About ...About the Ballbal_Direct Spreadsheet ...

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

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, fiCF, fiU and fiO 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, fiU and fiO, such that the objective functions :

fi = [ wCF (fiCF - fiCF)2 + wU (fiU - fiU)2 + wO(fiO - fiO)2 ] ,for every particle size di

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

fiCF CF = fiU U + fiO 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 iwhere 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;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, d50c 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, d50c 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.&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&C&8Page &P&R&8&D / &T

Data_FileMoly-Cop Tools TMBALLBAL : Mass Balance Closure around a Ball Mill Grinding CircuitCircuit TypeDIRECTSample N1RemarksBalance circuito de molienda Molino # 1 , Fecha de muestreo 03/06/15Mill Dimensions and Operating Conditions1827BallsChargeMill Charge Weight, tonsApparentDiameterLengthSpeedChargeBallsInterstitialLift0OverfillingVolume,BallSlurryDensityftft% CriticalFilling,%Filling,%Slurry Filling,%Angle, ()338Slurrym3ChargeInterstitialExcesston/m315.519.575.242.0042.00100.0030.92165Net Power43.85203.8937.740.005.511NO DATA INPUT REQUIRED IN THIS SECTORrpm14.635.3% Losses2286Gross kWFeedrate, ton/hr (dry)275.4Cyclone Dimensions (inches) and Operating Pressure (psi)NumberDiameterHeightInletVortexApexpsiOre Density, ton/m33.00326.075.010.0010.005.506.90Balls Density, ton/m37.75EXPERIMENTAL SIZE DISTRIBUTIONSFresh FeedMill DischargeCyclone FeedCyclone U'flowCyclone O'flowCirc.LambdaCyclone Feed (pre-adjusted)Cyclone O'flow (pre-adjusted)Cyclone U'flow (pre-adjusted)iMeshOpeningMid-Sizeton/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% PassingLoadton/hr% Retained% Passingadj.ton/hr% Retained% Passingadj.ton/hr% Retained% Passingadj.11.0525400100.00100.00100.00100.00100.00100.000.00100.000.00100.000.0020.74219050219970.000.00100.00.000.00100.00.000.00100.000.000.00100.00.000.00100.00.000000.000.00100.000.000.000.00100.000.000.000.00100.000.0030.52512700155540.000.00100.00.000.00100.00.000.00100.000.000.00100.00.000.00100.00.000000.000.00100.000.000.000.00100.000.000.000.00100.000.0040.37195001098482.6530.0170.078.114.2795.789.874.2795.7340.142.2097.80.000.00100.00.3491861.822.9497.061.330.480.1799.83(0.17)61.343.3596.65(1.16)50.256730799665.3223.7246.398.485.3990.3113.315.3990.3496.315.2792.50.000.00100.00.11937103.724.9392.131.790.160.0699.77(0.23)103.565.6690.98(1.56)644750565429.4210.6835.656.443.0987.364.943.0987.2660.473.3189.20.000.00100.00.0313862.422.9789.161.910.040.0299.75(0.25)62.373.4187.57(1.66)782360334838.2213.8821.7124.526.8180.4143.286.8180.45147.148.0581.20.000.00100.0(0.02710)145.466.9182.251.81-0.04-0.0199.76(0.24)145.507.9679.61(1.57)810170020039.943.6118.172.373.9676.583.273.9676.4992.735.0776.10.190.0799.9(0.06779)88.714.2278.031.550.100.0499.73(0.20)88.614.8574.77(1.34)914118014167.012.5415.696.785.2971.2111.365.2971.19122.786.7169.41.280.4699.5(0.08913)118.525.6372.401.211.150.4299.31(0.16)117.376.4268.35(1.05)102085010014.931.7913.8122.596.7064.5141.066.7064.49159.008.7060.73.221.1798.3(0.14853)152.997.2765.130.643.011.0998.21(0.08)149.988.2060.14(0.56)11286007143.651.3212.5191.9410.5054.0220.8510.5053.99231.2812.6548.15.932.1596.17.095(0.11492)230.0810.9454.190.205.782.1096.12(0.03)224.3112.2747.88(0.17)12354255053.431.2511.2225.0012.3141.7258.8912.3141.69279.4615.2832.818.196.6089.55.365(0.27212)280.7613.3540.85(0.84)17.826.4789.650.11262.9414.3833.500.7313483003572.991.0910.1178.229.7531.9205.069.7531.94198.2010.8421.924.889.0380.54.851(0.12648)215.2210.2330.62(1.32)24.708.9780.680.17190.5210.4223.081.1514652122522.971.089.0124.576.8125.1143.336.8125.13116.686.3815.532.6311.8568.74.544(0.04196)146.716.9723.64(1.48)32.5811.8368.850.19114.136.2416.831.29151001501783.021.097.986.414.7320.499.434.7320.4065.873.6011.932.8411.9256.74.2960.0050299.024.7118.94(1.46)32.8511.9356.930.1966.183.6213.221.27161501061262.380.867.151.482.8217.659.242.8217.5834.081.8610.120.837.5649.24.2090.0304456.792.7016.24(1.35)20.877.5849.350.1835.921.9611.251.171720075892.450.896.246.092.5215.153.032.5215.0625.011.378.724.849.0240.23.9500.0223351.242.4413.80(1.26)24.879.0340.320.1726.371.449.811.101827053632.150.785.435.251.9313.140.561.9313.1419.411.067.712.654.5935.64.0880.0597235.761.7012.10(1.03)12.734.6235.700.1423.031.268.550.901932544481.010.365.016.070.8812.318.490.8812.268.110.447.26.272.2833.34.1630.0288416.170.7711.33(0.92)6.312.2933.410.129.860.548.010.802040038410.860.314.714.160.7711.516.290.7711.487.260.406.85.522.0031.3Circ. Load0.0246514.310.6810.65(0.83)5.552.0231.390.118.760.487.530.7221-40001913.054.740.00209.9611.480.00241.5811.480.00124.506.810.0086.1631.280.00W. Factors0.21712224.1410.6586.4631.39137.687.53Totals275.42100.001828.43100.002103.85100.001828.43100.00275.42100.0014.7292103.85100.00275.42100.001828.43100.00% Solids93.0880.3070.0076.8339.7718.548(0.00005)69.13(0.87)39.800.0477.760.93Slurry Density, ton/m32.6352.1521.8752.0501.361Weighting Factor0.0001.0001.0001.0001.000CL (ave)6.63993.088552915880.267299404481.804442483236.1884721402

