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Moly-Cop Tools, Version 2.0
About the BallSim_Dual Spreadsheet ...
Scope : The BallSim_Dual spreadsheet was designed to simulate the Size-by-Size Mass Balance around any given Conventional Ball Mill grinding section, of the Dual configuration (see Flowsheet), operating under various conditions, on the basis of well accepted mathematical models for the grinding and hydroclassification processes. Theoretical Framework : - The Grinding Model : For the simulation of the ball mill response, this routine 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 Figure below helps define both concepts with greater clarity. Consider that at any given instant t, the size distribution of the mineral charge in a hypothetical batch mill is quantified by the fractions f i (i = 1, n) retained on the n different
screens represented on the left of such Figure. After a time interval Dt, the resulting size distribution is represented on the right of the same Figure. During this time interval, some particles will be fractured and their fragments redistributed to the lower screens. For the particles retained on mesh ‘i+1’ (the ‘i’ fraction), the Selection Function Si (min-1) denotes the fractional breakage velocity; that is, the fraction of the particles in the size range [di+1 , di] which are fractured, per unit of
time. Therefore, the product (SiDt) represents the fraction of the material retained on mesh ‘i+1’, at time t, that will be
fractured by the action of the grinding media, during the following time period Dt. Complementarily, the Breakage Function bij denotes the fraction, by weight, of the fragments arising from the breakage of the particles retained on mesh ‘j+1’ to be retained on the lower ‘i+1’ mesh.
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Moly-Cop Tools, Version 2.0
About the Ballsim_Dual Spreadsheet ...
It is customary to define mesh ‘1’ as the coarsest opening and ‘n’ as the finest opening. Then, by definition : i+1
Bij = S bkj (1)
k=n represents the cummulative fraction of fragments from the breakage of particles retained on mesh ‘j’ that will become finer than mesh ‘i’. With reference to the Figure above, it is then possible to establish, for each size fraction ‘i’, the following population balance of particles :
[Particles in fraction ‘i’ at time (t+Dt)] = [Particles in fraction ‘i’ at time t]
- [Particles in fraction ‘i’ broken during the time interval Dt] + [New particles added to fraction ‘i’ as a result of the breakage of particles originally retained in the coarser fractions (j = 1, i-1)] then, if H represents the total weight of ore in the mill :
fi(t+Dt) H = fi(t) H - SiDtfi(t) H + bi1S1Dtf1(t) H + bi2S2Dtf2(t) H + … + bi,i-1Si-1Dtfi-1(t) H ; for i = 1, 2, …, n (2)
Considering the limiting condition when Dt approaches zero, the expression above reduces to the system of first order differential equations : 1
d(fi)/dt = -Si fi + S bij Sj fj ; for i = 1, 2, …, n (3)
j = i-1 which constitutes the General Grinding Model, in its differential form. The analytical solution of this complex system of differential equations is fortunately known, under the restrictive assumption that the parameters S and B are invariant with time; so giving rise to particular solution of the general system denoted ‘Linear Model’, which in its matrix form is expressed as : f = ( T J T-1 ) f° (4) where : f = {fi | i = 1, 2, …, n} = vector containing the size distribution of the mill discharge (ground product), f° = {fi° | i = 1, 2, …, n} = vector containing the size distribution of the mill feed, T = {Tij | i,j = 1, 2, …, n} = lower triangular matrix of values Tij recursively defined as : Tij = 0 ; when i < j Tij = 1 ; when i = j i - 1
Tij = S ( bik Sk Tkj )/( Si – Sj ) ; when i > j
k = j
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Moly-Cop Tools, Version 2.0
About the Ballsim_Dual Spreadsheet ...
J = {Jij | i,j = 1, 2, …, n} = diagonal matrix of values Jij defined as : Jij = exp (-Sit) ; when i = j ( batch grinding)
Jij = (1 + Sit/N)-N ; when i = j (continuous grinding) Jij = 0 ; in all other cases
and where t - the average mean residence time - and N are parameters characteristic of the Residence Time Distribution (RTD) of the mineral slurry in the mill, here represented by :
E(t) = [ NN (t/t)N-1 / t G(N) ] exp (-Nt/t) (5) referred to as the ‘N-Mixers in Series Model’ and where the parameter N may be approximated by the effective (Lenght/Diameter) ratio of the mill. The grinding model parameters (the Selection and Breakage parameters) are different for different particle sizes. Such dependence is here represented by the following relationships : - For the Selection Function :
Si = a0 (di*)a1 / [ 1 + (di* / dcrit)
a2 ] (6) 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 :
Si = [1/(1+a02/a01)] { a01 (di*)a11 / [ 1 + (di* / dcrit)
a2 ] + a02 (di*)a12 } (6e)
- For the Breakage Function :
Bij = b0 (di/dj+1)b1 + (1- b0) (di/dj+1)
b2 (7)
An expanded form of this expression - also available in this simulation routine - is obtained by replacing b0 in Equation 7 by :
b0j = b00(dj+1/1000) -b01 , never > 1 (7e) 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 (see Files BallParam_Batch and BallParam_Open) 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 a02 and b01 are set equal to zero. Not considering the expanded forms, the above expressions considerably reduce the number of ore characteristic
parameters to a maximum of seven (a0, a1, a2, dcrit, b0, b1 and b2) and simplify the computation of the (n-1) Si‘s values and the n(n-1)/2 Bij’s values required for the evaluation of the model.
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Moly-Cop Tools, Version 2.0
About the Ballsim_Dual Spreadsheet ...
The critical role of the Specific Energy Consumption E (kWh/ton) becomes explicit in the above formulations through a simple change of variables, when introducing the Specific Selection Function parameter as : Si
Eballs = Si (H/Pballs) ; i = 1, 2, ..., n (8)
and recognizing that (see Equations 2 and 5) : Eballs = t (Pballs/H) (batch grinding)
Eballs = t (Pballs/H) (continuous grinding) (9) where Pballs represents the contribution of the balls to the Net Mill Power Draw (kW) (see Mill Power_Ball Mills), it may be concluded that : Si
Eballs Eballs = Si t (batch grinding)
or : SiE
balls Eballs = Si t (continuous grinding) (10)
Therefore, it is enough to replace in Equations 4 above the products (Sit) or (Sit) by the product (SiE
ballsEballs) to obtain the equations of the Linear Grinding Model in terms of the Specific Selection Function, Si
Eballs.
- The Hydrocyclone Model : (see Files Cyclosim_Single and Cyclobal_Single) - Simulation of Grinding/Classification Circuits : The mathematical simulation of the response of grinding/classification circuits, like the one represented here in Flowsheet, requires the proper combination of the unit grinding and classification models. As a result of the circulating load stream, both models can not be solved independently : the feed to the mill is affected by the cyclones discharge stream which depends on the cyclones feed and this cyclones feed is affected by the mill discharge, which in turns depends on the mill feed. Such interdependence condition implies that the system must be solved with the aid of numerical convergence algorithms, starting from an initial guessed value for the Circulating Load ratio (defined as the ratio of the massflowrate of solids in the cyclones discharge stream to the massflowrate of solids in the cyclones overflow stream). For such purposes, the present Ballsim_Dual simulator makes use of the Goal Seek tool available in Microsoft Excel. Data Input and Program Execution : The data required by the simulator 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. In addition to the above, the user is requested to provide an initial guess of the Circulating Load ratio in Cell E25. Finally, the system is solved by single clicking on the macro button Iterate, next to Cell E25. Important Notice : Iterate ... must be clicked every time any element of input data gets to be modified. After clicking ITERATE, Cell E27 must display a zero value; otherwise, the current outputs are not valid.
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Moly-Cop Tools, Version 2.0
About the Ballsim_Dual Spreadsheet ...
Calculation results are presented in the Reports worksheet and graphically summarized in the Flowsheet 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.
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Moly-Cop Tools TM (Version 2.0)
Circuit Type DUAL FEED (see Flowsheet ) Simulation N° 0
Remarks
Mill Dimensions and Operating Conditions 3348 Balls
Eff. Diam. Eff. Length Speed Charge Balls App. Dens. Interstitial Lift 0 Overfilling
ft ft % Critical Filling,% Filling,% ton/m3 Slurry, % Angle, (°) 536 Slurry
18.5 22.0 72.0 38.0 38.0 5.39 100.0 35.0 3885 Net kW
rpm 12.82 10.0 % Losses
4316 Gross kW
Cyclone Dimensions (inches) and Operating Conditions
Number Diameter Height Inlet Vortex Apex
10 20.0 75.0 3.50 7.50 3.97
Suggested Default Values: 60.0 5.0 7.0 3.5
% Solids O'flow 40.0 P80 157.7
% Solids U'flow 76.0 Wio 14.61
% Solids Mill Discharge 72.0 % Fines MD 19.53
Q 1799
Circulating Load 3.532 (Guess) Bpf 0.405
3.532 (Actual) Cycl. Psi 9.6
0.000 (Delta) Total Water 615.1
Ore Density, ton/m3 2.80 Arbiter's
Balls Density, ton/m3 7.75 Flow # 2.48
Feedrate to Sump, ton/hr (dry) 300.0 Feedrate to Ball Mill, ton/hr (dry) 125.0
Moisture in Feedrate to Sump, % 5.0 Moisture in Feedrate to Ball Mill, % 5.0
i Mesh Opening Mid-Size ton/hr % Retained % Passing ton/hr % Passing
1 1.05 25400 100.00 100.00
2 0.742 19050 21997 0.00 0.00 100.00 0.00 100.00
3 0.525 12700 15554 15.00 5.00 95.00 6.25 95.00
4 0.371 9500 10984 49.80 16.60 78.40 20.75 78.40
5 3 6700 7978 42.21 14.07 64.33 17.59 64.33
6 4 4750 5641 30.99 10.33 54.00 12.91 54.00
7 6 3350 3989 25.02 8.34 45.66 10.43 45.66
8 8 2360 2812 20.52 6.84 38.82 8.55 38.82
9 10 1700 2003 16.23 5.41 33.41 6.76 33.41
10 14 1180 1416 15.30 5.10 28.31 6.38 28.31
11 20 850 1001 11.70 3.90 24.41 4.88 24.41
12 28 600 714 10.62 3.54 20.87 4.43 20.87
13 35 425 505 9.03 3.01 17.86 3.76 17.86
14 48 300 357 7.77 2.59 15.27 3.24 15.27
15 65 212 252 6.63 2.21 13.06 2.76 13.06
16 100 150 178 5.64 1.88 11.18 2.35 11.18
17 150 106 126 4.86 1.62 9.56 2.03 9.56
18 200 75 89 4.14 1.38 8.18 1.73 8.18
19 270 53 63 3.54 1.18 7.00 1.48 7.00
20 400 38 45 2.55 0.85 6.15 1.06 6.15
21 -400 0 19 18.45 6.15 0.00 7.69 0.00
Make-up Ball Size, mm 77.0 3.03 inches
Selection Function Parameters : Expanded Form :
alpha0 alpha1 alpha2 dcrit alpha02 alpha12
0.009180 0.65 2.5 6532 0 1
5.75 <<< 5.73 7.30 >>> 7.27 0 1 Suggested Default Values
4.60 <<< 4.60 0.50 >>> 0.50
4.20 <<< 4.20
Breakage Function Parameters : Expanded Form :
beta0 beta1 beta2 beta01
0.2 0.25 4 0
0 Suggested Default Value
Classifier Constants :
a1 a2 a3 a4 l Bpc
9.680 1.401 54.964 0.523 0.950 0.000
9.680 1.401 54.964 0.523 0.950 0.000 Suggested Default Values
Defaults ^
Feed Size Distribution
BALLSIM : Conventional Closed Circuit Grinding Simulator
Base Case Example
Secondary Feed
Main Simulated Outputs
Simulation results are not valid until the Iterate button has been clicked.
