Learning from the Pioneers ...
THE LAWS OF COMMINUTION
2.0
(*) M. Siddique, M. S. Thesis, Univ. of Utah, USA.
(*) M. Siddique, M. S. Thesis, Univ. of Utah, USA.
“Existe una clara relación entre el Consumo el Consumo de Energía Específica y Específica y la Fineza de Producto resultante”. Más kWh/ton kWh/ton,, menor P80 P80 ! !
La Energía Específica (kWh/ton) requerida es proporcional a la nueva Superficie Específica (m2/m3) de los fragmentos así creados
El requerimiento de Energía Específica (kWh/ton) es proporcional a la Razón de Reducción que se desea lograr
El requerimiento de Energía Específica (kWh/ton) es proporcional a la Longitud de las Nuevas Fisuras creadas
12 11 10 9 8 7 6 5 4 80
100
120
140
160
180
200
,
220
240
260
Equipo de Apoyo
Mina “RRICA”
Sra. Yolanda Secretaria (Alias “La Cachorra”)
Srta. Betsy Asistente (Alias “La Cachorrita”)
10 9 8 7 6 5 4 3 2 1 0
Diamond Corundum Topaz Quartz Feldspar Apatite Fluorite Calcite Gypsum Talc
Escala Mohs
Primera Entrevista ... Bueno, Joven, después de su extensa visita a la Planta ... ¿Cuáles serían sus primeras impresiones? Emeterio
Don Emeterio, con todo respeto ... habiendo yo estudiado en profundidad el “Libro Negro de la Metalurgia” ... y siendo yo un fiel creyente de los 10 Mandamientos de la Molienda, ... me permito manifestarle que es muy posible que esta operación esté muy por debajo de sus máximos niveles de eficiencia.
Saturnino
Grrrrr ... ¿Cómo así? Para empezar, el Nivel de Llenado del molino está muy bajo. Eso significa que la Potencia demandada no está maximizada ... y por lo tanto, tampoco el Tonelaje procesado.
Moly-Cop Tools TM (Version 2.0) BOND'S LAW APPLICATION Estimation of the Operating Work Index from Plant Data Remarks
Mina RRica : Molino 1.
GRINDING TASK : Ore Work Index, kWh/ton (metric) Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 9795 150.0 100.00
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 36.00
Balls Filling,% 36.00
Charge Volume, m3 17.91
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
9.32 932 1 932 Mill Power, kW 804 0 129 932 10.0 1036
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 83.26 13.33 0.00
Balls Overfilling Slurry Net Total % Losses Gross Total Apparent Density ton/m3 5.395
Spreadsheet ... Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of the Operating Work Index from Plant Data
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh/ton (metric) Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 9795 150.0 100.00
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 36.00
Balls Filling,% 36.00
Charge Volume, m3 17.91
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
9.32 932 1 932 Mill Power, kW 804 0 129 932 10.0 1036
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 83.26 13.33 0.00
Balls Overfilling Slurry Net Total % Losses Gross Total Apparent Density ton/m3 5.395
Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Conventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Pl ant Throughput, ton/hr
13.03 9795 150.0 #VALUE!
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
Mill Pow er, kW #VALUE! #VALUE! #VALUE! #VALUE! 10.0 #VALUE!
Balls Overfilling Slurry Net Total % Losses Gross Total
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Apparent Density ton/m3 5.395
MILL DIMENSIONS AND OPERATING CONDITIONS :
Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Interstitial Lift Filling,% Slurry Filling,% Angle, (°) 40.00 100.00 Same as in 1a
Charge Volume, m3 19.89
9.32 #VALUE! 1 #VALUE!
