MOLY-COP TOOLS 3.0Jaime E. Sepúlveda
XII Simposio sobreProcesamiento de MineralesNoviembre, 2012
MOLY-COP TOOLS 3.0
Moly-Cop Tools 3.0 es un conjunto de 63 planillas EXCEL 2007 diseñadas para ayudar al Ingeniero de Procesos a caracterizar y evaluar la eficiencia operacional de un circuito dado de molienda, sobre la base de metodologías y criterios de amplia aceptación práctica.
Moly-Cop Tools 3.0 contiene una completa variedad de simuladores para diversas aplicaciones de trituración (Chancado y HPGR’s) y molienda (Semiautógena, de Barras, de Bolas y en Molinos Verticales), con sus correspondientes rutinas para balances de materiales y estimación de parámetros.
Lo anterior complementado con otras aplicaciones para cálculos típicos relativos a la Ley de Bond, el ‘algebra’ de las bolas y otras funciones de utilidad general.
Moly-Cop Tools 3.0UN POCO DE HISTORIA…
La primera versión de Moly-Cop Tools , con un total de 30 aplicaciones, nació precisamente en el X Simposio, que se llevó a efecto en Noviembre, 2001 en Termas de Puyehue, Chile.
Desde entonces - gracias a los continuos esfuerzos de distribución, aplicación e intercambio de experiencias con la comunidad minera internacional - Moly-Cop Tools ha llegado a ser reconocido como un conjunto de herramientas computacionales de verdadera utilidad para el análisis de procesos de trituración y molienda de minerales.
Resultado de este sostenido proceso de adaptación y desarrollo, la tercera versión - que hoy por primera vez presentamos - expande significativamente el alcance de las primeras dos versiones, incorporando ahora un total de 63 planillas de aplicación.
¡Lady Gaga!
Moly-Cop Tools 3.0CONTENIDOS
Moly-Cop Tools 3.0CONTENIDOS
Moly-Cop Tools 3.0¿QUÉ HAY DE NUEVO?
Moly-Cop Tools 3.0HPGR’s
HPGRSim_Open permite simular la respuesta de un HPGR bajo determinadas condiciones de operación y diseño.
HPGRParam_Open permite ‘sintonizar’ el simulador a la condición de interés, a partir de resultados a escala laboratorio, piloto o industrial.
La aplicación HPGRSim_Open puede ser integrada con otras aplicaciones de Moly-Cop Tools 3.0 para representar configuraciones de circuitos de mayor complejidad.
HPGR’sBASE TEORICA DEL MODELO
El modelo HPGR – adaptado de la Tesis de Magíster de Magín Torres (Univ. de Chile, 2010) - consiste de 3 ecuaciones para el cálculo del ‘Gap’ Operacional (mm), la Capacidad de Molienda (tph) y la Potencia Neta Demandada (kW), respectivamente; las que debidamente combinadas permiten la estimación de la Energía Específica (kWh/ton) aplicada al mineral, información clave para la posterior solución de las ecuaciones del ya tradicional Modelo Lineal de Molienda supuestamente aplicable a este diseño específico de dispositivos de trituración.
M
c gD/2
p
HPGR’s‘GAP’ OPERACIONAL
El ‘Gap’ Operacional o separación entre los rodillos se determina a partir de la relación geométrica:
g = 1000 D cos c (1 - cos c) / (rc/ra - cos c)
Valores típicos de c están en el rango de 7° - 9°.
M
c gD/2
p
HPGR’sCAPACIDAD DE MOLIENDA
La Capacidad de Molienda del HPGR está dada por:
M = 3.6 rc g L U c
donde c es un factor empírico que permite considerar la posibilidad de extrusión del mineral en su paso entre los rodillos.
Krupp Polysius recomienda U = 1.35 D0.5 cuando D < 1.82 m ó U = D cuando D > 1.82 m, con el propósito de evitar dicha posibilidad de extrusión.
M
c gD/2
p
Ensayos Piloto con Rodillos de 0.92x0.25 mCAPACIDAD DE MOLIENDA
565
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70
Pred
icte
d Ca
paci
ty, t
ph
Actual Capacity, tph
Extrusion/Slippage Factor = 1.12
HPGR’sPOTENCIA NETA DEMANDADA
La Potencia Neta Demandada es función directa de la fuerza de compresión aplicada entre los rodillos, definida como:
F = 100 p D L Luego, considerando ambos rodillos:
P = 2 * Torque = 2 (2 p N/60) (D/2) ( m F) = m p N D F /30
donde m representa el Coeficiente de Fricción contra los rodillos.
