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Moly-Cop Tools, Version 2.0
About the BallSim_Reverse Spreadsheet ...
Scope : The BallSim_Reverse spreadsheet was designed to simulate the Size-by-Size Mass Balance around any given Conventional Ball Mill grinding section, of the Reverse 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_Reverse 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 cumulative 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_Reverse 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 (Length/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_Reverse 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_Reverse 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 E21. Finally, the system is solved by single clicking on the macro button ITERATE, next to Cell E21. Important Notice : ITERATE ... must be clicked every time any element of input data gets to be modified. After clicking ITERATE, Cell E23 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_Reverse 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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. Finally,
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Moly-Cop Tools TM (Version 2.0)
Circuit Type REVERSE (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 3.82
Suggested Default Values: 60.0 5.0 7.0 3.5
% Solids O'flow 40.0
% Solids U'flow 76.0
% Solids Mill Discharge 72.0 P80 148.8
Wio 15.01
Circulating Load 3.366 (Guess) % Fines MD 21.80
3.366 (Actual) Q 1649
0.000 (Delta) Bpf 0.394
Pressure 8.5
Ore Density, ton/m3 2.80 Total Water 578.9
Balls Density, ton/m3 7.75
Arbiter's
Feedrate, ton/hr (dry) 400.0 Flow # 2.05
Feed Moisture, % 5.0
i Mesh Opening Mid-Size ton/hr % Retained % Passing
1 1.05 25400 100.00
2 0.742 19050 21997 0.00 0.00 100.00
3 0.525 12700 15554 20.00 5.00 95.00
4 0.371 9500 10984 66.40 16.60 78.40
5 3 6700 7978 56.28 14.07 64.33
6 4 4750 5641 41.32 10.33 54.00
7 6 3350 3989 33.36 8.34 45.66
8 8 2360 2812 27.36 6.84 38.82
9 10 1700 2003 21.64 5.41 33.41
10 14 1180 1416 20.40 5.10 28.31
11 20 850 1001 15.60 3.90 24.41
12 28 600 714 14.16 3.54 20.87
13 35 425 505 12.04 3.01 17.86
14 48 300 357 10.36 2.59 15.27
15 65 212 252 8.84 2.21 13.06
16 100 150 178 7.52 1.88 11.18
17 150 106 126 6.48 1.62 9.56
18 200 75 89 5.52 1.38 8.18
19 270 53 63 4.72 1.18 7.00
20 400 38 45 3.40 0.85 6.15
21 -400 0 19 24.60 6.15 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 0.650 2.50 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
Main Simulated Outputs
Very Important : Simulation results are not valid until the Iterate button has been clicked after any input data changes.
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Moly-Cop Tools TM (Version 2.0)
Simulation N° 0
Remarks
40.00 % Solids
60.58 % - Size 18
148.8 P80 Bpc 0.000 8.52 psi
Bpf 0.394
Bpw 0.415 10 # of Cyclones
7.50 Vortex
3.82 Apex
ton/hr 400.0
F80 9795 76.00 % Solids
Water, 98.4 Water, m3/hr
m3/hr 480.5
Gross kW 4316.1
% Balls 38.00 Circ. Load 336.60
% Critical 72.00 m3/hr 1649
% Solids 72.00 % Solids 63.01
kWh/ton 10.79
Wio 15.01
Base Case Example
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Simulation N° 0
Remarks : Base Case Example
Fresh Mill Mill Sump Cyclone Cyclone Cyclone
Feed Feed Discharge Water Feed U'flow O'flow
Ore, ton/hr 400.0 1346.4 1346.4 0.0 1746.4 1346.4 400.0
Water, m3/hr 21.1 425.2 523.6 480.5 1025.2 425.2 600.0
Slurry, ton/hr 421.1 1771.6 1870.0 480.5 2771.6 1771.6 1000.0
Slurry, m3/hr 163.9 906.0 1004.4 480.5 1648.9 906.0 742.9
Slurry Dens., ton/m3 2.569 1.955 1.862 1.000 1.681 1.955 1.346
% Solids (by volume) 87.2 53.1 47.9 0.0 37.8 53.1 19.2
% Solids (by weight) 95.0 76.0 72.0 0.0 63.0 76.0 40.0
i Mesh Opening
1 1.05 25400 100.00 100.00 100.00 0.00 100.00 100.00 100.00
2 0.742 19050 100.00 100.00 100.00 0.00 100.00 100.00 100.00
3 0.525 12700 95.00 97.72 99.21 0.00 98.24 97.72 100.00
4 0.371 9500 78.40 91.20 97.62 0.00 93.22 91.20 100.00
5 3 6700 64.33 85.40 95.99 0.00 88.74 85.40 100.00
6 4 4750 54.00 80.77 94.44 0.00 85.18 80.77 100.00
7 6 3350 45.66 76.57 92.72 0.00 81.94 76.57 100.00
8 8 2360 38.82 72.43 90.61 0.00 78.75 72.43 100.00
9 10 1700 33.41 68.21 87.99 0.00 75.49 68.21 100.00
10 14 1180 28.31 63.10 84.39 0.00 71.55 63.10 100.00
11 20 850 24.41 57.51 79.96 0.00 67.24 57.51 100.00
12 28 600 20.87 50.66 74.15 0.00 61.95 50.66 99.94
13 35 425 17.86 42.71 66.90 0.00 55.67 42.71 99.30
14 48 300 15.27 34.18 58.29 0.00 48.44 34.18 96.43
15 65 212 13.06 26.36 49.17 0.00 40.90 26.36 89.85
16 100 150 11.18 20.21 40.73 0.00 33.96 20.21 80.25
17 150 106 9.56 15.85 33.76 0.00 28.22 15.85 69.86
18 200 75 8.18 12.92 28.49 0.00 23.84 12.92 60.58
19 270 53 7.00 10.94 24.60 0.00 20.57 10.94 52.98
20 400 38 6.15 9.60 21.80 0.00 18.22 9.60 47.22
D80, microns 9795 4461 852 0 2713 4461 148.8
Specific Energy Consumption : 10.79 kWh/ton (Gross)
Operational Work Index : 15.01 kWh/ton
Configuration : REVERSE