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TMill Diameter, inside liners.Effective Grinding Lenght.Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill.See Mill Power_Ball Mills for further details.Free Cyclone Height,defined as the distance from the bottom end of the vortex finder to the top end of the apex.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.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.Component of the Total Mill Power Draw (Cell K11) contributed by the Ball Charge.Component of the Total Mill Power Draw (Cell K11) contributed by the Overfilling Slurry on top of the "kidney".Component of the Total Mill Power Draw (Cell K11) contributed by the Interstitial Slurry in the ball charge.Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids).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).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.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.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.&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &T

Control_PanelMoly-Cop Tools TMBallbal_Direct : MASS BALANCE CLOSURE AROUND A BALL MILL GRINDING CIRCUITSample N1Weighting Factors :Streams :Fresh Feed0Mill Discharge1Cyclone Feed1Cyclone U'flow1Cyclone O'flow1Size Distributions1% Solids1Initial Guesses :BpfBpcd50cm0.5350.015293.92.4244Obj. Function :0.018Classifier Constants :a14.11a20.856a351.82a41.205l1.129Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TRelative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams.Default Value : 1Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams.Default Value : 1Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses.Default Value : 1Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses.Default Value : 1Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams.Default Value : 1Fractional short-circuit of slurry to the cyclone overflow.Default Value : 0To minimize this value, use Tools / Solver / Min, by changing any combination of Cells C20:F20.See Cyclosim_Single spreadsheet for further reference.See Cyclosim_Single spreadsheet for further reference.See Cyclosim_Single spreadsheet for further reference.See Cyclosim_Single spreadsheet for further reference.See Cyclosim_Single spreadsheet for further reference.