M
c gD/2
p
Ensayos Piloto con Rodillos de 0.92x0.25 mPOTENCIA DEMANDADA
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
Pred
icte
d Po
wer
, kW
Actual Power, kW
Friction Coefficient = sin(3.48� ) = 0.0608
HPGR’sMODELO LINEAL DE LA MOLIENDA
JCii exp(-Si
EE) R(E) dE (1 + SiEE /N)-N
0
(T JC T-1) f INf OUT =
Finalmente, conocida la Energía Específica, E = P/M, es posible calcularla granulometría del producto molido:
con:
HPGRParam_Open_Data FileESTIMACION DE PARAMETROSMoly-Cop Tools TM (Version 3.0)
Circuit Type OPEN (see Flowsheet ) Test N° 0
Remarks
HPGR Dimensions and Operating Conditions
Roll Diameter, D, m 0.90Roll Length, L, m 0.25
Peripheral Speed, U, m/sec 0.43Rotational Speed, , rpm 9.12Operating Pressure, p, Bars 30.00Specific Grinding Force, Newton/mm2 3.00Compression Force, kNewton 675Friction Coefficient, m 0.114Net Power Draw, P, kW 66.0
Critical Compression Angle, c, (°) 8.13Operational Gap, g, mm 19.0
As % of Roll Diameter 2.1Nipping Gap, mm 28.1
Extrusion/Slippage Factor 1.08 Edge By-Pass, Le, mm 57.0Grinding Capacity, M, ton/hr (wet) 21.1 As # of gaps 3.0Feed Moisture, % 5.0Grinding Capacity, M, ton/hr (dry) 20.0Specific Throughput, ton sec / m3 hr) 206.7Specific Energy, E, kWh/ton 3.30
Ore Density, r s, ton/m3 2.80Bulk Feed Particles % Voids 35.0 App. Density, rap, ton/m3 1.82Product Particles (Cake) % Voids 5.0 App. Density, rc, ton/m3 2.66
HPGRParam: Estimation of HPGR Grinding Parameters from Experimental Data.
Base Case Example
M
c gD/2
p
HPGRParam_Open_Data FileESTIMACION DE PARAMETROS
i Mesh Opening Mid-Size ton/hr % Retained % Passing % Retained % Passing % Retained % Passing % Retained % PassingDISCHARGE CENTER EDGES
1 1" 25400 100.00 100.00 100.00 100.002 3/4" 19050 21997 7.13 35.64 64.36 0.72 99.28 0.72 99.28 0.72 99.283 1/2" 12700 15554 5.01 25.03 39.33 7.26 92.02 7.26 92.02 7.26 92.024 3/8" 9525 10999 2.07 10.33 29.00 11.91 80.11 11.91 80.11 11.91 80.115 1/4" 6350 7777 1.80 9.00 20.00 11.99 68.12 11.99 68.12 11.99 68.126 4 4750 5492 0.81 4.03 15.97 6.42 61.70 6.42 61.70 6.42 61.707 6 3350 3989 0.79 3.97 12.00 6.87 54.83 6.87 54.83 6.87 54.838 8 2360 2812 0.41 2.04 9.96 5.52 49.31 5.52 49.31 5.52 49.319 10 1700 2003 0.31 1.56 8.40 5.72 43.59 5.72 43.59 5.72 43.59
10 14 1180 1416 0.26 1.31 7.09 4.32 39.27 4.32 39.27 4.32 39.2711 20 850 1001 0.20 0.98 6.11 3.74 35.53 3.74 35.53 3.74 35.5312 28 600 714 0.18 0.90 5.21 4.47 31.06 4.47 31.06 4.47 31.0613 35 425 505 0.15 0.73 4.48 2.74 28.32 2.74 28.32 2.74 28.3214 48 300 357 0.13 0.65 3.83 3.34 24.98 3.34 24.98 3.34 24.9815 65 212 252 0.12 0.58 3.25 2.22 22.76 2.22 22.76 2.22 22.7616 100 150 178 0.10 0.52 2.73 2.74 20.02 2.74 20.02 2.74 20.0217 150 106 126 0.09 0.45 2.28 2.21 17.81 2.21 17.81 2.21 17.8118 200 75 89 0.07 0.34 1.94 2.10 15.71 2.10 15.71 2.10 15.7119 270 53 63 0.06 0.30 1.64 1.91 13.80 1.91 13.80 1.91 13.8020 325 45 49 0.02 0.10 1.54 1.08 12.72 1.08 12.72 1.08 12.7221 -325 0 23 0.31 1.54 0.00 12.72 0.00 12.72 0.00 12.72 0.00
F99/Gap Ratio 1.33F99/Nipping Gap Ratio 0.90 1.00 0.00 0.00
Selection Function Parameters : 1.80 0.00 0.00alpha0 alpha1 alpha2 dcrit0.031595 0.324510724 3 90002 Ave. Error, % 1.80
473.7 % of GapBreakage Function Parameters :
beta0 beta1 beta20.378331715 0.363039662 4
Weighting Factors
Feed Size Distribution Product Size Distributions
HPGRParam_Open_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Test N° 0
Weighting Factors: Center Sample 0.00 Edge Sample 0.00 Overall 1.00
Edge By-Pass, As # of gaps 3.0
SELECTION FUNCTION PARAMETERS: alpha0 0.060000 alpha1 0.250 alpha2 3.0 Dcrit 7000
BREAKAGE FUNCTION PARAMETERS: beta0 0.40000 beta1 0.400 beta2 4.0
Objective Function 31.37
HPGRParam_Open : Estimation of HPGR Grinding Parameters.