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Moly-Cop Tools TM (Version 2.0)
Simulation N° 0
Remarks
40.00 % Solids
58.82 % - Size 18
157.7 P80 Bpc 0.000 9.55 psi
Bpf 0.405
Bpw 0.426 10 # of Cyclones
7.50 Vortex
3.97 Apex
ton/hr 300.0 76.00 % Solids
F80 9795
125.0 Sec. Feed, ton/hr
Water, 151.8 Water, m3/hr
m3/hr 470.0
Gross kW 4316.1
% Balls 38.00 Circ. Load 353.16
% Critical 72.00 m3/hr 1799
% Solids 72.00 % Solids 63.41
kWh/ton 10.16
Wio 14.61
Base Case Example
Moly-Cop Tools / 226529973.xls.ms_office / Flowsheet 5/5/2014 / 3:35 PM
Simulation N° 0
Remarks : Base Case Example
Prim. Feed Mill Mill Sump Cyclone Cyclone Cyclone Sec. Feed
to Sump Feed Discharge Water Feed U'flow O'flow to Mill
Ore, ton/hr 300.0 1625.9 1625.9 0.0 1925.9 1500.9 425.0 125.0
Water, m3/hr 15.8 480.6 632.3 470.0 1111.5 474.0 637.5 6.6
Slurry, ton/hr 315.8 2106.5 2258.3 470.0 3037.4 1974.9 1062.5 131.6
Slurry, m3/hr 122.9 1061.3 1213.0 470.0 1799.3 1010.0 789.3 51.2
Slurry Dens., ton/m3 2.569 1.985 1.862 1.000 1.688 1.955 1.346 2.569
% Solids (by volume) 87.2 54.7 47.9 0.0 38.2 53.1 19.2 87.2
% Solids (by weight) 95.0 77.2 72.0 0.0 63.4 76.0 40.0 95.0
i Mesh Opening
1 1.05 25400 100.00 100.00 100.00 0.00 100.00 100.00 100.00 100.00
2 0.742 19050 100.00 100.00 100.00 0.00 100.00 100.00 100.00 100.00
3 0.525 12700 95.00 97.81 99.12 0.00 98.48 98.05 100.00 95.00
4 0.371 9500 78.40 91.69 97.33 0.00 94.38 92.79 100.00 78.40
5 3 6700 64.33 86.18 95.50 0.00 90.65 88.00 100.00 64.33
6 4 4750 54.00 81.74 93.76 0.00 87.57 84.05 100.00 54.00
7 6 3350 45.66 77.64 91.84 0.00 84.65 80.30 100.00 45.66
8 8 2360 38.82 73.51 89.50 0.00 81.61 76.40 100.00 38.82
9 10 1700 33.41 69.22 86.63 0.00 78.34 72.20 100.00 33.41
10 14 1180 28.31 63.96 82.70 0.00 74.22 66.93 100.00 28.31
11 20 850 24.41 58.14 77.90 0.00 69.57 60.95 100.00 24.41
12 28 600 20.87 50.97 71.64 0.00 63.73 53.48 99.93 20.87
13 35 425 17.86 42.64 63.89 0.00 56.72 44.70 99.16 17.86
14 48 300 15.27 33.73 54.81 0.00 48.65 35.27 95.92 15.27
15 65 212 13.06 25.65 45.44 0.00 40.39 26.70 88.74 13.06
16 100 150 11.18 19.43 37.05 0.00 33.02 20.11 78.60 11.18
17 150 106 9.56 15.12 30.40 0.00 27.15 15.58 68.01 9.56
18 200 75 8.18 12.29 25.53 0.00 22.83 12.63 58.82 8.18
19 270 53 7.00 10.40 22.02 0.00 19.68 10.68 51.47 7.00
20 400 38 6.15 9.13 19.53 0.00 17.45 9.38 45.94 6.15
D80, microns 9795 4106 984 0 2012 3263 157.7 9794.6
Specific Energy Consumption : 10.16 kWh/ton (Gross)
Operational Work Index : 14.61 kWh/ton (neglecting Sec. F80)
Conventional Closed Circuit Grinding Simulator
Configuration : DUAL FEED
Particle Size Distributions (Cummulative % Passing)
CIRCUIT MASS BALANCE
Moly-Cop ToolsTM
, Version 2.0
BALLSIM
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Simulation N° 0
Remarks : Base Case Example
Number of Cyclones : 10 Operating Conditions :
Cyclone Dimensions, in : Feed Flowrate, m3/hr 1799.3
Diameter 20.00 Pressure, psi 9.6
Height 75.00 D50 (corr.), microns 181.7
Inlet 3.50 Water By-Pass, % 42.6
Vortex 7.50 Solids By-Pass, % 40.5
Apex 3.97 Plitt's Parameter 1.50
Ore Density, ton/m3 2.80 Circulating Load, % 353
i Mesh Opening Mid-Size Feed U'flow O'flow Actual Corrected
1 1.05 25400 21997 100.00 100.00 100.00 1.000 1.000
2 0.742 19050 15554 100.00 100.00 100.00 1.000 1.000
3 0.525 12700 10984 98.48 98.05 100.00 1.000 1.000
4 0.371 9500 7978 94.38 92.79 100.00 1.000 1.000
5 3 6700 5641 90.65 88.00 100.00 1.000 1.000
6 4 4750 3989 87.57 84.05 100.00 1.000 1.000
7 6 3350 2812 84.65 80.30 100.00 1.000 1.000
8 8 2360 2003 81.61 76.40 100.00 1.000 1.000
9 10 1700 1416 78.34 72.20 100.00 1.000 1.000
10 14 1180 1001 74.22 66.93 100.00 1.000 1.000
11 20 850 714 69.57 60.95 100.00 0.997 0.995
12 28 600 505 63.73 53.48 99.93 0.976 0.959
13 35 425 357 56.72 44.70 99.16 0.911 0.851
14 48 300 252 48.65 35.27 95.92 0.808 0.678
15 65 212 178 40.39 26.70 88.74 0.697 0.490
16 100 150 126 33.02 20.11 78.60 0.602 0.330
17 150 106 89 27.15 15.58 68.01 0.531 0.212
18 200 75 63 22.83 12.63 58.82 0.484 0.132
19 270 53 45 19.68 10.68 51.47 0.454 0.082
20 400 38 19 17.45 9.38 45.94 0.419 0.023
Ore, ton/hr 1925.9 1500.9 425.0
Water, m3/hr 1111.5 474.0 637.5 a1 9.680
Slurry, ton/hr 3037.4 1974.9 1062.5 a2 1.401
Slurry, m3/hr 1799.3 1010.0 789.3 a3 54.964
Slurry Dens., ton/m3 1.688 1.955 1.346 a4 0.523
% Solids (by volume) 38.2 53.1 19.2 l 0.950
% Solids (by weight) 63.4 76.0 40.0 Bpc 0.000
CLASSIFIERS PERFORMANCE
Size Distributions, % Passing Classifier Efficiency
Mass Balance around the Classifiers
Classifier Constants
Moly-Cop ToolsTM
, Version 2.0
BALLSIMConventional Closed Circuit Grinding Simulator
Moly-Cop Tools / 226529973.xls.ms_office Page 9 5/5/2014 / 3:35 PM
Simulation N° 0
Remarks : Base Case Example
Eff. Diameter, ft 18.5 Mill Power, kW (Gross) 4316
Eff. Length, ft 22.0 Mill Power, kW (Net) 3885
Speed, % Critical 72.0 Throughput, ton/hr 1625.9
App. Density, ton/m3 5.39 % Solids (by weight) 72.0
Charge Level, % 38.0 Sp. Energy, kWh/ton 2.65
Balls Filling, % 38.0 Reduction Ratio 4.17
Lift Angle, (°) 35.0 Arbiter's Flow Number 2.48
Mill Mill
i Mesh Opening Mid-Size Feed Discharge
1 1.05 25400 21997 100.00 100.00
2 0.742 19050 15554 100.00 100.00
3 0.525 12700 10984 97.81 99.12
4 0.371 9500 7978 91.69 97.33
5 3 6700 5641 86.18 95.50
6 4 4750 3989 81.74 93.76
7 6 3350 2812 77.64 91.84
8 8 2360 2003 73.51 89.50
9 10 1700 1416 69.22 86.63
10 14 1180 1001 63.96 82.70
11 20 850 714 58.14 77.90
12 28 600 505 50.97 71.64
13 35 425 357 42.64 63.89
14 48 300 252 33.73 54.81
15 65 212 178 25.65 45.44
16 100 150 126 19.43 37.05
17 150 106 89 15.12 30.40
18 200 75 63 12.29 25.53
19 270 53 45 10.40 22.02
20 400 38 19 9.13 19.53
D80, microns 4106 984
alpha0 alpha02 alpha1 alpha12 alpha2 dcrit beta0 beta01 beta1 beta2
0.0091800 0.0000000 0.650 1.000 2.50 6532 0.200 0.000 0.25 4.00
BALLSIM
Breakage Function Parameters :Selection Function Parameters :
Size Distributions
BALL MILL PERFORMANCE
Conventional Closed Circuit Grinding Simulator
Moly-Cop ToolsTM
, Version 2.0
Moly-Cop Tools / 226529973.xls.ms_office Page 10 5/5/2014 / 3:35 PM
Mill
Power, kW
Mill Dimensions and Operating Conditions 3348 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 0 Overfilling
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, (°) 536 Slurry
18.50 22.00 72.00 38.00 38.00 100.00 35.00 3885 Net Total
10.00 % Losses
4316 Gross Total
% Solids in the Mill 72.00 Charge Apparent
Ore Density, ton/m3 2.80 Volume, Ball Density
Slurry Density, ton/m3 1.86 m3 Charge Interstitial above Balls ton/m3
Balls Density, ton/m3 7.75 63.76 296.48 47.48 0.00 5.395
Mill Charge Weight, tons
CONVENTIONAL BALL MILL POWER ESTIMATION
Slurry
Hogg & Fuerstenau Model
Moly-Cop Tools / 226529973.xls.ms_office 5/5/2014 / 3:35 PM
SiE
Selection Function :
alpha01 alpha02 alpha11 alpha12 alpha2 dcrit
0.00918 0 0.65 1 2.5 6532
i Mesh Opening Mid-Size SiE
1 1.05 25400
2 0.742 19050 21997.05 0.279706
3 0.525 12700 15554.26 0.499505
4 0.371 9500 10984.08 0.832367
5 3 6700 7978.095 1.191379
6 4 4750 5641.365 1.487783
7 6 3350 3989.048 1.557154
8 8 2360 2811.761 1.428406
9 10 1700 2002.998 1.221491
10 14 1180 1416.333 1.00391
11 20 850 1001.499 0.811496
12 28 600 714.1428 0.654772
13 35 425 504.9752 0.523899
14 48 300 357.0714 0.41863
15 65 212 252.1904 0.334071
16 100 150 178.3255 0.266734
17 150 106 126.0952 0.212948
18 200 75 89.16277 0.170001
19 270 53 63.0476 0.135714
20 400 38 44.87761 0.108808
21 -400 0 19 0
Page 12
Bij
Breakage Function :
Beta00 Beta01 Beta1 Beta2
0.2 0 0.25 4
i Mesh Opening Beta0J Cummulative
1 1.05 25400 0.2 1
2 0.742 19050 0.2 1 1
3 0.525 12700 0.2 0.338745 1 1
4 0.371 9500 0.2 0.217546 0.436477 1 1
5 3 6700 0.2 0.16626 0.232419 0.381203 1 1