Control_Panel10010010010010010010010010010010010010010010010010010010010010095.72809360397.804450342610097.061716218296.574685471599.709235203569.990290286990.342108609992.536950163410092.131634035490.827425036199.221367302146.275153179187.255500445189.229813168210089.164869046287.368908441198.927784080635.594468811780.445122726781.182481216110082.25098541879.309024577598.243604431721.718507605976.487345796876.111144728899.929395982678.034300414274.393409382397.826332429418.108056829771.194200686869.396240630699.465762935272.400728210267.826053010297.268849014915.564558431364.489380643560.700388988198.298119987565.128616901859.348569068496.549192460313.775515898353.992114968848.051255055796.143651635654.192418430246.614596550995.385766960812.450753897841.686379244632.767122086989.538988930640.847360839731.598773430891.123058872611.205232084531.939463309221.927315967780.506875134830.617362009321.465880612480.365187804310.118190645225.126542032315.546090350668.658179634723.644174784715.638304741767.16441057659.041193736720.40061045411.943476267556.73424715418.937399867412.190080849855.6161009997.946339884617.584891262910.079829438849.172015682516.23793623310.357998200548.20151898437.083626298815.06422485068.711771190440.154441068113.80257094288.766774027341.17736818366.194127297713.13620755447.650214725635.562449227812.10264637857.675321348536.16976565425.414002075912.2574081147.206513832933.286420394611.33399055787.184992209333.88811465135.049050791811.48289456956.809237023931.282342901510.6536328826.752026798631.86292254084.7376703385

Mill DischargeCyclone U'flowCyclone O'flowFresh FeedParticle Size, microns% Passing

FlowsheetMoly-Cop Tools TMSample N1RemarksBalance circuito de molienda Molino # 1 , Fecha de muestreo 03/06/1539.80% Solids51.80% - Size malla 150psi6.90297.4P80# of Cyclones3Vortex10.00Circ. Load543.60Apex5.500.535Bpfm3/hr13820.474Bpw% Solids79.97Water,m3/hr356.6ton/hr275.4Water,39.5F8010591m3/hrGross kW2285.5kWh/ton8.30% Balls42.00Wio17.19% Critical75.19% Solids80.30% Solids69.13

