SAGParam Open

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About the SAGParam_Open Spreadsheet ...

Scope :

The SAGParam_Open spreadsheet was designed to be used - in conjunction with the SAG Mill Grinding SimulatorsSAGSim_Open and SAGSim_Recycle - in the "tuning" of such simulators to any specific actual grinding system, via theestimation of the various Model Parameters that characterize the grindability of any given ore. In other words, theattached spreadsheets provide an effective algorithm to search for the set of parameter values that best approximate themodel response to the actual experimental measurements available, based on a typical non-linear, least-squares criterio

Theoretical Framework :

The reference SAG mill model is described with further details in the About ... worksheets of the SAGSim_Open orSAGSim_Recycle files.

On the basis ofPilot or Industrial Scale Data, like those typically obtained from plant sampling or audit campaigns, the

SAGParam_Open routine allows for the calculation of all the Model Parameters (a's, b's and dcrit's) that minimize theleast-squares Objective Function :

n

f = S { wi [(fi - fi)/fi]2 + ui [(fiL - fiL)/fiL]2} (3)i = 1

where the fi's represent the experimental size distribution of the mill product (as % retained on screen 'i' ) and the fi'srepresent the model response for each corresponding fi, for a given set of model parameters. Similarly, the fi

L's represethe experimental size distribution of the mill internal load and the fi

L's represent the corresponding model response. The

Model Parameters (a's, b's and dcrit's) that yield the minimum possible value off are so considered to be representativeof the particular ore under analysis.

Also in Equation 3, the w i's and ui's represent user defined Weighting Factors - for the mill product and mill internal loadrespectively - that quantify the relative quality and reliability of each particular mesh value with respect to the otherscreens data. Relatively high values of such weighting factors indicate more reliable measurements. At the extreme, aweighting factor equal to zero means that this particular measurement is not being included in the Objective Function.

The minimization problem stated above may be readily solved with the aid of the Excel Subroutine Solver.

Data Input and Program Execution :

Most of the data required by the algorithm 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 resuof 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 isrequested to provide initial guesses of the grinding parameters listed above.

To run the program, select the objective function Cell E27 in Control_Panel and then, from the Tools Menu, selectSolver..., then Min and then By Changing any combination ofCells E10:E24 (see Useful Hints below). Clicking on theSolve button will execute the desired calculations.Important Notice : Solver ... must be run every time any element of input data gets to be modified . Otherwise, thecurrent 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 bycopying the Data_File worksheet into as many as required Test 1, Test 2, etc. worksheets. For reprocessing these datasimply copy the information back to the Data_File and re-run the Solverroutine.

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

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To run the program, select the objective function Cell E29 in Control_Panel and then, from the Tools Menu, selectSolver ..., then Min and then By Changing any combination ofCells E10:G29 (see Useful Hints below). Clicking on thSolve 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 currenoutputs 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 bycopying the Data_File worksheet into as many as required Test 1, Test 2, etc. worksheets. For reprocessing these datasimply copy the information back to the Data_File and re-run the Solverroutine.

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

Useful Hints :

The proper utilization of the parameter estimation spreadsheets - like SAGParam_Open - is by far the most complex tasto be undertaken with Moly-Cop Tools. There is no set of firm recommendations to obey, but the following hints mayhelp guiding the user in the search of the most representative set of grinding parameters :

1. It is not required to run the Solversearch for all parameters at the same time. In fact, this is strongly not recommendeas the search algorithm will most likely fail to find the minimizing optimum when dealing with too many parameters at oncTo exclude any given parameter off the search, remove the corresponding cell reference off the By Changing list of cellsin Solverand that parameter value will then remain constant and equal to its original guess during the whole search.