Particle Size Distributions (Cummulative % Passing)
Moly-Cop ToolsTM
, Version 2.0
BALLSIMConventional Closed Circuit Grinding Simulator
CIRCUIT MASS BALANCE
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Simulation N° 0
Remarks : Base Case Example
Number of Cyclones : 10 Operating Conditions :
Cyclone Dimensions, in : Feed Flowrate, m3/hr 1648.9
Diameter 20.00 Pressure, psi 8.5
Height 75.00 D50 (corr.), microns 186.1
Inlet 3.50 Water By-Pass, % 41.5
Vortex 7.50 Solids By-Pass, % 39.4
Apex 3.82 Plitt's Parameter 1.55
Ore Density, ton/m3 2.80 Circulating Load, % 337
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 98.24 97.72 100.00 1.000 1.000
4 0.371 9500 7978 93.22 91.20 100.00 1.000 1.000
5 3 6700 5641 88.74 85.40 100.00 1.000 1.000
6 4 4750 3989 85.18 80.77 100.00 1.000 1.000
7 6 3350 2812 81.94 76.57 100.00 1.000 1.000
8 8 2360 2003 78.75 72.43 100.00 1.000 1.000
9 10 1700 1416 75.49 68.21 100.00 1.000 1.000
10 14 1180 1001 71.55 63.10 100.00 1.000 1.000
11 20 850 714 67.24 57.51 100.00 0.998 0.996
12 28 600 505 61.95 50.66 99.94 0.976 0.961
13 35 425 357 55.67 42.71 99.30 0.909 0.850
14 48 300 252 48.44 34.18 96.43 0.800 0.670
15 65 212 178 40.90 26.36 89.85 0.683 0.477
16 100 150 126 33.96 20.21 80.25 0.586 0.316
17 150 106 89 28.22 15.85 69.86 0.515 0.199
18 200 75 63 23.84 12.92 60.58 0.468 0.122
19 270 53 45 20.57 10.94 52.98 0.439 0.074
20 400 38 19 18.22 9.60 47.22 0.406 0.020
Ore, ton/hr 1746.4 1346.4 400.0
Water, m3/hr 1025.2 425.2 600.0 a1 9.680
Slurry, ton/hr 2771.6 1771.6 1000.0 a2 1.401
Slurry, m3/hr 1648.9 906.0 742.9 a3 54.964
Slurry Dens., ton/m3 1.681 1.955 1.346 a4 0.523
% Solids (by volume) 37.8 53.1 19.2 l 0.950
% Solids (by weight) 63.0 76.0 40.0 Bpc 0.000
Size Distributions, % Passing Classifier Efficiency
Mass Balance around the Classifiers
CLASSIFIERS PERFORMANCE
Classifier Constants
Moly-Cop ToolsTM
, Version 2.0
BALLSIMConventional Closed Circuit Grinding Simulator
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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 1346.4
App. Density, ton/m3 5.39 % Solids (by weight) 72.0
Charge Level, % 38.0 Sp. Energy, kWh/ton 3.21
Balls Filling, % 38.0 Reduction Ratio 5.23
Lift Angle, (°) 35.0 Arbiter's Flow Number 2.05
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 97.72 99.21
4 0.371 9500 7978 91.20 97.62
5 3 6700 5641 85.40 95.99
6 4 4750 3989 80.77 94.44
7 6 3350 2812 76.57 92.72
8 8 2360 2003 72.43 90.61
9 10 1700 1416 68.21 87.99
10 14 1180 1001 63.10 84.39
11 20 850 714 57.51 79.96
12 28 600 505 50.66 74.15
13 35 425 357 42.71 66.90
14 48 300 252 34.18 58.29
15 65 212 178 26.36 49.17
16 100 150 126 20.21 40.73
17 150 106 89 15.85 33.76
18 200 75 63 12.92 28.49
19 270 53 45 10.94 24.60
20 400 38 19 9.60 21.80
D80, microns 4461 852
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
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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
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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 17
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 18
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 19
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 20
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 21
J&T
Mill Throughput, ton/hr 1346.389366 Reynolds Number 5.587257531
Water 523.5958645 Slurry Viscosity, cp 9.07347824
Slurry, m3/hr 1004.449209
Slurry Dens., ton/m3 1.861702128
% Solids (by volume) 47.87234043
Ebar 2.486878203 N 3.335901404
Matrix J
1 2 3 4 5 6 7 8 9
1 0.531633188 0 0 0 0 0 0 0 0
2 0 0.347859094 0 0 0 0 0 0 0
3 0 0 0.199808167 0 0 0 0 0 0
4 0 0 0 0.11999457 0 0 0 0 0
5 0 0 0 0 0.08295179 0 0 0 0
6 0 0 0 0 0 0.076512274 0 0 0
7 0 0 0 0 0 0 0.089033804 0 0
8 0 0 0 0 0 0 0 0.115355642 0
9 0 0 0 0 0 0 0 0 0.155085311
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 22
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 23
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 24
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 25
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
0.206343391 0 0 0 0 0 0 0 0 0
0 0.265516642 0 0 0 0 0 0 0 0
0 0 0.332914344 0 0 0 0 0 0 0
0 0 0 0.404102578 0 0 0 0 0 0
0 0 0 0 0.476237224 0 0 0 0 0
0 0 0 0 0 0.546074256 0 0 0 0
0 0 0 0 0 0 0.611696046 0 0 0
0 0 0 0 0 0 0 0.671627783 0 0
0 0 0 0 0 0 0 0 0.725060108 0
0 0 0 0 0 0 0 0 0 0.770915
0 0 0 0 0 0 0 0 0 0
Page 26
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 27
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 28
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 29
J&T
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
Page 30
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 31
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 32
J&T
0
0
0
0
0
0
0
0
1
Page 33
C
Cyclone Cyclone Cyclone Number of Cyclones 10
Feed U'flow O'flow Classifier Dimensions, inches.
