76 0.00 0.00 100.007 6 3350 3989 33.36 8.34 45.66 29.03 2.37 89.16 38.53 2.37 89.16 38.53 3.15 85.61 0.00 0.00 100.008 8 2360 2812 27.36 6.84 38.82 33.26 2.72 86.44 44.14 2.72 86.44 44.14 3.61 82.00 0.00 0.00 100.009 10 1700 2003 21.64 5.41 33.41 38.59 3.16 83.28 51.21 3.16 83.28 51.21 4.19 77.81 0.00 0.00 100.00

10 14 1180 1416 20.40 5.10 28.31 50.47 4.13 79.16 66.98 4.13 79.16 66.98 5.48 72.34 0.00 0.00 100.0011 20 850 1001 15.60 3.90 24.41 59.40 4.86 74.30 78.83 4.86 74.30 78.83 6.45 65.89 0.00 0.00 100.0012 28 600 714 14.16 3.54 20.87 75.81 6.20 68.10 100.61 6.20 68.10 100.51 8.22 57.67 0.10 0.02 99.9713 35 425 505 12.04 3.01 17.86 92.58 7.57 60.53 122.86 7.57 60.53 120.92 9.89 47.78 1.94 0.49 99.4914 48 300 357 10.36 2.59 15.27 107.08 8.76 51.77 142.11 8.76 51.77 131.20 10.73 37.05 10.90 2.73 96.7615 65 212 252 8.84 2.21 13.06 108.22 8.85 42.92 143.62 8.85 42.92 116.40 9.52 27.54 27.23 6.81 89.9616 100 150 178 7.52 1.88 11.18 94.65 7.74 35.18 125.60 7.74 35.18 85.79 7.02 20.52 39.81 9.95 80.0017 150 106 126 6.48 1.62 9.56 74.57 6.10 29.08 98.97 6.10 29.08 56.90 4.65 15.87 42.06 10.52 69.4918 200 75 89 5.52 1.38 8.18 55.19 4.51 24.57 73.25 4.51 24.57 36.44 2.98 12.89 36.81 9.20 60.2919 270 53 63 4.72 1.18 7.00 40.68 3.33 21.24 53.99 3.33 21.24 24.14 1.97 10.91 29.86 7.46 52.8220 400 38 45 3.40 0.85 6.15 29.37 2.40 18.84 38.98 2.40 18.84 16.23 1.33 9.59 22.75 5.69 47.1321 -400 0 19 24.60 6.15 0.00 230.40 18.84 0.00 305.76 18.84 0.00 117.22 9.59 0.00 188.54 47.13 0.00

Totals 400.00 100.00 1222.84 100.00 1622.84 100.00 1222.84 100.00 400.00 100.00

% Solids 95.00 72.00 62.20 76.00 40.00Slurry Density, ton/m3 2.569 1.862 1.666 1.955 1.346Weighting Factor 0.000 1.000 1.000 1.000 1.000ave)

Moly-Cop Tools TM

BALLBAL : Mass Balance Closure around a Ball Mill Grinding Circuit

L10

Component of the Total Mill Power Draw (Cell K11) contributed by the Ball Charge.

L11

Component of the Total Mill Power Draw (Cell K11) contributed by the Overfilling Slurry on top of the "kidney".

L12

Component of the Total Mill Power Draw (Cell K11) contributed by the Interstitial Slurry in the ball charge.

D13

Mill Diameter, inside liners.

E13

Effective Grinding Lenght.

F13

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

G13

Total Apparent Volumetric Charge Filling - including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners).

H13

See Mill Power_Ball Mills for further details.

I13

This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases - particularly in Grate Discharge Mills - it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between Cells F9 and G9.

K13

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. See Mill Power_Ball Mills for further details. A reasonable default value for this angle is 35°, but may be easily "tuned" to specific applications against any available actual power data.

L13

Net Mill Power Draw. See About ... in the Mill Power_Ball Mills spreadsheet. This value can be set equal to the actual measured value by selecting Tools / Goal Seek, by changing Cell J11.

S13

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

F18

Free Cyclone Height, defined as the distance from the bottom end of the vortex finder to the top end of the apex.

E24

The top Mesh Opening must always be defined to allow 100% of the material passing through such screen.

