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About ... Moly-Cop Tools, Version 3.0 About the BallParam_Direct Spreadsheet ... Moly-Cop Tools, Version 3.0 About the BallParam_Direct Spreadsheet ... &"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F &8Page &P &8&D / &T Scope : The BallParam_Direct spreadsheet was designed to be used - in conjunction with the BallSim_Direct spreadsheet in the "tuning" of such simulator to any specific actual grinding system. The attached spreadsheets provide an effective algorithm to search for the set of parameter values that best approximate the model response to the actual experimental measurements obtained from a Pilot or Full Scale Ball Mill, operating in close circuit with hydrocyclones in a Direct Circuit Configuration. BallParam_Direct combines in a single application the simultaneous closure of the Circuit Mass Balance, plus the evaluation of the corresponding Classifier Constants (see About ... in CycloSim_Single) and the estimation of the characteristic Ore Grinding Parameters, as an alternative to the concatenated use of the BallBal_Direct and BallParam_Open spreadsheets, as originally proposed in Moly-Cop Tools, Version 1.0. Theoretical Framework : The reference ball mill model is described in the About ... worksheet of the BallSim_Direct spreadsheet. Similarly, the reference hydrocyclone model is described in the About ... worksheet of the CycloSim_Single spreadsheet. On the basis of Pilot or Full Scale Data, like those typically obtained from sampling campaigns around continuous grinding/classification circuits, the BallParam_Direct routine allows for the calculation of all a's and b's (including dcrit) - plus the classification parameters (Bpf, d50c and m; see CycloSim_Single) that minimize the least-squares Objective Function: 3 n f = S S wik [(fik - fik)/fik]2 (3) k = 1 i = 1 where the fik's represent the experimental size distribution of the mill product (as % retained on screen 'i', i = 1,n) and the fik's represent the model response for each corresponding fik, for a given set of model parameters. Also, the subscript k = 1, 2, 3 represents the cyclone feed, overflow and underflow streams, respectively. The a's and b's (including dcrit) and the above listed classification parameters that yield the minimum possible value of f are so considered to be representative of the particular ore and test conditions under analysis. This evaluation methodology imposes the condition that the hydrocylones perform in good agreement with the Plitt´s Classification Efficiency Curve (see About ... in CycloSim_Single). Also in Equation 3, the wik's represent user defined Weighting Factors that quantify the relative quality and reliability of each particular mesh value with respect to the other screens data. Relatively high values of such weighting factors indicate more reliable measurements. At the extreme, a wi factor equal to zero means that this particular measurement is not being included in the Objective Function. The minimization problem stated above may be readily solved with the aid of the Excel Subroutine Solver. Data Input and Program Execution : Most of the data required by the algorithm must be defined in each corresponding unprotected white background cell - inside the red double-lined border - of the here attached Data_File worksheet. Gray background cells contain the results of the corresponding formula there defined and are protected to avoid any accidental editing. The remaining information required to run the program is entered in the Control_Panel worksheet, where the user is requested to provide initial guesses of the grinding and classification parameters referred above. To run the program, select the objective function Cell E36 in Control_Panel and then, from the Tools Menu, select Solver ..., then Min and then By Changing any combination of Cells C19:F19, C21:D21, C25:E25, C27, C32:F32 and E34. The same "parameter reduction hints" provided in About ... of BallParam_Batch apply in this case, but very importantly, Cell E34 must always be included in the By Changing list. Clicking on the Solve button will execute the desired calculations. Important Notice : Solver ... must be run every time any element of input data gets to be modified. Otherwise, the current outputs are not valid. Calculation results are summarized in the Reports worksheet. New Moly-Cop Tools users are invited to explore the brief comments inserted in each relevant cell, rendering the whole utilization of the worksheets self-explanatory. Eventually, the user may wish to remove the view of the comments by selecting Tools / Options / View / Comments / None. Control_Panel Moly-Cop Tools TM (Version 3.0) BallParam_Direct : SIMULTANEOUS MASS BALANCE CLOSURE AND GRINDING PARAMETERS ESTIMATION alpha0 intercepção da função seleção em 0,01 ton/kwh Sample N° 1 alpha1 tangente da curva da função seleção - velocidade de quebra dcrit valor pelo qual a moagem deixa de ser eficiente (inflexão pra baixo da função seleção) Weighting Factors : alpha2 inclinação de quando a curva de função seleção cai Streams : beta0 ponto da função quebra de fratura máxima Mill Discharge 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 beta1 inclinação da função quebra Cyclone U'flow 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 beta2 limite superior paralelo ao eixo y da função quebra (manter fixo) Cyclone O'flow 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 Size Distributions 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1 alpha - parâmetros da função seleção % Solids 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1 beta - parâmetros da função quebra Grinding Parameter Guesses : Num primeiro momento deve-se variar apenas alpha0 / dcrit / Bpf / d50c / m / carga circulante ESSES SÃO OS PARÂMETROS QUE MAIS INFLUENCIAM NO MODELO alpha0 alpha1 alpha2 dcrit Os pontos são os dados amostrados 0.00581 0.720 2.52 9415 A linha eh o modelo alpha02 alpha12 0 1 Os parâmetros alpha02 / alpha12 e beta01 seriam para uma moagem não linearizada 0 1 Default Values Quando Delta é igual a zero é uma forma de buscar uma solução para encontra uma solução Se o Delta for diferente de zero é pq não foi encontrado uma carga circulante que faça sentido para o circuito (geralmente dados inputados errados de % de sólidos e/ou dados incosistentes) beta0 beta1 beta2 0.179 0.319 4.00 Se os parâmetros iniciais forem muito distantes entre curvas e pontos, deve-se ajustar manualmente de forma a aproximar os pontos das curvas antes de rodar o Solver beta01 0 Caso a função solução não tenha dado um resultado satisfatório, sugere-se rodar o Solver modificando os parâmetros da função quebra 0 Default Value Manter ou variar os parâmetros da primeira solução do Solver vai da avaliação crítica do engenheiro que está simulando O parâmetro Beta0 vai modificar a inclinação da curva de OF - Num segundomomento poderia variar os mesmos parâmetros do primeiro Solver adicionando o Beta0 Classifiers Parameter Guesses : Bpf Bpc d50c m 0.363 0.000 Jaime E. Sepúlveda J.: Fractional short-circuit of slurry to the cyclone overflow. Default Value : 0 232.5 1.313 Jaime Sepulveda: Limited to the maximum value defined in cell H32, hidden behind the Chart. 4 Classifier Constants : Circulating Load : 2.695 Jaime Sepulveda: This cell must always be included in the "By Changing List" of Subroutine Solver. Delta : -0.000 Jaime Sepulveda: This cell must be set to zero, by running Subroutine Solver. a1 a2 a3 a4 l 10.637 Jaime E. Sepúlveda J.: See Cyclosim_Single spreadsheet for further reference. 