2. When multiple experimental data sets are available (the most desirable condition) for various ore types (hard, soft, etcorgrinding conditions (mill filling, ball size, % solids, etc.), always attempt to obtain a reasonable model fit of these datawith the same average parameter values for all sets. If that is not acceptable, proceed to allow differences in the most

critical parameters in the following sequence : a0, dcrit, b0, a1and b1. Keep in mind that a larger number of adjustable

parameters in the search (that is, included in the By Changing list) will necessarily yield lowerObjective Function (CelE29) values, but the values of the parameters that achieve such minimum will be less reliable in statistical terms andtherefore, from one data set to another, these parameters will exhibit significant variability and covariance amongst themrendering them meaningless.

3. An advisable starting run of the algorithm for each independent available data set should considered a search for

parameters a0, a1, dcrit and b0; leaving the others fix at nominal values : a2 = 3.0, b1 = 0.5 and b2 = 4.0. Use thegreen background table below the Control_Panel area to summarize the results of your search with the variousavailable data sets. Be careful to follow the instructions provided at the bottom of such table. If the model fits appeto be reasonable, then you should attempt to reduce the number of adjustable parameters. Look for the one parameterthat exhibit the least Coefficient of Variation (the ratio of its standard deviation to its average value, for all data sets) anset it fix at its average value and equal for all data sets, for the next runs of the search. Continue removing the remainingadjustable parameters off the By Changing list, one at a time, until the model fit is no longer judged acceptable. Theconcept behind this parameter screening process is to lump the impact of whatever



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ore properties orprocess variable are being investigated into the least possible number of parameters in order toimprove the statistical significance of the estimations and facilitate the derivation of valid conclusions regarding such

effects. For instance, it is believed that the distribution of ball sizes in the mill only affects the parameters a0 and dcrit.

Similarly, hardness variations of the same ore source may be well described by changes in the a0 parameter only. Not agrinding systems require a finite value of dcrit; whenever the estimated value of this parameter tends to be greater thathe top mesh opening, set it fix at 100,000 and remove it from the By Changing list.

4. If the step above does not provide satisfactory model fits, then you should add other parameters to the list, one at a

time. If the model fits are still not satisfactory, there is a good chance the data contains significant experimental errors anshould be discarded.

5. Never run a search fora2's orb2's, as these parameters have little effect on the objective function and may just confusthe search algorithm. When in doubt, simply try assigning them values between 2 and 4 and observe the response of theObjective Function (Cell E29). In other words, these two parameters are better optimized by a very basic trial-and-errorprocedure, not via the Solverroutine.



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Moly-Cop Tools TM

Test N 1

Selection Function :

Balls on Rocks on Self Particles Particles Breakage

alpha0 0.00358000 0.00228000 0.00018

alpha1 0.650 0.650 0.650

alpha2 3.500 3.500

Dcrit 25400 9500

Breakage Function :

beta00 0.400 beta01 0.050

beta1 0.650 (default : 0.0)

beta2 2.500

beta30 0.127 beta31 0.000

(default : 1.0)

Grate Parameters : Default

Inefficiency 0.400 0.400

D50/DGrate 0.600 0.700

m 2.000 3.000

Incr. Sp. Energy, KWH/ton :

(default value : 0.2) 0.50

Obj. Function 0.00

Exp. Adj. % Dev.

Fresh Feedrate 1.79 1.79 0.00

SAGPARAM_OPEN : Estimation of Semiautogenous Grinding Parameters from Plant or Pilot S

Note : Current calculations are not valid, if SOLVER has

last data modification.

0

1

10

100

10 100 1000 1000

%P

assing

Particle Size, microns

Moly-Cop Tools / 138335796.xls.ms_office Page 7


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Moly-Cop Tools TM

Circuit Type OPEN

Remarks

Power, KW

Mill Dimensions and Operating Conditions 5.9 BallsDiameter Length Speed Charge Balls Intersticial Lift 2.4 Roc

