ion presentation
TRANSCRIPT
MINERAL PROCESSINGMINERAL PROCESSINGComminution
Peter GronHatch, Brisbane, Australia
COMMINUTION
Min
Com
• Comminution is a mineral processing technique used in extractive metallurgy to
d th ti l i f i l
neram
m reduce the particle size of a mineral ore.
• Comminution processes are employed b b t i ll
al Proinut
because subsequent processing generally requires finer particle sizes, where the valuable mineral is liberated from the oces
tion gangue minerals.
• Coarse particle reduction is completed via ssing
Coa se pa c e educ o s co p e ed aCrushing, while finer reduction is completed via Grinding.g
PRESENTATION OUTLINE
Min
Com
1. Types of Comminution Equipment– Crushers
HPGR
neram
m – HPGR– Sizers– Grinding Millsal Proinut 2. Comminution Circuit Configurations
3. Sizing Comminution Equipmentocestion
g q p– Comminution Characteristics– Bond’s Law
Si i C h
ssing
– Sizing Crushers– Sizing Rod & Ball Mills– Sizing AG & SAG Millsg Sizing AG & SAG Mills
TYPES OF COMMINUTION EQUIPMENT
Types of Comminution EquipmentM
iC
om Equipment Type Reduction Ratio neram
min
Jaw 3 to 4
Gyratory 3 to 4
Cone 4 to 5 Compression Crushers al Prnutio
Rolls Crusher
High Pressure Grinding Rolls
Sizers
3 to 6
Vertical Type 3 to 8
roceon Eq
Vertical Type 3 to 8 Impactors
Horizontal Type 10 to 15
Rod Mill 100
Ball Mill 1 000 Tumbling Type Grinding
Reduction Ratio P d t 80% P i Si (P ) / F d 80% P i Si (F )
ssinuipm
Ball Mill 1,000 Mills
AG & SAG Mill 5,000
= Product 80% Passing Size (P80) / Feed 80% Passing Size (F80)
g m
ent
TYPES OF COMMINUTION EQUIPMENT
JAW, GYRATORY & CONE CRUSHERS
CRUSHERS
Min
Cru • Jaw, Gyratory and Cone Crushers are
mainly used for the size reduction of neraushe
hard, abrasive materials.
• Range in size from large primary jaw and
al Proers Range in size from large primary jaw and gyratory crushers to cone crusher for secondary, tertiary and quaternary oces
qcrushing.
• Sticky material can be problematic in ssing
• Sticky material can be problematic in these crushers.
g
Jaw Crushers (Primary)Jaw Crushers (Primary)Min
Cru neraushe al Pro
ersocesssingg
JAW CRUSHERS
Min
Cru • Tonnages from 25 tph to greater than neraushe
g p g1000 tph
• Openings range from
al Proers Openings range from
17” x 25” to oces
to 47” x 63”ssing
• Product size from 38 mm to 300 mm
g
Gyratory Crushers (Primary)Gyratory Crushers (Primary)Min
Cru neraushe al Pro
ersocesssingg
GYRATORY CRUSHERS
Min
Cru • Tonnages from 400 tph to greater than
6400 tphneraushe • Sizes range from
30” 60”
al Proers 30” x 60”
to 72” 112”
oces
72” x 112”
• (Size refers to feed opening x crusher ssing
( p gcone diameter)
• Product size from -100 mm to +250 mmg
Cone Crushers (Secondary / Tertiary)M
inC
ru neraushe al Pro
ersocesssingg
CONE CRUSHERS
Min
Cru neraushe • Tonnages from 15 tph to greater than
2000 tph
al Proers 2000 tph
P d t i f 6 t 75
oces
• Product size from –6 mm to +75 mm
ssingg
TYPES OF COMMINUTION EQUIPMENT
ROLLS CRUSHERS
Rolls Crushers / d /(Primary/Secondary/Tertiary)M
inRol nera
lls C al ProC
rush
• Rolls Crushers are used for the crushing of oceshers
• Rolls Crushers are used for the crushing of medium-hard rock as well as for sticky and soft materials such as lignite and mineral ssing
soft materials such as lignite and mineral coal, clay, marble, limestone and similar raw materials.g
Rolls Crushers (Krupp)Min
Rol neralls C al Pro
Crush oces
hers ssingg
Rolls Crushers (McLanahan)Min
Rol neralls C al Pro
Crush oces
hers ssingg
TYPES OF COMMINUTION EQUIPMENT
HIGH PRESSURE GRINDING ROLLS
(HPGR)
HPGR
Min
HP • HPGR’S are an autogenous crushing
system based on inter-particle breakage neraG
R
y p gin a packed bed.