6 4 4750 0.2 0.144421 0.172061 0.218179 0.38562 1 1
7 6 3350 0.2 0.130279 0.147204 0.166491 0.218179 0.381203 1 1
8 8 2360 0.2 0.118843 0.132267 0.144244 0.166393 0.216662 0.380272 1 1
9 10 1700 0.2 0.109363 0.121231 0.130901 0.145262 0.167818 0.221856 0.399649 1 1
10 14 1180 0.2 0.099788 0.11048 0.118923 0.130333 0.144244 0.166393 0.218179 0.368257 1 1
11 20 850 0.2 0.091923 0.101742 0.109435 0.119569 0.130901 0.145262 0.1684 0.218179 0.399649 1
12 28 600 0.2 0.084255 0.093247 0.100275 0.109459 0.119436 0.130932 0.145359 0.166568 0.222364 0.38194
13 35 425 0.2 0.077296 0.085542 0.091984 0.100384 0.109435 0.119569 0.131128 0.144546 0.1684 0.218179
14 48 300 0.2 0.07085 0.078408 0.084311 0.092004 0.100275 0.109459 0.11963 0.130404 0.145359 0.166568
15 65 212 0.2 0.064959 0.071889 0.077301 0.084353 0.09193 0.100325 0.109545 0.119044 0.131043 0.144434
16 100 150 0.2 0.059577 0.065933 0.070896 0.077363 0.084311 0.092004 0.100434 0.109052 0.11963 0.130404
17 150 106 0.2 0.054624 0.060451 0.065002 0.070931 0.077301 0.084353 0.092075 0.099953 0.109545 0.119044
18 200 75 0.2 0.050098 0.055443 0.059616 0.065054 0.070896 0.077363 0.084445 0.091664 0.100434 0.109052
19 270 53 0.2 0.045933 0.050833 0.05466 0.059646 0.065002 0.070931 0.077423 0.084041 0.092075 0.099953
20 400 38 0.2 0.042267 0.046776 0.050297 0.054885 0.059814 0.06527 0.071244 0.077333 0.084725 0.091968
Page 13
Bij
i Mesh Opening Partial
1 1.05 25400 0
2 0.742 19050 0.661255 0
3 0.525 12700 0.121199 0.563523 0
4 0.371 9500 0.051286 0.204057 0.618797 0
5 3 6700 0.021839 0.060359 0.163024 0.61438 0
6 4 4750 0.014142 0.024856 0.051689 0.167441 0.618797 0
7 6 3350 0.011436 0.014937 0.022246 0.051787 0.164542 0.619728 0
8 8 2360 0.00948 0.011036 0.013344 0.021131 0.048844 0.158416 0.600351 0
9 10 1700 0.009575 0.010751 0.011978 0.014929 0.023573 0.055463 0.18147 0.631743 0
10 14 1180 0.007865 0.008738 0.009488 0.010764 0.013344 0.021131 0.049779 0.150078 0.600351 0
11 20 850 0.007668 0.008495 0.00916 0.01011 0.011464 0.01433 0.023041 0.051611 0.177284 0.61806
12 28 600 0.00696 0.007705 0.008291 0.009075 0.010001 0.011363 0.014231 0.022022 0.053965 0.16376
13 35 425 0.006446 0.007134 0.007673 0.00838 0.00916 0.01011 0.011497 0.014143 0.023041 0.051611
14 48 300 0.00589 0.006519 0.00701 0.007651 0.008345 0.009135 0.010085 0.011359 0.014316 0.022134
15 65 212 0.005382 0.005956 0.006405 0.006989 0.007619 0.008321 0.009111 0.009992 0.011413 0.01403
16 100 150 0.004953 0.005482 0.005894 0.006432 0.00701 0.007651 0.008359 0.009099 0.010085 0.011359
17 150 106 0.004526 0.005009 0.005386 0.005877 0.006405 0.006989 0.007631 0.00829 0.009111 0.009992
18 200 75 0.004165 0.004609 0.004956 0.005409 0.005894 0.006432 0.007021 0.007623 0.008359 0.009099
19 270 53 0.003666 0.004057 0.004362 0.00476 0.005188 0.005661 0.006179 0.006708 0.007351 0.007985
20 400 38 0.042267 0.046776 0.050297 0.054885 0.059814 0.06527 0.071244 0.077333 0.084725 0.091968
1 1 1 1 1 1 1 1 1 1
Page 14
Bij
1
1 1
0.384872 1 1
0.218179 0.38194 1 1
0.166666 0.217611 0.382875 1 1
0.144546 0.166568 0.218179 0.383928 1 1
0.130443 0.144434 0.166666 0.218179 0.382875 1 1
0.119116 0.130404 0.144546 0.166776 0.218179 0.383928 1 1
0.109083 0.119044 0.130443 0.144546 0.166666 0.218179 0.382875 1 1
0.100345 0.109416 0.119521 0.13096 0.145185 0.16797 0.221458 0.395446 1 1
Page 15
Bij
0
0.615128 0
0.166692 0.61806 0
0.051513 0.164328 0.617125 0
0.02212 0.051043 0.164696 0.616072 0
0.014103 0.022134 0.051513 0.165749 0.617125 0
0.011327 0.01403 0.02212 0.051403 0.164696 0.616072 0
0.010034 0.011359 0.014103 0.02223 0.051513 0.165749 0.617125 0
0.008738 0.009628 0.010922 0.013586 0.021481 0.05021 0.161417 0.604554 0
0.100345 0.109416 0.119521 0.13096 0.145185 0.16797 0.221458 0.395446 1 0
1 1 1 1 1 1 1 1 1 0
Page 16
J&T
Mill Throughput, ton/hr 1625.946769 Reynolds Number 6.747367113
Water 632.3126322 Slurry Viscosity, cp 9.07347824
Slurry, m3/hr 1213.007907
Slurry Dens., ton/m3 1.861702128
% Solids (by volume) 47.87234043
Ebar 2.059296425 N 3.75862556
L/D 1.189189189
Matrix J
1 2 3 4 5 6 7 8 9
1 0.585136844 0 0 0 0 0 0 0 0
2 0 0.402835812 0 0 0 0 0 0 0
3 0 0 0.243607537 0 0 0 0 0 0
4 0 0 0 0.151304354 0 0 0 0 0
5 0 0 0 0 0.106379609 0 0 0 0
6 0 0 0 0 0 0.098408247 0 0 0
7 0 0 0 0 0 0 0.113862173 0 0
8 0 0 0 0 0 0 0 0.14575978 0
9 0 0 0 0 0 0 0 0 0.192568379
10 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0
Page 17
J&T
Matrix T
1 2 3 4 5 6 7 8 9
1 1 0 0 0 0 0 0 0 0
2 0.841479517 1 0 0 0 0 0 0 0
3 0.489924706 0.845646271 1 0 0 0 0 0 0
4 0.386606149 0.776863059 1.434673772 1 0 0 0 0 0
5 0.315327151 0.721995978 1.809260508 2.469465661 1 0 0 0 0
6 0.315398548 0.821129855 2.752379842 6.760890822 13.27125741 1 0 0 0
7 0.369076182 1.119814584 5.378875108 30.3364626 -219.8118008 -7.495387989 1 0 0
8 0.466858773 1.731025768 14.05792487 926.1123762 695.2981701 18.41420805 -4.144433287 1 0
9 0.708619343 3.469245574 73.32817949 -3857.727067 -993.5316507 -22.32856376 6.923306307 -3.546579474 1
10 1.072318934 8.174042244 -2266.6272 5667.083733 719.386679 14.19119948 -5.647527469 4.766390864 -3.132289953
11 1.951780615 31.64779806 6321.137547 -4128.423662 -265.178432 -4.521554118 2.363786177 -3.215751289 3.98991189
12 4.136434003 579.4123252 -7291.835913 1637.493651 52.44048422 0.759028624 -0.536728391 1.185552683 -2.593549289
13 11.86901497 -2368.807417 4263.567153 -316.2594569 -3.563319081 -0.035929086 0.04690161 -0.208960629 0.875426291
14 65.27464493 3389.574616 -1299.667344 23.57249567 0.022118425 0.000571441 -0.000548141 0.013372277 -0.142675361
15 -1113.147784 -2364.754858 179.6652476 0.87956343 0.051890681 0.001273712 -0.000394096 0.000721126 0.006484297
16 2685.152419 856.6168972 -5.658794658 0.567041523 0.050134524 0.001235646 -0.000358363 0.000448085 -8.37579E-05
17 -2777.308627 -149.9772447 -0.227192911 0.503252696 0.046193336 0.001139325 -0.000327928 0.000394871 -0.000247519
18 1467.202241 8.265492719 -0.027516841 0.463327035 0.042695812 0.001053074 -0.000302823 0.00036313 -0.000242418
19 -391.529141 0.115726363 -0.009107059 0.407893608 0.037612933 0.000927721 -0.000266727 0.000319627 -0.000215062
20 40.4334073 -0.753099391 -0.078171917 4.760032272 0.437966052 0.01079788 -0.003106871 0.003728728 -0.002519118
Vector SiE
1 2 3 4 5 6 7 8 9
1 0.279705855 0.499505464 0.83236683 1.191379254 1.487783271 1.557153874 1.42840647 1.221491463 1.003910414
Matrix bij
1 2 3 4 5 6 7 8 9
1 0 0 0 0 0 0 0 0 0
2 0.661254908 0 0 0 0 0 0 0 0
3 0.121199143 0.563523311 0 0 0 0 0 0 0
4 0.051285933 0.204057415 0.618796531 0 0 0 0 0 0
Page 18
J&T
5 0.021839227 0.06035874 0.163024186 0.614379963 0 0 0 0 0
6 0.014141521 0.024856428 0.051688678 0.167440754 0.618796531 0 0 0 0
7 0.011436325 0.01493736 0.022246279 0.051786633 0.164541605 0.619727927 0 0 0
8 0.009480048 0.011036109 0.013343752 0.021130744 0.048844159 0.158416166 0.600351132 0 0
9 0.009574967 0.010750552 0.011977653 0.014928971 0.02357338 0.055463258 0.181469585 0.631742839 0
10 0.007864554 0.008737604 0.009487643 0.010763714 0.013343752 0.021130744 0.049779467 0.150077878 0.600351132
11 0.007667902 0.008495358 0.009160423 0.010109762 0.011464474 0.014329905 0.023040676 0.051611362 0.177284455
12 0.006959904 0.007704731 0.008291031 0.009075442 0.010000823 0.01136278 0.014231306 0.022021565 0.053964597
13 0.006446056 0.007134323 0.007672966 0.008379999 0.009160423 0.010109762 0.011497498 0.014142725 0.023040676
14 0.005890368 0.00651891 0.007010024 0.007651239 0.008345216 0.009134658 0.010085342 0.011359454 0.014315904
15 0.005382082 0.005956289 0.006404755 0.006989433 0.007618782 0.008320784 0.009110876 0.009992152 0.0114129