1.228 Jaime E. Sepúlveda J.: See Cyclosim_Single spreadsheet for further reference. 48.323 Jaime E. Sepúlveda J.: See Cyclosim_Single spreadsheet for further reference. 0.358 Jaime E. Sepúlveda J.: See Cyclosim_Single spreadsheet for further reference. 0.970 Jaime E. Sepúlveda J.: See Cyclosim_Single spreadsheet for further reference. Jaime Sepulveda: This cell must always be included in the "By Changing List" of Subroutine Solver. Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 Jaime Sepulveda: This cell must be set to zero, by running Subroutine Solver. Obj. Function : 0.007 Jaime E. Sepúlveda J.: To minimize this value, use Tools / Solver / Solve, as pre-programed. Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of this sample with respect to the measurements associated with the other 2 streams. Default Value : 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1 Jaime E. Sepúlveda J.: Relative Weighting Factor of the size distribution analyses with respect to the % solids analyses. Default Value : 1 Note : Current calculations are not valid, if SOLVER has not been run after the last data modification. &"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F &8&D / &T Mill Discharge 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100 100 99.44 98.83 98 96.84 95.12 92.58 89.11 84.12 77.87 69.7 59.89 49.23 39.24 31.1 25.08 20.82 17.739999999999998 15.49 Cyclone U'flow 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100 100 99.23 98.4 97.25 95.67 93.31 89.83 85.07 78.23 69.72 58.85 46.67 34.81 25.15 18.350000000000001 13.95 11.16 9.32 8.0500000000000007 Cyclone O'flow 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100 100 100 100 100 100 100 100 100 99.99 99.86 98.93 95.54 88.11 77.23 65.48 55.07 46.83 40.44 35.549999999999997 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100.00000000000001 100.00000000000004 99.436446887274215 98.832068087606288 97.996741874306736 96.840777672790765 95.123394647749649 92.580673780230342 89.108144601158003 84.120337451715343 77.87364240183328 69.697002652624434 59.893080122916786 49.232474649482718 39.242371498925507 31.104673723683884 25.075047633344834 20.816044779030086 17.741584755525562 15.490884102856251 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100.00000000000001 100.00000000000006 99.227364055803989 98.398755759640238 97.2535166 63359306 95.668680252865244 93.314134026191667 89.828042866846602 85.067201540019553 78.231450357809763 69.716012435175926 58.852581190476158 46.668129516508152 34.809008230801446 25.149030472298151 18.35122436017808 13.946999648882265 11.163920677675819 9.3195540923014217 8.0491987732069532 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100 100 100 100 100 100 99.999999999998934 99.999999932045213 99.999933393373666 99.992997243648674 99.861376774128374 98.926602365472945 95.539058453506314 88.108882336264813 77.228973021454038 65.479787338966574 55.069122403173608 46.831976089526506 40.441973698783279 35.548891266618377 Fresh Feed 25400 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 100 100 87.98 78.52 64.010000000000005 50.91 40.869999999999997 33.78 29.02 25.05 22.22 19.690000000000001 17.510000000000002 15.57 13.83 12.28 10.87 9.6199999999999992 8.49 7.52 Particle Size, microns % Passing Data_File Moly-Cop Tools TM (Version 3.0) BALLPARAM_Direct : Simultaneous Mass Balance Closure and Grinding Parameters Estimation. Circuit Type DIRECT Sample N° 1 Remarks Base Case Example Mill Dimensions and Operating Conditions 15028 Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Ball Charge. Balls Charge Mill Charge Weight, tons Apparent Eff. Diam. Eff. Length Speed Charge Balls Interstitial Lift 0 Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Overfilling Slurry on top of the "kidney". Overfilling Volume, Ball Slurry Density ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, (°) 2528 Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Interstitial Slurry in the ball charge. Slurry m3 Charge Interstitial Excess ton/m3 28.5 36.3 75.0 Jaime E. Sepúlveda J.: Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill. 35.00 Jaime E. Sepúlveda J.: Total Apparent Volumetric Charge Filling - including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners). 35.00 jsepulveda: See Mill Power_Ball Mills for further details. 100.00 Jaime E. Sepúlveda J.: This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases - particularly in Grate Discharge Mills - it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between Cells F9 and G9. 31.6 Jaime E. Sepúlveda J.: Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge ("the kidney") with respect to the horizontal. See Mill Power_Ball Mills for further details. 17556 jsepulveda: Net Mill Power Draw. See About ... in the Mill Power_Ball Mills spreadsheet. Net Power 229.96 1069.32 179.86 0.00 5.432 Jaime E. Sepúlveda J.: Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids). NO DATA INPUT REQUIRED IN THIS GREEN AREA rpm 10.76 5.0 % Losses 18480 Gross kW Feedrate, ton/hr (dry) 2289.0 Cyclone Dimensions (inches) and Operating Pressure (psi) Ore Density, ton/m3 2.80 Number Diameter Height Inlet Vortex Apex psi Balls Density, ton/m3 7.75 18 26.0 80.0 jsepulveda: Free Cyclone Height, defined as the distance from the bottom end of the vortex finder to the top end of the apex. 6.75 9.25 5.37 15.30 Make-up Ball Size, mm 88.90 Default Values: 78.0 6.5 9.1 4.6 EXPERIMENTAL SIZE DISTRIBUTIONS Fresh Feed Mill Discharge Cyclone Feed Cyclone U'flow Cyclone O'flow Circ. Lambda Cyclone Feed (pre-adjusted) Cyclone O'flow (pre-adjusted) Cyclone U'flow (pre-adjusted) i Mesh Opening Mid-Size ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing ton/hr % Retained % Passing Load ton/hr % Retained % Passing adj. ton/hr % Retained % Passing adj. ton/hr %Retained % Passing adj. 1 1.05 25400 jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. 100.00 jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. 100.00 jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. 100.00 100.00 jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. 100.00 jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. Jaime E. Sepúlveda J.: Rotational Mill Speed, expressed as a percentage of the critical centrifugation speed of the mill. Jaime E. Sepúlveda J.: Total Apparent Volumetric Charge Filling - including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls - expressed as a percentage of the net internal mill volume (inside liners). jsepulveda: See Mill Power_Ball Mills for further details. Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Ball Charge. Jaime E. Sepúlveda J.: This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases - particularly in Grate Discharge Mills - it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between Cells F9 and G9. Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Overfilling Slurry on top of the "kidney". Jaime E. Sepúlveda J.: Component of the Total Mill Power Draw (Cell L13) contributed by the Interstitial Slurry in the ball charge. Jaime E. Sepúlveda J.: Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge ("the kidney") with respect to the horizontal. See Mill Power_Ball Mills for further details. jsepulveda: Free Cyclone Height, defined as the distance from the bottom end of the vortex finder to the top end of the apex. jsepulveda: Net Mill Power Draw. See About ... in the Mill Power_Ball Mills spreadsheet. jsepulveda: The top Mesh Opening must always be defined to allow 100% of the material passing through such screen. Jaime E. Sepúlveda J.: Corresponds to the ratio between the Total Charge Weight and its Apparent Volume (including interstitial voids). 