Solids, tons 174.638937 134.638937 40 DC h DI DO DU
Water, m3/hr 102.517559 42.5175589 60 20 75 3.5 7.5 3.82427337
Slurry, tons 277.156496 177.156496 100
Slurry, m3/hr 164.888608 90.6028934 74.2857143 Classifier Constants
Solids Density, ton/m3 2.8 2.8 2.8 a1 a2 a3 a4 l
Slurry Density, ton/m3 1.6808711 1.95530726 1.34615385 9.67960522 1.40133094 54.9640283 0.52297758 0.95
% Solids (by volume) 37.8261723 53.0726257 19.2307692
% Solids (by weight) 63.0109485 76 40
Opening Mid-Size Classifier
Efficiency
1 25400 Circulating Load, CL 3.36597341
2 19050 21997.0453 1 Slurry Split, S 1.21965433
3 12700 15554.2599 1 Cyclone Pressure, ft 11.707604
4 9500 10984.0794 1 Cyclone Pressure, lb/in2 8.52099543
5 6700 7978.09501 1 Corrected Cut Size, d50c, microns 186.066609
6 4750 5641.36508 1 Water By-Pass 0.41473441
7 3350 3989.04751 1 Solids By-Pass 0.39399769
8 2360 2811.76101 1 Plitt's Parameter 1.54550776
9 1700 2002.99775 1
10 1180 1416.33329 0.99999993
11 850 1001.49888 0.99994691
12 600 714.142843 0.99761992
13 425 504.975247 0.97632372
14 300 357.071421 0.90915962
15 212 252.190404 0.80003647
16 150 178.325545 0.68330662
17 106 126.095202 0.58550784
18 75 89.1627725 0.51479583
19 53 63.0476011 0.4679361
20 38 44.8776113 0.43887649
21 0 19 0.40622475
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Bpc
0
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Matrix J
1 2 3 4 5 6 7 8 9
1 0.531633188 0 0 0 0 0 0 0 0
2 0 0.347859094 0 0 0 0 0 0 0
3 0 0 0.199808167 0 0 0 0 0 0
4 0 0 0 0.11999457 0 0 0 0 0
5 0 0 0 0 0.08295179 0 0 0 0
6 0 0 0 0 0 0.076512274 0 0 0
7 0 0 0 0 0 0 0.089033804 0 0
8 0 0 0 0 0 0 0 0.115355642 0
9 0 0 0 0 0 0 0 0 0.155085311
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 0.531633188 0 0 0 0 0 0 0 0
2 0.447358438 0.347859094 0 0 0 0 0 0 0
3 0.260460233 0.294165745 0.199808167 0 0 0 0 0 0
4 0.205532659 0.27023888 0.286659537 0.11999457 0 0 0 0 0
5 0.167638378 0.251152867 0.361505026 0.29632247 0.08295179 0 0 0 0
6 0.167676336 0.285637487 0.549947972 0.811270188 1.100874563 0.076512274 0 0 0
7 0.196213147 0.389537686 1.074743177 3.640210789 -18.23378243 -0.573489181 0.089033804 0 0
8 0.248197618 0.602153055 2.808888202 111.1284565 57.67622809 1.408912936 -0.368994659 0.115355642 0
9 0.37672556 1.206808622 14.65156915 -462.9063011 -82.41522927 -1.708409193 0.616408294 -0.409117951 0.155085311
10 0.570080333 2.843414928 -452.8906266 680.0192764 59.67441303 1.085800946 -0.502820851 0.549830077 -0.485772162
11 1.03763135 11.00897436 1263.014908 -495.3884226 -21.99702571 -0.345954389 0.210456874 -0.370955054 0.618776727
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12 2.199065594 201.5538464 -1456.968369 196.4903467 4.350032057 0.058075006 -0.04778697 0.136760191 -0.402221399
13 6.309962261 -824.0112016 851.8955384 -37.94941759 -0.295583698 -0.002749016 0.004175829 -0.024104787 0.135765759
14 34.70216755 1179.094354 -259.68415 2.828571485 0.001834763 4.37223E-05 -4.88031E-05 0.001542568 -0.022126853
15 -591.7863044 -822.601482 35.89858383 0.105542836 0.004304425 9.74546E-05 -3.50879E-05 8.3186E-05 0.001005619
16 1427.51614 297.9819776 -1.130673389 0.068041904 0.004158749 9.45421E-05 -3.19064E-05 5.16891E-05 -1.29896E-05
17 -1476.509438 -52.17094845 -0.045394999 0.060387591 0.00383182 8.71723E-05 -2.91966E-05 4.55506E-05 -3.83866E-05
18 780.0134042 2.875226807 -0.00549809 0.055596728 0.003541694 8.05731E-05 -2.69615E-05 4.18891E-05 -3.75955E-05
19 -208.1498852 0.040256468 -0.001819665 0.048945018 0.00312006 7.0982E-05 -2.37477E-05 3.68708E-05 -3.33529E-05
20 21.4957412 -0.261972472 -0.015619387 0.571178026 0.036330068 0.00082617 -0.000276617 0.00043013 -0.000390678
Matrix [T*J*T(inv.)]