16 0.00495316 0.005481582 0.00589424 0.00643202 0.007010024 0.007651239 0.008358675 0.009098808 0.010085342
17 0.004525766 0.005008586 0.005385619 0.005876921 0.006404755 0.006989433 0.007630916 0.008289505 0.009110876
18 0.004165093 0.004609434 0.004956416 0.005408546 0.00589424 0.00643202 0.007021151 0.007622823 0.008358675
19 0.003665972 0.004057066 0.004362466 0.004760411 0.005187884 0.005661149 0.006179388 0.006707902 0.007350789
20 0.042267071 0.046776203 0.050297337 0.054885446 0.059813955 0.065270176 0.071243988 0.077332987 0.084724654
1 1 1 1 1 1 1 1 1
Matrix Tij (inverse)
1 2 3 4 5 6 7 8 9
1 1 5.25748E-16 1.93926E-15 8.5578E-16 1.87274E-15 1.3342E-15 -7.86704E-17 4.73301E-16 6.16571E-16
2 -0.841479517 1 -2.71996E-15 4.61772E-16 -4.21497E-15 5.77416E-16 4.13531E-15 2.70627E-15 2.61689E-15
3 0.221669309 -0.845646271 1 -2.74282E-15 -1.02781E-15 -5.63128E-15 -3.76681E-15 -4.41018E-15 -4.52166E-15
4 -0.050914941 0.436363466 -1.434673772 1 4.24272E-15 1.0118E-14 -2.10088E-15 1.06845E-15 2.44948E-15
5 0.016892849 -0.269586172 1.733617105 -2.469465661 1 -1.53231E-14 9.42598E-15 4.60655E-15 2.8274E-16
6 -0.114511716 2.133951622 -16.05998595 26.01202362 -13.27125741 1 -1.03781E-13 -5.89913E-14 -1.04616E-14
7 3.780410278 -53.07233943 298.837724 -378.183947 120.3385774 7.495387989 1 5.58564E-13 -6.93702E-14
8 51.05724478 -465.7716277 1643.475343 -1255.446374 47.81673071 12.64992743 4.144433287 1 -2.50142E-12
9 -41.32753886 237.2572583 -484.3301577 150.7888644 33.64853718 15.29966978 7.775255718 3.546579474 1
10 434.8008115 -1570.713151 1714.998912 60.73349644 26.04755023 15.7677135 10.24789388 6.34252439 3.132289953
11 128.8492366 -292.1868256 142.4747979 40.65920132 23.58732467 16.89911633 12.73675229 9.362773003 6.034148485
Page 19
J&T
12 665.4479586 -894.0766415 62.85672783 29.75492881 20.6887971 16.5731401 13.79299314 11.33182435 8.572972006
13 -256.6484779 181.8593757 39.62689582 24.21696064 18.89503961 16.31073474 14.51041649 12.82746697 10.74617897
14 -263.3810526 68.63929497 28.98692082 20.66084374 17.4154862 15.82564587 14.73875319 13.69410094 12.281019
15 694.3656877 41.03090002 23.34380387 18.38326881 16.33778623 15.38137439 14.78245504 14.20893467 13.34628307
16 100.8942482 29.41043506 19.88106964 16.75548163 15.45157538 14.90805037 14.63934877 14.40144083 13.96387104
17 50.22584799 23.22757654 17.5364197 15.49727704 14.66723779 14.39135295 14.33799212 14.32635204 14.19521188
18 33.18190447 19.56068736 15.91783475 14.54941276 14.0239156 13.91695035 13.99639559 14.12712761 14.2012704
19 25.49443411 17.41629376 14.92724914 13.97347828 13.63942317 13.63456361 13.79066142 14.00449838 14.20635835
20 1 1 1 1 1 1 1 1 1
Page 20
J&T
10 11 12 13 14 15 16 17 18 19
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0.250934842 0 0 0 0 0 0 0 0 0
0 0.315929625 0 0 0 0 0 0 0 0
0 0 0.387337118 0 0 0 0 0 0 0
0 0 0 0.460180613 0 0 0 0 0 0
0 0 0 0 0.531658119 0 0 0 0 0
0 0 0 0 0 0.598891841 0 0 0 0
0 0 0 0 0 0 0.660490428 0 0 0
0 0 0 0 0 0 0 0.715533949 0 0
0 0 0 0 0 0 0 0 0.76370616 0
0 0 0 0 0 0 0 0 0 0.804413
0 0 0 0 0 0 0 0 0 0
Page 21
J&T
10 11 12 13 14 15 16 17 18 19
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
-3.200233862 1 0 0 0 0 0 0 0 0
4.019730654 -3.077548507 1 0 0 0 0 0 0 0
-2.530593821 3.757772347 -3.075947053 1 0 0 0 0 0 0
0.832985429 -2.306165209 3.732710868 -3.055242062 1 0 0 0 0 0
-0.127564321 0.73025418 -2.2666493 3.685801766 -3.056425977 1 0 0 0 0
0.005292183 -0.106586603 0.71123422 -2.232108597 3.696582328 -3.06045921 1 0 0 0
0.000184452 0.003946524 -0.103704512 0.700332 -2.242119399 3.696553716 -3.054735637 1 0 0
2.94815E-05 -2.02105E-07 0.003631191 -0.100905636 0.702373885 -2.240356841 3.692417034 -3.059747561 1 0
1.49222E-05 -0.000119238 2.01485E-05 0.003561575 -0.100555887 0.692528389 -2.206784169 3.653974344 -3.049400298 1
0.000154883 -0.001553292 -0.001295561 -0.001439046 0.000145051 -0.088266053 0.569102772 -1.594226783 2.049400298 -1
10 11 12 13 14 15 16 17 18 19
0.811495675 0.654771728 0.523898505 0.418629827 0.334071218 0.266733778 0.212948341 0.170001418 0.13571357 0.108808
10 11 12 13 14 15 16 17 18 19
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Page 22
J&T
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0.618060326 0 0 0 0 0 0 0 0 0
0.163760391 0.615128411 0 0 0 0 0 0 0 0
0.051611362 0.166692306 0.618060326 0 0 0 0 0 0 0
0.022134136 0.051513295 0.164328338 0.617125204 0 0 0 0 0 0
0.014030154 0.022119632 0.051043416 0.164695513 0.616071934 0 0 0 0 0
0.011359454 0.014103278 0.022134136 0.051513295 0.165748783 0.617125204 0 0 0 0
0.009992152 0.011327054 0.014030154 0.022119632 0.051403024 0.164695513 0.616071934 0 0 0
0.009098808 0.010033517 0.011359454 0.014103278 0.022229902 0.051513295 0.165748783 0.617125204 0 0
0.00798532 0.008737957 0.009627971 0.010921992 0.0135862 0.021480536 0.05020961 0.161417221 0.604554499 0
0.091967897 0.100344551 0.109416206 0.119521086 0.130960156 0.145185452 0.167969673 0.221457575 0.395445501 1
1 1 1 1 1 1 1 1 1 1
10 11 12 13 14 15 16 17 18 19
1.25681E-15 1.01632E-15 2.01985E-15 9.84979E-17 1.04446E-15 6.84368E-16 6.95081E-16 4.2833E-16 2.41454E-16 0
3.35029E-16 -4.77592E-16 -2.33312E-15 1.74901E-15 -9.73087E-16 -2.77962E-16 -7.63382E-16 -5.87353E-16 -5.23294E-16 0
-2.76229E-15 -1.60077E-15 -1.5009E-15 -2.1672E-15 1.68627E-16 -4.3391E-16 3.23172E-16 3.02503E-16 3.24227E-16 0
2.48189E-15 1.23815E-15 4.08597E-15 1.35742E-17 -1.32791E-15 2.15045E-16 -5.1531E-16 -1.60186E-16 -1.5198E-16 0
-2.02203E-15 -6.70058E-17 -6.36424E-15 2.88786E-15 3.48962E-15 2.55967E-16 1.02359E-15 1.36967E-16 9.03776E-17 0
1.69679E-14 -2.94452E-15 6.22662E-14 -3.39187E-14 -3.73233E-14 -3.64345E-15 -1.05823E-14 -1.22038E-15 -7.1076E-16 0
-3.7858E-13 -6.5583E-14 -1.04623E-12 3.89803E-13 5.27389E-13 2.48246E-14 1.6017E-13 2.46918E-14 1.79021E-14 0
-2.73633E-12 -1.29483E-12 -4.81748E-12 2.46987E-13 1.6753E-12 -2.00893E-13 6.20672E-13 1.74487E-13 1.61429E-13 0
1.06104E-12 6.24208E-13 1.10437E-12 4.94214E-13 -2.0846E-13 1.50489E-13 -1.36436E-13 -8.16858E-14 -8.59284E-14 0
1 -2.79573E-12 -2.33346E-12 -4.02751E-12 2.74036E-13 -7.6398E-13 5.90978E-13 5.68487E-13 6.07794E-13 0
3.200233862 1 1.2297E-13 -6.76332E-13 8.60787E-14 -6.14848E-14 1.29118E-13 1.2297E-13 1.24703E-13 0
Page 23
J&T
5.82914429 3.077548507 1 -1.65836E-12 7.2844E-13 1.54987E-13 6.122E-13 4.8821E-13 4.47063E-13 0
8.434982709 5.708603913 3.075947053 1 -3.26715E-13 -1.48162E-13 -2.19077E-13 -1.51327E-13 -1.19851E-13 0
10.55968629 8.259733243 5.66505195 3.055242062 1 -1.83965E-13 -2.02361E-13 -1.28775E-13 -8.50837E-14 0
12.18843133 10.44994986 8.244130165 5.65231944 3.056425977 1 4.69185E-13 2.87565E-13 1.55134E-13 0
13.28516759 12.10881402 10.44410681 8.236847875 5.657484706 3.06045921 1 3.6758E-14 1.60816E-14 0
13.88796723 13.197024 12.08035851 10.4171758 8.22599674 5.652340099 3.054735637 1 6.76758E-15 0
14.15882411 13.84382192 13.19640766 12.07824678 10.42479153 8.234598952 5.65430288 3.059747561 1 0
14.33835534 14.28871014 13.99708373 13.33353102 12.20052316 10.51832734 8.28709141 5.67642078 3.049400298 1
1 1 1 1 1 1 1 1 1 1
Page 24
J&T
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
Page 25
J&T
20 SiE
0 1 0.279705855
0 2 0.499505464
0 3 0.83236683
0 4 1.191379254
0 5 1.487783271
0 6 1.557153874
0 7 1.42840647
0 8 1.221491463
0 9 1.003910414
0 10 0.811495675
0 11 0.654771728
0 12 0.523898505
0 13 0.418629827
0 14 0.334071218
0 15 0.266733778
0 16 0.212948341
0 17 0.170001418
0 18 0.13571357
0 19 0.10880787
1 20 0
20
0
20
0
0
0
0
Page 26
J&T
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
0
0
0
0
0
0
Page 27
J&T
0
0
0
0
0
0
0
0
1
Page 28
C
Cyclone Cyclone Cyclone Number of Cyclones 10
Feed U'flow O'flow Classifier Dimensions, inches.