100.00 0.00 100.00 0.00 100.00 0.00 2 0.742 19050 21997 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.00 0.00 0.00 100.00 0.00000 0.00 0.00 100.00 0.00 0.00 0.00 100.00 0.00 0.00 0.00 100.00 0.00 3 0.525 12700 15554 275.14 12.02 87.98 34.55 0.56 99.44 47.37 0.56 99.44 47.51 0.77 99.23 0.00 0.00 100.00 (0.00055) 47.45 0.56 99.44 (0.00) -0.01 -0.00 100.00 0.00 47.46 0.77 99.23 0.00 4 0.371 9500 10984 216.54 9.46 78.52 37.64 0.61 98.83 51.60 0.61 98.83 51.21 0.83 98.40 0.00 0.00 100.00 0.00155 51.36 0.61 98.83 0.00 0.02 0.00 100.00 (0.00) 51.34 0.83 98.40 (0.00) 5 3 6700 7978 332.13 14.51 64.01 51.21 0.83 98.00 70.21 0.83 98.00 70.95 1.15 97.25 0.00 0.00 100.00 (0.00297) 70.67 0.84 98.00 (0.00) -0.03 -0.00 100.00 0.00 70.70 1.15 97.25 0.00 6 4 4750 5641 299.86 13.10 50.91 71.57 1.16 96.84 98.12 1.16 96.84 97.48 1.58 95.67 0.00 0.00 100.00 0.00255 97.72 1.16 96.84 0.00 0.03 0.00 100.00 (0.00) 97.69 1.58 95.67 (0.00) 7 6 3350 3989 229.82 10.04 40.87 106.12 1.72 95.12 145.49 1.72 95.12 145.60 2.36 93.31 0.00 0.00 100.00 (0.00046) 145.56 1.72 95.12 0.00 -0.01 -0.00 100.00 (0.00) 145.57 2.36 93.31 (0.00) 8 8 2360 2812 162.29 7.09 33.78 156.71 2.54 92.58 214.85 2.54 92.58 214.70 3.48 89.83 0.00 0.00 100.00 0.00058 214.76 2.54 92.58 0.00 0.01 0.00 100.00 (0.00) 214.75 3.48 89.83 (0.00) 9 10 1700 2003 108.96 4.76 29.02 214.09 3.47 89.11 293.52 3.47 89.11 293.68 4.76 85.07 0.00 0.00 100.00 (0.00064) 293.62 3.47 89.11 0.00 -0.01 -0.00 100.00 (0.00) 293.62 4.76 85.07 (0.00) 10 14 1180 1416 90.87 3.97 25.05 307.87 4.99 84.12 422.09 4.99 84.12 422.01 6.84 78.23 0.23 0.01 99.99 (0.00059) 422.18 4.99 84.12 (0.00) 0.22 0.01 99.99 0.00 421.96 6.84 78.23 0.00 11 20 850 1001 64.78 2.83 22.22 385.60 6.25 77.87 528.67 6.25 77.87 525.04 8.51 69.72 2.98 0.13 99.86 0.00260 528.26 6.25 77.87 0.00 3.01 0.13 99.86 (0.00) 525.26 8.51 69.72 (0.00) 12 28 600 714 57.91 2.53 19.69 504.06 8.17 69.70 691.07 8.17 69.70 670.64 10.87 58.85 21.29 0.93 98.93 (0.00342) 691.61 8.18 69.70 (0.00) 21.25 0.93 98.93 0.00 670.36 10.87 58.85 0.00 13 35 425 505 49.90 2.18 17.51 605.25 9.81 59.89 829.80 9.81 59.89 751.47 12.18 46.67 77.60 3.39 95.54 0.00292 829.34 9.80 59.89 0.00 77.63 3.39 95.54 (0.00) 751.71 12.18 46.67 (0.00) 14 48 300 357 44.41 1.94 15.57 657.69 10.66 49.23 901.69 10.66 49.23 731.72 11.86 34.81 170.07 7.43 88.11 (0.00040) 901.76 10.66 49.23 0.00 170.07 7.43 88.11 (0.00) 731.69 11.86 34.81 (0.00) 15 65 212 252 39.83 1.74 13.83 616.35 9.99 39.24 845.02 9.99 39.24 595.99 9.66 25.15 249.04 10.88 77.23 (0.00005) 845.03 9.99 39.24 0.00 249.04 10.88 77.23 (0.00) 595.99 9.66 25.15 (0.00) 16 100 150 178 35.48 1.55 12.28 502.21 8.14 31.10 688.54 8.14 31.10 419.54 6.80 18.35 268.96 11.75 65.48 0.00016 688.51 8.14 31.10 0.00 268.96 11.75 65.48 (0.00) 419.55 6.80 18.35 (0.00) 17 150 106 126 32.27 1.41 10.87 371.41 6.02 25.08 509.21 6.02 25.08 271.47 4.40 13.95 238.28 10.41 55.07 (0.00215) 509.55 6.02 25.08 (0.00) 238.26 10.41 55.07 0.00 271.29 4.40 13.95 0.00 18 200 75 89 28.61 1.25 9.62 262.83 4.26 20.82 360.34 4.26 20.82 172.13 2.79 11.16 188.61 8.24 46.83 (0.00163) 360.59 4.26 20.82 (0.00) 188.59 8.24 46.83 0.00 172.00 2.79 11.16 0.00 19 270 53 63 25.87 1.13 8.49 190.03 3.08 17.74 260.53 3.08 17.74 113.52 1.84 9.32 146.27 6.39 40.44 0.00294 260.07 3.07 17.74 0.00 146.30 6.39 40.44 (0.00) 113.77 1.84 9.32 (0.00) 20 400 38 45 22.20 0.97 7.52 138.82 2.25 15.49 190.32 2.25 15.49 78.35 1.27 8.05 111.93 4.89 35.55 Circ. Load 0.00013 190.30 2.25 15.49 0.00 111.93 4.89 35.55 (0.00) 78.37 1.27 8.05 (0.00) 21 -400 0 19 172.13 7.52 0.00 955.68 15.49 0.00 1310.25 15.49 0.00 496.66 8.05 0.00 813.74 35.55 0.00 W. Factors (0.00060) 1310.34 15.49 813.73 35.55 496.61 8.05 Totals 2289.00 100.00 6169.67 100.00 8458.67 100.00 6169.67 100.00 2289.00 100.00 1 8458.67 100.00 2289.00 100.00 6169.67 100.00 % Solids 97.00 76.00 64.51 78.00 44.00 1 0.00000 64.51 0.00 44.00 (0.00) 78.00 (0.00) Slurry Density, ton/m3 2.657 1.955 1.709 2.006 1.394 Weighting Factor 1.000 1.000 1.000 1.000 CL (ave) 2.695 &"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F &8&D / &T Flowsheet Moly-Cop Tools TM (Version 3.0) Simulation N° 0 Remarks Base Case Example 44.00 % Solids 46.83 % - Size 18 psi 15.30 232.6 P80 # of Cyclones 18 Vortex 9.25 Circ. Load 269.54 Apex 5.37 0.363 Bpf m3/hr 7674 0.374 Bpw % Solids 78.00 Water, m3/hr 1982.3 ton/hr 2289.0 Water, 860.2 F80 9964 m3/hr Gross kW 18480.0 kWh/ton (Gross) 8.07 % Balls 35.00 Wio (metric) 14.53 % Critical 75.00 % Solids 76.00 % Solids 64.51 &"Arial,Bold"Moly-Cop Tools&"Arial,Regular" / &F / &A &D / &T Reports Moly-Cop ToolsTM, Version 3.0 Sample N° 1 BALLPARAM Conventional Closed Circuit Grinding Simulator Remarks : Base Case Example CIRCUIT MASS BALANCE Configuration : DIRECT Fresh Mill Mill Sump Cyclone Cyclone Cyclone Feed Feed Discharge Water Feed U'flow O'flow Ore, ton/hr2289.0 8458.7 8458.7 0.0 8458.7 6169.7 2289.0 Water, m3/hr 70.8 1811.0 2671.2 1982.3 4653.5 1740.2 2913.3 Slurry, ton/hr 2359.8 10269.7 11129.8 1982.3 13112.1 7909.9 5202.3 Slurry, m3/hr 888.3 4831.9 5692.1 1982.3 7674.4 3943.6 3730.8 Slurry Dens., ton/m3 2.657 2.125 1.955 1.000 1.709 2.006 1.394 % Solids (by volume) 92.0 62.5 53.1 0.0 39.4 55.9 21.9 % Solids (by weight) 97.00 82.37 76.00 0.00 64.51 78.00 44.00 Particle Size Distributions (Cummulative % Passing) i Mesh Opening 1 1.05 25400 100.00 100.00 100.00 0.00 100.00 100.00 100.00 0 0 0 0 0 0 0 2 0.742 19050 100.00 100.00 100.00 0.00 100.00 100.00 100.00 0 0 0 0 0 0 0 3 0.525 12700 87.98 96.18 99.44 0.00 99.44 99.23 100.00 9963.6822961264 0 0 0 0 0 0 4 0.371 9500 78.52 93.02 98.83 0.00 98.83 98.40 100.00 0 0 0 0 0 0 0 5 3 6700 64.01 88.26 98.00 0.00 98.00 97.25 100.00 0 0 0 0 0 0 0 6 4 4750 50.91 83.56 96.84 0.00 96.84 95.67 100.00 0 3595.2326760925 0 0 0 0 0 7 6 3350 40.87 79.12 95.12 0.00 95.12 93.31 100.00 0 0 0 0 0 0 0 8 8 2360 33.78 74.66 92.58 0.00 92.58 89.83 100.00 0 0 0 0 0 0 0 9 10 1700 29.02 69.90 89.11 0.00 89.11 85.07 100.00 0 0 0 0 0 1300.7604511945 0 10 14 1180 25.05 63.84 84.12 0.00 84.12 78.23 99.99 0 0 953.1405358324 0 953.1405358324 0 0 11 20 850 22.22 56.86 77.87 0.00 77.87 69.72 99.86 0 0 0 0 0 0 0 12 28 600 19.69 48.25 69.70 0.00 69.70 58.85 98.93 0 0 0 0 0 0 0 13 35 425 17.51 38.78 59.89 0.00 59.89 46.67 95.54 0 0 0 0 0 0 0 14 48 300 15.57 29.60 49.23 0.00 49.23 34.81 88.11 0 0 0 0 0 0 232.6302336883 15 65 212 13.83 22.09 39.24 0.00 39.24 25.15 77.23 0 0 0 0 0 0 0 16 100 150 12.28 16.71 31.10 0.00 31.10 18.35 65.48 0 0 0 0 0 0 0 17 150 106 10.87 13.11 25.08 0.00 25.08 13.95 55.07 0 0 0 0 0 0 0 18 200 75 9.62 10.75 20.82 0.00 20.82 11.16 46.83 0 0 0 0 0 0 0 19 270 53 8.49 9.10 17.74 0.00 17.74 9.32 40.44 0 0 0 0 0 0 0 20 400 38 7.52 7.91 15.49 0.00 15.49 8.05 35.55 0 0 0 0 0 0 0 D80, microns 9964 3595 953 0 953 1301 232.6 9963.6822961264 3595.2326760925 953.1405358324 0 953.1405358324 1300.7604511945 232.6302336883 Specific Energy Consumption : 8.07 kWh/ton (Gross) Operational Work Index : 14.53 kWh/ton (metric) Moly-Cop ToolsTM, Version 3.0 Sample N° 1 BALLPARAM Conventional Closed Circuit Grinding Simulator Remarks : Base Case Example CLASSIFIERS PERFORMANCE Number of Cyclones : 18 Operating Conditions : Cyclone Dimensions, in : Feed Flowrate, m3/hr 7674.4 Diameter 26.00 Pressure, psi 15.30 Height 80.00 D50 (corr.), microns 232.5 Inlet 