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000 10000 100000
% P
assi
ng
Particle Size, microns
FeedDischarge (Exp.)Discharge (Adjusted)SiE * 10
Estimaciones Iniciales
HPGRParam_Open_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Test N° 0
Weighting Factors: Center Sample 0.00 Edge Sample 0.00 Overall 1.00
Edge By-Pass, As # of gaps 3.0
SELECTION FUNCTION PARAMETERS: alpha0 0.031595 alpha1 0.325 alpha2 3.0 Dcrit 90002
BREAKAGE FUNCTION PARAMETERS: beta0 0.37833 beta1 0.363 beta2 4.0
Objective Function 1.80
HPGRParam_Open : Estimation of HPGR Grinding Parameters.
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000 10000 100000
% P
assi
ng
Particle Size, microns
FeedDischarge (Exp.)Discharge (Adjusted)SiE * 10
Después de ejecutar SOLVER
HPGRSim_Open_Data FileSIMULADOR HPGR
Moly-Cop Tools TM (Version 3.0)
Circuit Type OPEN (see Flowsheet ) Simulation N° 0
Remarks
HPGR Dimensions and Operating ConditionsDefault Values
Roll Diameter, D, m 2.25Roll Length, L, m 1.40
Peripheral Speed, U, m/sec 2.01 2.25 MaxRotational Speed, , rpm 17.06Operating Pressure, p, Bars 40.00Specific Grinding Force, Newton/mm2 4.00Compression Force, kNewton 12600Friction Coefficient, m 0.056 0.077Net Power Draw, P, kW 2850.0
Critical Compression Angle, c, (°) 8.80 8.0Operational Gap, g, mm 54.6
As % of Roll Diameter 2.4Nipping Gap, mm 81.0
Extrusion/Slippage Factor 1.00 1.00 Edge By-Pass, Le, mm 163.7Grinding Capacity, M, ton/hr (wet) 1476.7 As # of gaps 3.0Feed Moisture, % 3.5Grinding Capacity, M, ton/hr (dry) 1425.0Specific Throughput, ton sec / m3 hr) 225.1Specific Energy, E, kWh/ton 2.00
Ore Density, r s, ton/m3 2.80Bulk Feed Particles % Voids 35.0 35.0 App. Density, rap, ton/m3 1.82Product Particles (Cake) % Voids 4.6 5.0 App. Density, rc, ton/m3 2.67
i Mesh Opening Mid-Size ton/hr % Retained % Passing
1 3" 76200 100.002 2" 50800 62217 45.87 3.22 96.783 1.5" 38100 43994 35.75 2.51 94.274 1" 25400 31109 319.60 22.43 71.845 0.742" 19050 21997 324.87 22.80 49.056 0.525" 12700 15554 290.67 20.40 28.657 0.371" 9500 10984 101.96 7.16 21.498 3 6700 7978 66.51 4.67 16.839 4 4750 5641 39.54 2.77 14.05
10 6 3350 3989 29.21 2.05 12.0011 8 2360 2812 23.96 1.68 10.3212 10 1700 2003 19.41 1.36 8.9613 14 1180 1416 18.93 1.33 7.6314 20 850 1001 14.92 1.05 6.5815 28 600 714 13.87 0.97 5.6116 35 425 505 11.92 0.84 4.7717 48 300 357 10.40 0.73 4.0418 65 212 252 8.89 0.62 3.4219 100 150 178 7.58 0.53 2.8920 150 106 126 6.48 0.45 2.4321 -150 0 53 34.66 2.43 0.00
F99/Gap Ratio 1.23F99/Nipping Gap Ratio 0.83
Selection Function Parameters :alpha0 alpha1 alpha2 dcrit
0.03160 0.325 3 90002165.0 % of Gap
Breakage Function Parameters :beta0 beta1 beta2
0.378 0.363 4
HPGRSIM: Open Circuit HPGR Simulator.