1 2 3 4 5 6 7 8 9
1 0.531633188 2.79505E-16 1.03097E-15 4.54961E-16 9.9561E-16 7.09304E-16 -4.18238E-17 2.51623E-16 3.2779E-16
2 0.154642136 0.347859094 -7.86191E-17 5.43472E-16 -6.28429E-16 7.97724E-16 1.40331E-15 1.15314E-15 1.18614E-15
3 0.057217122 0.125198714 0.199808167 -1.89303E-16 -9.57489E-16 -6.07813E-16 4.43336E-16 3.81768E-17 2.69271E-17
4 0.035566282 0.080187558 0.114506474 0.11999457 -5.39666E-16 3.01061E-17 -2.30535E-16 -3.07395E-16 -1.68341E-16
5 0.022747005 0.052389134 0.080185593 0.091475872 0.08295179 6.00575E-17 -1.76952E-16 -1.36545E-16 -1.24711E-16
6 0.017754409 0.04107764 0.065748835 0.082937342 0.085460477 0.076512274 -1.71657E-16 -1.48523E-16 -1.37795E-16
7 0.015556631 0.035685316 0.058718541 0.07914098 0.091341378 0.093853721 0.089033804 -1.36182E-16 -1.34763E-16
8 0.013812407 0.031088961 0.05180878 0.072702823 0.089819151 0.102395295 0.109089102 0.115355642 -1.52617E-16
9 0.013822729 0.030129 0.049967639 0.071162073 0.09091705 0.109251789 0.126674192 0.14090443 0.155085311
10 0.012026188 0.025283153 0.041322704 0.058763121 0.076017121 0.093683939 0.11349561 0.135738485 0.160555167
11 0.011453128 0.023152097 0.036887168 0.051414975 0.065781503 0.08085926 0.098858312 0.121290203 0.152544961
12 0.010320715 0.020113555 0.031116976 0.042066898 0.052400395 0.062980179 0.075866239 0.092851564 0.119159566
13 0.009356293 0.017698021 0.026621017 0.034772029 0.041764678 0.048330842 0.056141763 0.066751568 0.084356781
14 0.00838055 0.015518464 0.022825772 0.028915832 0.033478454 0.037086535 0.040996124 0.04636715 0.055904338
15 0.007507504 0.013717167 0.019871656 0.024616156 0.027677046 0.029501006 0.031028593 0.033087164 0.037200394
16 0.006784675 0.012303085 0.017661804 0.02157582 0.023796082 0.02468639 0.024984458 0.02529911 0.026435117
17 0.006117382 0.011050266 0.015786915 0.019140737 0.02088598 0.021331167 0.021084147 0.020619904 0.020365251
18 0.005567126 0.010037441 0.014305247 0.017279821 0.01875648 0.019008369 0.018562578 0.017816635 0.01702225
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19 0.004876199 0.008784766 0.012506956 0.015083515 0.016335536 0.016499479 0.016026998 0.015252687 0.01434402
20 0.05485833 0.098726568 0.140349754 0.168957434 0.18261688 0.184019754 0.178158079 0.168665457 0.157026842
Matrix [T*J*T(inv.)] (inverse)
1 2 3 4 5 6 7 8 9
1 1.88099619 1.83859E-15 -6.8735E-15 8.54758E-15 -4.77794E-15 -1.95907E-14 5.1551E-15 -1.80707E-17 2.32451E-15
2 -0.836204294 2.874727203 1.12928E-14 -3.94557E-14 4.42077E-14 2.69349E-14 -1.48157E-14 -2.8513E-15 -1.31538E-14
3 -0.014681515 -1.801288476 5.004800425 -1.18062E-14 -1.38548E-14 5.86722E-14 -1.48158E-14 1.83233E-15 3.66171E-15
4 0.015286252 -0.202160492 -4.775899864 8.333710424 5.04326E-14 -9.52798E-14 1.83989E-14 1.08422E-14 6.89957E-15
5 0.009643085 0.14858898 0.428763726 -9.190078093 12.05519489 8.56022E-16 1.21983E-14 -8.98823E-15 -2.56807E-15
6 -0.002264849 0.057687215 0.397299483 1.231340623 -13.46506451 13.06979841 -1.29499E-14 4.64867E-15 1.16217E-15
7 -0.004916002 0.002203453 0.085842826 0.722539963 1.826365836 -13.77734257 11.23168909 -8.24329E-15 1.31143E-15
8 -0.003753839 -0.007329453 -0.005448464 0.127050734 0.83858296 1.427516349 -10.62154273 8.668843457 -1.31715E-15
9 -0.004115934 -0.008243441 -0.017468409 -0.00944426 0.164723236 0.749210265 0.476236507 -7.876171123 6.448063919
10 -0.002730692 -0.004845393 -0.010553501 -0.02036827 -0.012118521 0.122025756 0.438795195 0.425815882 -5.017219004
11 -0.002985614 -0.004934482 -0.009613038 -0.019008133 -0.035138526 -0.020146357 0.083617709 0.261333649 -0.126235864
12 -0.002668928 -0.004250579 -0.007844821 -0.014861477 -0.031688248 -0.043441476 -0.023997368 0.040232029 0.106803584
13 -0.002517973 -0.00397828 -0.007183414 -0.013138437 -0.028348295 -0.043399097 -0.043721046 -0.024814039 0.012915861
14 -0.002322177 -0.003662501 -0.006567439 -0.011840232 -0.025441784 -0.039631176 -0.043615953 -0.036953002 -0.022762811