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

ReportsMoly-Cop Tools TMSample N1BALLBALGrinding Circuit Mass Balance EstimatorRemarks :Balance circuito de molienda Molino # 1 , Fecha de muestreo 03/06/15CIRCUIT MASS BALANCEConfiguration : DIRECTFreshMillMillSumpCycloneCycloneCycloneFeedFeedDischargeWaterFeedU'flowO'flowOre, ton/hr275.41772.61772.60.01772.61497.2275.4Water, m3/hr20.5395.4434.9356.6791.5374.9416.5Slurry, ton/hr295.92168.02207.5356.62564.11872.1691.9Slurry, m3/hr112.3986.31025.7356.61382.3874.0508.3Slurry Dens., ton/m32.6352.1982.1521.0001.8552.1421.361% Solids (by volume)81.859.957.60.042.757.118.1% Solids (by weight)93.181.880.30.069.180.039.8Particle Size Distributions (Cummulative % Passing)iMeshOpening11.0525400100.00100.00100.000.00100.00100.00100.00000000020.74219050100.00100.00100.000.00100.00100.00100.00000000030.52512700100.00100.00100.000.00100.00100.00100.0010591.4627307500000040.371950069.9992.4497.060.0097.0696.5799.71000000050.25673046.2883.9192.130.0092.1390.8399.2205006.69700578570000064475035.5979.3289.160.0089.1687.3798.93000002512.689479068078236021.7270.3682.250.0082.2579.3198.24001985.157986715801985.157986715800810170018.1165.6578.030.0078.0374.3997.830000000914118015.5659.7172.400.0072.4067.8397.270000000102085013.7852.2765.130.0065.1359.3596.550000000112860012.4541.3154.190.0054.1946.6195.390000000123542511.2128.4340.850.0040.8531.6091.120000000134830010.1219.7030.620.0030.6221.4780.37000000297.36786901314652129.0414.6123.640.0023.6415.6467.160000000151001507.9511.5318.940.0018.9412.1955.620000000161501067.089.8516.240.0016.2410.3648.20000000017200756.198.3713.800.0013.808.7741.18000000018270535.417.3212.100.0012.107.6836.17000000019325445.056.8511.330.0011.337.1833.89000000020400384.746.4410.650.0010.656.7531.860000000D80, microns1059150071985019852513297.410591.462730755006.69700578571985.157986715801985.15798671582512.689479068297.367869013Specific Energy Consumption :8.30KWH/ton (Gross)Operational Work Index :17.19KWH/tonMoly-Cop Tools TMSample N1BALLBALGrinding Circuit Mass Balance EstimatorRemarks :Balance circuito de molienda Molino # 1 , Fecha de muestreo 03/06/15CLASSIFIERS PERFORMANCENumber of Cyclones :3Operating Conditions :Cyclone Dimensions, in :Feed Flowrate, m3/hr1382.3Diameter26.00Pressure, psi6.9Height75.00D50 (corr.), microns293.9Inlet10.00Water By-Pass, %47.4Vortex10.00Solids By-Pass, %53.5Apex5.50Plitt's Parameter2.42Ore Density, ton/m33.00Circulating Load, %544Mass Balance around the ClassifiersSize Distributions, % PassingClassifier EfficiencyiMeshOpeningMid-SizeFeedU'flowO'flowActualCorrected11.052540021997100.00100.00100.000.9851.00020.7421905015554100.00100.00100.000.9851.00030.5251270010984100.00100.00100.000.9851.00040.3719500799697.0696.5799.710.9851.00050.256730565492.1390.8399.220.9851.000644750334889.1687.3798.930.9851.000782360200382.2579.3198.240.9851.0008101700141678.0374.3997.830.9851.0009141180100172.4067.8397.270.9851.000102085071465.1359.3596.550.9830.997112860050554.1946.6195.390.9500.924123542535740.8531.6091.120.8370.671134830025230.6221.4780.370.7060.380146521217823.6415.6467.160.6190.1871510015012618.9412.1955.620.5730.085161501068916.2410.3648.200.5520.03817200756313.808.7741.180.5420.01618270534812.107.6836.170.5390.00919325444111.337.1833.890.5380.00620400381910.656.7531.860.5350.001Ore, ton/hr1772.61497.2275.4Classifier ConstantsWater, m3/hr791.5374.9416.5Slurry, ton/hr2564.11872.1691.9a14.108Slurry, m3/hr1382.3874.0508.3a20.856Slurry Dens., ton/m31.8552.1421.361a351.824% Solids (by volume)42.757.118.1a41.205% Solids (by weight)69.180.039.8l1.129Moly-Cop Tools TMSample N1BALLBALGrinding Circuit Mass Balance EstimatorRemarks :Balance circuito de molienda Molino # 1 , Fecha de muestreo 03/06/15BALL MILL PERFORMANCEDiameter, ft15.5Mill Power, kW (Gross)2286Length, ft19.5Mill Power, kW (Net)2165Speed, % Critical75.2Throughput, ton/hr1772.6App. Density, ton/m35.51% Solids (by weight)81.8Charge Level, %42.0Sp. Energy, KWH/ton1.29Balls Filling, %42.0Reduction Ratio2.52Lift Angle, ()30.9Size DistributionsMillMilliMeshOpeningMid-SizeFeedDischarge11.052540021997100.00100.0020.7421905015554100.00100.0030.5251270010984100.00100.0040.3719500799692.4497.0650.256730565483.9192.13644750334879.3289.16782360200370.3682.258101700141665.6578.039141180100159.7172.40102085071452.2765.13112860050541.3154.19123542535728.4340.85134830025219.7030.62146521217814.6123.641510015012611.5318.9416150106899.8516.241720075638.3713.801827053487.3212.101932544416.8511.332040038196.4410.65D80, microns50071985

