Ballparam Batch jMultitest

About ...Moly-Cop Tools, Version 2.0About the BallParam_Batch_MultiTest Spreadsheet ...Moly-Cop Tools, Version 2.0About the BallParam_Batch_MultiTest Spreadsheet ...Moly-Cop Tools, Version 2.0About the BallParam_Batch_MultiTest Spreadsheet ...

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&C&8Page &P&R&8&D / &TScope :

The BallParam_Batch_MultiTest spreadsheet is fully analogous to the BallParam_Batch spreadsheet, but designed for the simultaneous grinding parameters estimation from up to 10 different batch scale sets of test results.

Theoretical Framework :

The reference ball mill model is described with further details in the About ... worksheets of the BallSim_Direct or BallSim_Reverse files.

Such model is based on the so called Modern Theory of Comminution. This theory introduced two new sets of parameters : the Selection Function S and the Breakage Function B. The first set also referred to as Grindability relates to the grinding kinetics of each independent particle and the second set also referred to as Distribution of Primary Fragments characterizes the size distribution of the fragments produced as a result of breakage events.

The size-dependence of the Selection and Breakage Parameters is represented by the following relationships :

- For the Selection Function :

SiE = a0 (di*)a1 / [ 1 + (di* / dcrit)a2 ] (1) with : di* = (di di+1)0.5 = average particle size of the i-th fraction.

An expanded form of this expression - also available in this simulation routine - is given by :

SiE = [1/(1+a02/a01)] { a01 (di*)a11 / [ 1 + (di* / dcrit)a2 ] + a02 (di*)a12 } (1e)

- For the Breakage Function :

Bij = b0 (di/dj+1)b1 + (1- b0) (di/dj+1)b2 (2)

An expanded form of this expression - also available in this estimation routine - is obtained by replacing b0 in Equation 2 by :

b0j = b00(dj+1/1000) -b01 , never > 1 (2e)

These expanded forms for Si and Bij are intended to provide the model greater descriptive flexibility when tuning the model to actual specific grinding systems but, since they increment the total number of ore characteristic parameters to be estimated, its use should be avoided whenever possible. In any case, the proposed expanded forms reduce to the normal forms if both a02 and b01 are set equal to zero.On the basis of Laboratory Scale Data, like those typically obtained from batch grinding tests in small diameter ball mills, the BallParam_Batch_MultiTest routine allows for the calculation of all ak's and bk's (including dcrit,k) that minimize the least-squares Objective Function :

K n f = S S wik [(fik - fik)/fik]2 (3) k = 1 i = 1

where the fik's represent the experimental size distribution of the mill product (as % retained on screen 'i', i = 1, n ) in the kth test (k = 1, K) and the fik's represent the model response for each corresponding fik, for a given set of model parameters for each independent test. The ak's and bk's (including dcrit,k) that yield the minimum possible value of f are so considered to be representative of the particular ore and test conditions under analysis.

Also in Equation 3, the wik's represent user defined Weighting Factors that quantify the relative quality and reliability of each particular mesh value with respect to the other screens data. Relatively high values of such weighting factors indicate more reliable measurements. At the extreme, a wik 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_All and Control Panel_All worksheets. Gray background cells contain the results of the corresponding formula there defined and are protected to avoid any accidental editing.

The Incl. (1) / Del. (0) Factors in Row 6 of Control Panel_All may be used to include (set equal to 1) or delete (set equal to 0) any particular set of test results.

The remaining information required to run the program is entered in the Data_File_kth worksheet, where the user is requested to provide complementary general information about each test.

To run the program, select the objective function Cell P27 in Control_Panel_All and then, from the Tools Menu, select Solver ..., then Min and then By Changing any combination of Cells E10:N24 (see Useful Hints below). 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.

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.Useful Hints :

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

1. It is not required to run the Solver search for all parameters at the same time. In fact, this is strongly not recommended, as the search algorithm will most likely fail to find the minimizing optimum when dealing with too many parameters at once. To exclude any given parameter off the search, remove the corresponding cell reference (in the E10:N24 range in Control_Panel_All) off the By Changing list of cells in Solver and 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 (as would be the case for this application) for various ore types (hard, soft, etc.) or grinding conditions (mill filling, ball size, % solids, etc.), always attempt to obtain a reasonable model fit of these data with 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 lower Objective Function (Cell P27) values, but the values of the parameters that achieve such minimum will be less reliable in statistical terms and therefore, from one data set to another, these parameters will exhibit significant variability and covariance amongst them, rendering 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. If the model fit appears to be reasonable, then you should attempt to reduce the number of adjustable parameters. Look for the one parameter that exhibit the lowest Coefficient of Variation (the ratio of its standard deviation to its average value, for all data sets) and set it fix at its average value and equal for all data sets, for the next runs of the search. Continue removing the remaining adjustable parameters off the By Changing list, one at a time, until the model fit is no longer judged acceptable. The concept behind this parameter screening process is to lump the impact of whatever ore properties or process variable are being investigated into the least possible number of parameters in order to improve 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 all grinding systems require a finite value of dcrit; whenever the estimated value of this parameter tends to be greater than the 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 a satisfactory model fit, then you should add b1 to the list of adjustable parameters and eventually, include b01, a02 and a12 (one at a time, in that order). If the model fit is still not satisfactory, there is a good chance the data contains significant experimental errors and should be discarded.