15 -0.002144764 -0.003386424 -0.006061521 -0.010868279 -0.023228267 -0.036191368 -0.040461847 -0.036698138 -0.030014966
16 -0.001994485 -0.003154625 -0.005645199 -0.01009915 -0.021493902 -0.033424111 -0.037445014 -0.034439011 -0.029864843
17 -0.001834567 -0.002905136 -0.005199102 -0.009292616 -0.019729744 -0.030639994 -0.034323171 -0.031654884 -0.027830225
18 -0.001699688 -0.002694924 -0.004823788 -0.008616357 -0.018253434 -0.028313163 -0.031704666 -0.02925454 -0.025803212
19 -0.001498515 -0.002376658 -0.004254334 -0.007598128 -0.016087716 -0.024946268 -0.027931191 -0.025774599 -0.022750536
20 -0.017591692 -0.027995986 -0.050143567 -0.089428315 -0.188273973 -0.291075205 -0.325595511 -0.300465679 -0.265301903
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Matrix { C(inv.)*[T*J*T(inv.)] (inverse)-I}
1 2 3 4 5 6 7 8 9
1 0.88099619 1.83859E-15 -6.8735E-15 8.54758E-15 -4.77794E-15 -1.95907E-14 5.1551E-15 -1.80707E-17 2.32451E-15
2 -0.836204294 1.874727203 1.12928E-14 -3.94557E-14 4.42077E-14 2.69349E-14 -1.48157E-14 -2.8513E-15 -1.31538E-14
3 -0.014681515 -1.801288476 4.004800425 -1.18062E-14 -1.38548E-14 5.86722E-14 -1.48158E-14 1.83233E-15 3.66171E-15
4 0.015286252 -0.202160492 -4.775899864 7.333710424 5.04326E-14 -9.52798E-14 1.83989E-14 1.08422E-14 6.89957E-15
5 0.009643085 0.14858898 0.428763726 -9.190078093 11.05519489 8.56022E-16 1.21983E-14 -8.98823E-15 -2.56807E-15
6 -0.002264849 0.057687215 0.397299483 1.231340623 -13.46506451 12.06979841 -1.29499E-14 4.64867E-15 1.16217E-15
7 -0.004916002 0.002203453 0.085842826 0.722539963 1.826365836 -13.77734257 10.23168909 -8.24329E-15 1.31143E-15
8 -0.003753839 -0.007329453 -0.005448464 0.127050734 0.83858296 1.427516349 -10.62154273 7.668843457 -1.31715E-15
9 -0.004115935 -0.008243442 -0.01746841 -0.00944426 0.164723248 0.749210318 0.47623654 -7.876171681 5.448064376
10 -0.002730837 -0.00484565 -0.010554061 -0.020369352 -0.012119165 0.122032235 0.438818491 0.425838489 -5.017485374
11 -0.002992737 -0.004946254 -0.009635973 -0.019053482 -0.035222358 -0.020194421 0.083817201 0.261957129 -0.126537033
12 -0.00273365 -0.004353657 -0.008035061 -0.015221874 -0.032456702 -0.044494951 -0.024579315 0.041207673 0.109393618
13 -0.002769561 -0.004375778 -0.007901159 -0.014451188 -0.031180768 -0.047735398 -0.048089515 -0.02729338 0.014206373
14 -0.002902589 -0.004577918 -0.008208925 -0.014799615 -0.03180078 -0.049536712 -0.054517455 -0.046189146 -0.028452217
15 -0.003138802 -0.004955936 -0.008870865 -0.01590542 -0.033993914 -0.052965048 -0.059214774 -0.053706692 -0.043926057
16 -0.003406419 -0.005387845 -0.009641543 -0.017248531 -0.036709844 -0.057085677 -0.063953053 -0.058819043 -0.051006735
17 -0.003563679 -0.005643278 -0.010099347 -0.018051071 -0.038325377 -0.059518729 -0.066673366 -0.061490172 -0.054060704
18 -0.003632309 -0.005759171 -0.010308647 -0.018413533 -0.039008389 -0.060506473 -0.067754264 -0.062518237 -0.055142598
19 -0.003414434 -0.005415324 -0.009693692 -0.017312678 -0.03665659 -0.056841202 -0.063642485 -0.058728593 -0.051838129
20 -0.043305317 -0.068917479 -0.123437989 -0.220144916 -0.463472428 -0.71653734 -0.801515682 -0.739653789 -0.653091422
Matrix { C(inv.)*[T*J*T(inv.)] (inverse)-I}(inverse)
1 2 3 4 5 6 7 8 9
1 1.135078689 3.85258E-15 5.20249E-15 3.43048E-15 4.46351E-15 3.72918E-15 2.11431E-15 2.87421E-15 3.10738E-15
2 0.506291087 0.53341094 2.68288E-15 3.28694E-15 1.67788E-15 3.79599E-15 4.26439E-15 3.89753E-15 3.82135E-15
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3 0.231881961 0.239918817 0.249700333 -6.09198E-17 -1.03654E-15 -1.73224E-16 1.18942E-15 6.40687E-16 6.06668E-16
4 0.162597909 0.170945236 0.162611246 0.136356625 -8.22703E-16 1.87516E-16 3.71505E-17 -9.36827E-17 6.31006E-17
5 0.118377829 0.125630766 0.125492822 0.113351962 0.090455212 1.13464E-16 -5.03153E-17 -3.05592E-17 -5.41525E-18
6 0.105634687 0.112267321 0.115191095 0.11254455 0.100911815 0.082851425 -6.8217E-17 -1.14846E-16 -4.92711E-17
