Energy Use in Comminution Lecture 7 MINE 292. COMMINUTION MECHANICAL CHEMICAL External Special Chemical forces forces forces - smashing - thermal shock

Energy Use in ComminutionEnergy Use in Comminution

Lecture 7Lecture 7

MINE 292MINE 292

COMMINUTIONCOMMINUTION

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

ComminutionComminution

• 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 SizesComminution and Sizes

Effective Range of 80% passing sizes by Process

Process F80 P80

1) Explosive shattering: infinite 1 m2) Primary crushing: 1 m 100 mm3) Secondary crushing: 100 mm 10 mm4) Coarse grinding: 10 mm 1 mm5) Fine grinding: 1 mm 100 µm6) Very fine grinding: 100 µm 10 µm7) Superfine grinding: 10 µm 1 µm

The 80% passing size is used because it can be measured.

Comminution - BlastingComminution - 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 CrushingPrimary Crushing

• Jaw crusher < 1,000 tph• Underground applications• Gyratory crusher > 1,000 tph• Open-pit and In-pit

Types of Jaw Crushers 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 CrusherSingle Toggle Blake Jaw Crusher

Primary CrushingPrimary 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 CrushingSecondary 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 FeederSecondary Crusher Feeder

Secondary Crushing PlantsSecondary Crushing Plants

• Fully-configured Plant


• No Internal Surge Bins

Scissor Conveyors Scissor Conveyors • Palabora Mining – South Africa


• No Screen Bin


• Open Circuit – gravity-flow

Impact CrushersImpact 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


• Barmac Crusher• Invented in New Zealand• Impact velocity = 60 -90 mps• High production of

fines by attrition• Used in quarries &

cement industry


• 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 CrusherSecondary Crushing - Rolls Crusher

Secondary Crushing - Rolls CrusherSecondary 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 ComminutionEnergy in ComminutionCrushing 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

nDKdDdE

Energy in ComminutionEnergy in ComminutionVon 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

2cr DfK

dDdE

)D1

D1

(fKEfp

cr

Energy in ComminutionEnergy in ComminutionKick's Law (1883)

• Energy is proportional to percent reduction in size• So change in comminution energy is given by:


where Kk = Kick's Constant and fc = crushing strength of the material

1ck DfK

dDdE

p

feck DD

logfKE

Energy in ComminutionEnergy in ComminutionBond'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:


where Kb = Bond's Constant and fc = crushing strength of the material

5.1cb DfK

dDdE

)D1

D1

(fKEfp

cb

Energy in ComminutionEnergy in ComminutionWhere 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

KickBondvon

Rittinger

Size ReductionSize 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 TensionBreakage 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 TheoryGriffith’s Crack Theory

Griffith’s Crack TheoryGriffith’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 TheoryGriffith’s 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 Young’s Modulus

= strain

s = specific surface energy

a = half-length of the ellipse

s

222

a42A

'Ea

'E2A

U

Young's ModulusYoung'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 ModulusYoung's Modulus

Low-carbon steel

Hooke's law is valid from the origin to the yield point (2).

1. Ultimate strength2. Yield strength3. Rupture4. Strain hardening region5. Necking region

A: Engineering stress (F/A0)B: True stress (F/A)

Griffith’s TheoryGriffith’s 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

0'Ea2

a42

s

'Ea

G2

Compression LoadingCompression 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 PInduced stresses-compressive load P

P

P

P

a2

a1

2a3

2a4

a5

1

2 3

45

KI =Yi(ai)1/2

At fracture:

KIC =Yic(ai)1/2

where

KIC =(EGIC)1/2

GIC = Fracture ToughnessKI = 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

P

P

D

(a)

P

kP kPP

kP kP

2a

(b)

2a

P

P

D

P

kP kPP

kP kP

Schematic of particle containing a crack (flaw) of Schematic of particle containing a crack (flaw) of radius 'radius 'a'a' subjected to compressive force ' subjected to compressive force 'P'P'

i = P( kcos - sin)

KI=Y P (kcos - sin) a1/2

At fracture KI=KIC. In theory there is a limiting average fine particle size:

Dlimit ~ π(KIC/kP)2 (where = 0)

Impact EfficiencyImpact Efficiency

Impact EfficiencyImpact 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 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

Change in mode of breakageChange in mode of breakage

• High-velocity breakage of magnetite

Comminution TestingComminution 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 TestDrop Weight Test2 to 3 inch pieces of rock are subjected to different drop weight energy levels to establish Wi(C)

Split Hopkinson Bar Test ApparatusSplit Hopkinson Bar Test Apparatus

Split Hopkinson Bar Test ApparatusSplit 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 pendulumPendulum Test – twin pendulum

Rebound Pendulum

Impact Pendulum

Rock Particle

Bond Impact Crushing Test – Bond Impact Crushing Test – Wi(C)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 – Bond Impact Crushing Test – Wi(C)Wi(C)Values measured are: 1. E = Energy applied at breakage (J) 2. w = Width of specimen (mm)3. 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 – Bond Impact Crushing Test – Wi(C)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 Bond Mill – to determine Wi(RM)Wi(RM)For a Wi(RM) test, the standard Closing screen size should beclosing sieve size is 1180μm. close to desired P80 Multiply desired P80 by √2Stage crush 1250 ml of feedto 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)