ft ft % Critical Filling,% Filling,% Filling,% Angle, () 1.0 Slur

5.7 1.8 75.0 18.0 8.5 50.0 47.5 9.3 Net

7.00 % L

10.0 Gro

% Solids in Mill Slurry 74.0 Charge App

Ore Density, ton/m3 2.80 Volume, m3 Balls Rocks Slurry to

Slurry Density, ton/m3 1.907 0.24 0.52 0.21 0.09

Balls Density, ton/m3 7.75

Feed Moisture, % 2.0

% Open Open # of Grate Area / Rat

Area Area, in2 Elements Element 1/

Grate Opening, mm 12.7 15.00 551 6 15.3

Slurry Top Size, mm 12.7

Fresh Feedrate, ton/hr 1.79 in2/(ton/hr) of Rocks 308.36 Min

Sp. Energy, KWH/ton 5.21 (net) in2/(m3/hr) of Slurry 435.23 Min

i Mesh Opening Mid-Size % Ret % Pass % Ret % Pass %

1 16" 406400 100.00 100.00

2 8" 203200 287368 4.52 95.48 0.00 100.00

3 4" 101600 143684 6.04 89.44 0.00 100.00

4 3" 76100 87930 9.43 80.01 0.00 100.00

5 2" 50800 62176 18.29 61.72 0.00 100.00

6 1.05 25400 35921 23.36 38.35 0.00 100.007 0.742 19050 21997 5.46 32.90 0.00 100.00

8 0.525 12700 15554 5.21 27.69 0.00 100.00

9 0.371 9500 10984 2.68 25.02 3.92 96.08

10 3 6700 7978 2.58 22.44 5.88 90.20

11 4 4750 5641 2.13 20.31 6.42 83.78

12 6 3350 3989 1.90 18.41 5.73 78.05

13 8 2360 2812 1.73 16.68 7.07 70.98

14 10 1700 2003 1.48 15.20 7.06 63.91

15 14 1180 1416 1.52 13.68 8.05 55.86

16 20 850 1001 1.26 12.42 6.99 48.86

17 28 600 714 1.23 11.19 6.80 42.06

18 35 425 505 1.11 10.08 5.98 36.09

19 48 300 357 1.03 9.05 5.24 30.85

20 65 212 252 0.93 8.12 4.55 26.30

21 100 150 178 0.84 7.27 3.90 22.4022 150 106 126 0.77 6.51 3.39 19.01

23 200 75 89 0.69 5.82 2.90 16.11

24 270 53 63 0.62 5.19 2.48 13.63

25 400 38 45 0.54 4.65 2.03 11.60

26 -400 0 0 4.65 0.00 11.60 0.00

Obj. Function

Mill Disch. 1 Mill Load 1 2.049E-07

Maximum Grate Transport Capacity

'Grinding Kinetics Controlled'

Specific Grate Area Demand

SAGParam_Open : SAG Model Parameter

Design Example : SAG Pilot Testing.

Charge Weight, tons

Fee

Relative Weighting Factors

Mill Discharge (exp)Mill Feed



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Moly-Cop Tools TM Test N 1

Remarks : Design Example : SAG Pilot Testing.

Diameter, ft 5.7 Throughput, ton/hr 1.79

Length, ft 1.8 Water, m3/hr 0.63

Speed, % Critical 75.0 Slurry, ton/hr 2.42

Charge Level, % 18.0 Slurry, m3/hr 1.27

Ball Filling, % 8.5 Slurry Dens., ton/m3 1.907

Interstitial Filling, % 50 % Solids (slurry) 74.00

Lift Angle, () 47.5

Grate Opening, mm 12.7 Power, kW (net) 9.3

App. Dens., ton/m3 3.464 Energy, kWh/ton 5.21

i Mesh Opening Feed

Exp. Adj. Exp. Adj.