5. Never run a search for a2 or b2, as these parameters have little effect on the objective function and may just confuse the search algorithm. When in doubt, simply try assigning them values between 2 and 4 and observe the response of the Objective Function (Cell P27). In other words, these two parameters are better optimized by a very basic trial-and-error procedure, not via the Solver routine.

Control_Panel_AllMoly-Cop Tools TM (Version 2.0)BALLPARAM_BATCH : Estimation of Grinding Parameters from Laboratory DataTest N12345678910Incl. (1) / Del. (0)1111110000SELECTION FUNCTION :AverageStd.Coeff.Dev.of Var.alpha00.0091800.0091800.0091800.0091800.0091800.0091800.0091800.0091800.0091800.0091800.0091800.0000000.000alpha10.6500.6500.6500.6500.6500.6500.6500.6500.6500.6500.6500.0000.000alpha22.52.52.52.52.52.52.52.52.52.52.50.00.000Dcrit6532653265326532653265326532653265326532653200.000Expanded Formalpha020.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000alpha121.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0000.0000.000BREAKAGE FUNCTION :beta00.200000.200000.200000.200000.200000.200000.200000.200000.200000.200000.200000.000000.000beta10.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.0000.000beta24.04.04.04.04.04.04.04.04.04.04.00.00.000Expanded Formbeta010.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000Objective Function0.000.000.000.000.000.000.000.000.000.000.00(*) Suggested Default Values : alpha02 = 0 and beta01 = 0.Test N12345678910AverageStd. Dev.Coeff. Var.Weighting Factor111111000065SELECTION FUNCTION:alpha00.009180.009180.009180.009180.009180.0091800000.0091800alpha10.650.650.650.650.650.6500000.6500alpha22.52.52.52.52.52.500002.500Dcrit6532653265326532653265320000653200Expanded Form:alpha020000000000000alpha121111110000100BREAKAGE FUNCTION:beta00.20.20.20.20.20.200000.200beta10.250.250.250.250.250.2500000.2500beta24444440000400Expanded Form:beta010000000000000Objective Function:00000000000