Bond Mill – to determine Bond Mill – to determine Wi(RM)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 Bond Mill – to determine Wi(BM)Wi(BM)For a Wi(BM) test, the standard Closing screen size should beclosing sieve size is 150μm. close to desired P80 Multiply desired P80 by √2Stage crush 700 ml of feedto 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)

Bond Mill – to determine Bond Mill – to determine Wi(BM)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 Effect of Circulating Load on Wi(BM)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 – Bond Mill – Wi(BM) or Wi(RM)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)

Size Ranges for Different Size Ranges for Different Comminution TestsComminution Tests

Property Soft Medium Hard Very HardBond Wi (kWh/t) 7 - 9 9 -14 14 -20 > 20

Material Number Tested S.G.Work Index

(kWh/t)All Materials 1,211 - 15.90

Andesite 6 2.84 20.12Barite 7 4.50 6.32Basalt 3 2.91 18.85Bauxite 4 2.20 9.68

Cement clinker 14 3.15 14.95Cement (raw) 19 2.67 11.59

Coke 7 1.31 16.73Copper ore 204 3.02 14.03

Diorite 4 2.82 23.04Dolomite 5 2.74 12.42Emery 4 3.48 62.50

Feldspar 8 2.59 11.90Ferro-chrome 9 6.66 8.42

Ferro-manganese 5 6.32 9.15

Table of Materials Reported by Fred Bond1

1 adjusted from short tons to metric tonnes


(kWh/t)Ferro-silicon 13 4.41 11.03

Flint 5 2.65 28.84Fluorspar 5 3.01 9.82Gabbro 4 2.83 20.34Glass 4 2.58 13.57Glass 4 2.58 13.57

Gneiss 3 2.71 22.19Gold ore 197 2.81 16.46Granite 36 2.66 16.59Graphite 6 1.75 48.02Gravel 15 2.66 17.70

Gypsum rock 4 2.69 7.42Iron ore – hematite 56 3.55 14.25

Hematite-specularite 3 3.28 15.26




(kWh/t)Hematite – Oolitic 6 3.52 12.49

Magnetite 58 3.88 10.99Taconite 55 3.54 16.09Lead ore 8 3.45 12.93

Lead-zinc ore 12 3.54 11.65Limestone 72 2.65 13.82

Manganese ore 12 3.53 13.45Magnesite 9 3.06 12.27

Molybdenum ore 6 2.70 14.11Nickel ore 8 3.28 15.05Oilshale 9 1.84 17.46

Phosphate rock 17 2.74 10.93Potash ore 8 2.40 8.87Pyrite ore 6 4.06 9.84

Pyrrhotite ore 3 4.04 10.55




(kWh/t)Quartzite 8 2.68 10.56Quartz 13 2.65 14.96

Rutile ore 4 2.80 13.98Shale 9 2.63 17.49

Silica sand 5 2.67 15.54Silicon carbide 3 2.75 28.52

Slag 12 2.83 10.35Slate 2 2.57 15.76

Sodium silicate 3 2.10 14.88Spodumene ore 3 2.79 11.43

Syenite 3 2.73 14.47Tin ore 8 3.95 12.02

Titanium ore 14 4.01 13.59Trap rock 17 2.87 21.30Zinc ore 12 3.64 12.74



Histogram of Wi Values Reported by Fred Bond1

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.

Average for 1055 tests = 14.85 kWh/t

Wi versus 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.

Average Wi for 1055 tests = 14.85 kWh/t and 3.10 for S.G.

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 < 3.81 m

Correction Factors for Bond WCorrection Factors for Bond W ii

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

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


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


MacPherson Autogeneous Mill Work Index Test

SMC Test

JK Rotary Breaker Test

JK Drop Weight Test

Other Energy Indices Other Energy Indices

Developed by Bond to predict wear rates of ball/rods and linersQuantifies 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 rpmProcedure is repeated 4 times and paddle is re-weighedLoss in weight in grams is the Abrasion Index

Some representative Bond abrasion indices:Limestone 0.026Quartz 0.180 Magnetite 0.250Quartzite 0.690Taconite 0.700

Does not account for wear by corrosion in milling circuits

Bond Abrasion Index - Bond Abrasion Index - AAii

• 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

Comminution Energy TestingComminution Energy Testing

Nc =42.3(D-0.5)

Critical Speed Equation for MillsCritical Speed Equation for Mills

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.

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 1512 12

Grinding MillsGrinding 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


• Ball Mills


• Ball Mills – grate-discharge


• Ball Mills – rubber-lined


• Ball Mills – conical mill (Hardinge mill)


• Ball Mills


• Ball Mills – Mufulira Mine Grinding Aisle - 1969


• Rod Mills





End-plate Liners in an overflow SAG Mill



Elements in a Grate-Discharge SAG Mill




• SAG Mill – Ball Mill Circuit (Lac des Iles)


• Grinding Control Diagram

Secondary CrushingSecondary 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.


• Stirred Mills


• Horizontal Stirred Mill with Pin Stirrers


• Vertical Stirred Mill (ultra-fine grinding)


• Micronizer Jet Mill (ultra-fine grinding)

Grinding CircuitsGrinding Circuits

• One Stage Ball Mill Circuit


• Two Stage Ball Mill Circuit


• Rod Mill / Ball Mill Circuit


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

Documents

Energy Use in Comminution Lecture 7 MINE 292. COMMINUTION MECHANICAL CHEMICAL External Special Chemical forces forces forces - smashing - thermal shock