7 0.108118963 0.114547283 0.11913021 0.1216827 0.119735102 0.111562466 0.097735573 -8.63891E-17 -1.17832E-16
8 0.115650068 0.121863446 0.127316969 0.132930029 0.137160713 0.139094473 0.135366249 0.130397759 -1.63316E-16
9 0.142285236 0.148798218 0.155093581 0.162870052 0.171212156 0.17994073 0.187153178 0.188513767 0.183551429
10 0.16042369 0.166605098 0.172907838 0.181360528 0.191570728 0.203962628 0.217989235 0.231463833 0.239426799
11 0.198901031 0.20518418 0.211732093 0.220811672 0.232286733 0.246939874 0.264946467 0.28525126 0.30727454
12 0.238603341 0.244709528 0.251141553 0.260183678 0.271830408 0.287023658 0.306332009 0.32938714 0.358130013
13 0.277719281 0.283411712 0.289436705 0.297944109 0.308974798 0.323477964 0.342154588 0.364952513 0.394780469
14 0.29249408 0.297208221 0.302212056 0.309281224 0.318458657 0.330548615 0.346193879 0.365462557 0.391165669
15 0.272485858 0.275789432 0.279304448 0.284264965 0.290698307 0.299167848 0.31014411 0.323713884 0.341973342
16 0.2283474 0.230224508 0.23222761 0.235048394 0.238697551 0.24349087 0.249702816 0.257398517 0.267810185
17 0.177250477 0.178017278 0.178840725 0.179994318 0.181477278 0.183413481 0.185919043 0.189030624 0.193271963
18 0.134938045 0.135018103 0.135109911 0.135231874 0.135378127 0.13555582 0.135781491 0.136070097 0.136498529
19 0.10098742 0.100732524 0.100466664 0.100085194 0.099580526 0.098903623 0.098021695 0.096937283 0.095505116
20 0.86690232 0.860644896 0.853977789 0.844591647 0.832457583 0.816536593 0.795960376 0.770595572 0.736638022
Circuit Balance
1 2 3 4 5 6 7
Fresh Mill Mill Sump Cyclone Cyclone Cyclone
Feed Feed Discharge Water Feed U'flow O'flow
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 20.000 30.668 10.668 0.000 30.668 30.668 0.000
3 66.400 87.778 21.378 0.000 87.778 87.778 0.000
4 56.280 78.170 21.890 0.000 78.170 78.170 0.000
5 41.320 62.282 20.962 0.000 62.282 62.282 0.000
6 33.360 56.522 23.162 0.000 56.522 56.522 0.000
7 27.360 55.753 28.393 0.000 55.753 55.753 0.000
8 21.640 56.846 35.206 0.000 56.846 56.846 0.000
9 20.400 68.862 48.462 0.000 68.862 68.862 0.000
Page 42
Mill
10 15.600 75.249 59.653 0.000 75.253 75.249 0.004
11 14.160 92.221 78.282 0.000 92.442 92.221 0.220
12 12.040 107.048 97.604 0.000 109.644 107.048 2.596
13 10.360 114.805 115.916 0.000 126.276 114.805 11.471
14 8.840 105.296 122.774 0.000 131.614 105.296 26.318
15 7.520 82.816 113.678 0.000 121.198 82.816 38.383
16 6.480 58.697 93.771 0.000 100.251 58.697 41.553
17 5.520 39.403 71.021 0.000 76.541 39.403 37.138
18 4.720 26.720 52.382 0.000 57.102 26.720 30.382
19 3.400 18.028 37.677 0.000 41.077 18.028 23.049
20 24.600 129.224 293.510 0.000 318.110 129.224 188.886
Total 400.000 1346.390 1346.390 0.000 1746.390 1346.390 400.000
CL = 3.365974434
Page 43
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
0.206343391 0 0 0 0 0 0 0 0
0 0.265516642 0 0 0 0 0 0 0
0 0 0.332914344 0 0 0 0 0 0
0 0 0 0.404102578 0 0 0 0 0
0 0 0 0 0.476237224 0 0 0 0
0 0 0 0 0 0.546074256 0 0 0
0 0 0 0 0 0 0.611696046 0 0
0 0 0 0 0 0 0 0.671627783 0
0 0 0 0 0 0 0 0 0.725060108
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
Page 44
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 45
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
0.206343391 0 0 0 0 0 0 0 0
-0.660347106 0.265516642 0 0 0 0 0 0 0
Page 46
Mill
0.829444853 -0.817140344 0.332914344 0 0 0 0 0 0
-0.522171309 0.997751093 -1.024026896 0.404102578 0 0 0 0 0
0.171881038 -0.612325241 1.24267299 -1.234631195 0.476237224 0 0 0 0
-0.026322055 0.193894637 -0.754600065 1.489441997 -1.455583823 0.546074256 0 0 0
0.001092007 -0.028300517 0.236780074 -0.902000839 1.760450106 -1.671237987 0.611696046 0 0
3.80605E-05 0.001047868 -0.03452472 0.283005967 -1.067780718 2.018592821 -1.868569711 0.671627783 0
6.08331E-06 -5.36621E-08 0.001208876 -0.040776228 0.334496589 -1.223401196 2.258636901 -2.055011472 0.725060108
3.07909E-06 -3.16597E-05 6.70771E-06 0.001439241 -0.047888456 0.378171925 -1.349881151 2.45411069 -2.210998509