• The machine consists of 2 counter al Pro
rotating drums – 1 fixed while high crushing forces (300 MPa) are applied via h d li h h h h
oces
hydraulic rams through the other moveable roll shaft.Th hi ti i k d
ssing
• The crushing action occurs in a packed bed between the rolls.
• Polysius KHD & Koepern
g • Polysius, KHD & Koepern
HPGR
Min
HP • Main advantage of HPGR – lower specific
energy consumption.neraG
R HPGR & SAG Specific Comminution Power 1
Ball Mill
al Pro 20
25
30
r (kW
h/t)
Pebble CrusherSAG MillRolls Crusheroces
5
10
15
ecifi
c P
ower Secondary Crusher
Primary Crusher
1. Source: Innovation in Mineral Processing P
ssing
0
5
Spe
RollsCrusher
SAG Mill
Mineral Processing - P Reese: 2000 NZ Minerals & Mining Conference Proceedings 29 - 31 October 2000g
HPGR
Min
HP nera
GR al Proocesssingg
TYPES OF COMMINUTION EQUIPMENT
SIZERS
Sizers
Min
Size
• Sizers are used for primary, secondary and tertiary sizing / crushing of materials nera
ers
y g gsuch as: – Coal, Salt, Gypsum, Limestoneal Pro
, , yp ,• A feature of these machines is their
ability to handle very wet, sticky and oces
hard material either separately or together through the same unit.ssing
• The generation of fines is minismised.
g
DDC Sizers
Min
Size neraers al Proocesssingg
MMD Sizers
Min
Size neraers al Proocesssingg
Abon Sizers
Min
Size neraers al Proocesssingg
TYPES OF COMMINUTION EQUIPMENT
IMPACT CRUSHERS
Impact Crushers
Min
Imp • “Low-Abrasion” materials.
h h h l
nerapact
• A rotor spins in either the horizontal or vertical planes (thus horizontal or vertical impact crushers)
al Pro C
ru
impact crushers).
• Hammers are attached to the rotor and ocesushe
impact the material against breaker plates.ssing
rs • Historically “hammer-mills” were used for gold.g
Horizontal Impact Crushers
Min
Imp nerapact al Pro
Cru ocesushe ssing
rsg
Vertical Impact Crushers
Min
Imp nerapact al Pro
Cru ocesushe ssing
rsg
TYPES OF COMMINUTION EQUIPMENT
GRINDING MILLS
Metso / Bradken / Fuller / Krupp-Polysius / Outokumpu
Rod Mills (Primary Mill)Rod Mills (Primary Mill)Min
Gri nera
ndin al Prong M
• Limited Size (due to rods) Max – 14’ dia x 22’ocesM
ills
Limited Size (due to rods) Max 14 dia x 22• Feed is product from tertiary crusher• F80 9,500 m to 16,000 mssing
s
80
• Uniform size distribution in product• P80 1,000 m to 4,750 mg
Ball Mills (Primary/Secondary)Min
Gri
f d f l
nerandin
• Largest Size – 25 ft dia x 40 ft long– Predicting 26’ x 40’ with 15 MW Wrap
Around Drive
al Prong M
• Feed is product from tertiary crusher or (S)AG Mill or HPGR
• F 6 350 m to 12 700 m
ocesM
ills
• F80 6,350 m to 12,700 m• P80 < 50 m (mill discharge: grates or o/f)• Ball Size – 9.5 mm to 75 mm
ssings
g
(S)AG Mills – (Primary)(S)AG Mills (Primary)Min
Gri
• AG – Autogenous Grinding Mill: Feed is used as grinding media
nerandin
• SAG – Semi-Autogenous Grinding: Feed plus steel balls used as grinding media
al Prong M
p g gocesM
ills ssings
g
(S)AG Mills – (Primary)Min
Gri nera
ndin al Prong M oces
Mills ssing
sg
(S)AG Mills – (Primary)Min
Gri nera
ndin al Prong M oces
Mills ssing
sg