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &T

Data_File_AllMoly-Cop Tools TM (Version 2.0)BALLPARAM_BATCH : Estimation of Grinding Parameters from Laboratory DataRemarksBase Case ExampleTest NAllOVERALL CONDITIONS (for all Tests) :Eff. Mill Diam.Eff. Mill LengthOre DensityBalls DensityVoids Fractionftftton/m3ton/m3/11.501.252.807.750.40INDEPENDENT TEST CONDITIONS :Test N12345678910Mill Speed, % Critical74.074.074.074.074.074.074.074.074.074.0Ore Weight, kg11.10011.10011.10011.10011.10011.10011.10011.10011.10011.100% Solids (by weight)72.072.072.072.072.072.072.072.072.072.0Balls Weight, kg102.0102.0102.0102.0102.0102.0102.0102.0102.0102.0Net Power, kW0.4500.4500.4500.4500.4500.4500.4500.4500.4500.450Grinding Time, min0.501.002.004.008.0015.005.005.005.005.00Experimental Size Distributions (% Passing)iMeshOpeningMid-SizeFeedProductFeedProductFeedProductFeedProductFeedProductFeedProductFeedProductFeedProductFeedProductFeedProduct11.0525400100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.0020.7421905021997100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.0030.525127001555497.6597.9797.6598.2597.6598.6997.6599.2797.6599.7797.6599.9797.6599.4697.6599.4697.6599.4697.6599.4640.37195001098491.0092.6091.0093.9091.0095.8391.0098.0091.0099.4991.0099.9491.0098.5991.0098.5991.0098.5991.0098.59536700797885.0287.5785.0289.7085.0292.9285.0296.6485.0299.1985.0299.9285.0297.6785.0297.6785.0297.6785.0297.67644750564180.1983.3080.1985.9780.1990.1880.1995.2780.1998.8880.1999.8980.1996.7280.1996.7280.1996.7280.1996.72763350398975.7679.1975.7682.2375.7687.2575.7693.6775.7698.4975.7699.8675.7695.5875.7695.5875.7695.5875.7695.58882360281271.3674.9271.3678.2071.3683.8271.3691.5671.3697.9271.3699.8171.3694.0171.3694.0171.3694.0171.3694.019101700200366.8770.4866.8773.8666.8779.8866.8788.7966.8797.0166.8799.7366.8791.8266.8791.8266.8791.8266.8791.8210141180141661.4965.1361.4968.5961.4974.8961.4984.8461.4995.3561.4999.5461.4988.5061.4988.5061.4988.5061.4988.501120850100155.6759.3155.6762.7955.6769.2555.6779.9355.6792.7055.6799.1155.6784.1355.6784.1355.6784.1355.6784.13122860071448.6052.2548.6055.7648.6062.3348.6073.5748.6088.5048.6098.0548.6078.2148.6078.2148.6078.2148.6078.21133542550540.4144.0440.4147.5440.4154.1640.4165.7640.4182.4840.4195.7940.4170.7240.4170.7240.4170.7240.4170.72144830035731.6835.1731.6838.5631.6845.0231.6856.6031.6874.4531.6891.5631.6861.7131.6861.7131.6861.7131.6861.71156521225223.9727.1323.9730.2223.9736.1923.9747.1223.9764.9623.9784.9123.9752.0723.9752.0723.9752.0723.9752.071610015017818.2220.9718.2223.6818.2228.9218.2238.6718.2255.2618.2276.1718.2243.1718.2243.1718.2243.1718.2243.171715010612614.3116.6914.3119.0214.3123.5514.3132.0014.3146.6114.3166.5014.3135.9214.3135.9214.3135.9214.3135.9218200758911.7313.8111.7315.8511.7319.7811.7327.0911.7339.6911.7357.3811.7330.4711.7330.4711.7330.4711.7330.471927053639.9511.809.9513.619.9517.099.9523.509.9534.419.9549.679.9526.449.9526.449.9526.449.9526.442040038458.7410.418.7412.048.7415.188.7420.918.7430.528.7443.728.7423.528.7423.528.7423.528.7423.5221-4000190.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TThe top Mesh Opening must always be defined to allow 100% of the material passing through such screen.