Solids, tons 192.594677 150.094677 42.5 DC h DI DO DU
Water, m3/hr 111.148319 47.398319 63.75 20 75 3.5 7.5 3.96903569
Slurry, tons 303.742996 197.492996 106.25
Slurry, m3/hr 179.932132 101.003561 78.9285714 Classifier Constants
Solids Density, ton/m3 2.8 2.8 2.8 a1 a2 a3 a4 l
Slurry Density, ton/m3 1.68809757 1.95530726 1.34615385 9.67960522 1.40133094 54.9640283 0.52297758 0.95
% Solids (by volume) 38.227643 53.0726257 19.2307692
% Solids (by weight) 63.407117 76 40
Opening Mid-Size Classifier
Efficiency
1 25400 Circulating Load, CL 3.53163946
2 19050 21997.0453 1 Slurry Split, S 1.27968312
3 12700 15554.2599 1 Cyclone Pressure, ft 13.0701614
4 9500 10984.0794 1 Cyclone Pressure, lb/in2 9.55358545
5 6700 7978.09501 1 Corrected Cut Size, d50c, microns 181.745672
6 4750 5641.36508 1 Water By-Pass 0.42644207
7 3350 3989.04751 1 Solids By-Pass 0.40511996
8 2360 2811.76101 1 Plitt's Parameter 1.49707364
9 1700 2002.99775 1
10 1180 1416.33329 0.99999982
11 850 1001.49888 0.99992044
12 600 714.142843 0.99724847
13 425 504.975247 0.97575022
14 300 357.071421 0.91143595
15 212 252.190404 0.80815153
16 150 178.325545 0.69667904
17 106 126.095202 0.60160368
18 75 89.1627725 0.53140733
19 53 63.0476011 0.48388583
20 38 44.8776113 0.45380331
21 0 19 0.41898295
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Bpc
0
Page 30
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Matrix J
1 2 3 4 5 6 7 8 9
1 0.585136844 0 0 0 0 0 0 0 0
2 0 0.402835812 0 0 0 0 0 0 0
3 0 0 0.243607537 0 0 0 0 0 0
4 0 0 0 0.151304354 0 0 0 0 0
5 0 0 0 0 0.106379609 0 0 0 0
6 0 0 0 0 0 0.098408247 0 0 0
7 0 0 0 0 0 0 0.113862173 0 0
8 0 0 0 0 0 0 0 0.14575978 0
9 0 0 0 0 0 0 0 0 0.192568379
10 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0
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Matrix T
1 2 3 4 5 6 7 8 9
1 1 0 0 0 0 0 0 0 0
2 0.841479517 1 0 0 0 0 0 0 0
3 0.489924706 0.845646271 1 0 0 0 0 0 0
4 0.386606149 0.776863059 1.434673772 1 0 0 0 0 0
5 0.315327151 0.721995978 1.809260508 2.469465661 1 0 0 0 0
6 0.315398548 0.821129855 2.752379842 6.760890822 13.27125741 1 0 0 0
7 0.369076182 1.119814584 5.378875108 30.3364626 -219.8118008 -7.495387989 1 0 0
8 0.466858773 1.731025768 14.05792487 926.1123762 695.2981701 18.41420805 -4.144433287 1 0
9 0.708619343 3.469245574 73.32817949 -3857.727067 -993.5316507 -22.32856376 6.923306307 -3.546579474 1
10 1.072318934 8.174042244 -2266.6272 5667.083733 719.386679 14.19119948 -5.647527469 4.766390864 -3.132289953
11 1.951780615 31.64779806 6321.137547 -4128.423662 -265.178432 -4.521554118 2.363786177 -3.215751289 3.98991189
12 4.136434003 579.4123252 -7291.835913 1637.493651 52.44048422 0.759028624 -0.536728391 1.185552683 -2.593549289
13 11.86901497 -2368.807417 4263.567153 -316.2594569 -3.563319081 -0.035929086 0.04690161 -0.208960629 0.875426291
14 65.27464493 3389.574616 -1299.667344 23.57249567 0.022118425 0.000571441 -0.000548141 0.013372277 -0.142675361
15 -1113.147784 -2364.754858 179.6652476 0.87956343 0.051890681 0.001273712 -0.000394096 0.000721126 0.006484297
16 2685.152419 856.6168972 -5.658794658 0.567041523 0.050134524 0.001235646 -0.000358363 0.000448085 -8.37579E-05
17 -2777.308627 -149.9772447 -0.227192911 0.503252696 0.046193336 0.001139325 -0.000327928 0.000394871 -0.000247519
18 1467.202241 8.265492719 -0.027516841 0.463327035 0.042695812 0.001053074 -0.000302823 0.00036313 -0.000242418
19 -391.529141 0.115726363 -0.009107059 0.407893608 0.037612933 0.000927721 -0.000266727 0.000319627 -0.000215062
20 40.4334073 -0.753099391 -0.078171917 4.760032272 0.437966052 0.01079788 -0.003106871 0.003728728 -0.002519118
Matrix T (inverse)
1 2 3 4 5 6 7 8 9
1 1 5.25748E-16 1.93926E-15 8.5578E-16 1.87274E-15 1.3342E-15 -7.86704E-17 4.73301E-16 6.16571E-16
2 -0.841479517 1 -2.71996E-15 4.61772E-16 -4.21497E-15 5.77416E-16 4.13531E-15 2.70627E-15 2.61689E-15
3 0.221669309 -0.845646271 1 -2.74282E-15 -1.02781E-15 -5.63128E-15 -3.76681E-15 -4.41018E-15 -4.52166E-15
4 -0.050914941 0.436363466 -1.434673772 1 4.24272E-15 1.0118E-14 -2.10088E-15 1.06845E-15 2.44948E-15
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5 0.016892849 -0.269586172 1.733617105 -2.469465661 1 -1.53231E-14 9.42598E-15 4.60655E-15 2.8274E-16
6 -0.114511716 2.133951622 -16.05998595 26.01202362 -13.27125741 1 -1.03781E-13 -5.89913E-14 -1.04616E-14
7 3.780410278 -53.07233943 298.837724 -378.183947 120.3385774 7.495387989 1 5.58564E-13 -6.93702E-14
8 51.05724478 -465.7716277 1643.475343 -1255.446374 47.81673071 12.64992743 4.144433287 1 -2.50142E-12
9 -41.32753886 237.2572583 -484.3301577 150.7888644 33.64853718 15.29966978 7.775255718 3.546579474 1
10 434.8008115 -1570.713151 1714.998912 60.73349644 26.04755023 15.7677135 10.24789388 6.34252439 3.132289953
11 128.8492366 -292.1868256 142.4747979 40.65920132 23.58732467 16.89911633 12.73675229 9.362773003 6.034148485
12 665.4479586 -894.0766415 62.85672783 29.75492881 20.6887971 16.5731401 13.79299314 11.33182435 8.572972006
13 -256.6484779 181.8593757 39.62689582 24.21696064 18.89503961 16.31073474 14.51041649 12.82746697 10.74617897
14 -263.3810526 68.63929497 28.98692082 20.66084374 17.4154862 15.82564587 14.73875319 13.69410094 12.281019
15 694.3656877 41.03090002 23.34380387 18.38326881 16.33778623 15.38137439 14.78245504 14.20893467 13.34628307
16 100.8942482 29.41043506 19.88106964 16.75548163 15.45157538 14.90805037 14.63934877 14.40144083 13.96387104
17 50.22584799 23.22757654 17.5364197 15.49727704 14.66723779 14.39135295 14.33799212 14.32635204 14.19521188
18 33.18190447 19.56068736 15.91783475 14.54941276 14.0239156 13.91695035 13.99639559 14.12712761 14.2012704
19 25.49443411 17.41629376 14.92724914 13.97347828 13.63942317 13.63456361 13.79066142 14.00449838 14.20635835
20 1 1 1 1 1 1 1 1 1
Matrix T*J
1 2 3 4 5 6 7 8 9
1 0.585136844 0 0 0 0 0 0 0 0
2 0.492380669 0.402835812 0 0 0 0 0 0 0
3 0.286672996 0.340656602 0.243607537 0 0 0 0 0 0
4 0.226217502 0.312948261 0.349497344 0.151304354 0 0 0 0 0
5 0.184509534 0.290845836 0.440749497 0.373640907 0.106379609 0 0 0 0
6 0.184551311 0.330780512 0.670500475 1.022952221 1.411791168 0.098408247 0 0 0
7 0.215960073 0.451101417 1.310334518 4.590038886 -23.38349332 -0.737607996 0.113862173 0 0
8 0.273176269 0.697319171 3.424616456 140.1248351 73.96554715 1.812109943 -0.471894181 0.14575978 0
9 0.414639286 1.397536357 17.86329722 -583.6909031 -105.6915081 -2.197314829 0.788302703 -0.516948642 0.192568379
10 0.627453317 3.292796943 -552.1674701 857.4544452 76.52807329 1.396531071 -0.643039752 0.694748082 -0.60318
11 1.14205875 12.74886642 1539.87675 -624.6484766 -28.20957778 -0.444958217 0.269145831 -0.468727199 0.768330867
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12 2.420379938 233.4080344 -1776.346189 247.7599196 5.578598183 0.074694677 -0.061113061 0.172805898 -0.499435584
13 6.944997962 -954.240459 1038.637094 -47.85143294 -0.379064489 -0.003535718 0.005340319 -0.030458055 0.168579422
14 38.19459973 1365.442042 -316.608761 3.566621238 0.002352949 5.62345E-05 -6.24125E-05 0.00194914 -0.027474763
15 -651.3437811 -952.607943 43.7678085 0.133081777 0.00552011 0.000125344 -4.48726E-05 0.000105111 0.001248671
16 1571.181612 345.0759632 -1.378525031 0.085795852 0.005333291 0.000121598 -4.08039E-05 6.53127E-05 -1.61291E-05
17 -1625.105605 -60.41620514 -0.055345906 0.076144324 0.004914029 0.000112119 -3.73385E-05 5.75563E-05 -4.76644E-05
18 858.514089 3.32963647 -0.00670331 0.070103398 0.004541964 0.000103631 -3.44801E-05 5.29298E-05 -4.66821E-05
19 -229.0981259 0.046618723 -0.002218548 0.061716079 0.004001249 9.12954E-05 -3.03701E-05 4.65888E-05 -4.14141E-05
20 23.65907634 -0.303375404 -0.019043268 0.72021361 0.046590657 0.0010626 -0.000353755 0.000543499 -0.000485102
Matrix [T*J*T(inv.)]
