Energy Use in Comminution
Lecture 7
MINE 292
COMMINUTION
MECHANICAL
External
forces
- smashing
- blasting (chemical)
- breaking
- attrition
- abrasion
- splitting or cutting
- crushing
- grinding
CHEMICAL
Special
forces
- thermal shock
- microwaves
- pressure changes
- photon bombardment
Chemical
forces
- digestion
- dissolution
- combustion
- bioleaching
Comminution
• Although considered a size-reduction process,
since minerals in an ore break preferentially,
some upgrading is achieved by size separation
with screens and/or classifiers
Comminution and Sizes
Effective Range of 80% passing sizes by Process
Process
1) Explosive shattering:
2) Primary crushing:
3) Secondary crushing:
4) Coarse grinding:
5) Fine grinding:
6) Very fine grinding:
7) Superfine grinding:
F80
infinite
1m
100 mm
10 mm
1 mm
100 µm
10 µm
P80
1m
100 mm
10 mm
1 mm
100 µm
10 µm
1 µm
The 80% passing size is used because it can be measured.
Comminution - Blasting
•
•
•
•
Blasting practices aim to minimize explosives use
Pattern widened/explosive type limited to needs
Requirements – maximum size to be loaded
However, "Mine-to-Mill" studies show that
– Increased breakage by blasting reduces grinding costs
– Blasting energy efficiency ranges from 10-20%
– Crushing and grinding energy efficiencies are 1-2%
• Limitations in blasting relate to
– Flyrock control
– Vibration control
• Improvements comes from reduced top-size & Wi
Primary Crushing
•
•
•
•
Jaw crusher < 1,000 tph
Underground applications
Gyratory crusher > 1,000 tph
Open-pit and In-pit
Types of Jaw Crushers
Two different types:
• Blake Jaw Crusher - plate pinned above
• Dodge Jaw Crusher - plate pinned below
Comparison:
1. product size of Dodge more uniform
2. Blake - largest force on smallest particles
3. Blake - higher capacity at same size
4. Dodge - frequent blockages
Single Toggle Blake Jaw Crusher
Primary Crushing
• Product size = 10 – 4 inches (250 – 100 mm)
• Open Side Setting (OSS) is used to operate
• Mantle and bowl are
lined with steel plates
• Spider holds spindle
around which the
mantle is wrapped
Secondary Crushing
• Symons Cone Crushers
• Standard and Shorthead
Secondaries Tertiaries
CSS (mm)
25-60
5-20
• Can process up to 1,000 tph
• Mech. Availability = 70-75%
Secondary Crusher Feeder
Secondary Crushing Plants
• Fully-configured Plant
Secondary Crushing Plants
• No Internal Surge Bins
Scissor Conveyors
• Palabora Mining – South Africa
Secondary Crushing Plants
• No Screen Bin
Secondary Crushing Plants
• Open Circuit – gravity-flow
Impact Crushers
•
•
•
•
Used in small-scale operations
Coarse liberation sizes
Hammer velocities (50mps)
Screen hole size controls
product size
• High wear rates of
hammers and screen
Impact Crushers
•
•
•
•
Barmac Crusher
Invented in New Zealand
Impact velocity = 60 -90 mps
High production of
fines by attrition
• Used in quarries &
cement industry
Impact Crushers
•
•
•
•
Barmac Crusher
Invented in New Zealand
Impact velocity = 60-90 mps
High production of
fines by attrition
• Used in quarries &
cement industry
Secondary Crushing - Rolls Crusher
Secondary Crushing - Rolls Crusher
•
•
•
•
Angle of Nip
Standard rolls
HPGR forces
Packed-bed
– 2a = bed thickness
• Now applied to fine
crushing
• Competitive with
SAG (or complementary)
Energy in Comminution
Crushing and Grinding
•
•
•
•
•
Very inefficient at creating new surface area (~1-2%)
Surface area is equivalent to surface energy
Comminution energy is 60-85 % of all energy used
A number of energy "laws" have been developed
Assumption - energy is a power function of D
dE
 K D n
dD
dE = differential energy required,
dD = change in a particle dimension,
D = magnitude of a length dimension,
K = energy use/weight of material, and
n = exponent
Energy in Comminution
Von Rittinger's Law (1867)
• Energy is proportional to new surface area produced
• Specific Surface Area (cm2/g)  inverse particle size
• So change in comminution energy is given by:
dE
 K r f c  D 2
dD
which on integration becomes:
1
1
E  K r f(c

)
D p Df
where
Kr = Rittinger's Constant and
fc = crushing strength of the material
Energy in Comminution
Kick's Law (1883)
• Energy is proportional to percent reduction in size
• So change in comminution energy is given by:
dE
 K k f c  D 1
dD
which on integration becomes:
 Df 
E  K k f c log e  
 D p 
where
Kk = Kick's Constant and
fc = crushing strength of the material
Energy in Comminution
Bond's Law
• Energy required is based on geometry of a crack
•
expansion as it opens up
His analysis resulting in a value for n of 1.5:
dE
 K b f c  D 1.5
dD
which on integration becomes:
E  K b f(c
where
1
1

)
Dp
Df
Kb = Bond's Constant and
fc = crushing strength of the material
Energy in Comminution
Where do these Laws apply?