6.75 Water By-Pass, % 37.4 Vortex 9.25 Solids By-Pass, % 36.3 Apex 5.37 Plitt's Parameter 1.31 Ore Density, ton/m3 2.80 Circulating Load, % 269.5 Mass Balance around the Classifiers Size Distributions, % Passing Classifier Efficiency 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 99.44 99.23 100.00 1.000 1.000 4 0.371 9500 7978 98.83 98.40 100.00 1.000 1.000 5 3 6700 5641 98.00 97.25 100.00 1.000 1.000 6 4 4750 3989 96.84 95.67 100.00 1.000 1.000 7 6 3350 2812 95.12 93.31 100.00 1.000 1.000 8 8 2360 2003 92.58 89.83 100.00 1.000 1.000 9 10 1700 1416 89.11 85.07 100.00 1.000 0.999 10 14 1180 1001 84.12 78.23 99.99 0.994 0.991 11 20 850 714 77.87 69.72 99.86 0.969 0.951 12 28 600 505 69.70 58.85 98.93 0.906 0.853 13 35 425 357 59.89 46.67 95.54 0.811 0.704 14 48 300 252 49.23 34.81 88.11 0.705 0.538 15 65 212 178 39.24 25.15 77.23 0.609 0.387 16 100 150 126 31.10 18.35 65.48 0.533 0.267 17 150 106 89 25.08 13.95 55.07 0.477 0.179 18 200 75 63 20.82 11.16 46.83 0.438 0.117 19 270 53 45 17.74 9.32 40.44 0.412 0.077 20 400 38 19 15.49 8.05 35.55 0.379 0.026 Ore, ton/hr 8458.7 6169.7 2289.0 Classifier Constants Water, m3/hr 4653.5 1740.2 2913.3 a1 10.637 Slurry, ton/hr 13112.1 7909.9 5202.3 a2 1.228 Slurry, m3/hr 7674.4 3943.6 3730.8 a3 48.323 Slurry Dens., ton/m3 1.709 2.006 1.394 a4 0.358 % Solids (by volume) 39.4 55.9 21.9 l 0.970 % Solids (by weight) 64.5 78.0 44.0 Bpc 0.000 Moly-Cop ToolsTM, Version 3.0 Sample N° 1 BALLPARAM Conventional Closed Circuit Grinding Simulator Remarks : Base Case Example BALL MILL PERFORMANCE Eff. Diameter, ft 28.5 Mill Power, kW (Gross) 18480 Eff. Length, ft 36.3 Mill Power, kW (Net) 17556 Speed, % Critical 75.0 Throughput, ton/hr 8458.7 App. Density, ton/m3 5.43 % Solids (by weight) 76.0 Charge Level, % 35.0 Sp. Energy, kWh/ton 2.18 Balls Filling, % 35.0 Reduction Ratio 3.77 Lift Angle, (°) 31.6 Arbiter's Flow Number 3.55 Size Distributions 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 96.18 99.44 4 0.371 9500 7978 93.02 98.83 5 3 6700 5641 88.26 98.00 6 4 4750 3989 83.56 96.84 7 6 3350 2812 79.12 95.12 8 8 2360 2003 74.66 92.58 9 10 1700 1416 69.90 89.11 10 14 1180 1001 63.84 84.12 11 20 850 714 56.86 77.87 12 28 600 505 48.25 69.70 13 35 425 357 38.78 59.89 14 48 300 252 29.60 49.23 15 65 212 178 22.09 39.24 16 100 150 126 16.71 31.10 17 150 106 89 13.11 25.08 18 200 75 63 10.75 20.82 19 270 53 45 9.10 17.74 20 400 38 19 7.91 15.49 D80, microns 3595 953 Selection Function Parameters Breakage Function Parameters alpha01 alpha02 alpha11 alpha12 alpha2 Dcrit Beta00 Beta01 Beta1 Beta2 0.00581 0.0000000 0.720 1.000 2.52 9415 0.179 0.000 0.32 4.00 &"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F &8Page &P &8&D / &T Class Number of Cyclones 18 Classifier Dimensions, inches. DC h DI DO DU 26 80 6.75 9.25 5.37 Classifier Constants a1 a2 a3 a4 l Cyclone Cyclone Cyclone 10.6367547994 1.2282598789 48.3232354267 0.3578672672 0.9699836829 Feed U'flow O'flow Circulating Load, CL 2.6953578995 Solids, tons 469.93 342.76 127.1666666667 Slurry Split, S 1.0570577026 Water, m3/hr 258.53 96.68 161.85 Cyclone Pressure, ft 20.6811936022 Slurry, tons 728.4522977486 439.4369454296 289.015352319 Cyclone Pressure, lb/in2 15.30 Slurry, m3/hr 426.3567894684 219.0914371494 207.265352319 Corrected Cut Size, d50c, microns 232.4719738419 Solids Density, ton/m3 2.80 2.80 2.80 Water By-Pass 0.3739557492 Slurry Density, ton/m3 1.7085509501 2.0057239623 1.3944219286 Fines By-Pass 0.3627309748 % Solids (by volume) 39.3639416749 55.8735534622 21.9123293684 Coarse By-Pass 0 % Solids (by weight) 64.51 78.00 44.00 Plitt's Parameter 1.3131070129 % Passing (model) % Passing (exp) (Weighted Error)^2 Opening Mid-Size Classifier Cyclone Cyclone Cyclone Cyclone Cyclone Cyclone Cyclone Cyclone Cyclone Efficiency Feed U'flow O'flow Feed U'flow O'flow Feed U'flow O'flow 1 1 1 1 25400 2 19050 21997.0452561247 1 100.00 100 100.00 100.00 100.00 100.00 0.000 0.000 0.000 3 12700 15554.2598666732 1 100.00 100 100.00 100.00 100.00 100.00 0.000 0.000 0.000 4 9500 10984.0793879141 1 99.44 99.2273640558 100.00 99.44 99.23 100.00 0.000 0.000 0.000 5 6700 7978.0950107153 1 98.83 98.3987557596 100.00 98.83 98.40 100.00 0.000 0.000 0.000 6 4750 5641.3650830273 1 98.00 97.2535166634 100.00 98.00 97.25 100.00 0.000 0.000 0.000 7 3350 3989.0475053576 1 96.84 95.6686802529 100.00 96.84 95.67 100.00 0.000 0.000 0.000 8 2360 2811.7610140266 0.9999999928 95.12 93.3141340262 100.00 95.12 93.31 100.00 0.000 0.000 0.000 9 1700 2002.9977533687 0.9999948147 92.58 89.8280428668 100.00 92.58 89.83 100.00 0.000 0.000 0.000 10 1180 1416.3332941084 0.9996236844 89.11 85.06720154 100.00 89.11 85.07 100.00 0.000 0.000 0.000 11 850 1001.4988766843 0.9942981394 84.12 78.2314503578 99.99 84.12 78.23 99.99 0.000 0.0000.000 12 600 714.1428428543 0.9690631982 77.87 69.7160124352 99.86 77.87 69.72 99.86 0.000 0.000 0.000 13 425 504.9752469181 0.906496358 69.70 58.8525811905 98.93 69.70 58.85 98.93 0.000 0.000 0.000 14 300 357.0714214271 0.8113917432 59.89 46.6681295165 95.54 59.89 46.67 95.54 0.000 0.000 0.000 15 212 252.1904042584 0.7052873568 49.23 34.8090082308 88.11 49.23 34.81 88.11 0.000 0.000 0.000 16 150 178.3255450013 0.6092943647 39.24 25.1490304723 77.23 39.24 25.15 77.23 0.000 0.000 0.000 17 106 126.0952021292 0.5327691051 31.10 18.3512243602 65.48 31.10 18.35 65.48 0.000 0.000 0.000 18 75 89.1627725006 0.4766257957 25.08 13.9469996489 55.07 25.08 13.95 55.07 0.000 0.000 0.000 19 53 63.0476010646 0.4375607315 20.82 11.1639206777 46.83 20.82 11.16 46.83 0.000 0.001 0.000 20 38 44.8776113446 0.411687251 17.74 9.3195540923 40.44 17.74 9.32 40.44 0.000 0.000 0.000 21 0 19 0.378997541 15.49 8.0491987732 35.55 15.49 8.05 35.55 0.000 0.000 0.000 Overall 0.000 0.000 0.000 0.000 SiE Selection Function : alpha01 alpha02 alpha11 alpha12 alpha2 dcrit 0.0058143557 0 0.7199253855 1 2.5191340556 9415.1485159774 i Mesh Opening Mid-Size SiE 1 1.05 25400 2 0.742 19050 21997.0452561247 0.8201112231 3 0.525 12700 15554.2598666732 1.3337977095 4 0.371 9500 10984.0793879141 1.9057944355 5 3 6700 7978.0950107153 2.258207865 6 4 4750 5641.3650830273 2.2889832791 7 6 3350 3989.0475053576 2.0398934762 8 8 2360 2811.7610140266 1.6877294227 9 10 1700 2002.9977533687 1.3575369993 10 14 1180 1416.3332941084 1.0701507542 11 20 850 1001.4988766843 0.8379408168 12 28 600 714.1428428543 0.6582023183 13 35 425 504.9752469181 0.5133113475 14 48 300 357.0714214271 0.4001110438 15 65 212 252.1904042584 0.3115439857 16 100 150 178.3255450013 0.2427658035 17 150 106 126.0952021292 0.1891644475 18 200 75 89.1627725006 0.1473956892 19 270 53 63.0476010646 0.114849004 20 400 38 44.8776113446 0.0899164438 21 -400 0 19 0 19050 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 0.82011122306267703 1.3337977094862761 1.9057944354632907 2.2582078650124973 2.2889832790778031 2.0398934762132326 1.687729422721892 1.3575369993421635 1.0701507541551614 0.83794081676934107 0.658202318291504 0.51331134750733587 0.40011104378036461 0.31154398572866626 0.24276580352961036 0.18916444749857503 0.14739568922800664 0.11484900402326827 8.9916443834196516E-2 Bij Breakage Function : Beta00 Beta01 Beta1 Beta2 0.1794342827 0 0.3194530094 4 i Mesh Opening Beta0J Cummulative 1 1.05 25400 0.1794342827 1 2 0.742 19050 0.1794342827 1 1 3 0.525 12700 0.1794342827 0.319722015 1 1 4 0.371 9500 0.1794342827 0.1944222786 0.420458829 1 1 5 3 6700 0.1794342827 0.1410637677 0.2098417285 0.3635050624 1 1 6 4 4750 0.1794342827 0.1183077603 0.1471153982 0.1950792646 0.3680575379 1 1 7 6 