ReportsMoly-Cop ToolsTM, Version 2.0Test N1BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min0.5Energy, kWh/ton0.34Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6597.97/97.9700040.371950091.0092.60/92.6000053670085.0287.57/87.5700064475080.1983.30/83.304679.91694096793595.03513058263595.035130582676335075.7679.19/79.1900088236071.3674.92/74.92000910170066.8770.48/70.480001014118061.4965.13/65.13000112085055.6759.31/59.31000122860048.6052.25/52.25000133542540.4144.04/44.04000144830031.6835.17/35.17000156521223.9727.13/27.130001610015018.2220.97/20.970001715010614.3116.69/16.69000182007511.7313.81/13.8100019270539.9511.80/11.8000020400388.7410.41/10.41000D80, microns46803595/35954679.91694096793595.03513058263595.0351305826MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N2BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min1.0Energy, kWh/ton0.68Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6598.25/98.2500040.371950091.0093.90/93.9000053670085.0289.70/89.7000064475080.1985.97/85.974679.91694096790076335075.7682.23/82.2302765.02324429192765.023244291988236071.3678.20/78.20000910170066.8773.86/73.860001014118061.4968.59/68.59000112085055.6762.79/62.79000122860048.6055.76/55.76000133542540.4147.54/47.54000144830031.6838.56/38.56000156521223.9730.22/30.220001610015018.2223.68/23.680001715010614.3119.02/19.02000182007511.7315.85/15.8500019270539.9513.61/13.6100020400388.7412.04/12.04000D80, microns46802765/27654679.91694096792765.02324429192765.0232442919MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N3BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min2.0Energy, kWh/ton1.35Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6598.69/98.6900040.371950091.0095.83/95.8300053670085.0292.92/92.9200064475080.1990.18/90.184679.91694096790076335075.7687.25/87.2500088236071.3683.82/83.8201716.9743891241716.974389124910170066.8779.88/79.880001014118061.4974.89/74.89000112085055.6769.25/69.25000122860048.6062.33/62.33000133542540.4154.16/54.16000144830031.6845.02/45.02000156521223.9736.19/36.190001610015018.2228.92/28.920001715010614.3123.55/23.55000182007511.7319.78/19.7800019270539.9517.09/17.0900020400388.7415.18/15.18000D80, microns46801717/17174679.91694096791716.9743891241716.974389124MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N4BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min4.0Energy, kWh/ton2.70Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.27/99.2700040.371950091.0098.00/98.0000053670085.0296.64/96.6400064475080.1995.27/95.274679.91694096790076335075.7693.67/93.6700088236071.3691.56/91.56000910170066.8788.79/88.790001014118061.4984.84/84.840854.0876464831854.0876464831112085055.6779.93/79.93000122860048.6073.57/73.57000133542540.4165.76/65.76000144830031.6856.60/56.60000156521223.9747.12/47.120001610015018.2238.67/38.670001715010614.3132.00/32.00000182007511.7327.09/27.0900019270539.9523.50/23.5000020400388.7420.91/20.91000D80, microns4680854/8544679.9169409679854.0876464831854.0876464831MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N5BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min8.0Energy, kWh/ton5.41Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.77/99.7700040.371950091.0099.49/99.4900053670085.0299.19/99.1900064475080.1998.88/98.884679.91694096790076335075.7698.49/98.4900088236071.3697.92/97.92000910170066.8797.01/97.010001014118061.4995.35/95.35000112085055.6792.70/92.70000122860048.6088.50/88.50000133542540.4182.48/82.480383.1479256902383.1479256902144830031.6874.45/74.45000156521223.9764.96/64.960001610015018.2255.26/55.260001715010614.3146.61/46.61000182007511.7339.69/39.6900019270539.9534.41/34.4100020400388.7430.52/30.52000D80, microns4680383/3834679.9169409679383.1479256902383.1479256902MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N6BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min15.0Energy, kWh/ton10.14Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.97/99.9700040.371950091.0099.94/99.9400053670085.0299.92/99.9200064475080.1999.89/99.894679.91694096790076335075.7699.86/99.8600088236071.3699.81/99.81000910170066.8799.73/99.730001014118061.4999.54/99.54000112085055.6799.11/99.11000122860048.6098.05/98.05000133542540.4195.79/95.79000144830031.6891.56/91.56000156521223.9784.91/84.910175.3574241086175.35742410861610015018.2276.17/76.170001715010614.3166.50/66.50000182007511.7357.38/57.3800019270539.9549.67/49.6700020400388.7443.72/43.72000D80, microns4680175/1754679.9169409679175.3574241086175.3574241086MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N7BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min5.0Energy, kWh/ton3.38Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.46/99.4600040.371950091.0098.59/98.5900053670085.0297.67/97.6700064475080.1996.72/96.724679.91694096790076335075.7695.58/95.5800088236071.3694.01/94.01000910170066.8791.82/91.820001014118061.4988.50/88.50000112085055.6784.13/84.130668.5136127336668.5136127336122860048.6078.21/78.21000133542540.4170.72/70.72000144830031.6861.71/61.71000156521223.9752.07/52.070001610015018.2243.17/43.170001715010614.3135.92/35.92000182007511.7330.47/30.4700019270539.9526.44/26.4400020400388.7423.52/23.52000D80, microns4680669/6694679.9169409679668.5136127336668.5136127336MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N8BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min5.0Energy, kWh/ton3.38Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.46/99.4600040.371950091.0098.59/98.5900053670085.0297.67/97.6700064475080.1996.72/96.724679.91694096790076335075.7695.58/95.5800088236071.3694.01/94.01000910170066.8791.82/91.820001014118061.4988.50/88.50000112085055.6784.13/84.130668.5136127336668.5136127336122860048.6078.21/78.21000133542540.4170.72/70.72000144830031.6861.71/61.71000156521223.9752.07/52.070001610015018.2243.17/43.170001715010614.3135.92/35.92000182007511.7330.47/30.4700019270539.9526.44/26.4400020400388.7423.52/23.52000D80, microns4680669/6694679.9169409679668.5136127336668.5136127336MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N9BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min5.0Energy, kWh/ton3.38Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.46/99.4600040.371950091.0098.59/98.5900053670085.0297.67/97.6700064475080.1996.72/96.724679.91694096790076335075.7695.58/95.5800088236071.3694.01/94.01000910170066.8791.82/91.820001014118061.4988.50/88.50000112085055.6784.13/84.130668.5136127336668.5136127336122860048.6078.21/78.21000133542540.4170.72/70.72000144830031.6861.71/61.71000156521223.9752.07/52.070001610015018.2243.17/43.170001715010614.3135.92/35.92000182007511.7330.47/30.4700019270539.9526.44/26.4400020400388.7423.52/23.52000D80, microns4680669/6694679.9169409679668.5136127336668.5136127336MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00Moly-Cop ToolsTM, Version 2.0Test N10BALL_PARAMBall Mill Grinding Model Parameter EstimatorRemarks :Base Case ExampleDESIGN AND OPERATING CONDITIONSConfiguration : BATCHOre, kg11.1Eff. Diameter, ft1.50Water, lt4.3Eff. Length, ft1.25Slurry, kg15.4Balls Filling, %35.0Slurry, lt8.3Speed, % Critical74.0Slurry Dens., kg/lt1.862App. Dens., ton/m35.353% Solids (by weight)72.0Power, kW0.45Grinding Time, min5.0Energy, kWh/ton3.38Particle Size Distributions (Cumm. % Passing)iMeshOpeningFeedDischargeExp.Adj.11.0525400100.00100.00/100.0000020.74219050100.00100.00/100.0000030.5251270097.6599.46/99.4600040.371950091.0098.59/98.5900053670085.0297.67/97.6700064475080.1996.72/96.724679.91694096790076335075.7695.58/95.5800088236071.3694.01/94.01000910170066.8791.82/91.820001014118061.4988.50/88.50000112085055.6784.13/84.130668.5136127336668.5136127336122860048.6078.21/78.21000133542540.4170.72/70.72000144830031.6861.71/61.71000156521223.9752.07/52.070001610015018.2243.17/43.170001715010614.3135.92/35.92000182007511.7330.47/30.4700019270539.9526.44/26.4400020400388.7423.52/23.52000D80, microns4680669/6694679.9169409679668.5136127336668.5136127336MODEL PARAMETERSSelectionBreakagealpha010.009180beta000.20000alpha020.0000000beta010.000alpha110.650beta10.250alpha121.000beta24.000alpha22.500Dcrit6532Obj. Function0.00