AG / SAG Mills (Primary)AG / SAG Mills (Primary)
• Largest Size – 40 ft dia x 24 ft long
Min
Gri Largest Size 40 ft dia x 24 ft long
– Predicting 44 ft dia with 30 MW Wrap Around Drive
nerandin
• Feed is product from primary crusher• F80 up to 250 mm
al Prong M
• P80 as fine as less than 100 m• Ball Size – 75 mm to 200 mm
ocesM
ills ssings
g
COMMINUTION CIRCUIT CONFIGURATIONS
Two Stage Crushing CircuitFEEDM
inC
om
FEED
J AW CRUS HER
Typically
Availabilities are in neram
min
S I ZI NG S CREEN
CONE CRUS HER
– Availabilities are in the order of 80%-85% al Pro
nutio
• For U/G operations Jaw Crushers are often used as the U/G Crusher (Size allows shaft access)
ocesn C
ir
P RODUCT( t o Rod M i l l or Ba l l M i l l )
as the U/G Crusher (Size allows shaft access)• Third Stage can be added with addition of
another cone crusher / screen
ssingrcuits
• Generally lower tonnage operations
g s
Rod Mill / Ball Mill CircuitRod Mill / Ball Mill CircuitMin
Com nera
mm
in
P RODUCT
CYCLONE
al Pronutio ROD M I LL
( ope n c c t )
CYCLONE
ocesn C
ir
FEED
BALL M I LL( c l ose d c c t )T picall
ssingrcuits
( c l ose d c c t )Typically
– Availabilities are in the order of +95% g s the order of +95%
SAG / AG CircuitSAG / AG CircuitMi
Com nera
mm
in
COARSE ORE STOCKPILEPRODUCT
Gyratory Crusher
FEED
Transfer Conveyoral Prnutio
(S)AG Mill
Discharge ScreenApron Feeders & Transfer
Conveyorsroceon C
i
Pebble Recycle System
Cyclone Feed System
T picallssinrcuits
Typically
– Availabilities are in the order of +92% g s the order of +92%
(S)ABC(S)AG – BALL – CRUSHERM
inC
om
Gyratory Crusher
FEED
Coarse Ore
neram
min
Crusher
Transfer Conveyor
Coarse Ore Stockpile
al Pronutio (S)AG Mill
Discharge Screen
Pebble Crushing & Recycle System
Apron Feeders & Transfer Conveyors
ocesn C
ir
PRODUCT
Ball Mill Grinding CircuitTypically
– Availabilities are in ssingrcuits (S)AG Transfer
Pump
BM Cyclone Feed
the order of +92%
g s
BM Cyclone Feed Pump
High Pressure Grinding Rolls CctHigh Pressure Grinding Rolls CctMin
Com nera
mm
in Apron Feeders & Coarse Ore Transfer Conveyor
Coarse Ore Stockpile
Pre-Crusher Feed Bin & Apron Feeder
Pre-Crushing Circuit Screen Feed Bin
Apron Feeder & Double Deck Screens (Top Deck Arranged As A Scalping
Grizzly)
Oversize Ore Transfer Conveyor
Pre-Crushed Ore Transfer Conveyors
al Pronutio
HPGR Circuit Feed Bin
Gyratory Pre-Crusher
Crushed Ore Transfer Conveyors
Covered Crushed Ore Stockpile
HPGR Feed Conveyor
Covered Ore Stockpile Conveyoroces
n Cir
& Belt Feeder
HPGR
HPGR Product Transfer Conveyor
HPGR Circuit Screen Feed Bins, Apron Feeders, Double Decked
Screens (Wet) & Oversize Transfer Conveyors
HPGR Oversize Ore Transfer
Conveyors
Typically Availabilities Are:ssingrcuits Ball Mill Circuit
PRODUCT
yp y80% - 85% for prim crushing90% for HPGR
f d
g s
+90% for grinding Cct
COMMINUTION COMMINUTION
SIZING COMMINUTION EQUIPMENT
Process of Sizing Comminution EquipmentM
inSizin
1 Determine the ore’s
nerang C
om
1. Determine the ore s ‘Comminution Characteristics’.al Pro
mm
inu
2. Determine the ‘Required Comminution Power’.oces
ution E
Comminution Power .