3350 0.1794342827 0.1037678881 0.1211973307 0.141304389 0.1950792646 0.3635050624 1 1 8 8 2360 0.1794342827 0.0922736318 0.105792605 0.1181247766 0.1412021722 0.1935051133 0.3625449648 1 1 9 10 1700 0.1794342827 0.0829715479 0.0946498871 0.1044000487 0.1191803313 0.1426891665 0.1988924594 0.3825160425 1 1 10 14 1180 0.1794342827 0.0738028501 0.0840564427 0.092353014 0.1038224628 0.1181247766 0.1412021722 0.1950792646 0.3501584715 1 1 11 20 850 0.1794342827 0.0664527625 0.0756552717 0.0830417431 0.09299505 0.1044000487 0.1191803313 0.1432965361 0.1950792646 0.3825160425 1 1 12 28 600 0.1794342827 0.059453136 0.0676780731 0.0742633926 0.0830651969 0.0928627296 0.1044320437 0.1192812402 0.1413850686 0.1994197566 0.3642639444 1 1 13 35 425 0.1794342827 0.0532510902 0.0606159758 0.0665086088 0.0743667253 0.0830417431 0.09299505 0.1046314602 0.1184379841 0.1432965361 0.1950792646 0.3672860812 1 1 14 48 300 0.1794342827 0.0476435804 0.0542324045 0.0595030794 0.0665272674 0.0742633926 0.0830651969 0.0930558125 0.1038943656 0.1192812402 0.1413850686 0.1950792646 0.3642639444 1 1 15 65 212 0.1794342827 0.0426417688 0.0485387442 0.0532557246 0.0595408876 0.0664585489 0.0743106679 0.0831481713 0.0924733974 0.1045453057 0.1183212381 0.1414874006 0.1944901099 0.3652278573 1 1 16 100 150 0.1794342827 0.038180273 0.0434602315 0.0476835974 0.0533107625 0.0595030794 0.0665272674 0.0744141623 0.0826702137 0.0930558125 0.1038943656 0.1184379841 0.1413850686 0.1950792646 0.366313539 1 1 17 150 106 0.1794342827 0.0341719809 0.0388976239 0.0426775844 0.0477138911 0.0532557246 0.0595408876 0.0665932739 0.0739591118 0.0831481713 0.0924733974 0.1039344892 0.1183212381 0.1414874006 0.1950792646 0.3652278573 1 1 18 200 75 0.1794342827 0.0305966626 0.0348278728 0.0382123411 0.0427216883 0.0476835974 0.0533107625 0.0596236547 0.0662129819 0.0744141623 0.0826702137 0.092544743 0.1038943656 0.1184379841 0.141602467 0.1950792646 0.366313539 1 1 19 270 53 0.1794342827 0.0273845247 0.0311715281 0.0342006825 0.0382366174 0.0426775844 0.0477138911 0.0533636279 0.0592597193 0.0665932739 0.0739591118 0.08269975 0.0924733974 0.1039344892 0.1184379841 0.1414874006 0.1950792646 0.3652278573 1 1 20 400 38 0.1794342827 0.0246233261 0.0280284834 0.0307522059 0.0343811934 0.038374369 0.0429028371 0.0479828076 0.0532840328 0.0598765124 0.0664938936 0.0743293635 0.0830232466 0.092947201 0.1044607105 0.1191009934 0.1428477305 0.1984793897 0.378184248 1 1 i Mesh Opening Partial 1 1.05 25400 0 2 0.742 19050 0.680277985 0 3 0.525 12700 0.1252997365 0.579541171 0 4 0.371 9500 0.0533585109 0.2106171005 0.6364949376 0 5 3 6700 0.0227560074 0.0627263303 0.1684257978 0.6319424621 0 6 4 4750 0.0145398722 0.0259180676 0.0537748756 0.1729782733 0.6364949376 0 7 6 3350 0.0114942563 0.0154047257 0.0231796124 0.0538770924 0.1699999491 0.6374550352 0 8 8 2360 0.0093020839 0.0111427179 0.0137247279 0.0220218408 0.0508159469 0.1636525054 0.6174839575 0 9 10 1700 0.0091686979 0.0105934444 0.0120470347 0.0153578685 0.0245643899 0.0576902873 0.1874367778 0.6498415285 0 10 14 1180 0.0073500875 0.008401171 0.0093112708 0.0108274128 0.0137247279 0.0220218408 0.0517827285 0.1550792069 0.6174839575 0 11 20 850 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0.1712342744 0.6347721427 0 17 150 106 0.0035753183 0.004069751 0.0044652432 0.0049922027 0.0055721272 0.0062301251 0.0069696192 0.0077461299 0.008734009 0.0098031837 0.0113897462 0.0144268724 0.0230494165 0.0534767976 0.1701485927 0.633686461 0 18 200 75 0.0032121379 0.0036563447 0.0040116587 0.004485071 0.005006013 0.0055968714 0.0062600268 0.0069532625 0.0078208884 0.0087111019 0.009844993 0.0114209682 0.0145034949 0.0231644829 0.053591864 0.1712342744 0.6347721427 0 19 270 53 0.0027611987 0.0031430447 0.0034484766 0.0038554239 0.0043032154 0.0048110539 0.0053808203 0.0059756865 0.0067167615 0.0074652182 0.0083703865 0.0094501508 0.0109872882 0.0139772737 0.0223864072 0.0522315341 0.1667484676 0.621815752 0 20 400 38 0.0246233261 0.0280284834 0.0307522059 0.0343811934 0.038374369 0.0429028371 0.0479828076 0.0532840328 0.0598765124 0.0664938936 0.0743293635 0.08302324660.092947201 0.1044607105 0.1191009934 0.1428477305 0.1984793897 0.378184248 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 12700 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38 0.31972201504621345 0.19442227858056962 0.14106376771028908 0.11830776028207698 0.10376788808134418 9.2273631822395411E-2 8.2971547928283707E-2 7.3802850055580613E-2 6.6452762512206331E-2 5.9453136043714647E-2 5.3251090158817418E-2 4.7643580405958619E-2 4.2641768837468667E-2 3.8180272964290489E-2 3.4171980927367583E-2 3.05966626332137E-2 2.7384524735381135E-2 2.4623326062661564E-2 J&T Mill Throughput, ton/hr 8458.674231846 Reynolds Number 8.6781099389 Water 2671.1602837408 Slurry Viscosity, cp 16.914635647 Slurry, m3/hr 5692.115366543 Slurry Dens., ton/m3 1.9553072626 % Solids (by volume) 53.0726256983 Ebar 1.7766694643 N 4.6184068332 L/D 1.2736842105 Matrix J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.281840538 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0.1476707015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0.0788791177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0.0557059232 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0.0541046034 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0.068886214 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0.0991911476 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0.1436233376 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0.203449911 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0.2751520349 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0.3526082753 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0.4350573076 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0.5162348967 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5928732783 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6620948327 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.722948763 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7751348487 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8190012771 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8546604883 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Matrix T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 SiE 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.8201112231 2 1.0860780359 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1.3337977095 3 0.8679216146 1.351390054 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1.9057944355 4 0.97467391 2.0772113533 3.4420609674 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2.258207865 5 1.2111563877 3.6450927708 13.6564614065 46.3700483474 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2.2889832791 6 1.8722283815 8.9153610566 159.1620793995 -311.2408798079 -5.8490000497 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2.0398934762 7 3.566655383 37.7032576623 -975.5894759146 677.5954112071 12.002523988 -3.6924278748 1 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1.6877294227 8 8.5180288676 1804.8575286211 1754.2617478596 -674.7125110927 -11.4575626817 5.1501155217 -3.1561773361 1 0 0 0 0 0 0 0 0 0 0 0 0 8 1.3575369993 9 36.0254063323 -6089.6389232616 -1506.1464292689 349.186720561 5.6963224747 -3.6019440506 3.9962298745 -3.0696803809 1 0 0 0 0 0 0 0 0 0 0 0 9 1.0701507542 10 1463.3075828637 7341.1784679878 658.8231517949 -95.3459569622 -1.4952368142 1.309298116 -2.4284286384 3.4987205993 -2.8457047544 1 0 0 0 0 0 0 0 0 0 0 10 0.8379408168 11 -4863.745313394 -4220.0368465348 -119.7653293907 7.6285217244 0.1095354448 -0.1791539297 0.6800702618 -1.9092680608 3.2042661907 -2.9638012677 1 0 0 0 0 0 0 0 0 0 11 0.6582023183 12 5917.3468510099 1249.1913114281 8.8387769243 -0.0963707779 -0.0009158473 0.0084233144 -0.0897187641 0.5357975824 -1.7797999085 3.3654352443 -2.8742561796 1 0 0 0 0 0 0 0 0 12 0.5133113475 13 -3444.8246512659 -149.7330787135 0.4039464279 -0.0425958967 -0.0005983713 0.0008654802 0.0011879971 -0.0592281728 0.4775013674 -1.8438651664 3.1950348649 -2.8827708106 1 0 0 0 0 0 0 0 13 0.4001110438 14 986.4347542168 3.2139387134 0.2086514154 -0.0354799404 -0.0005222149 0.000519803 -0.0002513869 0.0009412057 -0.0526926377 0.4943732111 -1.7200360203 3.1968371871 -2.8676502321 1 0 0 0 0 0 0 14 0.3115439857 15 -114.5267323245 0.7637525659 0.1761703658 -0.0315815383 -0.0004674456 0.0004447809 -0.0002902114 0.0003104991 -0.000115042 -0.0519793507 0.4458883975 -1.7081362351 3.1653746545 -2.8704045301 1 0 0 0 0 0 15 0.2427658035 16 1.0441792915 0.5791183355 0.1580618958 -0.0285091264 -0.0004223122 0.0003994486 -0.0002691944 0.0002508436 -0.0003370693 0.0000833636 -0.0447327411 0.4401066412 -1.6888133985 3.1785142974 -2.8749453501 1 0 0 0 0 16 0.1891644475 17 0.0400731644 0.5084726337 0.1414978106 -0.0255336588 -0.0003782783 0.0003575486 -0.000242326 0.000222019 -0.0003171754 -0.0000186527 -0.0001498672 -0.0444895196 0.4362365662 -1.7003297105 3.180411082 -2.869871029 1 0 0 0 17 0.1473956892 18 -0.0142752533 0.4581100723 0.1276694549 -0.023028177 -0.0003411547 0.0003225254 -0.0002189618 0.0002002547 -0.0002886494 -0.0000226324 -0.0001757955 -0.0001866473 -0.0434780313 0.4385406397 -1.699967777 3.1772854945 -2.8747221687 1 0 0 18 0.114849004 19 -0.0173676849 0.3947095755 0.1099815344 -0.0198327303 -0.0002938109 0.000277808 -0.000188706 0.0001725712 -0.0002491953 -0.0000201238 -0.000154235 -0.000134732 -0.0001365117 -0.0437100148 0.4331435358 -1.6750990099 3.1440922124 -2.8643235696 1 0 19 0.0899164438 20 -0.1672495362 3.5711256795 0.9909773174 -0.1784221314 -0.0026429269 0.0025015082 -0.0017026083 0.0015610395 -0.0022631259 -0.0001846253 -0.0014184236 -0.0012258837 -0.0015330471 -0.0026106817 -0.0386414907 0.3676845444 -1.2693700436 1.8643235696 -1 1 20 0 Vector SiE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.8201112231 1.3337977095 1.9057944355 2.258207865 2.2889832791 2.0398934762 1.6877294227 1.3575369993 1.0701507542 0.8379408168 0.6582023183 0.5133113475 0.4001110438 0.3115439857 0.2427658035 0.1891644475 0.1473956892 0.114849004 0.0899164438 0 Matrix bij 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.680277985 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0.1252997365 0.579541171 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0.0533585109 0.2106171005 0.6364949376 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0.0227560074 0.0627263303 0.1684257978 0.6319424621 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0.0145398722 0.0259180676 0.0537748756 0.1729782733 0.6364949376 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0.0114942563 0.0154047257 0.0231796124 0.0538770924 0.1699999491 0.6374550352 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0.0093020839 0.0111427179 0.0137247279 0.0220218408 0.0508159469 0.1636525054 0.6174839575 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0.0091686979 0.0105934444 0.0120470347 0.0153578685 0.0245643899 0.0576902873 0.1874367778 0.6498415285 0 0 0 0 0 0 0 0 0 0 0 0 10 0.0073500875 0.008401171 0.0093112708 0.0108274128 0.0137247279 0.0220218408 0.0517827285 0.1550792069 0.6174839575 0 0 0 0 0 0 0 0 0 0 0 11 0.0069996265 0.0079771986 0.0087783506 0.0099298531 0.0115373191 0.0147482876 0.0240152959 0.053694196 0.1830962858 0.6357360556 0 0 0 0 0 0 0 0 0 0 12 0.0062020459 0.0070620973 0.0077547838 0.0086984716 0.0098209865 0.0114369937 0.0146497801 0.0229470844 0.0561232205 0.1691846798 0.6327139188 0 0 0 0 0 0 0 0 0 13 0.0056075098 0.0063835714 0.0070055293 0.007839458 0.0087783506 0.0099298531 0.0115756477 0.0145436185 0.0240152959 0.053694196 0.1722068166 0.6357360556 0 0 0 0 0 0 0 0 14 0.0050018116 0.0056936603 0.0062473549 0.0069863798 0.0078048437 0.0087545291 0.0099076412 0.0114209682 0.0147359345 0.0230638305 0.053591864 0.1697738345 0.6347721427 0 0 0 0 0 0 0 15 0.0044614959 0.0050785127 0.0055721272 0.0062301251 0.0069554694 0.0077834005 0.008734009 0.0098031837 0.0114894933 0.0144268724 0.0230494165 0.0531050413 0.1701485927 0.633686461 0 0 0 0 0 0 16 0.004008292 0.0045626076 0.005006013 0.0055968714 0.0062473549 0.0069863798 0.0078208884 0.0087111019 0.0099076412 0.0114209682 0.0145034949 0.0230638305 0.053591864 0.1712342744 0.6347721427 0 0 0 0 0 17 0.0035753183 0.004069751 0.0044652432 0.0049922027 0.0055721272 0.0062301251 0.0069696192 0.0077461299 0.008734009 0.0098031837 0.01138974620.0144268724 0.0230494165 0.0534767976 0.1701485927 0.633686461 0 0 0 0 18 0.0032121379 0.0036563447 0.0040116587 0.004485071 0.005006013 0.0055968714 0.0062600268 0.0069532625 0.0078208884 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3.6924278748 1 0 -0 -0 -0 0 -0 -0 -0 -0 0 -0 0 0 8 2214.0114626651 -2145.42213446 56.3476403947 21.7078077103 11.6164386388 6.5038416517 3.156177336 1 -0 -0 -0 0 -0 -0 -0 -0 0 -0 0 0 9 -297.8379197164 125.016467972 33.783065519 18.8784767986 12.6884273203 8.8108685861 5.6922257725 3.0696803809 1 0 0 -0 0 0 0 0 -0 0 0 0 10 -1762.0427556495 49.7621041588 23.8095993495 16.3251292901 12.6015234646 9.9755053453 7.5842399218 5.2366834551 2.8457047544 1 0 -0 0 0 0 0 -0 0 0 0 11 133.5114853228 32.6953466056 20.3420632107 15.7729987789 13.2836185422 11.4186677432 9.5846916223 7.5936840631 5.2298371681 2.9638012677 1 -0 -0 -0 -0 -0 0 -0 0 0 12 52.9776912398 23.6501177788 17.1992952475 14.4794586932 12.9421669096 11.7679562765 10.554260278 9.1300935599 7.2346566318 5.1532888647 2.8742561796 1 -0 -0 -0 -0 0 -0 0 0 13 32.3373773545 19.1442624387 15.3626995125 13.6666733859 12.7166037731 12.0075229132 11.2541063897 10.307071682 8.9159393765 7.2301675012 5.0907869521 2.8827708106 1 -0 -0 -0 0 -0 0 0 14 23.3989943746 16.3388340495 13.9995769567 12.9336954649 12.3687651164 11.9805877184 11.5663780163 11.0029963376 10.0811370158 8.8628377609 7.1301033647 5.0699411972 2.8676502321 1 -0 -0 0 -0 0 0 15 18.827856997 14.6058656519 13.0869710571 12.4085543428 12.0880391876 11.9087869113 11.7253212894 11.4390571375 10.8885411893 10.0867148945 8.8157657402 7.1358687559 5.0659415624 2.8704045301 1 -0 0 -0 0 0 16 16.1161515846 13.4213363444 12.4072294308 11.9771999354 11.8133863698 11.7678417436 11.7363590858 11.6420225058 11.3683049655 10.9030002331 10.0588519577 8.8287074455 7.1382512748 5.0737418593 2.8749453501 1 0 -0 0 0 17 14.3358910521 12.5431839701 11.8547000435 11.5865433713 11.521566728 11.5575148229 11.6201775097 11.6507798464 11.5703504436 11.3557177618 10.860612076 10.0497467781 8.8137981679 7.1322481037 5.0703112882 2.869871029 1 -8.00495166178202E-16 0 0 18 13.1473482656 11.9146807316 11.4399119195 11.2766040946 11.2716937887 11.3536504506 11.4697228521 11.5754679068 11.6206435974 11.5788238111 11.3431251435 10.8718012881 10.0547930326 8.8235598926 7.1411818811 5.0727963739 2.8747221687 1 0 0 19 12.4471638406 11.56545855 11.2292028824 11.1319974189 11.161703409 11.2670727047 11.4101225531 11.5569933459 11.6777213902 11.7462370414 11.6875892276 11.4632652371 10.9772658376 10.1485176608 8.8958039149 7.1820900746 5.0900422515 2.8643235696 1 0 