3.1959E-05 -0.000412425 -0.000431311 -0.000581522 6.90786E-05 -0.048199819 0.348117915 -1.070727001 1.485938401
10 11 12 13 14 15 16 17 18
6.6816E-16 5.40309E-16 1.07382E-15 5.23647E-17 5.5527E-16 3.63833E-16 3.69528E-16 2.27714E-16 1.28365E-16
6.78786E-16 2.88524E-16 9.19971E-17 6.52473E-16 1.28751E-16 2.09466E-16 4.54012E-17 -1.2699E-17 -7.40162E-17
-1.26025E-16 -1.95627E-16 -4.60128E-16 1.07129E-16 1.94848E-17 9.7851E-18 2.10527E-17 -7.7353E-19 -2.62628E-17
-1.45169E-16 -2.30481E-16 -1.55309E-16 -1.26725E-16 -1.59298E-16 -3.30363E-17 -3.26275E-17 -3.19575E-18 -1.70817E-17
-1.36038E-16 -1.66927E-16 -1.0711E-16 -8.40974E-17 -1.1236E-16 -2.69897E-17 -2.61644E-17 -2.45933E-18 -1.12782E-17
-1.2694E-16 -1.40928E-16 -8.04428E-17 -8.07596E-17 -1.01424E-16 -2.57931E-17 -2.46669E-17 -2.13241E-18 -8.86273E-18
-1.25174E-16 -1.28605E-16 -6.67734E-17 -7.8127E-17 -9.58209E-17 -2.50776E-17 -2.391E-17 -1.90166E-18 -7.66722E-18
-1.09979E-16 -1.17835E-16 -5.76621E-17 -7.27824E-17 -8.70672E-17 -2.30086E-17 -2.20094E-17 -1.61406E-18 -6.61701E-18
-1.47147E-16 -1.22437E-16 -5.37709E-17 -6.90458E-17 -8.45235E-17 -2.235E-17 -2.11688E-17 -1.33553E-18 -6.30721E-18
0.206343391 -1.0084E-16 -6.20406E-17 -5.69967E-17 -7.16503E-17 -1.77892E-17 -1.69942E-17 -9.68395E-19 -5.18976E-18
0.189368241 0.265516642 -1.15914E-15 -1.67351E-16 -2.31312E-16 -2.53252E-16 -1.09796E-17 -1.61606E-17 1.08835E-17
0.155010403 0.207419699 0.332914344 -1.21765E-16 -1.98387E-16 -2.0015E-16 -8.39831E-18 -1.24726E-17 8.18477E-18
0.110263256 0.15312021 0.21897124 0.404102578 -1.18376E-16 -1.35195E-16 -5.94818E-18 -9.12378E-18 5.54931E-18
0.070840135 0.097633124 0.142921419 0.220388803 0.476237224 -9.89593E-17 -1.95426E-18 -6.53828E-18 2.76613E-18
0.044210992 0.057925255 0.082793931 0.128867212 0.21345172 0.546074256 5.36778E-17 9.52299E-18 8.09538E-19
0.028903363 0.034644877 0.046029895 0.068676686 0.113095933 0.200832811 0.611696046 5.13424E-16 2.60849E-16
0.020625803 0.022300074 0.026458138 0.035749088 0.055302212 0.09618009 0.183075613 0.671627783 7.73959E-17
0.01637973 0.016297897 0.017203687 0.020225147 0.027547915 0.044020367 0.080829579 0.163489425 0.725060108
Page 47
Mill
0.013444486 0.012748484 0.012402301 0.012849481 0.01491049 0.020436104 0.033767492 0.065052296 0.139830447
0.1446102 0.132393738 0.120305046 0.109141006 0.099454506 0.092456371 0.090631269 0.099830495 0.135109445
10 11 12 13 14 15 16 17 18
-2.32786E-15 9.53236E-16 -5.72511E-15 1.0686E-15 -1.53627E-15 -7.87906E-16 -9.25703E-16 -5.56686E-16 -3.33012E-16
-5.59862E-15 -2.63384E-15 4.86441E-15 -4.61092E-15 4.12212E-16 -6.82234E-16 1.64491E-16 2.30397E-16 4.41502E-16
3.58757E-15 -2.561E-16 6.39566E-15 1.37534E-15 2.79727E-17 6.23508E-16 -2.27073E-17 -2.33165E-17 -2.88399E-30
-9.85653E-16 6.24247E-15 -6.0782E-15 2.62841E-15 2.62841E-15 5.74964E-16 4.92827E-16 8.21378E-17 -1.64276E-16
1.92605E-15 -1.07003E-15 8.56022E-16 -5.35014E-16 -1.07003E-16 1.07003E-16 2.14006E-16 -1.07003E-16 1.07003E-16
0 -4.98072E-16 1.66024E-16 -8.3012E-17 -8.3012E-17 -8.3012E-17 -3.32048E-16 1.66024E-16 -8.3012E-17
7.4939E-16 7.4939E-16 -5.62043E-16 -3.74695E-16 9.36738E-17 0 3.74695E-16 0 1.87348E-16
3.29287E-16 1.64644E-16 8.23218E-16 3.29287E-16 -1.64644E-16 -8.23218E-17 8.23218E-17 1.64644E-16 0
-5.16885E-16 -2.58442E-16 -3.87663E-16 1.29221E-16 1.29221E-16 -1.29221E-16 -1.29221E-16 -1.93832E-16 0
4.846290431 0 1.94337E-16 -3.88673E-16 -9.71683E-17 9.71683E-17 -9.71683E-17 -9.71683E-17 -1.94337E-16
-3.456406685 3.766242274 1.17539E-14 5.87694E-16 8.81541E-16 1.61616E-15 0 1.46923E-16 1.46923E-16
-0.103025291 -2.346528024 3.003775649 -2.30076E-16 0 0 3.45115E-16 -1.15038E-16 -6.90229E-16
0.043151252 -0.155568565 -1.627657215 2.474619202 -3.67598E-16 -1.83799E-16 9.18996E-17 0 1.83799E-16
-0.001338868 0.004083437 -0.148216998 -1.145182142 2.099793863 0 -3.01496E-16 0 1.50748E-16
-0.019761416 -0.008618228 -0.013378355 -0.136348084 -0.820775941 1.83125278 -1.25385E-16 1.25385E-16 0