3 Size Comminution Equipment ssingEquipm
3. Size Comminution Equipment based on the ‘Required Comminution Power’.g
ment
Comminution CharacterisationComminution Characterisation• AI – Abrasion Index: Indicates the
abrasiveness of an ore in crushing and
Min
Sizin ggrinding. Used to estimate media & liner wear.
WI B d W k I d (I l d
nerang C
om
• WI - Bond Work Index: (Includes Crushing, Rod Milling and Ball Milling Indices) The work indices of an ore are
d t l l t hi d i di
al Prom
minu
used to calculate crushing and grinding mill power requirements.
• AUTOGENOUS MEDIA COMPETENCY -
ocesution E
• AUTOGENOUS MEDIA COMPETENCY -Provides a qualitative guide to the suitability of an ore for autogenous or semi-autogenous grinding
ssingEquipm
autogenous grinding.g m
ent
Comminution Characterisation
• DWI - JK Technology Drop Weight Testing:Determines the ore breakage parameters for use
Min
Sizin g pin the comminution processing simulator, JKSimMet, which models crushers, (S)AG, ball and rod mills, along with classification systems.
nerang C
om , g y
• SMC – SAG Mill Comminution: Developed by Dr. S Morrell. Again the parameters can be used in simulations of comminution circuits
al Prom
minu
in simulations of comminution circuits
• Piloting – Pilot scale milling circuits (particularly (S)AG mills used for scale up).
ocesution E p
• HPGR – laboratory scale to pilot scale tests undertaken for power requirements and wear rates
ssingEquipm
rates.
g m
ent
Bond’s Law (1952 – Third Theory of Comminution)M
inSizin nera
ng Com
The power required to reduce the feed from the Feed Size (F80) to the required ProductSize (P80) is as per the Bond Equation:
10 10
al Prom
minu
Power Required (kW / tonne) = Wi x10
P80
10
F80
ocesution E
W i = Bond Work Index of the ore.
P 80 = 80% passing size of the mill product.
F 80 = 80% passing size of the mill feed.ssingEquipm Efficiency factors are used to take into account conditions in the grinding circuit. A total
efficiency factor (which is the product of all of the efficiency factors) is multiplied by theBond Power to determine the power required at the mill pinion shaft
g m
ent
Bond Power to determine the power required at the mill pinion shaft.
CrushersCrushers
• Bond’s Law can be used to determine
Min
Sizin
• Bond s Law can be used to determine power requirements for crushers.
nerang C
om
• Crushers are flow through devices and the tonnage and F80 / P80 sizings determines the ‘size’ of crusher required
al Prom
minu
the size’ of crusher required.
• The ‘Nordberg Red Book’ is one source of
ocesution E
The Nordberg Red Book is one source of performance data for crusher sizing (can be downloaded from the internet.)
ssingEquipm g
ment
Bond’s Law - Rod & Ball MillsBond s Law Rod & Ball MillsMin
Sizin EFFICIENCY FACTORSnerang C
om
EF1: Mill Type - For the same range of work dry grinding requires 1.3 times as muchpower as wet grinding.
EF2: Open Circuit Grinding - When utilising open circuit ball mills the amount of extra
al Prom
minu
power required is a function of the degree of control required on the product produced.(EF2=1 for closed cct) The inefficiency factors are given below:
Product Size Control (P80) Inefficiencyocesution E
( 80) y Reference % Passing Multiplier 50% 1.035 60% 1.050 70% 1.100ssing
Equipm
80% 1.200 90% 1.400 92% 1.460 95% 1.570
98% 1 700
gment
98% 1.700
Bond’s Law - Rod & Ball MillsBond s Law Rod & Ball MillsMin
Sizin nerang C
om EFFICIENCY FACTORS (continued)al Prom
minu
EF3: Mill Diameter Efficiency Factor
F Di 3 81 EF (2 44/Di )0 2ocesution E
For Diameters < 3.81 m EF3 = (2.44/Diameter)0.2
For Diameters > or = 3.81 m EF3 = 0.914
ssingEquipm g
ment
Bond’s Law - Rod & Ball MillsMi
Sizin
EFFICIENCY FACTORS (continued)
EF4: Oversized Feed Efficiency Factor - This factor is used to take into account situationsnerang C
om
4 ywhere the mill feed is coarser than the optimum feed size:
R + (W i - 7) xF - F o
al Prm
minu
R r
EF4 =
R r + (W i - 7) x F o
roceution E
R r = Ratio of Reduction = F80 / P80
F o = Optimum Feed SizessinEquipm