Feed Size Distribution
Base Case Example
M
c gD/2
p
HPGRSim_Open_ChartSIMULADOR HPGR
Moly-Cop Tools TM (Version 3.0)
Simulation N° 0 Remarks :
HPGRSim_Open : Open Circuit HPGR Simulator
Base Case Example
1
10
100
10 100 1000 10000 100000
% P
assi
ng
Particle Size, microns
Fresh Feed
HPGR Discharge
Edges
Size Distributions
HPGRSim_Open_ReportsSIMULADOR HPGR
Simulation N° 0
Remarks:
Roll Diameter, D, m 2.25 Critical Compression Angle, c, (°) 8.80
Roll Length, L, m 1.40 Operational Gap, g, mm 54.6As % of Roll Diameter 2.4
Peripheral Speed, U, m/sec 2.01Rotational Speed, w, rpm 17.06 Grinding Capacity, M, ton/hr (wet) 1476.7Operating Pressure, p, Bars 40.0 Feed Moisture, % 3.50
Grinding Capacity, M, ton/hr (dry) 1425.0Friction Coefficient, m 0.056Net Power Draw, P, kW 2850.0 Specific Energy, E, kWh/ton 2.00
Ore Density, rs, ton/m3 2.80Bulk Feed Particles % Voids 35 Apparent Density, rap, ton/m3 1.82Product Particles (Cake) % Voids 4.5857275 Apparent Density, rc, ton/m3 2.67
Moly-Cop ToolsTM, Version 3.0HPGRSIM_Open
Open Circuit HPGR Simulator
Base Case Example
HPGRSim_Open_ReportsSIMULADOR HPGR
HPGR HPGR Rolls RollsFeed Discharge Center Edge
Ore, ton/hr 1425.0 1425.0 1091.8 333.2 Water, m3/hr 51.7 51.7 39.6 12.1 Slurry, ton/hr 1476.7 1476.7 1131.4 345.3 Slurry, m3/hr 560.6 560.6 429.5 131.1 Slurry Dens., ton/m3 2.634 2.634 2.634 2.634 % Solids (by volume) 90.8 90.8 90.8 90.8 % Solids (by weight) 96.50 96.50 96.50 96.50
i Mesh Opening
1 3" 76200 62217 100.00 100.00 100.00 100.002 2" 50800 43994 96.78 99.70 99.76 99.483 1.5" 38100 31109 94.27 98.95 99.14 98.354 1" 25400 21997 71.84 93.63 94.62 90.395 0.742" 19050 15554 49.05 84.40 86.47 77.636 0.525" 12700 10984 28.65 71.14 74.29 60.827 0.371" 9500 7978 21.49 61.32 64.82 49.888 3 6700 5641 16.83 52.43 55.95 40.899 4 4750 3989 14.05 45.57 48.92 34.60
10 6 3350 2812 12.00 40.05 43.16 29.8711 8 2360 2003 10.32 35.46 38.32 26.0912 10 1700 1416 8.96 31.69 34.33 23.0613 14 1180 1001 7.63 28.05 30.46 20.1414 20 850 714 6.58 25.05 27.26 17.7915 28 600 505 5.61 22.21 24.23 15.5916 35 425 357 4.77 19.67 21.51 13.6517 48 300 252 4.04 17.38 19.04 11.9318 65 212 178 3.42 15.33 16.84 10.4119 100 150 126 2.89 13.52 14.87 9.0920 150 106 53 2.43 11.90 13.11 7.92
D80, microns 29821 16777 15478 20164
alpha0 alpha1 alpha2 Dcrit Beta0 Beta1 Beta20.03160 0.325 3 90002 0.378 0.36 4.00
Breakage Function ParametersSelection Function Parameters
Size Distributions, % Passing
HPGRSim_OpenEFECTO VELOCIDAD DE GIRO
0
1000
2000
3000
4000
5000
6000
7000
1.60 1.80 2.00 2.20 2.40 2.60 2.80
Peripheral Speed, m/sec
Power, kW
Capacity, ton/hr
18.0
18.5
19.0
19.5
20.0
20.5
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1.60 1.80 2.00 2.20 2.40 2.60 2.80
% -
100#
kWh/
ton
Peripheral Speed, m/sec
Specific Energy, kWh/tonProduct Size, % - 100#
HPGRSim_OpenEFECTO PRESION DE COMPRESION
0
1000
2000
3000
4000
5000
6000
7000
8000
35.00 40.00 45.00 50.00 55.00 60.00 65.00
Pressure, Bars
Power, kW
Capacity, ton/hr
16
18
20
22
24
26
28
3.0
3.5
4.0
4.5
5.0
5.5
6.0
35.00 40.00 45.00 50.00 55.00 60.00 65.00
% -
100#
kWh/
ton
Pressure, Bars
Specific Energy, kWh/tonProduct Size, % - 100#
HPGRSim_OpenEFECTO TAMAÑO DE ALIMENTACION
0
1000
2000
3000
4000
5000
6000
7000
8000
5 10 15 20 25 30 35
F80, mm
Power, kW
Capacity, ton/hr
17
18
19
20
21