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

CNumber of Cyclones3Classifier Dimensions, inches.DChDIDODU267510105.5Classifier Constantsa1a2a3a4lCycloneCycloneCyclone4.10766467180.856107359251.823792161.20514616541.1291263638FeedU'flowO'flowCirculating Load, CL5.4360407498Solids, tons701.28592.32108.9619472191Slurry Split, S1.7193518295Water, m3/hr313.12148.33164.79Cyclone Pressure, ft8.5909768341Slurry, tons1014.4011563622740.6535521327273.7476042295Cyclone Pressure, lb/in26.90Slurry, m3/hr546.8788013749345.7724952914201.1063060835Corrected Cut Size, d50c, microns293.8699092649Solids Density, ton/m3333Water By-Pass0.4737260236Slurry Density, ton/m31.85489207812.14202564471.3612084552Fines By-Pass0.5348965424% Solids (by volume)42.74460390657.101282233118.0604227587Coarse By-Pass0.0153755019% Solids (by weight)69.1379.9739.80Plitt's Parameter2.4244024258ton/hr (model)% Retained (model)% Passing (model)% Passing (exp)(Weighted Error)^2OpeningMid-SizeClassifierCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneCycloneEfficiencyFeedU'flowO'flowFeedU'flowO'flowFeedU'flowO'flowFeedU'flowO'flowFeedU'flowO'flow111125400100.00100.00100.00100.00100.00100.0021905021997.04525612470.98462449810.0000.000.000.000.00100.00100.00100.00100.00100.00100.000.0000.0000.00031270015554.25986667320.98462449810.0000.000.000.000.00100.00100.00100.00100.00100.00100.000.0000.0000.0004950010984.07938791410.984624498161.8260.86663194580.952.943.430.2997.0696.5799.7197.0697.80100.000.0000.0000.000567307995.93646798170.9846244981103.72102.1267923611.594.935.750.4992.1390.8399.2292.1392.54100.000.0000.0000.000647505653.98089844670.984624498162.4261.45662096650.962.973.460.2989.1687.3798.9389.1689.23100.000.0000.0000.000723603348.13380855660.9846244981145.46143.22129561362.246.918.060.6882.2579.3198.2482.2581.18100.000.0000.0010.000817002002.99775336870.984624498188.7187.34874954811.364.224.920.4278.0374.3997.8378.0376.1199.930.0000.0010.000911801416.33329410840.9846244981118.52116.69960811931.825.636.570.5672.4067.8397.2772.4069.4099.470.0000.0010.000108501001.49887668430.9846239075152.99150.64190182322.357.278.480.7265.1359.3596.5565.1360.7098.300.0000.0000.00011600714.14284285430.98347074230.08226.27820364723.8010.9412.731.1654.1946.6195.3954.1948.0596.140.0000.0010.00012425504.97524691810.9503697623280.76266.825884635413.9313.3515.024.2640.8531.6091.1240.8532.7789.540.0000.0010.00013300357.07142142710.8366075572215.22180.057934124235.1710.2310.1310.7630.6221.4780.3730.6221.9380.510.0000.0000.00014212252.19040425840.7058631812146.71103.553969339243.156.975.8313.2023.6415.6467.1623.6415.5568.660.0000.0000.00015150178.32554500130.618779539299.0261.273723259837.754.713.4511.5518.9412.1955.6218.9411.9456.730.0000.0000.00016106126.09520212920.573233415756.7932.555462975324.242.701.837.4116.2410.3648.2016.2410.0849.170.0000.0010.000177589.16277250060.551862868851.2428.275492742722.962.441.597.0213.808.7741.1813.808.7140.150.0000.0000.001185363.04760106460.5422994735.7619.394729427716.371.701.095.0112.107.6836.1712.107.6535.560.0000.0000.000194448.29078587060.538790216916.178.71297599137.460.770.492.2811.337.1833.8911.337.2133.290.0000.0000.000203840.89009660050.537501687214.317.69364275236.620.680.432.0310.656.7531.8610.656.8131.280.0000.0000.000210190.5353038275224.14119.981136513104.1610.656.7531.86OverallTotal2103.851776.96326.89100.00100.00100.000.0000.0000.000