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &T

Control_Panel_01Moly-Cop Tools TM (Version 2.0)BALLPARAM_BATCH : Estimation of Grinding Parameters from Laboratory DataTest N1SELECTION FUNCTION :alpha00.009180alpha10.650alpha22.5Dcrit6532Expanded Formalpha020.000000alpha121.000BREAKAGE FUNCTION :beta00.20000beta10.250beta24.0Expanded Formbeta010.000Objective Function0.00Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.(*) Suggested Default Values : alpha02 = 0 and beta01 = 0.

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TTo minimize this value, use Tools / Solver / Min, by changing any combination of Cells E10:E24.

Control_Panel_011001001002.79705858081001001004.995054697997.647831285797.968564215997.96856421598.32366838990.999624813292.601371321692.601371321611.913792635285.020220866987.572689637287.572689637214.877832796380.1937528383.296439454783.296439454715.571538796775.763753819879.18562431679.18562431614.284064738371.35819893274.92478878274.92478878212.214914657466.869281850270.476899902370.476899902310.039104153561.485142579265.126542437865.12654243788.114956760755.666483899459.307816734859.30781673486.547717291348.60075361352.250907339152.25090733915.238985057340.407764359344.036903983544.03690398354.186298273331.684739374535.169618847635.16961884763.340712187723.96770355227.129648970727.12964897072.667337784718.217715336520.971216499820.97121649982.129483410114.312193150416.689893691916.68989369191.700014179911.72680269513.807198953913.80719895391.35713569849.948750593711.799329949811.79932994981.08807869958.738997608610.411385994410.4113859944

FeedDischarge (Exp.)Discharge (Adjusted)SiE * 10Particle Size, microns% Passing



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Control_Panel_031001001002.79705858081001001004.995054697997.647831285798.691399789698.69139978968.32366838990.999624813295.831152264595.831152264511.913792635285.020220866992.923973502192.923973502114.877832796380.1937528390.184605690490.184605690415.571538796775.763753819887.246634669387.246634669314.284064738371.35819893283.824230852783.824230852712.214914657466.869281850279.883406777279.883406777210.039104153561.485142579274.891220320474.89122032048.114956760755.666483899469.2529593569.252959356.547717291348.60075361362.334115008462.33411500845.238985057340.407764359354.163107401454.16310740144.186298273331.684739374545.018511807345.01851180733.340712187723.96770355236.186923310236.18692331022.667337784718.217715336528.918966314528.91896631452.129483410114.312193150423.552013792423.55201379241.700014179911.72680269519.784473693319.78447369331.35713569849.948750593717.090429066817.09042906681.08807869958.738997608615.175813787515.1758137875




Control_Panel_041001001002.79705858081001001004.995054697997.647831285799.271976325499.27197632548.32366838990.999624813297.996277322997.996277322911.913792635285.020220866996.638168291396.638168291314.877832796380.1937528395.270729625595.270729625515.571538796775.763753819893.666948095693.666948095614.284064738371.35819893291.562057329991.562057329912.214914657466.869281850288.78751508188.78751508110.039104153561.485142579284.837382373484.83738237348.114956760755.666483899479.930320848879.93032084886.547717291348.60075361373.567235284873.56723528485.238985057340.407764359365.756196514565.75619651454.186298273331.684739374556.598957471956.59895747193.340712187723.96770355247.117495048347.11749504832.667337784718.217715336538.670865771738.67086577172.129483410114.312193150431.995063595631.99506359561.700014179911.72680269527.089965137427.08996513741.35713569849.948750593723.499445065323.49944506531.08807869958.738997608620.90507053320.905070533