22
23
3.0
3.5
4.0
4.5
5.0
5.5
6.0
5 15 25 35 45 55
% -
100#
kWh/
ton
F80, mm
Specific Energy, kWh/tonProduct Size, % - 100#
Moly-Cop Tools 3.0MOLINOS DE BARRAS
RodSim_Open_Data FileSIMULADOR MOLINOS DE BARRAS
Moly-Cop Tools TM (Version 3.0)
Circuit Type OPEN (see Flowsheet ) Simulation N° 0
Remarks
Mill Dimensions and Operating Conditions 213 RodsEff. Diam. Eff. Length Speed Charge Rods App. Dens. Interstitial Lift 0 Overfilling
ft ft % Critical Filling,% Filling,% ton/m3 Slurry, % Angle, (°) 33 Slurry7.5 12.0 72.0 30.0 30.0 5.38 100.0 45.0 246 Net kW
rpm 20.14 10.0 % Losses274 Gross kW
Ore Density, ton/m3 2.70Rods Density, ton/m3 7.75 P80 3729% Solids Mill Discharge 71.9 Wio 54.30 0.946Feedrate, ton/hr (dry) 92.6 % Fines MD 9.19 2.297Feed Moisture, % 1.5
i Mesh Opening Mid-Size ton/hr % Retained % Passing
1 1.05 25400 100.002 0.742 19050 21997 0.00 0.00 100.003 0.525 12700 15554 0.00 0.00 100.004 0.371 9500 10984 8.00 8.64 91.365 3 6700 7978 25.78 27.84 63.526 4 4750 5641 18.66 20.15 43.377 6 3350 3989 10.05 10.86 32.518 8 2360 2812 8.05 8.70 23.819 10 1700 2003 4.61 4.97 18.84
10 14 1180 1416 3.40 3.67 15.1711 20 850 1001 2.24 2.42 12.7512 28 600 714 1.89 2.04 10.7013 35 425 505 1.42 1.54 9.1714 48 300 357 1.23 1.32 7.8415 65 212 252 0.98 1.06 6.7916 100 150 178 0.88 0.95 5.8417 150 106 126 0.73 0.79 5.0518 200 75 89 0.67 0.72 4.3319 270 53 63 0.55 0.60 3.7320 400 38 45 0.29 0.32 3.4221 -400 0 19 3.16 3.42 0.00
Selection Function Parameters : Expanded Form :alpha0 alpha1 alpha2 dcrit alpha02 alpha120.003642 0.65 3.5 14414 0 1
0 1 Suggested Default Values
Breakage Function Parameters : Expanded Form :beta0 beta1 beta2 beta01
00.2 0.3 4 0 Suggested Default Value
(*) Contributed by Javier Jofré from Moly-Cop Chile S. A.
RODSIM : Open Circuit Grinding Simulator(*)
Feed Size Distribution
Base Case Example
Main Simulated Outputs
fE, KWh/ton
Adaptación del Modelo General de la Molienda al caso particular de molienda no-lineal, característica de los molinos de barras, en que las partículas de mayor tamaño quedan preferentemente expuestas a la acción de las barras.
RodParam_Open_Data FileESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Remarks Test N° 0
Mill Dimensions and Operating Conditions 213 RodsEff. Diam. Eff. Length Speed Charge Rods Lift 0 Overfilling
ft ft % Critical Filling,% Filling,% Angle, (°) 33 Slurry7.50 12.00 72.0 30.00 30.00 45.02 246 Net Power
rpm 20.14 10.0 % Losses274 Gross kW
% Solids (by weight) 71.9 Charge Apparent Mill Flowrate, tph (dry) 92.6Ore Density, ton/m3 2.70 Volume, Rod DensitySlurry Density, ton/m3 1.83 m3 Charge Interstitial Excess ton/m3 Total Energy, kWh/ton 2.66Rods Density, ton/m3 7.75 4.51 20.98 3.30 0.00 5.381 Rods Energy, kWh/ton 2.30Feed Moisture, % 1.5
% wi wi (error) 2̂
i Mesh Opening Mid-Size % Ret % Pass % Ret % Pass % Ret % Pass Exp Adj. Error
1 1.05 25400 100.00 100.00 100.002 0.742 19050 21997 0.00 100.00 0.00 100.00 0.00 100.00 100.00 100.00 0.00 1 0.003 0.525 12700 15554 0.00 100.00 0.00 100.00 0.00 100.00 100.00 100.00 0.00 1 0.004 0.371 9500 10984 8.64 91.36 0.00 100.00 0.67 99.33 100.00 99.33 0.67 1 0.455 3 6700 7978 27.84 63.52 0.98 99.02 3.25 96.07 99.02 96.07 3.06 1 9.386 4 4750 5641 20.15 43.37 6.94 92.08 7.69 88.39 92.08 88.39 4.17 1 17.437 6 3350 3989 10.86 32.51 13.08 79.00 11.85 76.54 79.00 76.54 3.21 1 10.298 8 2360 2812 8.70 23.81 17.89 61.11 13.75 62.79 61.11 62.79 (2.68) 1 7.209 10 1700 2003 4.97 18.84 12.10 49.01 12.16 50.63 49.01 50.63 (3.20) 1 10.25