I24


L24


R24


U24


Moly-Cop Tools / document.xls / Flowsheet 04/22/2023 / 09:13:48

Sample N° 1


40.00 % Solids60.29 % - Size 18

psi 7.98 150.0 P80

# of Cyclones 10Vortex 7.50 Circ. Load 305.73

Apex 3.67 0.372 Bpf 15660.392 Bpw

% Solids 76.00

Water, 355.1

ton/hr 400.0 Water, 223.9F80 9795

Gross kW 4316.1kWh/ton 10.79 % Balls 38.00

Wio 15.08 % Critical 72.00% Solids 72.00

% Solids 62.20

Moly-Cop Tools TM

m3/hr

m3/hr

m3/hr


Sample N° 1BALLBAL

Grinding Circuit Mass Balance Estimator

Remarks : Base Case Example

CIRCUIT MASS BALANCEConfiguration : DIRECT

Fresh Mill Mill Sump Cyclone Cyclone CycloneFeed Feed Discharge Water Feed U'flow O'flow

Ore, ton/hr 400.0 1622.9 1622.9 0.0 1622.9 1222.9 400.0 Water, m3/hr 21.1 407.3 631.1 355.1 986.2 386.2 600.0 Slurry, ton/hr 421.1 2030.2 2254.1 355.1 2609.2 1609.2 1000.0 Slurry, m3/hr 163.9 986.9 1210.8 355.1 1565.8 823.0 742.9 Slurry Dens., ton/m3 2.569 2.057 1.862 1.000 1.666 1.955 1.346 % Solids (by volume) 87.2 58.7 47.9 0.0 37.0 53.1 19.2 % Solids (by weight) 95.0 79.9 72.0 0.0 62.2 76.0 40.0

i Mesh Opening

1 1.05 25400 100.00 100.00 100.00 0.00 100.00 100.00 100.002 0.742 19050 100.00 100.00 100.00 0.00 100.00 100.00 100.003 0.525 12700 95.00 97.65 98.88 0.00 98.88 98.51 100.004 0.371 9500 78.40 91.00 96.32 0.00 96.32 95.12 100.005 3 6700 64.33 85.02 93.81 0.00 93.81 91.79 100.006 4 4750 54.00 80.20 91.53 0.00 91.53 88.76 100.007 6 3350 45.66 75.77 89.16 0.00 89.16 85.61 100.008 8 2360 38.82 71.36 86.44 0.00 86.44 82.00 100.009 10 1700 33.41 66.87 83.28 0.00 83.28 77.82 99.99

10 14 1180 28.31 61.49 79.16 0.00 79.16 72.34 99.9911 20 850 24.41 55.67 74.30 0.00 74.30 65.89 99.9912 28 600 20.87 48.60 68.10 0.00 68.10 57.68 99.9613 35 425 17.86 40.41 60.53 0.00 60.53 47.79 99.4814 48 300 15.27 31.69 51.77 0.00 51.77 37.06 96.7615 65 212 13.06 23.97 42.92 0.00 42.92 27.54 89.9616 100 150 11.18 18.22 35.18 0.00 35.18 20.52 80.0117 150 106 9.56 14.31 29.08 0.00 29.08 15.87 69.4918 200 75 8.18 11.73 24.57 0.00 24.57 12.89 60.2919 270 53 7.00 9.95 21.24 0.00 21.24 10.91 52.8220 400 38 6.15 8.74 18.84 0.00 18.84 9.59 47.13

D80, microns 9795 4679 1273 0 1273 2021 150.0

Specific Energy Consumption : 10.79 KWH/ton (Gross) Operational Work Index : 15.08 KWH/ton

Moly-Cop Tools TM

Particle Size Distributions (Cummulative % Passing)


Sample N° 1BALLBAL



CLASSIFIERS PERFORMANCE

Number of Cyclones : 10 Operating Conditions :Cyclone Dimensions, in : Feed Flowrate, m3/hr 1565.8

Diameter 20.00 Pressure, psi 8.0Height 75.00 D50 (corr.), microns 179.8Inlet 3.50 Water By-Pass, % 39.2Vortex 7.50 Solids By-Pass, % 37.2Apex 3.67 Plitt's Parameter 1.62

Ore Density, ton/m3 2.80 Circulating Load, % 306

Mass Balance around the Classifiers

Size Distributions, % Passing Classifier Efficiencyi Mesh Opening Mid-Size Feed U'flow O'flow Actual Corrected

1 1.05 25400 21997 100.00 100.00 100.00 1.000 1.0002 0.742 19050 15554 100.00 100.00 100.00 1.000 1.0003 0.525 12700 10984 98.88 98.51 100.00 1.000 1.0004 0.371 9500 7978 96.32 95.12 100.00 1.000 1.0005 3 6700 5641 93.81 91.79 100.00 1.000 1.0006 4 4750 3989 91.53 88.76 100.00 1.000 1.0007 6 3350 2812 89.16 85.61 100.00 1.000 1.0008 8 2360 2003 86.44 82.00 100.00 1.000 1.0009 10 1700 1416 83.28 77.82 99.99 1.000 1.000