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Control_Panel_091001001002.79705858081001001004.995054697997.647831285799.456981331399.45698133138.32366838990.999624813298.592836324298.592836324211.913792635285.020220866997.666760612497.666760612414.877832796380.1937528396.719468324596.719468324515.571538796775.763753819895.577900050995.577900050914.284064738371.35819893294.012893429794.012893429712.214914657466.869281850291.823885353891.823885353810.039104153561.485142579288.504053291288.50405329128.114956760755.666483899484.127249860984.12724986096.547717291348.60075361378.208644592378.20864459235.238985057340.407764359370.722288850970.72228885094.186298273331.684739374561.710218698561.71021869853.340712187723.96770355252.071759246952.07175924692.667337784718.217715336543.172664825643.17266482562.129483410114.312193150435.916487549835.91648754981.700014179911.72680269530.470262616730.47026261671.35713569849.948750593726.442391281126.44239128111.08807869958.738997608623.517480362623.5174803626




Control_Panel_101001001002.79705858081001001004.995054697997.647831285799.456981331399.45698133138.32366838990.999624813298.592836324298.592836324211.913792635285.020220866997.666760612497.666760612414.877832796380.1937528396.719468324596.719468324515.571538796775.763753819895.577900050995.577900050914.284064738371.35819893294.012893429794.012893429712.214914657466.869281850291.823885353891.823885353810.039104153561.485142579288.504053291288.50405329128.114956760755.666483899484.127249860984.12724986096.547717291348.60075361378.208644592378.20864459235.238985057340.407764359370.722288850970.72228885094.186298273331.684739374561.710218698561.71021869853.340712187723.96770355252.071759246952.07175924692.667337784718.217715336543.172664825643.17266482562.129483410114.312193150435.916487549835.91648754981.700014179911.72680269530.470262616730.47026261671.35713569849.948750593726.442391281126.44239128111.08807869958.738997608623.517480362623.5174803626


Data_File_01Moly-Cop Tools TM (Version 2.0)BALLPARAM_BATCH : Estimation of Grinding Parameters from Laboratory DataRemarksBase Case ExampleTest N1Mill Dimensions and Operating ConditionsNetDiameterLengthSpeedChargeBallsInterstitialPowerPower Decomposition, kWftft% CriticalFilling, %Filling, %Slurry Filling,%kWBallsOverfillingSlurry1.501.2574.035.035.094.40.4500.3910.0000.059rpm46.28Ore Weight,11.1kgBalls Weight,102.0kgApp.Grinding Time,0.50minOre Density,2.80ton/m3Balls Density,7.75ton/m3Charge% Solids (by weight)72.0%Voids Fraction,0.40/1Density,Total Energy,0.34kWh/tonSlurry Density,1.862ton/m3Balls Volume (app.),21.9literston/m3Balls Energy,0.29kWh/tonSlurry Weight,15.4kgMill Volume,62.7liters5.353Slurry Volume,8.3litersOverfilling,0.0litersFeed Size DistributionsObjective FunctionMill FeedMill Disch. (exp)Mill Disch. (adj)% Passing%wiwi (error)^2iMeshOpeningMid-Size% Ret% Pass% Ret% Pass% Ret% PassExpAdj.Error11.0525400100.00100.00100.0020.74219050219970.00100.000.00100.00-0.00100.00100.00100.000.0010.0030.52512700155542.3597.652.0397.972.0397.9797.9797.970.0010.0040.3719500109846.6591.005.3792.605.3792.6092.6092.600.0010.0053670079785.9885.025.0387.575.0387.5787.5787.570.0010.0064475056414.8380.194.2883.304.2883.3083.3083.300.0010.0076335039894.4375.764.1179.194.1179.1979.1979.190.0010.0088236028124.4171.364.2674.924.2674.9274.9274.920.0010.00910170020034.4966.874.4570.484.4570.4870.4870.480.0010.001014118014165.3861.495.3565.135.3565.1365.1365.130.0010.00112085010015.8255.675.8259.315.8259.3159.3159.310.0010.0012286007147.0748.607.0652.257.0652.2552.2552.250.0010.0013354255058.1940.418.2144.048.2144.0444.0444.040.0010.0014483003578.7231.688.8735.178.8735.1735.1735.170.0010.0015652122527.7223.978.0427.138.0427.1327.1327.130.0010.00161001501785.7518.226.1620.976.1620.9720.9720.970.0010.00171501061263.9114.314.2816.694.2816.6916.6916.690.0010.001820075892.5911.732.8813.812.8813.8113.8113.810.0010.001927053631.789.952.0111.802.0111.8011.8011.800.0010.002040038451.218.741.3910.411.3910.4110.4110.410.0010.0021-4000198.740.0010.410.0010.410.000.000.000.0000.00sum19.000.00