F o = Rod Milling = 16,000 x 13 / W i
g m
ent
F o = Ball Milling = 4,000 x 13 / W i
Bond’s Law - Rod & Ball MillsMin
Sizin
EFFICIENCY FACTORS (continued)
EF5: Finess of Grind Factor - This applies to fine grinding when 80% passing size ofth d t i fi th 75 i
nerang C
om
the product is finer than 75 microns:
EF5 = (P80 + 10.3) / (1.145 * P80)al Prom
minu
EF6: Ratio of Reduction Factor For Ball Mills - This applies to ball mills only whenRr < 6. (Most often this factor is applied in regrinding operations.) The equation to use isas follows:
EF2 x (R r - 1.35) + 0.26oces
ution E EF6: Ratio of Reduction Factor For Rod Mills - This applies whenever the absolutel f (R R ) > 2
EF 6 =2 x (R r - 1.35)
ssingEquipm
value of (R r - R ro) > 2:
(R r - R ro) 2
EF6 = 1 +150
R ro = 8 + 5L / Dg m
ent
R ro 8 5L / D
Bond’s Law - Rod & Ball MillsMin
Sizin
EFFICIENCY FACTORS (continued)
EF7: Mill Liner Type Factornerang C
om
For Rubber Liners: EF7 = 1.07 For Steel Liners: EF7 = 1.00al Pro
mm
inu
EF8: Rod Mill Inefficiency Factor - When calculating power for a 'rod mill onlyapplication', an inefficiency factor of 1.4 is used when open circuit crushing is used tofeed the rod mill. If closed circuit crushing is employed a factor of 1.2 is used.
Wh l l ti f ' d ill b ll ill li ti ' i ffi i f t f 1 2
ocesution E
When calculating power for a 'rod mill - ball mill application', an inefficiency factor of 1.2is used when open circuit crushing is used to feed the rod mill. If closed circuit crushingis employed a factor of 1.0 is used.
EFT: Total Efficiency Factor
ssingEquipm
EFT: Total Efficiency Factor
EFT = EF1 x EF2 x EF3 x EF4 x EF5 x EF6 X EF7 X EF8
Power is calculated according to the Bond Formula and the Total Efficiency Factor is
g m
ent
Power is calculated according to the Bond Formula and the Total Efficiency Factor isapplied to arrive at a corrected power requirement.
Bond Operating Work Index Min
Sizin • An Operating Work Index can be calculated as follows:nera
ng Com Specific Energy (kWh/t) = E =
Mill Power Draw
(Fresh Feed Rate x Drive Efficiency)
al Prom
minu
10 10
E
O ti W k I d (kWh/t) W
ocesution E
10
P80
10
F80
Operating Work Index (kWh/t) = Wi Op =
ssingEquipm
• Bond’s Law can then be used to evaluate different tonnage and / or F80 - P80 scenariosg
ment
Rod & Ball Mill SizingRod & Ball Mill SizingMin
Sizin
• There are numerous models that may be used
nerang C
om
• There are numerous models that may be used to calculate Rod & Ball Mill Dimensions based on the Power Requirements, such as:al Pro
mm
inu 1. Kelly & Spottiswood Model.2 H & F M d l (B ll Mill O l )
ocesution E
2. Hogg & Fuerstenau Model (Ball Mills Only).3. Mular & Bhappu Model.ssing
Equipm g m
ent
Kelly & Spottiswood Rod & B ll Mill M d lBall Mill ModelM
inSizin
Power Delivered At Pinion =nerang C
om
Power Delivered At Pinion
8.44 x Dia2.5 x Length x KMt x KSP x KL al Prom
minu
Where:
Dia = Diameter inside linersocesution E
Length = Length inside linersKMt is the Mill Factor (1.0 for wet grinding, 1.3 for ssing
Equipm
dry grinding)KSP is a factor based on the mill critical speedK is a factor based on the mill charge
g m
ent
KL is a factor based on the mill charge
Kelly & Spottiswood ModelKelly & Spottiswood ModelMin
Sizin Factors For Calculating Power Draftnerang C
om 5.50
6.00
al Prom
minu 4.50
5.00
K L Ball Mill
Rod Millocesution E
3.50
4.00
ssingEquipm
3.0020% 25% 30% 35% 40% 45% 50%
Percent Mill Loading
g m
ent
Percent Mill Loading
Kelly & Spottiswood ModelKelly & Spottiswood ModelMin
Sizin Factors For Calculating Power Draftnerang C
om 0.220
0.240al Prom
minu 0.180
0.200
K S
Pocesution E
0 120
0.140
0.160
K
ssingEquipm
0.100
0.120
60% 65% 70% 75% 80% 85%g m
ent
Percent of Critical Speed
Kelly & Spottiswood Modely pMin
Sizin nerang C
om • By assuming an aspect ratio we can replace Length in terms of the Diameter & use ‘Goal
al Prom
minu
Length in terms of the Diameter & use Goal Seek’ or ‘Solver’ in Excel to calculate the Mill Dimensions based on the Grinding Power
d f d
ocesution E
Required from Bond’s Law.