Spreadsheet ... 3.4% Higher Throughput Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Co nventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 9795 150.0 103.43
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
Mill Pow er, kW 831 0 133 964 10.0 1072
Balls Overfilling Slurry Net Total % Losses Gross Tota l
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Apparent Density ton/m3 5.395
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Interstitial Filling,% Slurry Filling,% 40.00 100.00
Charge Volume, m3 19.89
9.32 964 1 964
Lift Angle, (°) 35.99
Spreadsheet ... 5.6% Higher Throughput Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Conventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 9795 150.0 109.18
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 76.00 rpm 16.81 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Filling,% 40.00
Charge Volume, m3 19.89
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
9.32 1018 1 1018 Mill Power, kW 877 0 141 1018 10.0 1131
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Balls Overfilling Slurry Net Total % Losses Gross Total Apparent Density ton/m3 5.395
Moly-Cop Tools TM Run N° :
1
Simulation Data : 10
8
6
4
2
0 -10
-8
-6
-4
-2
0
2
4
6
-2
-4
-6
-8
-10
Developed by Alvaro Videla L. (Consultant to Moly-Cop Chile S. A.)
8
10
Effective Mill Diameter Ball Size
11.9 feet 2.5 inches
Static Friction Coefficient Dynamic Friction Coefficient
0.05 0.2
Lifter Face Angle Lifter Height % Critical Speed
10.0 degrees 4.0 inches 72.0 %
Apparent Mill Filling Angle of Repose,
38.0 % 33.0 degrees
Always click on the Execute button before drawing any conclusions.
Velocity at Impact Angle wrt Horizontal (at Impact) Clock Equiv. Position Kidney's Toe (from central axis) Impact Spot (from central axis)
24.65 45.95 7.47 -4.21 -3.75
feet/sec degrees
Energy at Impact
29.36 Joules
feet feet
Moly-Cop Tools TM Run N° :
1
Simulation Data : 10 8 6 4 2 0 -10
-8
-6
-4
-2
0
2
4
6
-2 -4 -6 -8 -10
Developed by Alvaro Videla L. (Consultant to Moly-Cop Chile S. A.)
8
10
Effective Mill Diameter Ball Size
11.9 feet 2.5 inches
Static Friction Coefficient Dynamic Friction Coefficient
0.05 0.2
Lifter Face Angle Lifter Height % Critical Speed
10.0 degrees 4.0 inches 76.0 %
Apparent Mill Fillin g Angle of Repose,
38.0 % 33.0 degrees
Always click on the Execute button before drawing any conclusions.
Velocity at Impact Angle wrt Horizontal (at Im pact) Clock Equiv. Position Kidney's Toe (from central axis) Impact Spot (from central axis)
25.24 37.01 7.77 -4.21 -4.67
feet/sec degrees
Energy at Impact
30.79 Joules
feet feet
Algunas semanas después ...
Emeterio
Saturnino, veo que las cosas se dieron como Ud. anticipó ... pero me cuesta pensar que haya muchas otras variables que estén fuera de su punto de operación ... ¡ Llevamos tantos años en esto !
Con todo respeto Don Eme, ¡ No es así ! He estado estudiando la operación del chancador y me parece que está sobrado. Podríamos aprovechar mejor su capacidad reduciendo un poco el “setting” y la abertura de los harneros. Creo que podríamos pasar de un F80 = 9795 micrones a un F80 = 7000 micrones. Déjeme mostrarle algunos cálculos que hice ... con la ayuda de Moly-Cop Tools.
Saturnino
Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Conventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 7000 150.0 106.18
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
Mill Power, kW 831 0 133 964 10.0 1072
Balls Overfilling Slurry Net Total % Losses Gross Total
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Apparent Density ton/m3 5.395
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Filling,% 40.00
Charge Volume, m3 19.89
9.08 964 1 964
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
Spreadsheet ... 2.7% Higher Throughput Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Conventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 7000 150.0 106.18
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Filling,% 40.00
Charge Volume, m3 19.89
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
9.08 964 1 964 Mill Power, kW 831 0 133 964 10.0 1072
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Balls Overfilling Slurry Net Total % Losses Gross Total Apparent Density ton/m3 5.395
Algunas semanas después ...
Emeterio
Don Eme, ... ¿Y por qué tenemos que moler tan fino? Yo he estado estudiando los registros operacionales y me he percatado que podemos llegar fácilmente a un P80 = 170 micrones y la flotación no se da ni cuenta ...
Ah, qué interesante ... y no me diga que ya lo tiene todo analizado con la ayuda de Moly-Cop Tools. ¡Efectivamente, Don Eme!
Saturnino
Spreadsheet ... 7.7% Higher Throughput Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Estimation of a Conventional Ball Mill Grinding Capacity
Remarks
Mina RRica: Molino 1.