&APage &P&APage &P

Sample 1Moly-Cop Tools TMBALLBAL : Mass Balance Closure around a Ball Mill Grinding CircuitCircuit TypeDIRECTSample N1RemarksBase Case ExampleMill Dimensions and Operating Conditions3348BallsChargeMill Charge Weight, tonsApparentDiameterLengthSpeedChargeBallsInterstitialLift0OverfillingVolume,BallSlurryDensityftft% CriticalFilling,%Filling,%Slurry Filling,%Angle, ()536Slurrym3ChargeInterstitialExcesston/m318.522.072.038.0038.00100.0035.03885Net Power63.76296.4847.480.005.395NO DATA INPUT REQUIRED IN THIS SECTORrpm12.8210.0% Losses4316Gross kWFeedrate, ton/hr (dry)400.0Cyclone Dimensions (inches) and Operating Pressure (psi)NumberDiameterHeightInletVortexApexpsiOre Density, ton/m32.801020.075.03.507.503.677.98Balls Density, ton/m37.75EXPERIMENTAL SIZE DISTRIBUTIONSFresh FeedMill DischargeCyclone FeedCyclone U'flowCyclone O'flowCirc.LambdaCyclone Feed (pre-adjusted)Cyclone O'flow (pre-adjusted)Cyclone U'flow (pre-adjusted)iMeshOpeningMid-Sizeton/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% Passington/hr% Retained% PassingLoadton/hr% Retained% Passingadj.ton/hr% Retained% Passingadj.ton/hr% Retained% Passingadj.11.0525400100.00100.00100.00100.00100.00100.000.00100.000.00100.000.0020.74219050219970.000.00100.000.000.00100.000.000.00100.000.000.00100.000.000.00100.000.000000.000.00100.000.000.000.00100.000.000.000.00100.000.0030.525127001555420.005.0095.0013.691.1298.8818.171.1298.8818.171.4998.510.000.00100.000.0000018.171.1298.880.000.000.00100.00(0.00)18.171.4998.51(0.00)40.37195001098466.4016.6078.4031.262.5696.3241.492.5696.3241.493.3995.120.000.00100.000.0000041.492.5696.320.000.000.00100.00(0.00)41.493.3995.12(0.00)536700797856.2814.0764.3330.712.5193.8140.762.5193.8140.763.3391.790.000.00100.000.0000040.762.5193.810.000.000.00100.00(0.00)40.763.3391.79(0.00)644750564141.3210.3354.0027.882.2891.5337.012.2891.5337.013.0388.760.000.00100.000.0000037.012.2891.530.000.000.00100.00(0.00)37.013.0388.76(0.00)763350398933.368.3445.6629.032.3789.1638.532.3789.1638.533.1585.610.000.00100.000.0000038.532.3789.160.000.000.00100.00(0.00)38.533.1585.61(0.00)882360281227.366.8438.8233.262.7286.4444.142.7286.4444.143.6182.000.000.00100.000.0000044.142.7286.440.000.000.00100.00(0.00)44.143.6182.00(0.00)9101700200321.645.4133.4138.593.1683.2851.213.1683.2851.214.1977.810.000.00100.003.0570.0000051.213.1683.280.000.000.00100.00(0.00)51.214.1977.81(0.00)10141180141620.405.1028.3150.474.1379.1666.984.1379.1666.985.4872.340.000.00100.003.0570.0000066.984.1379.160.000.000.00100.00(0.00)66.985.4872.34(0.00)1120850100115.603.9024.4159.404.8674.3078.834.8674.3078.836.4565.890.000.00100.003.0570.0000078.834.8674.300.000.000.00100.00(0.00)78.836.4565.89(0.00)122860071414.163.5420.8775.816.2068.10100.616.2068.10100.518.2257.670.100.0299.973.0570.00000100.616.2068.100.000.100.0299.97(0.00)100.518.2257.67(0.00)133542550512.043.0117.8692.587.5760.53122.867.5760.53120.929.8947.781.940.4999.493.0570.00000122.867.5760.530.001.940.4999.49(0.00)120.929.8947.78(0.00)144830035710.362.5915.27107.088.7651.77142.118.7651.77131.2010.7337.0510.902.7396.763.0570.00000142.118.7651.770.0010.902.7396.76(0.00)131.2010.7337.05(0.00)15652122528.842.2113.06108.228.8542.92143.628.8542.92116.409.5227.5427.236.8189.963.0570.00000143.628.8542.920.0027.236.8189.96(0.00)116.409.5227.54(0.00)161001501787.521.8811.1894.657.7435.18125.607.7435.1885.797.0220.5239.819.9580.003.057(0.00000)125.607.7435.180.0039.819.9580.00(0.00)85.797.0220.52(0.00)171501061266.481.629.5674.576.1029.0898.976.1029.0856.904.6515.8742.0610.5269.493.057(0.00000)98.976.1029.080.0042.0610.5269.49(0.00)56.904.6515.87(0.00)1820075895.521.388.1855.194.5124.5773.254.5124.5736.442.9812.8936.819.2060.293.057(0.00000)73.254.5124.570.0036.819.2060.29(0.00)36.442.9812.89(0.00)1927053634.721.187.0040.683.3321.2453.993.3321.2424.141.9710.9129.867.4652.823.057(0.00000)53.993.3321.240.0029.867.4652.82(0.00)24.141.9710.91(0.00)2040038453.400.856.1529.372.4018.8438.982.4018.8416.231.339.5922.755.6947.13Circ. Load3.057(0.00000)38.982.4018.840.0022.755.6947.13(0.00)16.231.339.59(0.00)21-40001924.606.150.00230.4018.840.00305.7618.840.00117.229.590.00188.5447.130.00W. Factors(0.00000)305.7618.84188.5447.13117.229.59Totals400.00100.001222.84100.001622.84100.001222.84100.00400.00100.0013.0571622.84100.00400.00100.001222.84100.00% Solids95.0072.0062.2076.0040.0013.0570.0000062.200.0040.00(0.00)76.00(0.00)Slurry Density, ton/m32.5691.8621.6661.9551.346Weighting Factor0.0001.0001.0001.0001.000CL (ave)3.057