ssingEquipm g
ment
BALL MILL SIZING EXAMPLEMin
Sizin
BALL MILL SIZING EXAMPLEBall Mill - 25' x 40' Pwr @ Pinion = 12,190kW
(F80 = 1.080mm P80 = 75micron)(Wet Grinding Mill In Closed Circuit With Grate Discharge and Rubber Liners)
nerang C
om
(Wet Grinding Mill In Closed Circuit With Grate Discharge and Rubber Liners)
Grinding Circuit Parameters
Feed Rate 931 tph
al Prom
minu
Mill Feed - F80 Passing Size 1,080 micronMill Product - P80 Passing Size 75 micron
Total Mill Charge (Ore plus Media) 28% vol/vol%ocesution E
Media Charge 28% vol/vol%
Liner Thickness 75 mm
Mill Speed 75% % criticalssingEquipm
Drive Efficiency 93% %
Ball Mill Work Index 15.50 kWh/tAbrasion Index 0.388 -g
ment
Power Required To Achieve Grind RequirementsMin
Sizin
q q
Net Power - kW Gross Power - kW
11,995 12,898
Net Power kW Gross Power kW
Bond's Law Power Required (Delivered To Pinion Shaft)
A l P D (D li d
nerang C
om
Net Power - kW Gross Power - kW
12,190 13,108
Ball Mill Dimensions
Actual Power Draw (Delivered To Pinion Shaft)
al Prom
minu
Ball Mill Dimensions - Inside Shell (feet)
Based On Bond's Law
Based On Actual Mill Power Draw
Calculation Methodocesution E
Law Mill Power Draw
Diameter Length Diameter Length
Kelly & Spottiswood 25.0 39.9 25.1 40.1ssingEquipm
Hogg & Fuerestenau 24.6 39.4 24.7 39.6
Mular & Bhappu 25.8 41.2 25.9 41.4
Average 25.1 40.2 25.2 40.4g m
ent
SAG & AG Power RequirementsM
inSizin
• There are numerous methods that may be
nerang C
om
• There are numerous methods that may be used to calculate SAG & AG Power Requirements. Two such methods are:al Prom
minu 1. the Barratt Method.
2 h A i M h d
ocesution E
2. the Austin Method.
• Both of these methods are very similar and ssingEquipm
• Both of these methods are very similar and yield similar results.
g m
ent
Barratt Method To Determine /SAG/AG Power Requirements
• Barratt proposed the use of an empirical f l b d B d W k I di t
Min
Sizin
formula, based on Bond Work Indices, to calculate the power requirements, where:
F F Si f F d
nerang C
om
FC = F80 Size of FeedPC = P80 Size of Equivalent Crusher Product
F P F Si f F d t R d Mill
al Prom
minu
FR = PC = F80 Size of Feed to Rod MillPR = P80 Size of Equivalent Rod Mill Product
F P F Size of Feed to Ball Mill
ocesution E
FB = PR = F80 Size of Feed to Ball Mill
P(S)AG = P80 Size of (S)AG Product
ssingEquipm g
ment
Barratt Method To Determine /SAG/AG Power RequirementsM
inSizin nera
ng Com
KR = Rod Mill Efficiency Factor (generally 1.0)KB = Ball Mill Efficiency Factor (generally 1.0)al Prom
minu
K(S)AG = (S)AG Efficiency Factor (generally 1.25)
WI B d C h W k I d
ocesution E
WIC = Bond Crusher Work Index
WIR = Bond Rod Mill Work IndexWI B d B ll Mill W k I d
ssingEquipm
WIB = Bond Ball Mill Work Index
g m
ent
Barratt Method To Determine /SAG/AG Power RequirementsM
inSizin nera
ng Com )10(WIC
10 + )10(WIR
10KR +[al Pro
mm
inu
)( PC FC)( PR FR
-)10(WIB
10KB K(S)AG
[]oces
ution E )10(WIB10
KB
)( 110 FB]
ssingEquipm
)(WIB
110 P(S)AG
KB
g m
ent
SAG/AG SizingSAG/AG Sizing
• Most (S)AG Sizing Models use empirical f l t d t i th
Min
Sizin
formulae to determine the power required to rotate the various components in the mill charge:
nerang C
om
components in the mill charge:
» Rocks Slurry
al Prom
minu
» Slurry» Balls
h l h d b l l h
ocesution E
• This is accomplished by calculating the volume and weight of each component.