•
•
•
•
Hukki put together the diagram below (modified on right)
Kick applies to coarse sizes (> 10 mm)
Bond applies down to 100 µm
Rittinger applies to sizes < 100 µm
von
Rittinger
Bond
Kick
Size Reduction
• Different fracture modes
• Leads to different size
distributions
• Bimodal distribution not
often seen in a crushed
or ground product
Cumulative
Weight% Passing
Breakage in Tension
• All rocks (or brittle material) break in tension
• Compression strength is 10x tensile strength
• Key issue is how a compression or torsion
force is translated into a tensile force
• As well, the density and orientation of internal
flaws is a key issue (i.e., microcracks, grain
boundaries, dislocations)
Griffith’s Crack Theory
Griffith’s Crack Theory
• Three ways to cause a crack to propagate:
Mode I – Opening (tensile stress normal to the crack plane)
Mode II – Sliding
(shearing in the crack plane normal to tip)
Mode III – Tearing (shearing in the crack plane parallel to tip)
Griffith’s Crack Theory
• Based on force (or stress) needed to propagate
an elliptical plate-shaped or penny-shaped crack
 2 A  2 a 2 A
U 


 4 a s
2 E'
E'
2
where
A
E'

s
a
=
area of the elliptical plate
= effective Young’s Modulus
=
strain
=
specific surface energy
=
half-length of the ellipse
Young's Modulus
• Also called Tensile Modulus or Elastic Modulus
• A measure of the stiffness of an elastic material
• Ratio of uniaxial stress to uniaxial strain
• Over the range where Hooke's law holds
• E' is the slope of a stress-strain curve of a tensile
test conducted on a sample of the material
Young's Modulus
Low-carbon steel
Hooke's law is valid from the
origin to the yield point (2).
1. Ultimate strength
2. Yield strength
3. Rupture
4. Strain hardening region
5. Necking region
A: Engineering stress (F/A0)
B: True stress (F/A)
Griffith’s Theory
Differentiating with respect to 'a' gives:
2  2 a
4 a s 
0
E'
Rearranging derives the fracture stress to initiate a
crack as well as the strain energy release rate, G:
 2 a
G
E'
where
G = energy/unit area to extend the crack
Compression Loading
• Fracture under point-contact loading
D. Tromans and J.A. Meech, 2004. "Fracture Toughness and Surface Energies of Covalent Materials:
Theoretical Estimates and Application to Comminution", Minerals Engineering 17(1), 1–15.