10 14 1180 1416 3.67 15.17 9.38 39.63 10.34 40.30 39.63 40.30 (1.65) 1 2.7211 20 850 1001 2.42 12.75 6.29 33.34 7.12 33.17 33.34 33.17 0.51 1 0.2612 28 600 714 2.04 10.70 5.42 27.93 5.50 27.67 27.93 27.67 0.92 1 0.8413 35 425 505 1.54 9.17 4.04 23.89 4.13 23.55 23.89 23.55 1.44 1 2.0814 48 300 357 1.32 7.84 3.43 20.46 3.29 20.26 20.46 20.26 0.97 1 0.9515 65 212 252 1.06 6.79 2.87 17.58 2.65 17.61 17.58 17.61 (0.14) 1 0.0216 100 150 178 0.95 5.84 2.29 15.30 2.26 15.34 15.30 15.34 (0.30) 1 0.0917 150 106 126 0.79 5.05 1.93 13.36 1.93 13.41 13.36 13.41 (0.39) 1 0.1518 200 75 89 0.72 4.33 1.62 11.74 1.70 11.72 11.74 11.72 0.23 1 0.0519 270 53 63 0.60 3.73 1.53 10.22 1.46 10.26 10.22 10.26 (0.37) 1 0.1320 400 38 45 0.32 3.42 1.04 9.17 1.06 9.19 9.17 9.19 (0.19) 1 0.0421 -400 0 19 3.42 0.00 9.17 0.00 9.19 0.00 0.00 0.00 0.00 0 0.00
(*) Contributed by Javier Jofré from Moly-Cop Chile S.A. sum 19.00 62.35
% Passing
Objective Function
Base Case Example
Feed Size Distributions
Mill Feed Mill Disch. (exp) Mill Disch. (adj)
Mill Charge Weight, tonsSlurry
InterstitialSlurry Filling,%
100.00
RODPARAM_OPEN : Estimation of Grinding Parameters from Plant Scale Data(*)
RodParam_Open_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Test N° 0
SELECTION FUNCTION :
alpha0 0.006000 alpha1 0.650 alpha2 3.5 Dcrit 10000 Expanded Form alpha02 0.000 alpha12 1.000
BREAKAGE FUNCTION :
beta0 0.2 beta1 0.3 beta2 4.0 Expanded Form beta01 0.000f 0.946
Objective Function 19.08
RODPARAM_OPEN : Estimation of Grinding Parameters from Plant Scale Data
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000 10000 100000
% P
assi
ng
Particle Size, microns
FeedDischarge (Exp.)Discharge (Adjusted)SiE * 10
Estimaciones Iniciales
RodParam_Open_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Test N° 0
SELECTION FUNCTION :
alpha0 0.003642 alpha1 0.650 alpha2 3.5 Dcrit 14414 Expanded Form alpha02 0.000 alpha12 1.000
BREAKAGE FUNCTION :
beta0 0.2 beta1 0.3 beta2 4.0 Expanded Form beta01 0.000f 0.946
Objective Function 1.81
RODPARAM_OPEN : Estimation of Grinding Parameters from Plant Scale Data
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000 10000 100000
% P
assi
ng
Particle Size, microns
FeedDischarge (Exp.)Discharge (Adjusted)SiE * 10
Después de ejecutar SOLVER
Moly-Cop Tools 3.0MOLINOS VERTICALES (VERTIMILLS)
VertimillsBASE TEORICA DEL MODELO
El modelo matemático aquí propuesto para describir la operación de Molinos Verticales (Vertimills) es una simple extensión del Modelo Lineal de la Molienda, normalmente aplicable a molinos de bolas, modificando la ecuación que permite el cálculo de la Potencia Neta Demandada en función de sus condiciones específicas de diseño y operación.
VertimillsPOTENCIA NETA DEMANDADA
Para tal efecto, se hace referencia al modelo publicado Nitta, Furuyama, Bissombolo y Mori (“Estimation of the Motor Power of the Tower Mill through Dimensional Analysis”, Proc. XXIII International Mineral Processing Congress, pp.158-161, Sep. 2006), según el cual:
Pnet = h Pgross = K (H*Jb)0.884 S2.232 DG N1.232
donde K es una constante ajustable con un valor nominal 312.