10 14 1180 1001 79.16 72.34 99.99 1.000 1.00011 20 850 714 74.30 65.89 99.99 0.999 0.99812 28 600 505 68.10 57.68 99.96 0.984 0.97513 35 425 357 60.53 47.79 99.48 0.923 0.87814 48 300 252 51.77 37.06 96.76 0.811 0.69815 65 212 178 42.92 27.54 89.96 0.683 0.49516 100 150 126 35.18 20.52 80.01 0.575 0.32317 150 106 89 29.08 15.87 69.49 0.497 0.20018 200 75 63 24.57 12.89 60.29 0.447 0.11919 270 53 45 21.24 10.91 52.82 0.416 0.07120 400 38 19 18.84 9.59 47.13 0.383 0.018

Ore, ton/hr 1622.9 1222.9 400.0 Classifier Constants Water, m3/hr 986.2 386.2 600.0 Slurry, ton/hr 2609.2 1609.2 1000.0 a1 9.680 Slurry, m3/hr 1565.8 823.0 742.9 a2 1.401 Slurry Dens., ton/m3 1.666 1.955 1.346 a3 54.950 % Solids (by volume) 37.0 53.1 19.2 a4 0.524 % Solids (by weight) 62.2 76.0 40.0 l 0.950

Moly-Cop Tools TM


Sample N° 1BALLBAL



BALL MILL PERFORMANCE

Diameter, ft 18.5 4316Length, ft 22.0 3885Speed, % Critical 72.0 Throughput, ton/hr 1622.9App. Density, ton/m3 5.39 % Solids (by weight) 79.9Charge Level, % 38.0 Sp. Energy, KWH/ton 2.66Balls Filling, % 38.0 Reduction Ratio 3.67Lift Angle, (°) 35.0

Size DistributionsMill Mill

i Mesh Opening Mid-Size Feed Discharge

1 1.05 25400 21997 100.00 100.002 0.742 19050 15554 100.00 100.003 0.525 12700 10984 97.65 98.884 0.371 9500 7978 91.00 96.325 3 6700 5641 85.02 93.816 4 4750 3989 80.20 91.537 6 3350 2812 75.77 89.168 8 2360 2003 71.36 86.449 10 1700 1416 66.87 83.28

10 14 1180 1001 61.49 79.1611 20 850 714 55.67 74.3012 28 600 505 48.60 68.1013 35 425 357 40.41 60.5314 48 300 252 31.69 51.7715 65 212 178 23.97 42.9216 100 150 126 18.22 35.1817 150 106 89 14.31 29.0818 200 75 63 11.73 24.5719 270 53 45 9.95 21.2420 400 38 19 8.74 18.84

D80, microns 4679 1273

Moly-Cop Tools TM

Mill Power, kW (Gross)Mill Power, kW (Net)

Sample 1

Circuit Type DIRECT


Mill Dimensions and Operating ConditionsDiameter Length Speed Charge Balls Interstitial

ft ft % Critical Filling,% Filling,% Slurry Filling,%18.5 22.0 72.0 38.00 38.00 100.00

rpm 12.82

Cyclone Dimensions (inches) and Operating Pressure (psi)Number Diameter Height Inlet Vortex Apex psi

10 20.0 75.0 3.50 7.50 3.67 7.98

EXPERIMENTAL SIZE DISTRIBUTIONSFresh Feed Mill Discharge

i Mesh Opening Mid-Size ton/hr % Retained % Passing ton/hr

1 1.05 25400 100.002 0.742 19050 21997 0.00 0.00 100.00 0.003 0.525 12700 15554 20.00 5.00 95.00 13.694 0.371 9500 10984 66.40 16.60 78.40 31.265 3 6700 7978 56.28 14.07 64.33 30.716 4 4750 5641 41.32 10.33 54.00 27.887 6 3350 3989 33.36 8.34 45.66 29.038 8 2360 2812 27.36 6.84 38.82 33.269 10 1700 2003 21.64 5.41 33.41 38.59

10 14 1180 1416 20.40 5.10 28.31 50.4711 20 850 1001 15.60 3.90 24.41 59.4012 28 600 714 14.16 3.54 20.87 75.8113 35 425 505 12.04 3.01 17.86 92.5814 48 300 357 10.36 2.59 15.27 107.0815 65 212 252 8.84 2.21 13.06 108.2216 100 150 178 7.52 1.88 11.18 94.6517 150 106 126 6.48 1.62 9.56 74.5718 200 75 89 5.52 1.38 8.18 55.1919 270 53 63 4.72 1.18 7.00 40.6820 400 38 45 3.40 0.85 6.15 29.3721 -400 0 19 24.60 6.15 0.00 230.40

Totals 400.00 100.00 1222.84

% Solids 95.00Slurry Density, ton/m3 2.569Weighting Factor 0.000

Moly-Cop Tools TM


D13

Mill Diameter, inside liners.