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Mill2 Matrix J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.281840538 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0.1476707015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0.0788791177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0.0557059232 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0.0541046034 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0.068886214 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0.0991911476 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0.1436233376 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0.203449911 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0.2751520349 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0.3526082753 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0.4350573076 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0.5162348967 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5928732783 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6620948327 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.722948763 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7751348487 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8190012771 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8546604883 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 Matrix T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1.0860780359 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0.8679216146 1.351390054 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0.97467391 2.0772113533 3.4420609674 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1.2111563877 3.6450927708 13.6564614065 46.3700483474 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1.8722283815 8.9153610566 159.1620793995 -311.2408798079 -5.8490000497 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3.566655383 37.7032576623 -975.5894759146 677.5954112071 12.002523988 -3.6924278748 1 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8.5180288676 1804.8575286211 1754.2617478596 -674.7125110927 -11.4575626817 5.1501155217 -3.1561773361 1 0 0 0 0 0 0 0 0 0 0 0 0 9 36.0254063323 -6089.6389232616 -1506.1464292689 349.186720561 5.6963224747 -3.6019440506 3.9962298745 -3.0696803809 1 0 0 0 0 0 0 0 0 0 0 0 10 1463.3075828637 7341.1784679878 658.8231517949 -95.3459569622 -1.4952368142 1.309298116 -2.4284286384 3.4987205993 -2.8457047544 1 0 0 0 0 0 0 0 0 0 0 11 -4863.745313394 -4220.0368465348 -119.7653293907 7.6285217244 0.1095354448 -0.1791539297 0.6800702618 -1.9092680608 3.2042661907 -2.9638012677 1 0 0 0 0 0 0 0 0 0 12 5917.3468510099 1249.1913114281 8.8387769243 -0.0963707779 -0.0009158473 0.0084233144 -0.0897187641 0.5357975824 -1.7797999085 3.3654352443 -2.8742561796 1 0 0 0 0 0 0 0 0 13 -3444.8246512659 -149.7330787135 0.4039464279 -0.0425958967 -0.0005983713 0.0008654802 0.0011879971 -0.0592281728 0.4775013674 -1.8438651664 3.1950348649 -2.8827708106 1 0 0 0 0 0 0 0 14 986.4347542168 3.2139387134 0.2086514154 -0.0354799404 -0.0005222149 0.000519803 -0.0002513869 0.0009412057 -0.0526926377 0.4943732111 -1.7200360203 3.1968371871 -2.8676502321 1 0 0 0 0 0 0 15 -114.5267323245 0.7637525659 0.1761703658 -0.0315815383 -0.0004674456 0.0004447809 -0.0002902114 0.0003104991 -0.000115042 -0.0519793507 0.4458883975 -1.7081362351 3.1653746545 -2.8704045301 1 0 0 0 0 0 16 1.0441792915 0.5791183355 0.1580618958 -0.0285091264 -0.0004223122 0.0003994486 -0.0002691944 0.0002508436 -0.0003370693 0.0000833636 -0.0447327411 0.4401066412 -1.6888133985 3.1785142974 -2.8749453501 1 0 0 0 0 17 0.0400731644 0.5084726337 0.1414978106 -0.0255336588 -0.0003782783 0.0003575486-0.000242326 0.000222019 -0.0003171754 -0.0000186527 -0.0001498672 -0.0444895196 0.4362365662 -1.7003297105 3.180411082 -2.869871029 1 0 0 0 18 -0.0142752533 0.4581100723 0.1276694549 -0.023028177 -0.0003411547 0.0003225254 -0.0002189618 0.0002002547 -0.0002886494 -0.0000226324 -0.0001757955 -0.0001866473 -0.0434780313 0.4385406397 -1.699967777 3.1772854945 -2.8747221687 1 0 0 19 -0.0173676849 0.3947095755 0.1099815344 -0.0198327303 -0.0002938109 0.000277808 -0.000188706 0.0001725712 -0.0002491953 -0.0000201238 -0.000154235 -0.000134732 -0.0001365117 -0.0437100148 0.4331435358 -1.6750990099 3.1440922124 -2.8643235696 1 0 20 -0.1672495362 3.5711256795 0.9909773174 -0.1784221314 -0.0026429269 0.0025015082 -0.0017026083 0.0015610395 -0.0022631259 -0.0001846253 -0.0014184236 -0.0012258837 -0.0015330471 -0.0026106817 -0.0386414907 0.3676845444 -1.2693700436 1.8643235696 -1 1 Matrix T (inverse) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 -9.91243276993069E-16 4.50292221529256E-16 -0 -0 -0 -0 -7.7870534843126E-16 -0 -0 -7.86435364900846E-16 -4.12767869735151E-19 -2.56658280817759E-16 -5.12970493342246E-16 -1.81526628193981E-16 -3.17219817863824E-16 1.27601535945552E-16 -1.12291621869412E-16 0 0 2 -1.0860780359 1 -0 2.81713232803521E-16 6.41290714888983E-16 0 0 -1.50613328903025E-16 0 0 9.79302389083299E-16 -3.1348964556553E-16 2.40683907638598E-16 5.75979360163233E-16 1.97152083819448E-16 3.44525476746294E-16 -1.38585225542475E-16 1.21957464132274E-16 0 0 3 0.5997934411 -1.351390054 1 0 0 -0 -0 0 -0 -8.20474728586048E-17 -7.45760423630121E-16 2.78634127910712E-16 -2.04872127657582E-16 -3.33154599822832E-16 -1.08878480968593E-16 -1.90266366129148E-16 7.65345643293981E-17 -6.73517782833278E-17 0 0 4 -0.7831858752 2.5743556032 -3.4420609674 1 -0 0 0 -0 0 -0 0 -3.04842337809415E-16 4.55389138513845E-16 4.50286534425783E-16 1.42169091167421E-16 2.48442080672578E-16 -9.99357206016077E-17 8.79452121472219E-17 0 0 5 30.8730097262 -104.5628804381 145.9520720657 -46.3700483474 1 -0 -0 0 -0 0 -0 0 -0 -0 -0 -0 0 -0 0 0 6 -150.8370472615 395.8311000218 -376.7984864768 40.0224647204 5.8490000497 1 0 -0 0 -0 0 -0 0 0 0 0 -0 0 0 0 7 225.7083909225 -383.880447597 164.8197117949 26.7422707594 9.594486835 3.6924278748 1 0 -0 -0 -0 0 -0 -0 -0 -0 0 -0 0 0 8 2214.0114626651 -2145.42213446 56.3476403947 21.7078077103 11.6164386388 6.5038416517 3.156177336 1 -0 -0 -0 0 -0 -0 -0 -0 0 -0 0 0 9 -297.8379197164 125.016467972 33.783065519 18.8784767986 12.6884273203 8.8108685861 5.6922257725 3.0696803809 1 0 0 -0 0 0 0 0 -0 0 0 0 10 -1762.0427556495 49.7621041588 23.8095993495 16.3251292901 12.6015234646 9.9755053453 7.5842399218 5.2366834551 2.8457047544 1 0 -0 0 0 0 0 -0 0 0 0 11 133.5114853228 32.6953466056 20.3420632107 15.7729987789 13.2836185422 11.4186677432 9.5846916223 7.5936840631 5.2298371681 2.9638012677 1 -0 -0 -0 -0 -0 0 -0 0 0 12 52.9776912398 23.6501177788 17.1992952475 14.4794586932 12.9421669096 11.7679562765 10.554260278 9.1300935599 7.2346566318 5.1532888647 2.8742561796 1 -0 -0 -0 -0 0 -0 0 0 13 32.3373773545 19.1442624387 15.3626995125 13.6666733859 12.7166037731 12.0075229132 11.2541063897 10.307071682 8.9159393765 7.2301675012 5.0907869521 2.8827708106 1 -0 -0 -0 0 -0 0 0 14 23.3989943746 16.3388340495 13.9995769567 12.9336954649 12.3687651164 11.9805877184 11.5663780163 11.0029963376 10.0811370158 8.8628377609 7.1301033647 5.0699411972 2.8676502321 1 -0 -0 0 -0 0 0 15 18.827856997 14.6058656519 13.0869710571 12.4085543428 12.0880391876 11.9087869113 11.7253212894 11.4390571375 10.8885411893 10.0867148945 8.8157657402 7.1358687559 5.0659415624 2.8704045301 1 -0 0 -0 0 0 16 16.1161515846 13.4213363444 12.4072294308 11.9771999354 11.8133863698 11.7678417436 11.7363590858 11.6420225058 11.3683049655 10.9030002331 10.0588519577 8.8287074455 7.1382512748 5.0737418593 2.8749453501 1 0 -0 0 0 17 14.3358910521 12.5431839701 