VertiMillSim_ReverseSIMULADOR PARA VERTIMILLS
Moly-Cop Tools TM (Version 3.0)
Circuit Type REVERSE (see Flowsheet ) Simulation N° 0
Remarks
Mill Dimensions and Operating Conditions 869 BallsChamber Chamber Screw Screw Balls Wall/Screw App. Dens. Power 0 Overfilling
Diameter, m Height, m Diameter, m Speed, rpm Filling, % Gap, m ton/m3 Constant 128 Slurry4.10 4.80 3.10 24.0 40.0 0.50 5.34 312.0 997 Net kW
Tip Velocity, m/sec >>> 5.2 117.9 <<< tons of Balls 10.0 % Losses1108 Gross kW
Cyclone Dimensions (inches) and Operating ConditionsNumber Diameter Height Inlet Vortex Apex
26 10.0 30.0 2.50 3.50 1.09Suggested Default Values: 30.0 2.5 3.5 1.8
% Solids O'flow 25.0% Solids U'flow 76.0% Solids Mill Discharge 65.0 49.7 microns
19.97 kWh/tonCirculating Load 1.988 (Guess) 20.79
1.988 (Actual) 563 m3/hr0.000 (Delta) 0.164
4.7 psiOre Density, ton/m3 2.80 180.0 m3/hrBalls Density, ton/m3 7.75
Feedrate, ton/hr (dry) 120.0Feed Moisture, % 60.0
i Mesh Opening Mid-Size ton/hr % Retained % Passing
1 1.05 25400 100.002 0.742 19050 21997 0.00 0.00 100.003 0.525 12700 15554 0.00 0.00 100.004 0.371 9500 10984 0.00 0.00 100.005 3 6700 7978 0.00 0.00 100.006 4 4750 5641 0.00 0.00 100.007 6 3350 3989 0.00 0.00 100.008 8 2360 2812 0.00 0.00 100.009 10 1700 2003 0.00 0.00 100.00
10 14 1180 1416 0.00 0.00 100.0011 20 850 1001 0.00 0.00 100.0012 28 600 714 0.00 0.00 100.0013 35 425 505 0.00 0.00 100.0014 48 300 357 6.68 5.57 94.4315 65 212 252 2.98 2.48 91.9516 100 150 178 4.95 4.13 87.8317 150 106 126 10.27 8.56 79.2718 200 75 89 15.96 13.30 65.9719 270 53 63 13.38 11.15 54.8220 400 38 45 13.33 11.11 43.7121 -400 0 19 52.46 43.71 0.00
Make-up Ball Size, mm 25.4 1.00 inches
# Reactor in Series 20.0
Selection Function Parameters : Expanded Form :alpha0 alpha1 alpha2 dcrit1 alpha3 dcrit20.014286 0.650000 2.500000 50000 2.0 100
0 Suggested Default Value
Breakage Function Parameters : Expanded Form :beta0 beta1 beta2 beta01
0.4 0.65 4 00 Suggested Default Value
Classifier Constants :a1 a2 a3 a4 l Bpc
9.680 1.401 54.964 0.523 0.950 0.000 9.044 1.514 60.607 0.818 0.950 0.000 Suggested Default Values
(*) Application contributed by Dr. Alvaro Videla, Moly-Cop Chile S. A.
VertiMillSim : Simulation of a Closed Circuit Regrinding VertMill (*).
Base Case Example
Feed Size Distribution
P80 Wio % Fines MD Q Bpf Pressure Total Water
Main Simulated Outputs
Very Important :Simulation results are not valid until the Iterate button has been clicked after any input data changes.
Iterate
Moly-Cop Tools TM (Version 3.0)Simulation N° 0
Remarks
25.00 % Solids97.86 % - Size 1849.7 P80 Bpc 0.000 4.65 psi
Bpf 0.164 Bpw 0.173 26 # of Cyclones
3.50 Vortex 1.09 Apex
ton/hr 120.0F80 109 76.00 % Solids
Water, 53.1 Water, m3/hr m3/hr 126.9
Gross kW 1107.9% Balls 40.00 Circ. Load 198.80
% Critical 24.00 m3/hr 563% Solids 65.00 % Solids 45.16
kWh/ton 9.23Wio 19.97
Base Case Example
VertiMillParam_Reverse_Data FileESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Circuit Type REVERSE Sample N° 1
Remarks
Mill Dimensions and Operating Conditions 869 Balls Charge ApparentChamber Chamber Screw Screw Balls Wall/Screw Power 0 Overfilling Volume, Ball Density
Diameter, m Height, m Diameter, m Speed, rpm Filling, % Gap, m Constant 128 Slurry m3 Charge Interstitial Excess ton/m3
4.10 4.80 3.10 24.0 40.0 0.5 312.0 997 Net Power 25.35 117.87 17.42 0.00 5.337rpm 1.17 10.0 % Losses
1108 Gross kW Feedrate, ton/hr (dry) 120.0Cyclone Dimensions (inches) and Operating Pressure (psi) Ore Density, ton/m3 2.80
Number Diameter Height Inlet Vortex Apex psi Balls Density, ton/m3 7.7526 10.0 30.0 2.50 3.50 1.09 4.65 Make-up Ball Size, mm 25.40
Default Values: 30.0 2.5 3.5 1.8
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