Induced stresses-compressive load P
P
KI =Yi(ai)1/2
a1
a5
5
4
At fracture:
1
2
2a4
2a3
a2
3 P
KIC =Yic(ai)1/2
where
KIC =(EGIC)1/2
GIC = Fracture Toughness
P
KI = Stress intensity (at fracture KI = KIC, i = ic)
i = Tensile stress, ai = crack length Y = Geometric factor (2 π -½)
E = Young's modulus, GIC = critical energy release rate/m2
Schematic of particle containing a crack (flaw) of
radius 'a' subjected to compressive force 'P'
(a)
(b)
P
kP
P
q
kP
kP
P
kP
P
kP
2a
D
2a
kP
P
kP
D
P
kP
P
P
i = P( kcosq - sinq )
KI=Y P (kcosq - sinq ) a1/2
At fracture KI=KIC. In theory there is a limiting average fine particle size:
Dlimit ~ π(KIC/kP)2
(where q = 0)
Impact Efficiency
Impact Efficiency
• KIC, P, and flaw orientation (θ) determine impact efficiency
• Impact without fracture elastically deforms the particle with the
elastic strain energy released as thermal energy (heat)
• Impact inefficiency leads directly to high-energy consumption
• In ball and rod mills with the random nature of particle/steel
interactions, a wide distribution of "P" occurs leading to very
inefficient particle fracture. A way to narrow this distribution
is to use HPGR
• Such mills consume less energy and exhibit improved interparticle separation in mineral aggregates (i.e., liberation via
inter-phase cracking), particularly with diamond ores
• Diamond liberation without fracture damage is attributable
to the high KIC of diamond relative to that of the host rock
Change in mode of breakage
• High-velocity breakage of magnetite
Comminution Testing
• Single Particle Breakage Tests
– Drop weight testing
– Split Hopkinson Bar tests
– Pendulum testing
• Multiple Particle Breakage Tests
–
–
–
–
Bond Ball Mill test
Bond Rod Mill test
Comparison test
High-velocity Impact Testing
Drop Weight Test
2 to 3 inch pieces of rock are subjected to different
drop weight energy levels to establish Wi(C)
Split Hopkinson Bar Test Apparatus
Split Hopkinson Bar Test Apparatus
- Method to obtain material properties in a dynamic regime
- Sample is positioned between two bars:
- incident bar
- transmission bar
- A projectile accelerated by compressed air strikes the
incident bar causing an elastic wave pulse.
- Pulse runs through first bar - part reflected at the bar end,
the other part runs through sample into transmission bar.
- Strain gauges installed on surfaces of incident and
transmission bars measure pulse strain to determine
amplitudes of applied, reflected, and transmitted pulses.
Pendulum Test – twin pendulum
Impact Pendulum
Rebound Pendulum
Rock Particle
Bond Impact Crushing Test – Wi(C)
Low-energy impact test pre-dates Bond “Third Theory” paper.
Published by Bond in 1946
Test involves 2 hammers
striking a 2"-3" specimen
simultaneously on 2 sides.
Progressively more energy
(height) added to hammers
until the specimen breaks
Doll et al (2006) have shown that drill core samples
can be used to establish range of energy requirements
Bond Impact Crushing Test – Wi(C)
Values measured are:
1.
2.
3.
E = Energy applied at breakage (J)
w = Width of specimen (mm)
ρ = Specific gravity
Wi(C) = _59.0·E_
w·ρ
where Wi(C) = Bond Impact Crushing Work Index (kWh/t)
F.C. Bond, 1947. "Crushing Tests by Pressure and Impact", Transactions of AIME, 169, 58-66.
A. Doll, R. Phillips, and D. Barratt, 2010. "Effect of Core Diameter on Bond Impact Crushing
Work Index", 5th International Conference on Autogenous and Semiautogenous
Grinding Technology, Paper No. 75, pp.19.
Bond Impact Crushing Test – Wi(C)
Some example results:
A. Doll, R. Phillips, and D. Barratt, 2010. "Effect of Core Diameter on Bond Impact Crushing
Work Index", 5th International Conference on Autogenous and Semiautogenous
Grinding Technology, Paper No. 75, pp.19.
Bond Mill – to determine Wi(RM)
For a Wi(RM) test, the standard
closing sieve size is 1180μm.