ssingEquipm g
ment
SAG/AG SizingSAG/AG Sizing• There are numerous models available to
determine (S)AG Power Requirements:
Min
Sizin q
1. Austin Model. 2. Morrell Charge Model.
nerang C
om
3. Morrell Empirical Model.4. Sastri & Rao Model.5 Morgardshammar Model
al Prom
minu
5. Morgardshammar Model.6. Hogg & Fuerstenau Model.7. Barratt Model.
ocesution E
8. Marcy Model.
• All of these models yield similar results.
ssingEquipm g
ment
Min
Sizin
SAG MILL SIZING EXAMPLEExample: SAG - 36' x 22' Power @ Pinion = 15,670 kW (F80 = 134mm P80 = 1.08mm)nera
ng Com
Grinding Circuit Parameters
Feed Rate 1,861 tph
SAG New Feed Size - F80 Passing Size 134 mmS G f S S
al Prom
minu
SAG Transfer Size - P80 Passing Size 1,080 micron
Total Mill Charge (Ore plus Media) 26% vol/vol%Media Charge 13% vol/vol%
Liner Thickness 75 mmocesution E
Mill Speed 75% % critical
Drive Efficiency 93% %
Crushing Work Index 16.00 kWh/tssingEquipm
Rod Mill Work Index 16.00 kWh/tBall Mill Work Index 16.00 kWh/t
Abrasion Index 0.230 -g m
ent
Min
Sizin nerang C
om
Power Required To Achieve Grind Sizing
Net Power - kW Gross Power - kWActual Power Requirements for a 36' x 22' SAG
al Prom
minu
15,670 16,850
Calculation Method Net Power - kW Gross Power - kW
Barratt 15,145 16,285
SAG
ocesution E
Austin 16,640 17,895
Calculated Average 15,895 17,090
ssingEquipm g
ment
SAG Mill Dimensions (To Draw Power Required To Achieve Grind Sizing)
SAG Mill Dimensions - Inside Shell (feet)Min
Sizin
Based On Barratt Method To Determine
SAG Power Requirements
Based On Austin Method To Determine
SAG Power Requirements
Based On SAG Power Requirements
For a 36' x 22' SAG
Calculation Method Used To Determine SAG
Dimensionsnerang C
om
Requirements Requirements
Diameter Length Diameter Length Diameter Length
Austin 35.2 21.5 36.2 22.1 35.5 21.7
al Prom
minu
Morrell Charge 36.0 22.0 36.9 22.6 36.3 22.2
Morrell Empirical 36.1 22.1 37.1 22.7 36.4 22.3
Sastri & Rao 36.7 22.5 37.7 23.1 37.1 22.7
Morgardshammer 36.4 22.2 37.3 22.8 36.7 22.4ocesution E
Morgardshammer 36.4 22.2 37.3 22.8 36.7 22.4
Hogg & Fuerstenau 36.5 22.3 37.5 22.9 36.9 22.5
Barratt 35.0 21.4 35.9 22.0 35.3 21.6
Marcy 35.3 21.6 36.2 22.1 35.6 21.8ssingEquipm
Minimum (Occurs With Barratt) 35.0 21.4 35.9 22.0 35.3 21.6
Average Of All Calculation 35.9 21.9 36.9 22.5 36.2 22.1
Maximum (Occurs
g m
ent
Maximum (Occurs With Sastri & Rao) 36.7 22.5 37.7 23.1 37.1 22.7
QUESTIONS