E13

Effective Grinding Lenght.

F13

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

G13

Total Apparent Volumetric Charge Filling - including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners).

H13

See Mill Power_Ball Mills for further details.

I13

This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases - particularly in Grate Discharge Mills - it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between Cells F9 and G9.

F18

Free Cyclone Height, defined as the distance from the bottom end of the vortex finder to the top end of the apex.

E24


I24


Sample 1

Sample 1

Sample N°

Base Case Example

3348 Balls Charge Mill Charge Weight, tonsLift 0 Overfilling Volume, Ball Slurry

Angle, (°) 536 Slurry m3 Charge Interstitial Excess35.0 3885 Net Power 63.76 296.48 47.48 0.00

10.0 % Losses4316 Gross kW Feedrate, ton/hr (dry) 400.0

Ore Density, ton/m3 2.80Balls Density, ton/m3 7.75

EXPERIMENTAL SIZE DISTRIBUTIONSMill Discharge Cyclone Feed Cyclone U'flow

% Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing

100.00 100.00 100.000.00 100.00 0.00 0.00 100.00 0.00 0.00 100.001.12 98.88 18.17 1.12 98.88 18.17 1.49 98.512.56 96.32 41.49 2.56 96.32 41.49 3.39 95.122.51 93.81 40.76 2.51 93.81 40.76 3.33 91.792.28 91.53 37.01 2.28 91.53 37.01 3.03 88.762.37 89.16 38.53 2.37 89.16 38.53 3.15 85.612.72 86.44 44.14 2.72 86.44 44.14 3.61 82.003.16 83.28 51.21 3.16 83.28 51.21 4.19 77.814.13 79.16 66.98 4.13 79.16 66.98 5.48 72.344.86 74.30 78.83 4.86 74.30 78.83 6.45 65.896.20 68.10 100.61 6.20 68.10 100.51 8.22 57.677.57 60.53 122.86 7.57 60.53 120.92 9.89 47.788.76 51.77 142.11 8.76 51.77 131.20 10.73 37.058.85 42.92 143.62 8.85 42.92 116.40 9.52 27.547.74 35.18 125.60 7.74 35.18 85.79 7.02 20.526.10 29.08 98.97 6.10 29.08 56.90 4.65 15.874.51 24.57 73.25 4.51 24.57 36.44 2.98 12.893.33 21.24 53.99 3.33 21.24 24.14 1.97 10.912.40 18.84 38.98 2.40 18.84 16.23 1.33 9.59

18.84 0.00 305.76 18.84 0.00 117.22 9.59 0.00100.00 1622.84 100.00 1222.84 100.00

72.00 62.20 76.001.862 1.666 1.9551.000 1.000 1.000


L10

Component of the Total Mill Power Draw (Cell K11) contributed by the Ball Charge.

L11

Component of the Total Mill Power Draw (Cell K11) contributed by the Overfilling Slurry on top of the "kidney".

L12

Component of the Total Mill Power Draw (Cell K11) contributed by the Interstitial Slurry in the ball charge.

K13

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. See Mill Power_Ball Mills for further details. A reasonable default value for this angle is 35°, but may be easily "tuned" to specific applications against any available actual power data.

L13

Net Mill Power Draw. See About ... in the Mill Power_Ball Mills spreadsheet. This value can be set equal to the actual measured value by selecting Tools / Goal Seek, by changing Cell J11.

L24


R24


Sample 1

Sample 1

1

ApparentDensityton/m3

5.395

EXPERIMENTAL SIZE DISTRIBUTIONSCyclone O'flow

ton/hr % Retained % Passing

100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.00 0.00 100.000.10 0.02 99.971.94 0.49 99.49

10.90 2.73 96.7627.23 6.81 89.9639.81 9.95 80.0042.06 10.52 69.4936.81 9.20 60.2929.86 7.46 52.8222.75 5.69 47.13

188.54 47.13 0.00400.00 100.00

40.001.3461.000

S13

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

U24


Sample 1

ballbal direct

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