Stage crush 1250 ml of feed
to pass 12.7 mm (0.5 in)
Perform series of batch
grinds in standard Bond
rod mill - 1' D x 2' L
(0.305 m x 0.610 m)
Wave liners
Mill speed = 40 rpm
Charge = 8 rods (33.38 kg)
Closing screen size should be
close to desired P80
Multiply desired P80 by √2
Bond Mill – to determine Wi(RM)
• Initial sample = 1250 ml stage-crushed to pass 12.7 cm (0.5 in)
• Grind initial sample for 100 revolutions, applying "tilting" cycle
Run level for 8 revs, then tilt up 5° for one rev, then down
at 5° for one rev, then return to level and repeat the cycle
• Screen on selected ‘closing’ screen to remove undersize. Add
back an equal weight of fresh feed to return to original weight.
• Return to the mill and grind for a predetermined number of
revolutions calculated to produce a 100% circulating load.
• Repeat at least 6 times until undersize produced per mill rev
reaches equilibrium. Average net mass per rev of last 3 cycles
to obtain rod mill grindability (Gbp) in g/rev.
• Determine P80 of final product.
Bond Mill – to determine Wi(BM)
For a Wi(BM) test, the standard
closing sieve size is 150μm.
Stage crush 700 ml of feed
to pass 3.35 mm (0.132 in)
Perform series of batch
grinds in standard Bond
ball mill - 1' D x 1' L
(0.305 m x 0.305 m)
Smooth liners / rounded corners
Mill speed = 70 rpm
Charge = 285 balls (20.125 kg)
Closing screen size should be
close to desired P80
Multiply desired P80 by √2
Bond Mill – to determine Wi(BM)
• Initial sample = 700 ml stage-crushed to pass 3.35 cm
• Grind initial sample for 100 revolutions, no "tilting" cycle used
• Screen on selected ‘closing’ screen to remove undersize. Add
back an equal weight of fresh feed to return to original weight.
• Return to the mill and grind for a predetermined number of
revolutions calculated to produce a 250% circulating load.
• Repeat at least 7 times until undersize produced per mill rev
reaches equilibrium. Average net mass per rev of last 3 cycles
to obtain ball mill grindability (Gbp) in g/rev.
• Determine P80 of final product.
Effect of Circulating Load on Wi(BM)
From S. Morrell, 2008. "A method for predicting the specific energy requirement of
comminution circuits and assessing their energy utilization
efficiency", Minerals Engineering, 21(3), 224-233.
Bond Mill – Wi(BM) or Wi(RM)
Procedure: use lab mill of set diameter with a set ball or
rod charge and run several cycles (5-7) of
grinding and screening to recycle coarse
material into next stage until steady state
(i.e., recycle weight becomes constant).
Formula:
where
Wi
P
F
Gbp
P1
=
=
=
=
=
work index (kWh/t);
80% passing size of the product;
80% passing size of the feed;
net grams of screen undersize per mill revolution;
closing screen size (mm)
Size Ranges for Different
Comminution Tests
Property
Soft
Bond Wi (kWh/t) 7 - 9
Medium
9 -14
Hard
Very Hard
14 -20 > 20
Table of Materials Reported by Fred Bond1
1
Material
Number Tested
S.G.
All Materials
Andesite
Barite
Basalt
Bauxite
Cement clinker
Cement (raw)
Coke
Copper ore
Diorite
Dolomite
Emery
Feldspar
Ferro-chrome
Ferro-manganese
1,211
6
7
3
4
14
19
7
204
4
5
4
8
9
5
2.84
4.50
2.91
2.20
3.15
2.67
1.31
3.02
2.82
2.74
3.48
2.59
6.66
6.32
adjusted from short tons to metric tonnes
Work Index
(kWh/t)
15.90
20.12
6.32
18.85
9.68
14.95
11.59
16.73
14.03
23.04
12.42
62.50
11.90
8.42
9.15
Table of Materials Reported by Fred Bond1
Material
Number Tested
S.G.
Ferro-silicon
Flint
Fluorspar
Gabbro
Glass
Glass
Gneiss
Gold ore
Granite
Graphite
Gravel
Gypsum rock
Iron ore – hematite
Hematite-specularite
13
5
5
4
4
4
3
197
36
6
15
4
56
3
4.41
2.65
3.01
2.83
2.58
2.58
2.71
2.81
2.66
1.75
2.66
2.69
3.55
3.28
1
adjusted from short tons to metric tonnes
Work Index
(kWh/t)
11.03
28.84
9.82
20.34
13.57
13.57
22.19
16.46
16.59
48.02
17.70
7.42
14.25
15.26
Table of Materials Reported by Fred Bond1
1
Material
Number Tested
S.G.