11.8547000435 11.5865433713 11.521566728 11.5575148229 11.6201775097 11.6507798464 11.5703504436 11.3557177618 10.860612076 10.0497467781 8.8137981679 7.1322481037 5.0703112882 2.869871029 1 -8.00495166178202E-16 0 0 18 13.1473482656 11.9146807316 11.4399119195 11.2766040946 11.2716937887 11.3536504506 11.4697228521 11.5754679068 11.6206435974 11.5788238111 11.3431251435 10.8718012881 10.0547930326 8.8235598926 7.1411818811 5.0727963739 2.8747221687 1 0 0 19 12.4471638406 11.56545855 11.2292028824 11.1319974189 11.161703409 11.2670727047 11.4101225531 11.5569933459 11.6777213902 11.7462370414 11.6875892276 11.4632652371 10.9772658376 10.1485176608 8.8958039149 7.1820900746 5.0900422515 2.8643235696 1 0 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Matrix T*J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.281840538 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.306100818 0.1476707015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0.2446154948 0.1995607173 0.0788791177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0.2747026192 0.3067432578 0.2715067322 0.0557059232 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0.3413529679 0.5382734067 1.0772096269 2.5830863519 0.0541046034 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0.5276698543 1.3165376218 12.554564397 -17.3379605463 -0.3164578279 0.068886214 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1.0052280721 5.5676665096 -76.953637114 37.7460779352 0.6493918 -0.2543573767 0.0991911476 0 0 0 0 0 0 0 0 0 0 0 0 0 8 2.400725839 266.524577445 138.3746189157 -37.5854833228 -0.6199068846 0.3547719599 -0.313064852 0.1436233376 0 0 0 0 0 0 0 0 0 0 0 0 9 10.1534199033 -899.2612519697 -118.8035014932 19.4517686369 0.3081972682 -0.2481242887 0.3963906273 -0.4408777417 0.203449911 0 0 0 0 0 0 0 0 0 0 0 10 412.4193964501 1084.076974554 51.967388945 -5.3113345557 -0.0808991948 0.0901925902 -0.2408786235 0.5024979298 -0.5789583791 0.2751520349 0 0 0 0 0 0 0 0 0 0 11 -1370.8005959427 -623.1758016846 -9.4469835154 0.4249538453 0.0059263718 -0.0123412359 0.0674569497 -0.2742154513 0.6519076714 -0.8154959498 0.3526082753 0 0 0 0 0 0 0 0 0 12 1667.7482201681 184.4689573258 0.6971949255 -0.0053684232 -0.0000495516 0.0005802502 -0.0088993072 0.0769530371 -0.362100133 0.9260063558 -1.0134865142 0.4350573076 0 0 0 0 0 0 0 0 13 -970.891233114 -22.1111887785 0.0318629378 -0.0023728438 -0.0000323746 0.0000596197 0.0001178388 -0.0085065479 0.0971476107 -0.5073432526 1.1265957332 -1.2541705072 0.5162348967 0 0 0 0 0 0 0 14 278.0173018549 0.4746045845 0.0164582396 -0.0019764428 -0.0000282542 0.0000358073 -0.0000249354 0.0001351791 -0.0107203125 0.136027795 -0.6064989345 1.3908073794 -1.4803811214 0.5928732783 0 0 0 0 0 0 15 -32.2782758566 0.1127838772 0.013896163 -0.0017592787 -0.000025291 0.0000306393 -0.0000287864 0.0000445949 -0.0000234053 -0.0143022241 0.1572239388 -0.7431371514 1.6340768579 -1.7017861437 0.6620948327 0 0 0 0 0 16 0.2942920533 0.0855188109 0.0124677829 -0.0015881272 -0.000022849 0.0000275165 -0.0000267017 0.000036027 -0.0000685767 0.0000229377 -0.0157731347 0.1914716104 -0.8718244104 1.8844561915 -1.9034864605 0.722948763 0 0 0 0 17 0.0112942422 0.0750865105 0.0111612225 -0.001422376 -0.0000204666 0.0000246302 -0.0000240366 0.0000318871 -0.0000645293 -0.0000051323 -0.0000528444 -0.0193554906 0.2252005387 -1.0080800496 2.1057337432 -2.0747697104 0.7751348487 0 0 0 18 -0.0040233451 0.0676494358 0.010070454 -0.0012828059 -0.000018458 0.0000222176 -0.0000217191 0.0000287612 -0.0000587257 -0.0000062274 -0.000061987 -0.0000812023 -0.022444877 0.2599990267 -1.1255398809 2.2970146179 -2.2282973334 0.8190012771 0 0 19 -0.0048949177 0.0582870399 0.0086752464 -0.0011048006 -0.0000158965 0.0000191371 -0.000018718 0.0000247852 -0.0000506988 -0.0000055371 -0.0000543846 -0.0000586162 -0.0000704721 -0.0259144998 0.2867820969 -1.2110107571 2.4370954415 -2.3458846615 0.8546604883 0 20 -0.0471376993 0.5273506344 0.0781674165 -0.0099391695 -0.0001429945 0.0001723194 -0.0001688837 0.0002242017 -0.0004604328 -0.0000508 -0.0005001479 -0.0005333297 -0.0007914124 -0.0015478034 -0.0255843313 0.2658170865 -0.9839329568 1.5268833844 -0.8546604883 1 Matrix [T*J*T(inv.)] 1 2 3 4 5 67 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.281840538 -2.7937253850121E-16 1.26910601984196E-16 -5.35055097965371E-16 -3.9156151065524E-16 -5.37508702937065E-16 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0.0551745614 0.0788592039 0.1453395117 1 Matrix [T*J*T(inv.)] (inverse) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 3.548105631 0 -0 0 -0 -0 0 -0 -2.41757051407453E-16 0 0 -3.31722539686001E-16 1.04274880860976E-16 7.47984304285373E-16 1.64947980633259E-16 4.66753423872372E-16 -1.86924087301114E-16 1.37107993613477E-16 -3.26306241496661E-31 0 2 -3.5012097085 6.7718239943 0 0 0 0 -0 0 -0 0 -8.44440607434542E-16 6.84086968398635E-16 8.72776474041085E-17 -3.18000067654785E-17 -1.77739783408234E-30 -4.70726615714142E-30 3.45906252858783E-30 -1.26157582865973E-30 2.24487023165442E-30 0 3 0.744326813 -7.9810428858 12.6776265879 -0 0 -0 0 -0 7.5221161294512E-16 -0 1.2536860215752E-16 5.0147440863008E-16 1.2536860215752E-16 0 6.268430107876E-17 6.268430107876E-17 6.268430107876E-17 0 0 0 4 0.2949106901 1.3089998379 -18.1526922676 17.9514123923 0 -0 0 -0 1.65256768201065E-16 -8.26283841005323E-16 6.61027072804258E-16 -2.47885152301597E-16 0 -1.65256768201065E-16 0 -8.26283841005323E-17 -2.47885152301597E-16 1.65256768201065E-16 3.30513536402129E-16 0 5 0.0187707014 1.0235676261 5.5235598227 -24.6365579912 18.4827156553 0 4.96805332672316E-16 -0 -9.93610665344633E-16 7.45207999008475E-16 -4.96805332672316E-16 3.72603999504237E-16 2.48402666336158E-16 6.21006665840395E-17 -1.24201333168079E-16 1.24201333168079E-16 1.24201333168079E-16 1.24201333168079E-16 2.48402666336158E-16 0 6 -0.0332221458 0.0387735971 1.2508555785 6.6332813154 -23.1972684462 14.5166927028 0 2.65507285215883E-16 2.65507285215883E-16 -3.98260927823824E-16 0 1.32753642607941E-16 -1.32753642607941E-16 1.99130463911912E-16 0 -1.32753642607941E-16 1.99130463911912E-16 -2.65507285215883E-16 -2.65507285215883E-16 0 7 -0.0176410648 -0.0733259932 -0.0556534378 1.424088972 5.0493176359 -16.3764636773 10.0815448183 4.27119358420792E-16 -6.40679037631187E-16 6.40679037631187E-16 2.13559679210396E-16 -2.13559679210396E-16-2.13559679210396E-16 -1.06779839605198E-16 -1.06779839605198E-16 2.66949599012995E-16 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-0.017221619 -0.0546368816 -0.1986398195 1.2209993171 -4.00847759204666E-16 0 19 -0.0016482648 -0.0017822961 -0.0038274171 -0.0102261442 -0.0191850949 -0.0225661587 -0.0210627607 -0.0178125563 -0.0152582625 -0.0125900935 -0.0107185504 -0.0090456014 -0.0077049301 -0.0068519345 -0.007558529 -0.014139041 -0.0420544386 -0.1459202627 1.1700552602 0 20 -0.0150365793 -0.016495126 -0.0352193903 -0.0929530575 -0.1734096721 -0.2036833469 -0.1900907797 -0.1608200699 -0.1378134804 -0.1138309253 -0.0971225537 -0.082324332 -0.0702973186 -0.060250538 -0.0522358039 -0.0471889774 -0.0494038476 -0.0750790543 -0.1700552602 1 Matrix { [T*J*T(inv.)] (inverse) - C} 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2.548105631 0 -0 0 -0 -0 0 -0 -2.41757051407453E-16 0 0 -3.31722539686001E-16 1.04274880860976E-16 7.47984304285373E-16 1.64947980633259E-16 4.66753423872372E-16 -1.86924087301114E-16 1.37107993613477E-16 -3.26306241496661E-31 0 2 -3.5012097085 5.7718239943 0 0 0 0 -0 0 -0 0 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