1 2 3 4 5 6 7 8 9
1 0.585136844 3.07635E-16 1.13473E-15 5.00748E-16 1.09581E-15 7.80689E-16 -4.60329E-17 2.76946E-16 3.60778E-16
2 0.153402585 0.402835812 -1.40844E-16 6.07388E-16 -7.75839E-16 8.89537E-16 1.62711E-15 1.32323E-15 1.35776E-15
3 0.054017758 0.134650797 0.243607537 -2.65536E-16 -1.14937E-15 -7.92642E-16 4.68544E-16 -1.67632E-17 -3.32953E-17
4 0.032647133 0.083420828 0.132424956 0.151304354 -6.12694E-16 4.52998E-17 -3.58022E-16 -4.25695E-16 -2.5126E-16
5 0.020242506 0.052492438 0.089118196 0.110940117 0.106379609 8.25593E-17 -2.54242E-16 -1.8009E-16 -1.72739E-16
6 0.015332388 0.039552325 0.069967999 0.09638007 0.105789984 0.098408247 -2.26824E-16 -1.83273E-16 -1.76999E-16
7 0.013023531 0.032861953 0.059388921 0.087249904 0.107504229 0.11583317 0.113862173 -1.5695E-16 -1.61601E-16
8 0.011201179 0.027288381 0.049488941 0.075320247 0.099251308 0.118930598 0.132197501 0.14575978 -1.7397E-16
9 0.010918641 0.025313416 0.045129949 0.069080037 0.093698715 0.118189588 0.143111935 0.16601042 0.192568379
10 0.009252178 0.020361683 0.035286648 0.053269294 0.072556221 0.093425325 0.117972209 0.147082629 0.182820684
11 0.008678321 0.018161404 0.030302777 0.044213284 0.058855996 0.074904064 0.094850563 0.120831309 0.159311133
12 0.00774328 0.015532651 0.024940296 0.03484282 0.04454786 0.05472525 0.067520317 0.085079204 0.113771057
13 0.006998198 0.013615256 0.021173361 0.028353304 0.034571539 0.040350139 0.047312483 0.057128532 0.074321742
14 0.006273211 0.011972118 0.018209036 0.023596102 0.027589648 0.030555782 0.033657937 0.038053288 0.046381141
15 0.005636028 0.010641907 0.015973669 0.020271116 0.023020675 0.024480765 0.025506855 0.026894357 0.030023079
16 0.00511186 0.009600469 0.014310236 0.017953396 0.020049338 0.020795083 0.02086509 0.020843364 0.021431884
17 0.004623375 0.008661579 0.012867715 0.016054439 0.017780677 0.018208253 0.01790074 0.017321346 0.016848238
18 0.004218533 0.007894387 0.011709737 0.014572904 0.016079951 0.016372885 0.015946732 0.015196473 0.014360154
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19 0.003699997 0.006921031 0.010259609 0.012755449 0.014053825 0.014277397 0.013853526 0.013118664 0.012243256
20 0.041842453 0.078221566 0.115840418 0.143843165 0.158270424 0.160543451 0.155441938 0.146680634 0.135919254
Matrix [T*J*T(inv.)] (inverse)
1 2 3 4 5 6 7 8 9
1 1.709001937 1.30253E-15 -5.74965E-15 6.11659E-15 -4.16962E-15 -1.50966E-14 3.98777E-15 -8.25949E-17 1.62937E-15
2 -0.650799424 2.482400945 8.97408E-15 -2.97124E-14 3.42661E-14 1.97624E-14 -1.24611E-14 -3.17535E-15 -1.09423E-14
3 -0.019235005 -1.372113804 4.1049633 -8.20227E-15 -9.29577E-15 4.54735E-14 -1.11469E-14 1.90736E-15 3.32095E-15
4 0.006896086 -0.167753478 -3.592755707 6.609195117 3.61297E-14 -7.11489E-14 1.50313E-14 1.02173E-14 6.15991E-15
5 0.004857154 0.099489177 0.307895621 -6.89253223 9.4002978 -3.50736E-16 8.7684E-15 -8.59303E-15 -1.40294E-15
6 -0.002998721 0.035184663 0.269100484 0.936569734 -10.10542694 10.16174991 -5.40155E-15 7.7165E-16 1.28608E-15
7 -0.004433871 -0.00195647 0.047490793 0.490407689 1.404960628 -10.33765361 8.782547975 -2.91302E-15 -2.91302E-16
8 -0.003364181 -0.00686975 -0.009498705 0.06908054 0.57025564 1.084448514 -7.965372198 6.860603128 7.74975E-16
9 -0.003645416 -0.007198641 -0.015282901 -0.016026002 0.092566638 0.510981227 0.339865473 -5.914426899 5.192960561
10 -0.002539092 -0.004546448 -0.009400245 -0.018154256 -0.017898634 0.068820927 0.292254568 0.287740146 -3.783374974
11 -0.002719532 -0.004656014 -0.008828851 -0.016565751 -0.030121845 -0.023356746 0.045908518 0.169053065 -0.127750226
12 -0.002442217 -0.004095811 -0.00749356 -0.013429801 -0.026486633 -0.036233937 -0.02417302 0.019233878 0.060992806
13 -0.002296729 -0.003837424 -0.006933849 -0.012107253 -0.023846651 -0.035283993 -0.036013154 -0.023119516 0.001973462
14 -0.002114768 -0.003531227 -0.006357654 -0.010997707 -0.021532565 -0.032202958 -0.035190182 -0.030362928 -0.020501816
15 -0.001949201 -0.003257124 -0.005859154 -0.010103219 -0.019696853 -0.029442175 -0.03256221 -0.029651817 -0.024693162
16 -0.001808966 -0.003025751 -0.0054424 -0.009373722 -0.018223733 -0.02719766 -0.030127335 -0.027743631 -0.0241961
17 -0.001661798 -0.002781411 -0.005003125 -0.008613391 -0.016720315 -0.024929427 -0.027613702 -0.025486827 -0.022475087
18 -0.001537621 -0.002575322 -0.004632842 -0.007973683 -0.015457863 -0.023027462 -0.025500048 -0.023546343 -0.020819106
19 -0.001355214 -0.002270182 -0.004084023 -0.007028675 -0.013621435 -0.020287352 -0.022463863 -0.020744385 -0.018353082
20 -0.015853422 -0.026605926 -0.047877183 -0.08234739 -0.159047239 -0.23638526 -0.261560824 -0.24154787 -0.213763279
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Matrix { C(inv.)*[T*J*T(inv.)] (inverse)-I}
1 2 3 4 5 6 7 8 9
1 0.709001937 1.30253E-15 -5.74965E-15 6.11659E-15 -4.16962E-15 -1.50966E-14 3.98777E-15 -8.25949E-17 1.62937E-15
2 -0.650799424 1.482400945 8.97408E-15 -2.97124E-14 3.42661E-14 1.97624E-14 -1.24611E-14 -3.17535E-15 -1.09423E-14
3 -0.019235005 -1.372113804 3.1049633 -8.20227E-15 -9.29577E-15 4.54735E-14 -1.11469E-14 1.90736E-15 3.32095E-15
4 0.006896086 -0.167753478 -3.592755707 5.609195117 3.61297E-14 -7.11489E-14 1.50313E-14 1.02173E-14 6.15991E-15
5 0.004857154 0.099489177 0.307895621 -6.89253223 8.4002978 -3.50736E-16 8.7684E-15 -8.59303E-15 -1.40294E-15
6 -0.002998721 0.035184663 0.269100484 0.936569734 -10.10542694 9.161749909 -5.40155E-15 7.7165E-16 1.28608E-15
7 -0.004433871 -0.00195647 0.047490793 0.490407689 1.404960628 -10.33765361 7.782547975 -2.91302E-15 -2.91302E-16
8 -0.003364181 -0.00686975 -0.009498705 0.06908054 0.57025564 1.084448514 -7.965372198 5.860603128 7.74975E-16
9 -0.003645417 -0.007198642 -0.015282904 -0.016026005 0.092566655 0.510981322 0.339865536 -5.914427991 4.19296152
10 -0.002539294 -0.00454681 -0.009400992 -0.018155701 -0.017900058 0.068826403 0.292277823 0.287763041 -3.783676014
11 -0.002727036 -0.004668861 -0.008853211 -0.016611458 -0.030204955 -0.02342119 0.046035186 0.169519504 -0.128102704
12 -0.002502912 -0.004197602 -0.007679793 -0.013763564 -0.027144891 -0.037134439 -0.024773778 0.019711886 0.062508626
13 -0.002519902 -0.004210305 -0.007607609 -0.013283712 -0.026163825 -0.038712531 -0.039512545 -0.025366035 0.002165223
14 -0.002616797 -0.004369512 -0.007866908 -0.013608472 -0.026644217 -0.039847673 -0.043544039 -0.037570836 -0.025368777
15 -0.002797847 -0.004675214 -0.008410119 -0.01450197 -0.028272492 -0.042260745 -0.046739185 -0.04256166 -0.0354441
16 -0.003006907 -0.005029476 -0.009046488 -0.015581225 -0.030291924 -0.045208601 -0.050078375 -0.046116127 -0.040219335
17 -0.003127164 -0.005234048 -0.009414858 -0.016208641 -0.031464216 -0.046912087 -0.051963345 -0.047961001 -0.04229352
18 -0.003177652 -0.00532217 -0.009574247 -0.016478439 -0.031945269 -0.047588625 -0.05269848 -0.048660947 -0.043024831
19 -0.002986346 -0.005002569 -0.008999545 -0.015488373 -0.030016164 -0.044705165 -0.049501319 -0.045712282 -0.040442811
20 -0.037837869 -0.063501216 -0.114270005 -0.19654115 -0.379603133 -0.564188263 -0.624275586 -0.57651003 -0.510195656
Matrix { C(inv.)*[T*J*T(inv.)] (inverse)-I}(inverse)
1 2 3 4 5 6 7 8 9
1 1.410433382 5.63488E-15 7.27958E-15 4.90569E-15 6.15236E-15 5.188E-15 3.16951E-15 4.16003E-15 4.47477E-15
2 0.61920443 0.674581329 3.90461E-15 4.70474E-15 2.63506E-15 5.37307E-15 5.97328E-15 5.45004E-15 5.29343E-15
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3 0.282370049 0.298104121 0.322064998 -1.34387E-18 -1.18004E-15 -1.51303E-16 1.5696E-15 7.88794E-16 7.28926E-16
4 0.197645796 0.211113826 0.206286434 0.178278698 -1.08088E-15 1.29763E-16 -1.15532E-16 -3.08281E-16 -6.44222E-17
5 0.143671654 0.154305286 0.157455548 0.146279537 0.119043399 9.69752E-17 -1.63489E-16 -1.58684E-16 -1.29836E-16
6 0.128055386 0.137271058 0.143126158 0.143121865 0.131305087 0.109149454 -2.20907E-16 -2.47236E-16 -2.24377E-16
7 0.130942635 0.139529952 0.146727039 0.152469093 0.152923595 0.144984554 0.128492623 -2.16689E-16 -2.70429E-16
8 0.13995747 0.148010892 0.155707768 0.164408414 0.171964311 0.176857049 0.174639289 0.170630902 -2.06474E-16
9 0.172101348 0.180384948 0.188786142 0.199559814 0.211540978 0.224414102 0.235924246 0.240685296 0.238494915
10 0.193952086 0.201701052 0.209804712 0.2208069 0.234243789 0.250661671 0.269594191 0.288594321 0.302265308
11 0.240305146 0.248124725 0.256392822 0.267861281 0.282361466 0.300882415 0.323818499 0.350125899 0.379846189
12 0.287224372 0.294763645 0.302776099 0.313978036 0.328333799 0.346997493 0.370772988 0.399377395 0.435640146
13 0.330200603 0.337120041 0.344490608 0.354817299 0.368106926 0.385487463 0.407858876 0.435248483 0.471353055
14 0.338861698 0.344414885 0.350339731 0.358641118 0.369330306 0.383327046 0.401406243 0.423688387 0.453503148