&APage &PComponent of the Total Mill Power Draw (Cell K11) contributed by the Ball Charge.Component of the Total Mill Power Draw (Cell K11) contributed by the Overfilling Slurry on top of the "kidney".Component of the Total Mill Power Draw (Cell K11) contributed by the Interstitial Slurry in the ball charge.Mill Diameter, inside liners.Effective Grinding Lenght.Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill.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).See Mill Power_Ball Mills for further details.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.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.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.Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids).Free Cyclone Height,defined as the distance from the bottom end of the vortex finder to the top end of the apex.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.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.&APage &P

Graficos

Graficos10010010010010010097.061716218292.444134373792.131634035483.905114629989.164869046279.324453528282.25098541870.360896495378.034300414265.648071255972.400728210259.705921921865.128616901852.26765473954.192418430241.306388604340.847360839728.430126410230.617362009319.702732986723.644174784714.613278446618.937399867411.530709486216.2379362339.849242580513.80257094288.367048974312.10264637857.323968807311.33399055786.853120255610.6536328826.4390461109

DischargeFeedParticle SizeSize Distributions, %Ball mill performance (Grinding circuit M1)Date: June 3th, 2015

0.984624498110.984624498110.984624498110.984624498110.984624498110.984624498110.984624498110.984624498110.98462390750.99999868680.983470740.99743454230.95036976230.92383231820.83660755720.67087449410.70586318120.38015568430.61877953920.18651941850.57323341570.08524458580.55186286880.03772575440.542299470.01646090150.53879021690.00865784410.53750168720.00579271260.53530382750.0009056254

Curva convencional para ciclones crebb D-26BActualCorrectedParticle SizeFraction betwen Feed and Discharge (U/F)Classifier Efficiency (Grinding circuit M1)Date: June 03th, 2015