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TRotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.Actual measurement of the Net Mill Power Draw, i. e. discounting all losses.The top Mesh Opening must always be defined to allow 100% of the material passing through such screen.The top Mesh Opening must always be defined to allow 100% of the material passing through such screen.The top Mesh Opening must always be defined to allow 100% of the material passing through such screen.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.See Mill Power_Ball Mills for further details.User defined Weighting Factor, included to represent the relative quality and reliability of this particular measurement with respect to the rest of the available data.At the extreme, a value equal to zero means that this measurement is not included in the Objective Function calculation.



Data_File_03Moly-Cop Tools TM (Version 2.0)BALLPARAM_BATCH : Estimation of Grinding Parameters from Laboratory DataRemarksBase Case ExampleTest N3Mill Dimensions and Operating ConditionsNetDiameterLengthSpeedChargeBallsInterstitialPowerPower Decomposition, kWftft% CriticalFilling, %Filling, %Slurry Filling,%kWBallsOverfillingSlurry1.501.2574.035.035.094.40.4500.3910.0000.059rpm46.28Ore Weight,11.1kgBalls Weight,102.0kgApp.Grinding Time,2.00minOre Density,2.80ton/m3Balls Density,7.75ton/m3Charge% Solids (by weight)72.0%Voids Fraction,0.40/1Density,Total Energy,1.35kWh/tonSlurry Density,1.862ton/m3Balls Volume (app.),21.9literston/m3Balls Energy,1.17kWh/tonSlurry Weight,15.4kgMill Volume,62.7liters5.353Slurry Volume,8.3litersOverfilling,0.0litersFeed Size DistributionsObjective FunctionMill FeedMill Disch. (exp)Mill Disch. (adj)% Passing%wiwi (error)^2iMeshOpeningMid-Size% Ret% Pass% Ret% Pass% Ret% PassExpAdj.Error11.0525400100.00100.00100.0020.74219050219970.00100.00-0.00100.00-0.00100.00100.00100.000.0010.0030.52512700155542.3597.651.3198.691.3198.6998.6998.690.0010.0040.3719500109846.6591.002.8695.832.8695.8395.8395.830.0010.0053670079785.9885.022.9192.922.9192.9292.9292.920.0010.0064475056414.8380.192.7490.182.7490.1890.1890.180.0010.0076335039894.4375.762.9487.252.9487.2587.2587.250.0010.0088236028124.4171.363.4283.823.4283.8283.8283.820.0010.00910170020034.4966.873.9479.883.9479.8879.8879.880.0010.001014118014165.3861.494.9974.894.9974.8974.8974.890.0010.00112085010015.8255.675.6469.255.6469.2569.2569.250.0010.0012286007147.0748.606.9262.336.9262.3362.3362.330.0010.0013354255058.1940.418.1754.168.1754.1654.1654.160.0010.0014483003578.7231.689.1445.029.1445.0245.0245.020.0010.0015652122527.7223.978.8336.198.8336.1936.1936.190.0010.00161001501785.7518.227.2728.927.2728.9228.9228.920.0010.00171501061263.9114.315.3723.555.3723.5523.5523.550.0010.001820075892.5911.733.7719.783.7719.7819.7819.780.0010.001927053631.789.952.6917.092.6917.0917.0917.090.0010.002040038451.218.741.9115.181.9115.1815.1815.180.0010.0021-4000198.740.0015.180.0015.180.000.000.000.0000.00sum19.000.00
