1 16" 406400 100.00 100.00 / 100.00 100.00 / 100.00

2 8" 203200 95.48 100.00 / 100.00 94.40 / 94.40

3 4" 101600 89.44 100.00 / 100.00 79.42 / 79.42

4 3" 76100 80.01 100.00 / 100.00 58.81 / 58.81

5 2" 50800 61.72 100.00 / 100.00 31.51 / 31.51

6 1.05 25400 38.35 100.00 / 100.00 17.16 / 17.16

7 0.742 19050 32.90 100.00 / 100.00 13.46 / 13.46

8 0.525 12700 27.69 100.00 / 100.00 9.83 / 9.83

9 0.371 9500 25.02 96.08 / 96.08 8.21 / 8.21

10 3 6700 22.44 90.20 / 90.20 7.05 / 7.05

11 4 4750 20.31 83.78 / 83.78 6.25 / 6.25

12 6 3350 18.41 78.05 / 78.05 5.70 / 5.70

13 8 2360 16.68 70.98 / 70.98 5.11 / 5.11

14 10 1700 15.20 63.91 / 63.91 4.57 / 4.57

15 14 1180 13.68 55.86 / 55.86 3.97 / 3.97

16 20 850 12.42 48.86 / 48.86 3.47 / 3.47

17 28 600 11.19 42.06 / 42.06 2.98 / 2.98

18 35 425 10.08 36.09 / 36.09 2.56 / 2.56

19 48 300 9.05 30.85 / 30.85 2.18 / 2.18

20 65 212 8.12 26.30 / 26.30 1.86 / 1.86

21 100 150 7.27 22.40 / 22.40 1.59 / 1.5922 150 106 6.51 19.01 / 19.01 1.35 / 1.35

23 200 75 5.82 16.11 / 16.11 1.14 / 1.14

24 270 53 5.19 13.63 / 13.63 0.96 / 0.96

25 400 38 4.65 11.60 / 11.60 0.82 / 0.82

D80, microns 76085 3783 / 3783 104624 / 104624

SAG_ParamSAG Model Parameter Estimator

DESIGN AND OPERATING CONDITIONS

Configuration : OPEN

Mill LoadMill Discharge

Particle Size Distributions (Cumm. % Passing)



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Moly-Cop Tools TM Test N 1SAG_Param

SAG Model Parameter Estimator

Balls on Particles : Self-Breakage : beta00 0.4000alpha0 0.003580 alpha0 0.000180 beta01 0.050

alpha1 0.650 alpha1 0.650 beta1 0.650

alpha2 3.50 beta2 2.50

Dcrit 25400 beta30 0.1270

beta31 0.000

Rocks on Particles :

alpha0 0.002280

alpha1 0.650 Inefficiency 0.400

alpha2 3.50 D50/DGrate 0.600

Dcrit 9500 m 2.000

Obj. Function 0.000

Selection Function

SAGParam_Open MODEL PARAMETERS

Breakage Function

Grate Parameters



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Test 1

Moly-Cop Tools TM

Circuit Type OPEN

Remarks

Mill Dimensions and Operating Conditions

Diameter Length Speed Charge Balls Intersticial Lift

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

5.7 1.8 75.0 18.0 8.5 50.0 47.5

% Solids in Mill Slurry 74.0 Charge

Ore Density, ton/m3 2.80 Volume, m3 Balls RocksSlurry Density, ton/m3 1.907 0.24 0.52 0.21