Hematite – Oolitic
Magnetite
Taconite
Lead ore
Lead-zinc ore
Limestone
Manganese ore
Magnesite
Molybdenum ore
Nickel ore
Oilshale
Phosphate rock
Potash ore
Pyrite ore
Pyrrhotite ore
6
58
55
8
12
72
12
9
6
8
9
17
8
6
3
3.52
3.88
3.54
3.45
3.54
2.65
3.53
3.06
2.70
3.28
1.84
2.74
2.40
4.06
4.04
adjusted from short tons to metric tonnes
Work Index
(kWh/t)
12.49
10.99
16.09
12.93
11.65
13.82
13.45
12.27
14.11
15.05
17.46
10.93
8.87
9.84
10.55
Table of Materials Reported by Fred Bond1
1
Material
Number Tested
S.G.
Quartzite
Quartz
Rutile ore
Shale
Silica sand
Silicon carbide
Slag
Slate
Sodium silicate
Spodumene ore
Syenite
Tin ore
Titanium ore
Trap rock
Zinc ore
8
13
4
9
5
3
12
2
3
3
3
8
14
17
12
2.68
2.65
2.80
2.63
2.67
2.75
2.83
2.57
2.10
2.79
2.73
3.95
4.01
2.87
3.64
adjusted from short tons to metric tonnes
Work Index
(kWh/t)
10.56
14.96
13.98
17.49
15.54
28.52
10.35
15.76
14.88
11.43
14.47
12.02
13.59
21.30
12.74
Histogram of Wi Values Reported by Fred Bond1
Average for 1055 tests = 14.85 kWh/t
F.C. Bond, 1953. "Work Indexes Tabulated", Trans. AIME, March, 194, 315-316.
F.C. Bond, 1952. "The Third Theory of Comminution", Trans. AIME, May, 193, 484-494.
Wi versus S.G.
Average Wi for 1055 tests = 14.85 kWh/t and 3.10 for S.G.
F.C. Bond, 1953. "Work Indexes Tabulated", Trans. AIME, March, 194, 315-316.
F.C. Bond, 1952. "The Third Theory of Comminution", Trans. AIME, May, 193, 484-494.
Correction Factors for Bond Wi
Basic Assumption for Bond Equation: Mill Size = 2.44m C.L. = 250%
1. Dry Grinding
EF1 = 1.3 for dry grinding in closed circuit ball mill
2. Wet Open Circuit
EF2 = 1.2 for wet open circuit factor for same product size
3. Large Diameter Mills
EF3 = (2.44/Dm)0.2
= 0.914
for Dm ≥ 3.81 m
for Dm < 3.81 m
Correction Factors for Bond Wi
4. Oversize Feed
Fo = Z ( 14.71/ [Wi
(RM)]0.5
where Fo = optimal feed size in mm
Z = 16 for rod mills and 4 for ball mills
If actual F80 size (in mm) is coarser, then
(adjusted to metric tonnes)
EF4 = 1 + 1.1(Wi(BM)– 6.35)(F80 - Fo)/(Rr Fo)
Wi (RM)
10
12
14
16
18
20
22
24
26
28
30
Fo (mm)
for a BM
4.85
4.43
4.10
3.83
3.62
3.43
3.27
3.13
3.00
2.90
2.80
where Rr = F80 / P80
5. Reduction Ratio (only apply when product size is less than 75 microns)
EF5 = (P80 + 10.3) / (1.145 P80) where P80 is in microns
Correction Factors for Bond Wi
6. High or Low Reduction Ratio for Rod Mills
where Rr - Rro is not between -2 and +2
EF6 = 1 + (Rr – Rro)2 / 159
where Rro = 8 + 5L/D
L = rod length (m)
D = inside mill diameter (m)
7. Low Reduction Ratio for Ball Mill
EF7 = 1 + 0.013/(Rr - 1.35) if Rr < 6.0
Correction Factors for Bond Wi
8. Rod Mills
Rod Mill only circuit
EF8 = 1.4 if feed is from open-circuit crushing
= 1.2 if feed is from closed-circuit crushing
Rod Mill/Ball Mill circuit
EF9 = 1.2 if feed is from open-circuit crushing
= 1.0 if feed is from closed-circuit crushing
9. Rubber Liners (due to energy absorption properties of rubber)
EF9 = 1.07
Other Energy Indices
MacPherson Autogeneous Mill Work Index Test
SMC Test
JK Rotary Breaker Test
JK Drop Weight Test