1 1.05 25400 100.00 100.00 100.00 100.00 100.002 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 0.00 100.003 0.525 12700 15554 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 0.00 100.004 0.371 9500 10984 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 0.00 100.005 3 6700 7978 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 0.00 100.006 4 4750 5641 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 0.00 100.007 6 3350 3989 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 0.00 100.008 8 2360 2812 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 0.00 100.009 10 1700 2003 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
10 14 1180 1416 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 0.00 100.0011 20 850 1001 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 0.00 100.0012 28 600 714 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 0.00 100.0013 35 425 505 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 0.00 100.0014 48 300 357 6.68 5.57 94.43 0.94 0.40 99.60 7.62 2.13 97.87 7.62 3.20 96.80 0.00 0.00 100.0015 65 212 252 2.98 2.48 91.95 2.44 1.02 98.58 5.42 1.51 96.36 5.41 2.27 94.53 0.00 0.00 100.0016 100 150 178 4.95 4.13 87.83 6.03 2.53 96.05 10.98 3.06 93.30 10.98 4.61 89.93 0.00 0.00 100.0017 150 106 126 10.27 8.56 79.27 18.30 7.68 88.37 28.57 7.97 85.32 28.54 11.97 77.95 0.03 0.02 99.9818 200 75 89 15.96 13.30 65.97 52.06 21.85 66.52 68.02 18.98 66.34 65.46 27.47 50.49 2.54 2.12 97.8619 270 53 63 13.38 11.15 54.82 67.71 28.41 38.11 81.09 22.63 43.71 64.75 27.17 23.32 16.34 13.62 84.2420 400 38 45 13.33 11.11 43.71 41.30 17.33 20.79 54.63 15.25 28.46 31.06 13.03 10.28 23.57 19.65 64.5921 -400 0 19 52.46 43.71 0.00 49.54 20.79 0.00 101.99 28.46 0.00 24.51 10.28 0.00 77.51 64.59 0.00
Totals 120.00 100.00 238.32 100.00 358.32 100.00 238.32 100.00 120.00 100.00
% Solids 40.00 65.00 45.16 76.00 25.00Slurry Density, ton/m3 1.346 1.718 1.409 1.955 1.191Weighting Factor 1.000 1.000 1.000 1.000
Slurry
Cyclone U'flow Cyclone O'flowCyclone FeedFresh Feed Mill DischargeEXPERIMENTAL SIZE DISTRIBUTIONS
VertiMillParam_Reverse : Simultaneous Mass Balance Closure and Grinding Parameters Estimation.
Base Case Example
Mill Charge Weight, tons
VertiMillParam_Reverse_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Sample N° 1
Weighting Factors :Streams : Mill Discharge 1 Cyclone U'flow 1 Cyclone O'flow 1
Size Distributions 1% Solids 1
Grinding Parameter Guesses :alpha0 alpha1 alpha2 dcrit1
0.02 0.65 2.5 50000 4alpha3 dcrit2
2 1000 0 Default Values
beta0 beta1 beta20.4 0.65 4
beta0100 Default Value
Classifiers Parameter Guesses :Bpf Bpc d50c m0.200 0.000 50.0 2.500
Circulating Load: 2.000 Delta: 0.376
Obj. Function: 5.254
VertiMillParam_Reverse : SIMULTANEOUS MASS BALANCE CLOSURE AND GRINDING PARAMETERS ESTIMATION
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000
% P
assi
ng
Particle Size, microns
Mill DischargeCyclone U'f lowCyclone O'f lowFresh Feed
VertiMillParam_Reverse_Control PanelESTIMACION DE PARAMETROS
Moly-Cop Tools TM (Version 3.0)
Sample N° 1
Weighting Factors :Streams : Mill Discharge 1 Cyclone U'flow 1 Cyclone O'flow 1
Size Distributions 1% Solids 1
Grinding Parameter Guesses :alpha0 alpha1 alpha2 dcrit1
0.014286 0.65 2.5 50000 4alpha3 dcrit2
2 1000 0 Default Values
beta0 beta1 beta20.4 0.65 4
beta0100 Default Value
Classifiers Parameter Guesses :Bpf Bpc d50c m0.164 0.000 45.8 2.253
Circulating Load: 1.986 Delta: 0.002
Obj. Function: 0.028
VertiMillParam_Reverse : SIMULTANEOUS MASS BALANCE CLOSURE AND GRINDING PARAMETERS ESTIMATION
Note : Current calculations are not valid, if SOLVER has not been run after the last data modification.
1
10
100
10 100 1000
% P
assi
ng
Particle Size, microns
Mill DischargeCyclone U'flowCyclone O'flowFresh Feed
AGRADECIMIENTOS
Oscar De GaticaJavier JofréAlvaro VidelaRodrigo MurandaLevi Guzmán
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