Balls Density, ton/m3 7.75

Feed Moisture, % 2.0

% Open Open # of Grate

Area Area, in2 Elements

Grate Opening, mm 12.7 15.00 551 6

Slurry Top Size, mm 12.7

Fresh Feedrate, ton/hr 1.79 in2/(ton/hr) of Rocks 308.36

Sp. Energy, KWH/ton 5.21 (net) in2/(m

3/hr) of Slurry 435.23

i Mesh Opening Mid-Size % Ret % Pass % Ret

1 16" 406400 100.00

2 8" 203200 287368 4.52 95.48 0.00

3 4" 101600 143684 6.04 89.44 0.00

4 3" 76100 87930 9.43 80.01 0.00

5 2" 50800 62176 18.29 61.72 0.00

6 1.05 25400 35921 23.36 38.35 0.00

7 0.742 19050 21997 5.46 32.90 0.00

8 0.525 12700 15554 5.21 27.69 0.009 0.371 9500 10984 2.68 25.02 3.92

10 3 6700 7978 2.58 22.44 5.88

11 4 4750 5641 2.13 20.31 6.42

12 6 3350 3989 1.90 18.41 5.73

13 8 2360 2812 1.73 16.68 7.07

14 10 1700 2003 1.48 15.20 7.06

15 14 1180 1416 1.52 13.68 8.05

16 20 850 1001 1.26 12.42 6.99

Specific Grate Area

SAGParam_Open : SAG

Design Example : SAG Pilot Testing.

Charge Weight, t

Maximum Grate Transp

'Grinding Kinetics Co

Mill Feed Mill Disch

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Test 1

17 28 600 714 1.23 11.19 6.80

18 35 425 505 1.11 10.08 5.98

19 48 300 357 1.03 9.05 5.24

20 65 212 252 0.93 8.12 4.55

21 100 150 178 0.84 7.27 3.90

22 150 106 126 0.77 6.51 3.39

23 200 75 89 0.69 5.82 2.9024 270 53 63 0.62 5.19 2.48

25 400 38 45 0.54 4.65 2.03

26 -400 0 0 4.65 0.00 11.60

Obj. Function

Mill Disch. 1 Mill Load 1 2.04904E-07

Relative Weighting Factors

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Test 1

Test N 1

Power, KW

5.9 Balls

2.4 Rocks

1.0 Slurry

9.3 Net Total

7.00 % Losses

10.0 Gross Total

App. Dens.

Slurry ton/m30.09 3.464

Area / Rate Const.

Element 1/in2/min

15.3 10.000

Min 27.50

Min 4.23

% Pass % Ret % Pass % Ret % Pass % Ret % Pass

100.00 100.00 100.00 100.00

100.00 0.00 100.00 5.60 94.40 5.60 94.40

100.00 0.00 100.00 14.98 79.42 14.98 79.42

100.00 0.00 100.00 20.61 58.81 20.61 58.81

100.00 0.00 100.00 27.30 31.51 27.30 31.51

100.00 0.00 100.00 14.35 17.16 14.35 17.16

100.00 0.00 100.00 3.71 13.46 3.71 13.46

100.00 0.00 100.00 3.63 9.83 3.63 9.8396.08 3.92 96.08 1.62 8.21 1.62 8.21

90.20 5.88 90.20 1.15 7.05 1.15 7.05

83.78 6.42 83.78 0.81 6.25 0.81 6.25

78.05 5.73 78.05 0.55 5.70 0.55 5.70

70.98 7.07 70.98 0.59 5.11 0.59 5.11

63.91 7.06 63.91 0.54 4.57 0.54 4.57

55.86 8.05 55.86 0.59 3.97 0.59 3.97

48.86 6.99 48.86 0.51 3.47 0.51 3.47

emand

Feed Size Distributions

odel Parameter Estimator

ns

rt Capacity

trolled'

Mill Discharge (adj) Mill Load (exp) Mill Load (adj)rge (exp)

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Test 1

42.06 6.80 42.06 0.49 2.98 0.49 2.98

36.09 5.98 36.09 0.43 2.56 0.43 2.56

30.85 5.24 30.85 0.37 2.18 0.37 2.18

26.30 4.55 26.30 0.32 1.86 0.32 1.86

22.40 3.90 22.40 0.28 1.59 0.28 1.59

19.01 3.39 19.01 0.24 1.35 0.24 1.35

16.11 2.90 16.11 0.20 1.14 0.20 1.1413.63 2.48 13.63 0.18 0.96 0.18 0.96

11.60 2.03 11.60 0.14 0.82 0.14 0.82

0.00 11.60 0.00 0.82 0.00 0.82 0.00

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Documents

SAGParam Open