Bond Abrasion Index - Ai
Developed by Bond to predict wear rates of ball/rods and liners
Quantifies the abrasiveness of an ore
A 400g sample is stage-crushed & sized into the range -19+12.7 mm
A standard weighed test paddle and enclosure are used
Paddle is abraded by rotation with the sample for 15 min. at 632 rpm
Procedure is repeated 4 times and paddle is re-weighed
Loss in weight in grams is the Abrasion Index
Some representative Bond abrasion indices:
Limestone
Quartz
Magnetite
Quartzite
Taconite
0.026
0.180
0.250
0.690
0.700
Does not account for wear by corrosion in milling circuits
Comminution Energy Testing
• Mines today perform Bond Work Index Tests on multiple samples
• A map of the drill core data is produced to show contours of ore
with different Work Index Ranges
• Ball Mill, Rod Mill and Low Energy Crushing tests are done
• The mill will be designed based on Mine Production Schedule
to allow the mill to achieve desired liberation on the hardest ore
• Some consideration is now being given to using these maps
to do mine planning, so hard and soft ores can be blended to
provide a more consistent mill feed
Critical Speed Equation for Mills
Critical speed defines the velocity at which steel balls will
centrifuge in the mill rather than cascade
D
Nc
2
30
-0.5
c
3
24
4
21
8
15
where
12
12
Nc = critical speed (revolutions per minute)
D = mill effective inside diameter (m)
N =42.3(D
)
Typically , a mill is designed to achieve 75-80% of critical
speed. SAG and AG mills operate with variable speed. Ball
and rod mills have not in the past , but this is changing.
Grinding Mills
• Ball Mills
• Rod Mills - limited to 20' (6m) ft. by rod length (bending)
• Autogenous Mills - cascade mills for iron ore
• Pebble Mills - pioneered in Scandinavia, South Africa
• Semi-Autogenous Mills - pioneered in N.A.
variable speed drives
Grinding Mills
• Ball Mills
Grinding Mills
• Ball Mills – grate-discharge
Grinding Mills
• Ball Mills – rubber-lined
Grinding Mills
• Ball Mills – conical mill (Hardinge mill)
Grinding Mills
• Ball Mills
Grinding Mills
• Ball Mills – Mufulira Mine Grinding Aisle - 1969
Grinding Mills
• Rod Mills
Grinding Mills
• Semi-Autogenous Mills
Grinding Mills
• Semi-Autogenous Mills
End-plate Liners in an overflow SAG Mill
Grinding Mills
• Semi-Autogenous Mills
Elements in a Grate-Discharge SAG Mill
Grinding Mills
• Semi-Autogenous Mills
Grinding Mills
• SAG Mill – Ball Mill Circuit (Lac des Iles)
Grinding Mills
• Grinding Control Diagram
Secondary Crushing
• Hydroset Control
• Automatic change
in closed-side setting
(C.S.S.)
• Motor load can be
used to adjust feed
tonnage and/or C.S.S.
Grinding Mills
• Stirred Mills
Grinding Mills
• Horizontal Stirred Mill with Pin Stirrers
Grinding Mills
• Vertical Stirred Mill (ultra-fine grinding)
Grinding Mills
• Micronizer Jet Mill (ultra-fine grinding)
Grinding Circuits
• One Stage Ball Mill Circuit
Grinding Circuits
• Two Stage Ball Mill Circuit
Grinding Circuits
• Rod Mill / Ball Mill Circuit
Grinding Circuits
• SAG/AG – Crusher - Ball Mill Circuit (ABC)