15 0.303863884 0.307562538 0.311515171 0.317049012 0.324168361 0.333484195 0.345527969 0.360411871 0.38045871
16 0.243807077 0.24575455 0.247840487 0.250756769 0.254501429 0.259391767 0.265712868 0.273536667 0.284120601
17 0.181844793 0.182531303 0.183270967 0.184301115 0.185616735 0.187324848 0.189529148 0.19226384 0.195991796
18 0.134571139 0.134541088 0.134514107 0.134471712 0.134408827 0.134314853 0.134189336 0.134041917 0.133877309
19 0.099260968 0.098917711 0.098554983 0.098043441 0.097378601 0.096499136 0.095358504 0.093954115 0.092086771
20 0.860427161 0.853715505 0.846535616 0.836496217 0.823606772 0.806782943 0.785083927 0.758341253 0.72250905
Circuit Balance
1 2 3 4 5 6 7 8
Fresh Mill Mill Sump Cyclone Cyclone Cyclone Secondary
Feed Feed Discharge Water Feed U'flow O'flow Feed
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 15.000 35.585 14.335 0.000 29.335 29.335 0.000 6.250
3 49.800 99.606 29.056 0.000 78.856 78.856 0.000 20.750
4 42.210 89.498 29.700 0.000 71.910 71.910 0.000 17.588
5 30.990 72.263 28.361 0.000 59.351 59.351 0.000 12.913
6 25.020 66.651 31.206 0.000 56.226 56.226 0.000 10.425
7 20.520 67.092 38.022 0.000 58.542 58.542 0.000 8.550
8 16.230 69.772 46.780 0.000 63.010 63.010 0.000 6.763
9 15.300 85.563 63.888 0.000 79.188 79.188 0.000 6.375
Page 37
Mill
10 11.700 94.604 78.036 0.000 89.736 89.729 0.007 4.875
11 10.620 116.517 101.782 0.000 112.402 112.092 0.309 4.425
12 9.030 135.490 125.971 0.000 135.001 131.727 3.274 3.763
13 7.770 144.820 147.571 0.000 155.341 141.583 13.758 3.238
14 6.630 131.352 152.485 0.000 159.115 128.589 30.526 2.763
15 5.640 101.268 136.345 0.000 141.985 98.918 43.067 2.350
16 4.860 70.032 108.182 0.000 113.042 68.007 45.036 2.025
17 4.140 45.983 79.145 0.000 83.285 44.258 39.027 1.725
18 3.540 30.788 57.039 0.000 60.579 29.313 31.266 1.475
19 2.550 20.593 40.488 0.000 43.038 19.531 23.507 1.063
20 18.450 148.467 317.554 0.000 336.004 140.780 195.224 7.688
Total 300.000 1625.947 1625.947 0.000 1925.947 1500.947 425.000 125.000
CL = 3.531640097
Page 38
Mill
10 11 12 13 14 15 16 17 18
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0.250934842 0 0 0 0 0 0 0 0
0 0.315929625 0 0 0 0 0 0 0
0 0 0.387337118 0 0 0 0 0 0
0 0 0 0.460180613 0 0 0 0 0
0 0 0 0 0.531658119 0 0 0 0
0 0 0 0 0 0.598891841 0 0 0
0 0 0 0 0 0 0.660490428 0 0
0 0 0 0 0 0 0 0.715533949 0
0 0 0 0 0 0 0 0 0.76370616
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
Page 39
Mill
10 11 12 13 14 15 16 17 18
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
-3.200233862 1 0 0 0 0 0 0 0
4.019730654 -3.077548507 1 0 0 0 0 0 0
-2.530593821 3.757772347 -3.075947053 1 0 0 0 0 0
0.832985429 -2.306165209 3.732710868 -3.055242062 1 0 0 0 0
-0.127564321 0.73025418 -2.2666493 3.685801766 -3.056425977 1 0 0 0
0.005292183 -0.106586603 0.71123422 -2.232108597 3.696582328 -3.06045921 1 0 0
0.000184452 0.003946524 -0.103704512 0.700332 -2.242119399 3.696553716 -3.054735637 1 0
2.94815E-05 -2.02105E-07 0.003631191 -0.100905636 0.702373885 -2.240356841 3.692417034 -3.059747561 1
1.49222E-05 -0.000119238 2.01485E-05 0.003561575 -0.100555887 0.692528389 -2.206784169 3.653974344 -3.049400298
0.000154883 -0.001553292 -0.001295561 -0.001439046 0.000145051 -0.088266053 0.569102772 -1.594226783 2.049400298
10 11 12 13 14 15 16 17 18
1.25681E-15 1.01632E-15 2.01985E-15 9.84979E-17 1.04446E-15 6.84368E-16 6.95081E-16 4.2833E-16 2.41454E-16
3.35029E-16 -4.77592E-16 -2.33312E-15 1.74901E-15 -9.73087E-16 -2.77962E-16 -7.63382E-16 -5.87353E-16 -5.23294E-16
-2.76229E-15 -1.60077E-15 -1.5009E-15 -2.1672E-15 1.68627E-16 -4.3391E-16 3.23172E-16 3.02503E-16 3.24227E-16
2.48189E-15 1.23815E-15 4.08597E-15 1.35742E-17 -1.32791E-15 2.15045E-16 -5.1531E-16 -1.60186E-16 -1.5198E-16
Page 40
Mill
-2.02203E-15 -6.70058E-17 -6.36424E-15 2.88786E-15 3.48962E-15 2.55967E-16 1.02359E-15 1.36967E-16 9.03776E-17
1.69679E-14 -2.94452E-15 6.22662E-14 -3.39187E-14 -3.73233E-14 -3.64345E-15 -1.05823E-14 -1.22038E-15 -7.1076E-16
-3.7858E-13 -6.5583E-14 -1.04623E-12 3.89803E-13 5.27389E-13 2.48246E-14 1.6017E-13 2.46918E-14 1.79021E-14
-2.73633E-12 -1.29483E-12 -4.81748E-12 2.46987E-13 1.6753E-12 -2.00893E-13 6.20672E-13 1.74487E-13 1.61429E-13
1.06104E-12 6.24208E-13 1.10437E-12 4.94214E-13 -2.0846E-13 1.50489E-13 -1.36436E-13 -8.16858E-14 -8.59284E-14
1 -2.79573E-12 -2.33346E-12 -4.02751E-12 2.74036E-13 -7.6398E-13 5.90978E-13 5.68487E-13 6.07794E-13
3.200233862 1 1.2297E-13 -6.76332E-13 8.60787E-14 -6.14848E-14 1.29118E-13 1.2297E-13 1.24703E-13
5.82914429 3.077548507 1 -1.65836E-12 7.2844E-13 1.54987E-13 6.122E-13 4.8821E-13 4.47063E-13
8.434982709 5.708603913 3.075947053 1 -3.26715E-13 -1.48162E-13 -2.19077E-13 -1.51327E-13 -1.19851E-13
10.55968629 8.259733243 5.66505195 3.055242062 1 -1.83965E-13 -2.02361E-13 -1.28775E-13 -8.50837E-14
12.18843133 10.44994986 8.244130165 5.65231944 3.056425977 1 4.69185E-13 2.87565E-13 1.55134E-13
13.28516759 12.10881402 10.44410681 8.236847875 5.657484706 3.06045921 1 3.6758E-14 1.60816E-14
13.88796723 13.197024 12.08035851 10.4171758 8.22599674 5.652340099 3.054735637 1 6.76758E-15
14.15882411 13.84382192 13.19640766 12.07824678 10.42479153 8.234598952 5.65430288 3.059747561 1
14.33835534 14.28871014 13.99708373 13.33353102 12.20052316 10.51832734 8.28709141 5.67642078 3.049400298
1 1 1 1 1 1 1 1 1
10 11 12 13 14 15 16 17 18
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0.250934842 0 0 0 0 0 0 0 0
-0.803050178 0.315929625 0 0 0 0 0 0 0
Page 41
Mill
1.008690476 -0.972288747 0.387337118 0 0 0 0 0 0
-0.63501416 1.18719161 -1.191428466 0.460180613 0 0 0 0 0
0.209025067 -0.728585911 1.445817469 -1.405963164 0.531658119 0 0 0 0
-0.032010333 0.230708929 -0.877957407 1.696134514 -1.624973685 0.598891841 0 0 0
0.001327993 -0.033673865 0.275487413 -1.027173101 1.965318006 -1.83288405 0.660490428 0 0
4.62855E-05 0.001246824 -0.040168607 0.322279209 -1.192040981 2.213835859 -2.017623648 0.715533949 0
7.39793E-06 -6.38508E-08 0.001406495 -0.046434817 0.373422778 -1.341731433 2.438806107 -2.189353255 0.76370616
3.74449E-06 -3.76709E-05 7.80424E-06 0.001638968 -0.053461354 0.414749602 -1.45755982 2.614542691 -2.328845792
3.88654E-05 -0.000490731 -0.000501819 -0.000662221 7.71174E-05 -0.052861819 0.375886933 -1.140723385 1.565139632
10 11 12 13 14 15 16 17 18
7.35404E-16 5.94686E-16 1.18189E-15 5.76347E-17 6.11153E-16 4.00449E-16 4.06718E-16 2.50632E-16 1.41283E-16
7.53789E-16 3.08025E-16 5.46676E-17 7.53062E-16 1.22278E-16 2.24997E-16 3.47271E-17 -2.57053E-17 -9.19144E-17
-1.98491E-16 -2.61303E-16 -5.81389E-16 9.61019E-17 9.00917E-18 -4.2034E-18 1.79372E-17 -3.6029E-18 -3.0061E-17
-2.00732E-16 -2.91679E-16 -1.79558E-16 -1.85746E-16 -2.10234E-16 -5.12848E-17 -4.66802E-17 -5.42803E-18 -1.88215E-17
-1.75908E-16 -2.01428E-16 -1.17759E-16 -1.16045E-16 -1.40918E-16 -3.82381E-17 -3.49915E-17 -3.75145E-18 -1.1916E-17
-1.55389E-16 -1.61527E-16 -8.30627E-17 -1.03329E-16 -1.2074E-16 -3.37726E-17 -3.09817E-17 -2.99619E-18 -8.95926E-18
-1.44558E-16 -1.39045E-16 -6.44821E-17 -9.29691E-17 -1.07545E-16 -3.04916E-17 -2.81444E-17 -2.48257E-18 -7.37504E-18
-1.17682E-16 -1.20216E-16 -5.28193E-17 -8.04263E-17 -9.14241E-17 -2.5909E-17 -2.41371E-17 -1.95934E-18 -6.03087E-18
-1.56723E-16 -1.19698E-16 -4.66295E-17 -7.05213E-17 -8.30206E-17 -2.34114E-17 -2.15953E-17 -1.51666E-18 -5.46687E-18
0.250934842 -9.21598E-17 -5.84318E-17 -5.42342E-17 -6.63973E-17 -1.72232E-17 -1.60619E-17 -1.04246E-18 -4.28412E-18
0.207998507 0.315929625 -1.36274E-15 -1.84959E-16 -2.55819E-16 -2.97232E-16 -8.79458E-18 -1.91377E-17 1.47596E-17
0.154983052 0.219760021 0.387337118 -1.20456E-16 -2.00999E-16 -2.10235E-16 -6.6019E-18 -1.32256E-17 9.75061E-18
0.100883704 0.14750156 0.224062733 0.460180613 -1.03801E-16 -1.27241E-16 -4.52638E-18 -8.85392E-18 5.95828E-18
0.060126377 0.086254899 0.13302008 0.218381083 0.531658119 -8.90754E-17 -6.66222E-19 -6.04238E-18 2.72706E-18
0.035776821 0.047853092 0.071044502 0.116574557 0.205494895 0.598891841 5.97566E-17 1.13159E-17 7.53006E-19
0.023118527 0.02763942 0.03728383 0.057662164 0.099958076 0.188519964 0.660490428 5.54203E-16 2.8173E-16
0.016758641 0.017812728 0.02095182 0.028596809 0.045689448 0.083422214 0.168143405 0.715533949 7.11631E-17
0.013617721 0.013311068 0.013783392 0.015996123 0.021892995 0.035979933 0.069136639 0.147394806 0.76370616
Page 42
Mill
0.011357819 0.010632567 0.010172291 0.010337423 0.01181011 0.016195701 0.027418238 0.055046889 0.124130247
0.124443989 0.113305019 0.102344235 0.092271229 0.083496357 0.076990348 0.074811291 0.082024357 0.112163593
10 11 12 13 14 15 16 17 18
-2.08565E-15 4.58777E-16 -4.92754E-15 8.20237E-16 -1.44144E-15 -7.7132E-16 -8.83466E-16 -5.33489E-16 -3.1616E-16
-4.66942E-15 -2.08457E-15 3.9223E-15 -4.03978E-15 3.4339E-16 -6.07541E-16 1.67602E-16 2.30792E-16 4.19161E-16