Model_01Selection Function :Breakage Function :alpha01alpha02alpha11alpha12alpha2dcritBeta00Beta01Beta1Beta20.0091800.6512.565320.200.254iMeshOpeningMid-SizeSiEiMeshOpeningBeta0JCummulativeiMeshOpeningPartial11.052540021997.04525612470.279705858111.05254000.2111.052540002.797058580820.7421905015554.25986667320.499505469820.742190500.21120.742190500.661254907904.995054697930.5251270010984.07938791410.832366838930.525127000.20.33874509211130.525127000.1211991430.563523311308.32366838940.37195007978.09501071531.191379263540.37195000.20.21754594910.43647668871140.37195000.05128593260.20405741510.6187965309011.91379263525367005641.36508302731.48778327965367000.20.16626001650.23241927370.3812034691115367000.02183922730.060358740.1630241860.6143799633014.87783279636447503989.04750535761.55715387976447500.20.14442078910.17206053370.21817928310.3856200367116447500.01414152060.02485642780.05168867810.16744075360.6187965309015.57153879677633502811.76101402661.42840647387633500.20.13027926850.14720410590.16649060490.21817928310.3812034691117633500.01143632470.01493736010.0222462790.05178663330.16454160490.6197279266014.28406473838823602002.99775336871.22149146578823600.20.11884294380.13226674580.1442443260.16639264970.21666186410.3802720734118823600.00948004780.01103610850.01334375240.02113074410.04884415860.15841616570.6003511321012.214914657491017001416.33329410841.003910415491017000.20.1093628960.12123063730.13090057360.14526190560.16781770550.22185590780.39964886791191017000.00957496650.01075055190.01197765310.01492897130.02357337960.0554632580.18146958490.6317428388010.0391041535101411801001.49887668430.8114956761101411800.20.09978792950.11048008540.11892292040.13033293430.1442443260.16639264970.21817928310.368257161211101411800.0078645540.00873760420.00948764320.01076371440.01334375240.02113074410.04977946720.15007787820.600351132108.11495676071120850714.14284285430.654771729111208500.20.09192337550.10174248120.10943527720.11956921990.13090057360.14526190560.16839981580.21817928310.39964886791111208500.00766790240.00849535840.00916042260.01010976150.01146447370.01432990530.02304067620.05161136190.17728445530.618060325806.54771729131228600504.97524691810.523898505712286000.20.0842554730.09324712290.10027485460.10945945840.11943609990.13093200030.14535913970.16656792120.22236441260.38193967421112286000.00695990440.00770473060.00829103140.00907544220.01000082270.01136278040.0142313060.0220215650.05396459670.16376039120.615128410805.23898505731335425357.07142142710.418629827313354250.20.07729556870.08554239230.09198382320.10038401620.10943527720.11956921990.13112783370.14454635620.16839981580.21817928310.38487158921113354250.00644605620.00713432320.00767296580.00837999940.00916042260.01010976150.01149749780.01414272480.02304067620.05161136190.16669230610.618060325804.18629827331448300252.19040425840.334071218814483000.20.07084951240.07840806910.08431085740.09200401670.10027485460.10945945840.11963033590.13040363150.14535913970.16656792120.21817928310.38193967421114483000.00589036780.00651890960.00701002440.00765123890.00834521550.00913465770.01008534170.01135945440.01431590380.02213413560.05151329530.16432833750.61712520403.34071218771565212178.32554500130.266733778515652120.20.06495914470.07188915950.07730083310.08435277780.09192963910.10032480070.10954499410.11904417710.13104323580.14443378560.16666598780.21761133670.3828747961115652120.0053820820.00595628920.00640475450.00698943310.00761878170.0083207840.00911087630.00999215190.01141290.01403015410.02211963150.05104341550.1646955130.616071933802.667337784716100150126.09520212920.212948341161001500.20.05957706270.06593287030.07089607850.07736334480.08431085740.09200401670.10043411780.10905202520.11963033590.13040363150.14454635620.16656792120.21817928310.383928066211161001500.00495316040.00548158220.00589423950.00643202050.00701002440.00765123890.00835867450.00909880820.01008534170.01135945440.01410327810.02213413560.05151329530.16574878310.61712520402.12948341011715010689.16277250060.170001418171501060.20.05462390240.06045128820.0650018390.07093132430.07730083310.08435277780.09207544330.0999532170.10954499410.11904417710.13044307820.14443378560.16666598780.21817928310.38287479611171501060.00452576630.0050085860.00538561940.00587692140.00640475450.00698943310.00763091630.0082895050.00911087630.00999215190.01132705420.01403015410.02211963150.05140302450.1646955130.616071933801.7000141799182007563.04760106460.135713569818200750.20.05009813610.05544270220.05961621960.06505440280.07089607850.07736334480.0844445270.0916637120.10043411780.10905202520.1191160240.13040363150.14454635620.16677625860.21817928310.38392806621118200750.0041650930.00460943370.00495641590.00540854550.00589423950.00643202050.00702115110.00762282290.00835867450.00909880820.01003351680.01135945440.01410327810.02222990230.05151329530.16574878310.61712520401.3571356984192705344.87761134460.1088078719270530.20.04593304310.05083326850.05465980370.05964585730.0650018390.07093132430.07742337590.08404088910.09207544330.0999532170.10908250720.119044177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Ballparam Batch jMultitest