Energy Use in Comminution

1
Energy Use in Comminution

• Lecture 7
• MINE 292

2
COMMINUTION MECHANICAL
CHEMICAL External Special
Chemical forces
forces forces - smashing
- thermal shock - digestion
- blasting (chemical) - microwaves -
dissolution - breaking -
pressure changes - combustion -
attrition - photon bombardment
- bioleaching - abrasion -
splitting or cutting - crushing - grinding
3
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

4
Comminution and Sizes
Effective Range of 80 passing sizes by Process
Process F80 P80 1) Explosive
shattering infinite 1 m 2) Primary
crushing 1 m 100 mm 3) Secondary
crushing 100 mm 10 mm 4) Coarse grinding
10 mm 1 mm 5) Fine grinding 1 mm 100
µm 6) Very fine grinding 100 µm 10 µm 7)
Superfine grinding 10 µm 1 µm The 80
passing size is used because it can be measured.
5
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

6
Primary Crushing

• Jaw crusher lt 1,000 tph
• Underground applications
• Gyratory crusher gt 1,000 tph
• Open-pit and In-pit

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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

8
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

9
Secondary Crushing Plants

• Fully-configured Plant

10
Secondary Crushing Plants

• No Internal Surge Bins

11
Secondary Crushing Plants

• No Screen Bin

12
Secondary Crushing Plants

• Open Circuit gravity-flow

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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

14
Impact Crushers

• Barmac Crusher
• Invented in New Zealand
• Impact velocity 60 -90 mps
• High production of
• fines by attrition
• Used in quarries
• cement industry

15
Impact Crushers

• Barmac Crusher
• Invented in New Zealand
• Impact velocity 60-90 mps
• High production of
• fines by attrition
• Used in quarries
• cement industry

16
Secondary Crushing - Rolls Crusher
17
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)

18
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 differential energy required,
• dD change in a particle dimension,
• D magnitude of a length dimension,
• K energy use/weight of material, and
• n exponent

19
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
• which on integration becomes
• where Kr Rittinger's Constant and
• fc crushing strength of the material

20
Energy in Comminution

• Kick's Law (1883)
• Energy is proportional to percent reduction in
  size
• So change in comminution energy is given by
• which on integration becomes
• where Kk Kick's Constant and
• fc crushing strength of the material

21
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
• which on integration becomes
• where Kb Bond's Constant and
• fc crushing strength of the material

22
Energy in Comminution

• Where do these Laws apply?
• Hukki put together the diagram below (modified
  on right)
• Kick applies to coarse sizes (gt 10 mm)
• Bond applies down to 100 µm
• Rittinger applies to sizes lt 100 µm

23
Size Reduction

• Different fracture modes
• Leads to different size
• distributions
• Bimodal distribution not
• often seen in a crushed
• or ground product

24
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)

25
Griffiths Crack Theory
26
Griffiths 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)

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Griffiths Crack Theory

• Based on force (or stress) needed to propagate an
  elliptical plate-shaped or penny-shaped crack
• where
• A area of the elliptical plate
• E' effective Youngs Modulus
• ? strain
• ?s specific surface energy
• a half-length of the ellipse

28
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

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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)
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Griffiths Theory

• Differentiating with respect to 'a' gives
• Rearranging derives the fracture stress to
  initiate a crack as well as the strain energy
  release rate, G
• where
• G energy/unit area to extend the crack

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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), 115.
32
Induced stresses-compressive load P
KI Stress intensity (at fracture KI KIC, si
sic) si Tensile stress, ai crack length Y
Geometric factor (2 p -½) E Young's modulus,
GIC critical energy release rate/m2
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Schematic of particle containing a crack (flaw)
of radius 'a' subjected to compressive force 'P'
si sP( kcosq - sinq ) KIY sP (kcosq -
sinq ) a1/2 At fracture KIKIC. In theory there
is a limiting average fine particle size Dlimit
p(KIC/ksP)2 (where q 0)
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Impact Efficiency
35
Impact Efficiency

• KIC, P, and flaw orientation (?) 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 inter-particle 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

36
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

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Drop Weight Test
2 to 3 inch pieces of rock are subjected to
different drop weight energy levels to establish
Wi(C)
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Split Hopkinson Bar Test Apparatus
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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.

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Pendulum Test twin pendulum
41
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
42
Bond Impact Crushing Test Wi(C)

• Values measured are
• E Energy applied at breakage (J)
• w Width of specimen (mm)
• ? Specific gravity
• Wi(C) _59.0E_
• w?
• 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.
43
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.
44
Bond Mill to determine Wi(RM)
45
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.

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Bond Mill to determine Wi(BM)
47
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.