3.21481E-15 2.14135E-16 5.58569E-15 1.22492E-15 5.49338E-17 5.67109E-16 -2.19211E-17 -2.18857E-17 -2.29684E-30
3.13943E-16 4.64182E-15 -4.65881E-15 2.3579E-15 2.4353E-15 4.18575E-16 5.6324E-16 2.36048E-17 -3.9316E-30
1.92905E-15 -1.75368E-16 3.50736E-16 -7.89156E-16 -8.7684E-17 -8.7684E-17 8.7684E-17 -8.7684E-17 -1.75368E-16
-3.85825E-16 0 -1.28608E-16 6.43042E-16 -1.28608E-16 6.43042E-17 0 1.28608E-16 -1.28608E-16
7.28254E-16 0 1.45651E-16 -1.45651E-16 -2.18476E-16 -7.28254E-17 -1.45651E-16 -7.28254E-17 4.36953E-16
-1.29162E-15 -1.29162E-16 -3.87487E-16 -2.58325E-16 1.29162E-16 0 0 -1.29162E-16 -2.58325E-16
1.02748E-15 2.05496E-16 6.16489E-16 -1.02748E-16 3.08245E-16 2.05496E-16 0 -1.02748E-16 1.02748E-16
3.985098253 -3.14849E-16 -1.57424E-16 0 -1.57424E-16 0 1.57424E-16 7.87122E-17 -1.57424E-16
-2.623668124 3.165261879 9.96157E-15 6.07413E-16 2.42965E-16 1.57927E-15 -1.21483E-16 0 0
-0.105967966 -1.795846526 2.581730369 -1.94525E-16 3.8905E-16 -2.91788E-16 9.72625E-17 2.91788E-16 1.94525E-16
0.01892114 -0.140159715 -1.257048966 2.173059822 -1.5896E-16 -1.5896E-16 -3.1792E-16 -1.5896E-16 -3.1792E-16
-0.006284943 -0.006634839 -0.129606345 -0.892594583 1.880907984 1.33306E-16 1.33306E-16 -1.33306E-16 5.33225E-16
-0.017380892 -0.010319165 -0.01710556 -0.116715325 -0.645386967 1.669750583 -3.39704E-16 -1.13235E-16 -2.26469E-16
-0.019452522 -0.014897232 -0.011495536 -0.021314656 -0.100445991 -0.476587253 1.514026484 -1.14468E-15 -5.72338E-16
-0.018675681 -0.015483142 -0.012386326 -0.011236158 -0.021255047 -0.082678518 -0.355781257 1.397557728 -1.53309E-16
-0.01744867 -0.014808746 -0.01231327 -0.010330908 -0.01031856 -0.019564449 -0.06839593 -0.269727758 1.30940413
-0.015415394 -0.013169413 -0.011106611 -0.009381514 -0.008150438 -0.008696859 -0.016704466 -0.054014359 -0.202056329
-0.179725201 -0.153943099 -0.130667755 -0.111486678 -0.095350981 -0.082223503 -0.073144831 -0.073815611 -0.107347801
Page 43
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10 11 12 13 14 15 16 17 18
-2.08565E-15 4.58777E-16 -4.92754E-15 8.20237E-16 -1.44144E-15 -7.7132E-16 -8.83466E-16 -5.33489E-16 -3.1616E-16
-4.66942E-15 -2.08457E-15 3.9223E-15 -4.03978E-15 3.4339E-16 -6.07541E-16 1.67602E-16 2.30792E-16 4.19161E-16
3.21481E-15 2.14135E-16 5.58569E-15 1.22492E-15 5.49338E-17 5.67109E-16 -2.19211E-17 -2.18857E-17 -2.29684E-30
3.13943E-16 4.64182E-15 -4.65881E-15 2.3579E-15 2.4353E-15 4.18575E-16 5.6324E-16 2.36048E-17 -3.9316E-30
1.92905E-15 -1.75368E-16 3.50736E-16 -7.89156E-16 -8.7684E-17 -8.7684E-17 8.7684E-17 -8.7684E-17 -1.75368E-16
-3.85825E-16 0 -1.28608E-16 6.43042E-16 -1.28608E-16 6.43042E-17 0 1.28608E-16 -1.28608E-16
7.28254E-16 0 1.45651E-16 -1.45651E-16 -2.18476E-16 -7.28254E-17 -1.45651E-16 -7.28254E-17 4.36953E-16
-1.29162E-15 -1.29162E-16 -3.87487E-16 -2.58325E-16 1.29162E-16 0 0 -1.29162E-16 -2.58325E-16
1.02748E-15 2.05496E-16 6.16489E-16 -1.02748E-16 3.08245E-16 2.05496E-16 0 -1.02748E-16 1.02748E-16
2.985415343 -3.14874E-16 -1.57437E-16 0 -1.57437E-16 0 1.57437E-16 7.87185E-17 -1.57437E-16
-2.630907151 2.17399523 9.98906E-15 6.09089E-16 2.43636E-16 1.58363E-15 -1.21818E-16 0 0
-0.108601529 -1.840477698 1.645892673 -1.9936E-16 3.98719E-16 -2.99039E-16 9.96798E-17 2.99039E-16 1.9936E-16
0.020759703 -0.153779006 -1.37919616 1.384215605 -1.74406E-16 -1.74406E-16 -3.48812E-16 -1.74406E-16 -3.48812E-16
-0.007776936 -0.008209895 -0.160373816 -1.104489131 1.327419931 1.64952E-16 1.64952E-16 -1.64952E-16 6.59808E-16
-0.024948206 -0.014811936 -0.024553 -0.167530984 -0.926376324 1.396728608 -4.87604E-16 -1.62535E-16 -3.2507E-16
-0.032334447 -0.024762535 -0.019108154 -0.03542973 -0.166963724 -0.792194713 1.516650975 -1.90271E-15 -9.51353E-16
-0.035143815 -0.02913611 -0.023308534 -0.021144153 -0.039997656 -0.155584076 -0.669507625 1.629918066 -2.88496E-16
-0.036059477 -0.030603802 -0.025446643 -0.021349887 -0.021324368 -0.040431952 -0.141347246 -0.557420241 1.706018738
-0.033969328 -0.029020091 -0.024474504 -0.020673083 -0.017960287 -0.019164381 -0.036809926 -0.119025926 -0.445250891
-0.428955886 -0.36742092 -0.311868912 -0.266088822 -0.227577238 -0.196245466 -0.174577107 -0.176178081 -0.256210432
10 11 12 13 14 15 16 17 18
5.44857E-15 4.78998E-15 5.82877E-15 1.54605E-15 2.7122E-15 1.46561E-15 1.0892E-15 5.5104E-16 2.61382E-16
4.10907E-15 2.87424E-15 2.5515E-15 2.60151E-15 1.11656E-15 8.25951E-16 3.20998E-16 8.97147E-17 -5.09901E-17
Page 44
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3.379E-16 3.50965E-17 -2.59705E-16 7.78775E-16 4.09522E-16 2.47513E-16 1.55164E-16 4.7384E-17 -2.09138E-17
-1.15986E-16 -3.84478E-16 -1.66282E-16 -6.08331E-17 -1.07403E-16 8.95223E-17 4.02979E-17 2.97738E-17 -1.52418E-17
-1.88302E-16 -3.00705E-16 -1.1662E-16 -2.96984E-17 -1.03819E-16 6.21539E-17 2.18786E-17 3.19008E-17 9.50157E-19
-2.3447E-16 -3.34238E-16 -1.44435E-16 -1.07817E-16 -1.14977E-16 4.12565E-17 1.08454E-17 2.21693E-17 7.51748E-18
-2.77885E-16 -3.38676E-16 -1.30424E-16 -9.82749E-17 -9.78588E-17 4.87979E-17 1.70974E-17 1.98382E-17 -1.62556E-17
-1.69755E-16 -2.90845E-16 -6.67793E-17 -7.61463E-17 -1.03681E-16 6.39985E-17 3.21574E-17 4.22616E-17 2.49577E-18
-3.85043E-16 -4.70849E-16 -1.934E-16 -1.25432E-16 -1.94322E-16 5.12528E-17 4.75167E-17 6.56403E-17 -1.04576E-17
0.334961767 -4.25416E-16 -1.61155E-16 -1.09616E-16 -1.90876E-16 4.45614E-17 3.04044E-17 8.20261E-17 3.46524E-17
0.405361197 0.45998261 -3.54735E-15 -7.36031E-16 -6.64709E-16 -4.49973E-16 6.93407E-17 9.09487E-17 2.47642E-17
0.475386771 0.514363876 0.607573031 -8.77926E-16 -9.25243E-16 -4.56479E-16 -4.14661E-17 -5.13773E-17 -7.7019E-17
0.513672828 0.563600315 0.605369849 0.72243081 -6.59911E-16 -2.19338E-16 2.43027E-16 1.36804E-16 1.48707E-16
0.489309057 0.53393603 0.577106916 0.601103658 0.753341107 -3.93044E-16 8.60722E-17 9.16379E-17 -1.76924E-16
0.40478407 0.435652723 0.466056274 0.485332468 0.499651372 0.715958701 3.89931E-16 2.03697E-16 3.60228E-17
0.297046781 0.313491256 0.328764452 0.336554591 0.343916841 0.373967846 0.659347481 9.46636E-16 2.44747E-16
0.200591975 0.206347566 0.210235006 0.208693799 0.207448847 0.221953548 0.270834575 0.613527772 3.11215E-16
0.133731932 0.133370415 0.130827681 0.124128838 0.117533462 0.120472494 0.14312013 0.20046251 0.586160033
0.089856829 0.086818577 0.081671248 0.073318314 0.064844064 0.061829434 0.069122742 0.093298257 0.150046079
0.679267578 0.621627818 0.539910623 0.42845018 0.312842709 0.224729967 0.172783276 0.154026403 0.171089063
Page 45
Mill
Page 46
Mill
19 20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0.804412605 0
0 1
0
Page 47
Mill
19 20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
1 0
-1 1
19 20
0 0
0 0
0 0
0 0
Page 48
Mill
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
1 0
1 1
19 20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
Page 49
Mill
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0.804412605 0
-0.804412605 1
19 20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
Page 50
Mill
0.804412605 0
0.195587395 1
19 20
-1.31786E-30 0
2.64833E-30 0
1.39975E-30 0
-3.16549E-30 0
0 0
2.57217E-16 0
-2.91302E-16 0
0 0
0 0
-3.14849E-16 0
2.42965E-16 0
3.8905E-16 0
-6.3584E-16 0
0 0
0 0
7.63117E-16 0
-6.13237E-16 0
4.53869E-16 0
1.243143125 0
-0.243143125 1
Page 51
Mill
19 20
-1.31786E-30 0
2.64833E-30 0
1.39975E-30 0
-3.16549E-30 0
0 0
2.57217E-16 0
-2.91302E-16 0
0 0
0 0
-3.14874E-16 0
2.43636E-16 0
3.98719E-16 0
-6.97625E-16 0
0 0
0 0
1.26847E-15 0
-1.15399E-15 0
9.37968E-16 0
1.739387516 0
-0.580317475 1.386731991
Fresh C(inv)* Corrected Mill
19 20 Feed Sec. Feed Feed Discharge
-1.38078E-31 0 1 0.00 0 0.00 1 1.9757E-12
3.00558E-31 0 2 15.00 6.25 21.25 2 14.33485325
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Mill
1.51409E-31 0 3 49.80 20.75 70.55 3 29.0563982
-1.75748E-33 0 4 42.21 17.5875 59.80 4 29.70029718
2.96013E-33 0 5 30.99 12.9125 43.90 5 28.36092966
-1.61408E-17 0 6 25.02 10.425 35.45 6 31.20631411
7.91617E-20 0 7 20.52 8.55 29.07 7 38.02186086
3.09429E-18 0 8 16.23 6.7625 22.99 8 46.77998302
6.32528E-18 0 9 15.30 6.375001177 21.68 9 63.88840812
6.87194E-17 0 10 11.70 4.8753879 16.58 10 78.03649142
1.86885E-17 0 11 10.62 4.437209126 15.06 11 101.781664
-1.14482E-16 0 12 9.03 3.856007312 12.89 12 125.9710349
1.76326E-16 0 13 7.77 3.55208722 11.32 13 147.5705036
1.33127E-16 0 14 6.63 3.418294576 10.05 14 152.4851127
1.08627E-16 0 15 5.64 3.373145838 9.01 15 136.3451299
-4.05212E-16 0 16 4.86 3.366003356 8.23 16 108.1824575
2.56491E-16 0 17 4.14 3.246097511 7.39 17 79.1447482
-2.5953E-16 0 18 3.54 3.048239689 6.59 18 57.03898866
0.574915015 0 19 2.55 2.341322715 4.89 19 40.48806478
0.240589553 0.721119875 20 18.45 18.34800218 36.80 20 317.5538013
300 143.4742986 443.4742986 1625.947041
Page 53