GRINDING TASK : Ore Work Index, kWh (net)/metric ton Feed Size, F80, microns Product Size, P80, microns Total Plant Throughput, ton/hr
13.03 7000 170.0 114.30
Specific Energy, kWh/ton Net Power Available, kW Number of Mills for the Task Net kW / Mill
Mill Power, kW 831 0 133 964 10.0 1072
Balls Overfilling Slurry Net Total % Losses Gross Total
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 92.51 14.82 0.00
Apparent Density ton/m3 5.395
MILL DIMENSIONS AND OPERATING CONDITIONS : Eff. Diameter ft 12.00
Eff. Length ft 15.50 L/D 1.292
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 15.92 72.00 2.80 1.86 7.75
Charge Filling,% 40.00
Balls Filling,% 40.00
Charge Volume, m3 19.89
8.44 964 1 964
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 35.99
Algunas semanas después ...
Emeterio
“Sati” ... ¡ Buenas noticias ! La empresa desea ampliar esta Planta instalando otro molino adicional para unas 500 tph, más o menos.
¡ Buena noticia, pues !
Saturnino
Eeee ... el problema es que los Jefes me pidieron que les dimensionara el molino que se necesita. ¡ No hay problemas, Don Eme ! Moly-Cop Tools nos ayudará ...
Exercise 2
Moly-Cop Tools TM (Version 2.0) BOND'S LAW APPLICATION Conventional Ball Mill Sizing Remarks
Mina RRica: Molino 2.
GRINDING TASK : O re W ork In de x, k Wh (n et ) /m etric ton Feed Size, F80, microns Product Size, P80, microns Design Throughput, ton/hr
1 3. 03 7000 170.0 500.00
S pec if ic E ne rg y, k W h/to n Net Power Requirement, kW Number of Mills for the Task Net kW / Mill
MILL DESIGN PARAMETERS AND OPERATING CONDITIONS : Eff. Diameter ft 17.50
Eff. Length ft 23.63 L/D 1.350
% Solids in the Mill Ore Density, ton/m 3 Slurry Density, ton/m3 Balls Density, ton/m 3
Mill Speed % Critical 72.00 rpm 13.18
Charge Filling,% 38.00
Balls Filling,% 38.00
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 33.00
Guess
72.00 2.80 1.86 7.75
Charge Volume, m3 61.27
Guesses
Cyclone Diameter, in 26.00
Feed % Solids 62.00
Circulating Load, % 350.0
Power Oversize, %
ton/hr per Cyclone 375.0
Power, kW 2971 0 476 3447 10.0 3830
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 284.89 45.62 0.00 (18.3)
HYDROCYCLONES CLUSTER : (Preliminary Sizing) # Cyclones per Mill 6
8.44 4218 1 4218
m 3/hr per Cyclone 363.8
Pressure Loss, psi 12.96
Balls Overfilling Slurry Net Total % Losses Gross Total Apparent Density ton/m3 5.395
Spreadsheet ... Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Conventional Ball Mill Sizing
Remarks
Mina RRica: Molino 2.
GRINDING TASK : Ore Work Index, kWh(net) /metric ton Feed Size, F80, microns Product Size, P80, microns Design Throughput, ton/hr
13.03 7000 170.0 500.00
Specific Energy, kWh/ton Net Power Requirement, kW Number of Mills for the Task Net kW / Mill
MILL DESIGN PARAMETERS AND OPERATING CONDITIONS : Eff. Diameter ft 17.50
Eff. Length ft 23.63 L/D 1.350
% Solids in the Mill Ore Density, ton/m 3 Slurry Density, ton/m 3 Balls Density, ton/m 3
Mill Speed % Critical 72.00 rpm 13.18
Charge Filling,% 38.00
72.00 2.80 1.86 7.75
Balls Interstitial Filling,% Slurry Filling,% 38.00 100.00
Charge Volume, m3 61.27
Lift Angle, (°) 33.00
using Tools / Goal
(18.3)
HYDROCYCLONES CLUSTER : (Preliminary Sizing) Cyclone Diameter, in 26.00
Feed % Solids 62.00
Circulating Load, % 350.0
ton/hr per Cyclone 375.0
Power, kW 2971 Balls 0 Overfilling 476 Slurry 3447 Net Total May%be set to any 10.0 Losses 3830 Gross value, Total desired
Mill Charge Weight, tons Apparent Seek, changing Ball Slurry Density Cell C19 or ton/m3 D21. Charge Interstitial above Balls 284.89 45.62 0.00 5.395
Power Oversize, %
# Cyclones per Mill 6
8.44 4218 1 4218
m 3/hr per Cyclone 363.8
Pressure Loss, psi 12.96
Spreadsheet ... Moly-Cop Tools
TM
(Version 2.0) BOND'S LAW APPLICATION Conventional Ball Mill Sizing
Remarks
Mina RRica: Molino 2.