-0.023587506 -0.017194204 -0.011495615 -0.021334179 -0.11875082 -0.601239204 1.634798861 -1.24442E-15 -4.14808E-16
-0.022935733 -0.018746048 -0.014441069 -0.012081892 -0.022989762 -0.098354807 -0.445621536 1.488919941 0
-0.02149613 -0.018129575 -0.014887418 -0.012137434 -0.011525833 -0.02197685 -0.081766594 -0.335727565 1.379195999
-0.019004067 -0.016165433 -0.013550742 -0.011327292 -0.009622817 -0.009923393 -0.019173178 -0.064744771 -0.250161885
-0.221885987 -0.189375635 -0.160148238 -0.136208177 -0.11612869 -0.099758526 -0.088237553 -0.088447606 -0.129034114
Page 48
Mill
10 11 12 13 14 15 16 17 18
-2.32786E-15 9.53236E-16 -5.72511E-15 1.0686E-15 -1.53627E-15 -7.87906E-16 -9.25703E-16 -5.56686E-16 -3.33012E-16
-5.59862E-15 -2.63384E-15 4.86441E-15 -4.61092E-15 4.12212E-16 -6.82234E-16 1.64491E-16 2.30397E-16 4.41502E-16
3.58757E-15 -2.561E-16 6.39566E-15 1.37534E-15 2.79727E-17 6.23508E-16 -2.27073E-17 -2.33165E-17 -2.88399E-30
-9.85653E-16 6.24247E-15 -6.0782E-15 2.62841E-15 2.62841E-15 5.74964E-16 4.92827E-16 8.21378E-17 -1.64276E-16
1.92605E-15 -1.07003E-15 8.56022E-16 -5.35014E-16 -1.07003E-16 1.07003E-16 2.14006E-16 -1.07003E-16 1.07003E-16
0 -4.98072E-16 1.66024E-16 -8.3012E-17 -8.3012E-17 -8.3012E-17 -3.32048E-16 1.66024E-16 -8.3012E-17
7.4939E-16 7.4939E-16 -5.62043E-16 -3.74695E-16 9.36738E-17 0 3.74695E-16 0 1.87348E-16
3.29287E-16 1.64644E-16 8.23218E-16 3.29287E-16 -1.64644E-16 -8.23218E-17 8.23218E-17 1.64644E-16 0
-5.16885E-16 -2.58442E-16 -3.87664E-16 1.29221E-16 1.29221E-16 -1.29221E-16 -1.29221E-16 -1.93832E-16 0
3.846547726 0 1.94347E-16 -3.88694E-16 -9.71734E-17 9.71734E-17 -9.71734E-17 -9.71734E-17 -1.94347E-16
-3.464652847 2.77522763 1.17819E-14 5.89096E-16 8.83644E-16 1.62001E-15 0 1.47274E-16 1.47274E-16
-0.1055237 -2.403432362 2.076618531 -2.35656E-16 0 0 3.53484E-16 -1.17828E-16 -7.06968E-16
0.04746279 -0.171112488 -1.79028762 1.721875393 -4.04328E-16 -2.02164E-16 1.01082E-16 0 2.02164E-16
-0.001673509 0.005104064 -0.185262802 -1.431412422 1.624622676 0 -3.76853E-16 0 1.88427E-16
-0.028920276 -0.012612534 -0.019578845 -0.199541583 -1.201182483 1.67998689 -1.83497E-16 1.83497E-16 0
-0.040285551 -0.029366309 -0.01963358 -0.036437051 -0.202816788 -1.026867896 1.792104133 -2.12538E-15 -7.08459E-16
-0.044553067 -0.036414529 -0.028052032 -0.023469289 -0.044658019 -0.191055951 -0.865627711 1.892253308 0
-0.045938174 -0.038743697 -0.031815067 -0.02593823 -0.024631211 -0.046965493 -0.174738802 -0.717464548 1.947402407
-0.04330163 -0.036833671 -0.030875979 -0.025809749 -0.021926025 -0.0226109 -0.043686956 -0.147523897 -0.570005202
-0.546214833 -0.466184378 -0.394235546 -0.335302504 -0.285873002 -0.24557471 -0.217213629 -0.217730713 -0.317642174
10 11 12 13 14 15 16 17 18
3.8752E-15 3.39741E-15 4.27479E-15 1.09317E-15 1.98198E-15 1.07438E-15 8.0209E-16 4.07527E-16 1.94102E-16
2.96641E-15 2.05194E-15 1.84702E-15 1.87736E-15 8.26259E-16 6.10007E-16 2.43495E-16 7.09742E-17 -3.4354E-17
Page 49
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3.10977E-16 6.98038E-17 -1.6038E-16 5.80714E-16 3.09109E-16 1.88828E-16 1.1711E-16 3.64938E-17 -1.47403E-17
5.51136E-18 -2.49151E-16 -7.37424E-17 -1.8831E-17 -5.63404E-17 6.83285E-17 4.41767E-17 2.33151E-17 5.51713E-19
-7.63988E-17 -2.17731E-16 -9.95926E-17 -3.93887E-17 -7.40195E-17 3.01628E-17 1.99105E-17 2.17576E-17 -7.50139E-19
-8.97273E-17 -2.06954E-16 -9.89768E-17 -5.47882E-17 -7.83986E-17 2.72638E-17 2.36399E-17 1.18421E-17 -7.93129E-19
-1.29615E-16 -2.23827E-16 -7.93732E-17 -6.61932E-17 -1.08579E-16 1.17604E-17 2.78517E-18 8.49397E-18 -7.41071E-18
-2.22218E-16 -3.06036E-16 -1.41553E-16 -9.13145E-17 -1.14726E-16 6.11453E-18 -1.42137E-17 -4.25801E-18 -9.99179E-18
-2.21414E-16 -3.38334E-16 -1.44372E-16 -1.16363E-16 -1.32249E-16 3.23226E-17 -4.39881E-18 5.60698E-18 -2.0717E-17
0.259973376 -3.24446E-16 -1.0796E-16 -4.7327E-17 -1.1817E-16 4.71183E-17 2.40887E-17 3.02991E-17 9.52661E-19
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