48
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.
49
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 work index (kWh/t) P 80
passing size of the product F 80 passing
size of the feed Gbp net grams of screen
undersize per mill revolution P1 closing
screen size (mm)
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Size Ranges for Different Comminution Tests
Property Soft Medium Hard Very Hard Bond Wi
(kWh/t) 7 - 9 9 -14 14 -20 gt 20
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Table of Materials Reported by Fred Bond1
Material Number Tested S.G. Work Index (kWh/t)
All Materials 1,211 - 15.90
Andesite 6 2.84 20.12
Barite 7 4.50 6.32
Basalt 3 2.91 18.85
Bauxite 4 2.20 9.68
Cement clinker 14 3.15 14.95
Cement (raw) 19 2.67 11.59
Coke 7 1.31 16.73
Copper ore 204 3.02 14.03
Diorite 4 2.82 23.04
Dolomite 5 2.74 12.42
Emery 4 3.48 62.50
Feldspar 8 2.59 11.90
Ferro-chrome 9 6.66 8.42
Ferro-manganese 5 6.32 9.15
1 adjusted from short tons to metric tonnes
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Table of Materials Reported by Fred Bond1
Material Number Tested S.G. Work Index (kWh/t)
Ferro-silicon 13 4.41 11.03
Flint 5 2.65 28.84
Fluorspar 5 3.01 9.82
Gabbro 4 2.83 20.34
Glass 4 2.58 13.57
Glass 4 2.58 13.57
Gneiss 3 2.71 22.19
Gold ore 197 2.81 16.46
Granite 36 2.66 16.59
Graphite 6 1.75 48.02
Gravel 15 2.66 17.70
Gypsum rock 4 2.69 7.42
Iron ore hematite 56 3.55 14.25
Hematite-specularite 3 3.28 15.26
1 adjusted from short tons to metric tonnes
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Table of Materials Reported by Fred Bond1
Material Number Tested S.G. Work Index (kWh/t)
Hematite Oolitic 6 3.52 12.49
Magnetite 58 3.88 10.99
Taconite 55 3.54 16.09
Lead ore 8 3.45 12.93
Lead-zinc ore 12 3.54 11.65
Limestone 72 2.65 13.82
Manganese ore 12 3.53 13.45
Magnesite 9 3.06 12.27
Molybdenum ore 6 2.70 14.11
Nickel ore 8 3.28 15.05
Oilshale 9 1.84 17.46
Phosphate rock 17 2.74 10.93
Potash ore 8 2.40 8.87
Pyrite ore 6 4.06 9.84
Pyrrhotite ore 3 4.04 10.55
1 adjusted from short tons to metric tonnes
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Table of Materials Reported by Fred Bond1
Material Number Tested S.G. Work Index (kWh/t)
Quartzite 8 2.68 10.56
Quartz 13 2.65 14.96
Rutile ore 4 2.80 13.98
Shale 9 2.63 17.49
Silica sand 5 2.67 15.54
Silicon carbide 3 2.75 28.52
Slag 12 2.83 10.35
Slate 2 2.57 15.76
Sodium silicate 3 2.10 14.88
Spodumene ore 3 2.79 11.43
Syenite 3 2.73 14.47
Tin ore 8 3.95 12.02
Titanium ore 14 4.01 13.59
Trap rock 17 2.87 21.30
Zinc ore 12 3.64 12.74
1 adjusted from short tons to metric tonnes
55
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.
56
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.
57
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 for Dm 3.81 m
0.914 for Dm lt 3.81 m
58
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)
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
Wi (RM) Fo (mm) for a BM
10 4.85 12 4.43 14
4.10 16 3.83 18 3.62 20
3.43 22 3.27 24 3.13
26 3.00 28 2.90 30 2.80
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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 lt 6.0
60
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
61
Other Energy Indices
MacPherson Autogeneous Mill Work Index Test SMC
Test JK Rotary Breaker Test JK Drop Weight Test
62
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 -1912.7 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 0.026 Quartz 0.
180 Magnetite 0.250 Quartzite 0.690 Taco
nite 0.700 Does not account for wear by
corrosion in milling circuits
63
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

64
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 3 24 4 21 8 15 12 12
Nc 42.3(D-0.5)
where Nc critical speed (revolutions per
minute) D mill effective inside diameter
(m) 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.
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Grinding Mills

• Ball Mills
• Rod Mills
• Autogenous Mills
• Pebble Mills
• Semi-Autogenous Mills

- limited to 20' (6m) ft. by rod length (bending)

• cascade mills for iron ore

- pioneered in Scandinavia, South Africa

• pioneered in N.A.
• variable speed drives

66
Grinding Mills

• Ball Mills

67
Grinding Mills

• Ball Mills grate-discharge

68
Grinding Mills

• Ball Mills rubber-lined

69
Grinding Mills

• Ball Mills conical mill (Hardinge mill)

70
Grinding Mills

• Ball Mills

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Grinding Mills

• Ball Mills Mufulira Mine Grinding Aisle - 1969

72
Grinding Mills

• Rod Mills

73
Grinding Mills

• Semi-Autogenous Mills

74
Grinding Mills

• Semi-Autogenous Mills
• End-plate Liners in an overflow SAG Mill

75
Grinding Mills

• Semi-Autogenous Mills
• Elements in a Grate-Discharge SAG Mill

76
Grinding Mills

• Semi-Autogenous Mills

77
Grinding Mills

• SAG Mill Ball Mill Circuit (Lac des Iles)

78
Grinding Mills

• Grinding Control Diagram

79
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.

80
Grinding Mills

• Stirred Mills

81
Grinding Mills

• Horizontal Stirred Mill with Pin Stirrers

82
Grinding Mills

• Vertical Stirred Mill (ultra-fine grinding)

83
Grinding Mills

• Micronizer Jet Mill (ultra-fine grinding)

84
Grinding Circuits

• One Stage Ball Mill Circuit

85
Grinding Circuits

• Two Stage Ball Mill Circuit

86
Grinding Circuits

• Rod Mill / Ball Mill Circuit

87
Grinding Circuits

• SAG/AG Crusher - Ball Mill Circuit (ABC)