GRINDING TASK : Ore W ork Index, kW h(net) /metric ton Feed Size, F80, microns Product Size, P80, microns Design Throughput, ton/hr
13.03 7000 170.0 500.00
Specific Energy, kW h/ton Net Power Requirement, kW Number of Mills for the Task Net kW / Mill
MILL DESIGN PARAMETERS AND OPERATING CONDITIONS : Eff. Diameter ft 18.54
Eff. Length ft 25.03 L/D 1.350
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Mill Speed % Critical 72.00 rpm 12.81
Charge Filling,% 38.00
72.00 2.80 1.86 7.75
Balls Filling,% 38.00
Charge Volume, m3 72.84
Power, kW 3636 0 582 4218 10.0 4687
Balls Overfilling Slurry Net Total % Losses Gross Total
Mill Charge Weight, tons Ball Slurry Charge Interstitial above Balls 338.69 54.24 0.00
Apparent Density ton/m3 5.395
Interstitial Slurry Filling,% 100.00
Lift Angle, (°) 33.00
Power Oversize, %
(0.0)
HYDROCYCLONES CLUSTER : (Preliminary Sizing) # Cyclones per Mill 6
Cyclone Diameter, in 26.00
Feed % Solids 62.00
Circulating Load, % 350.0
ton/hr per Cyclone 375.0
8.44 4218 1 4218
m 3/hr per Cyclone 363.8
Pressure Loss, psi 12.96
Un rato después ...
Emeterio
A ver ... déjame revisar este catálogo de bombas que tengo por aquí ... ¡Pucha! … este catálogo me pide el flujo en gpm y el % Sólidos en Volumen ... ... ... Ya sé ... ya sé ... vamos a tu computador ...
¡ Listo, Don Eme ! Para 500 tph, necesitamos un molino de 19’ x 25’ con 6 ciclones de 26” y una bomba para 2300 tph al 62% sólidos.
Saturnino
Spreadsheet ... MINERAL SLUR RY CH ARACTERIZATION Ore Density, tons/m 3 : Given an d
Dry Solids (MS, tons)
Pulp Density MS (RHOP, tons/m3) MW MP QP RHOP PSV PS
W ater (MW, m3)
Pulp Weight (MP, tons)
2.80
Pulp Volume (QP, m3)
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
Percent Solids MS (PS, % by weight) MW MP QP RHOP PSV PS
2300.00 1409.68 3709.68 2231.11 1.663 36.82 62.00
MS MW MP QP 3 RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
MS MW MP QP RHOP PSV PS
100.00 70.00 170.00 105.71 1.608 33.78 58.82
Percent Solids (PSV, % by vol)
m /hr
Spreadsheet ...
Moly-Cop Tools
TM
(Version 2.0)
Frequently Used Conversion Factors En t er
VOLUMETRIC FLOW liters/sec 1.00000 3 m /hr 2,231.11000 gal/min 1.00000 3 ft /sec 1.00000 3 ft /min 1.00000
To Ob t ain
liters/sec 1.00000 619.75278 0.06309 28.31000 0.47190
3
m /hr 3.60000 2,231.11000 0.22710 101.91600 1.69884
gal/min 15.85000 9,823.57733 1.00000 448.80000 7.48100
3
ft /sec 0.03532 21.89165 0.00223 1.00000 0.01667
3
ft /min 2.11920 1,313.32059 0.13367 60.00000 1.00000
