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**Energy Use in Comminution**

Lecture 7 MINE 292

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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

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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

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**Comminution and Sizes Effective Range of 80% passing sizes by Process**

Process F P80 1) Explosive shattering: infinite 1 m 2) Primary crushing: 1 m mm 3) Secondary crushing: 100 mm 10 mm 4) Coarse grinding: mm mm 5) Fine grinding: mm 100 µm 6) Very fine grinding: 100 µm 10 µm 7) Superfine grinding: µm µm The 80% passing size is used because it can be measured.

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**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

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**Primary Crushing Jaw crusher < 1,000 tph Underground applications**

Gyratory crusher > 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

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**Secondary Crushing Symons Cone Crushers Standard and Shorthead**

Secondaries Tertiaries CSS (mm) Can process up to 1,000 tph Mech. Availability = 70-75%

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**Secondary Crushing Plants**

Fully-configured Plant

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**Secondary Crushing Plants**

No Internal Surge Bins

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**Secondary Crushing Plants**

No Screen Bin

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**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

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**Impact Crushers Barmac Crusher Invented in New Zealand**

Impact velocity = mps High production of fines by attrition Used in quarries & cement industry

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**Impact Crushers Barmac Crusher Invented in New Zealand**

Impact velocity = mps High production of fines by attrition Used in quarries & cement industry

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**Secondary Crushing - Rolls Crusher**

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**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)

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**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 % 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

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**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

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**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

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**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

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**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

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**Size Reduction Different fracture modes Leads to different size**

distributions Bimodal distribution not often seen in a crushed or ground product

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**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)

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**Griffith’s Crack Theory**

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**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)

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**Griffith’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

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**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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Griffith’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

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**Compression Loading Fracture under point-contact loading**

D. Tromans and J.A. Meech, "Fracture Toughness and Surface Energies of Covalent Materials: Theoretical Estimates and Application to Comminution", Minerals Engineering 17(1), 1–15.

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**Induced stresses-compressive load P**

KI =Ysi(ai)1/2 At fracture: KIC =Ysic(ai)1/2 where KIC =(EGIC)1/2 GIC = Fracture Toughness KI = Stress intensity (at fracture KI = KIC, si = sic) si = Tensile stress, ai = crack length Y = Geometric factor (2 π -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' P D (a) q s k 2 a (b) si = sP( kcosq - sinq ) KI=Y sP (kcosq - sinq ) a1/2 At fracture KI=KIC. In theory there is a limiting average fine particle size: Dlimit ~ π(KIC/ksP) (where q = 0)

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Impact Efficiency

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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 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

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**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**

Rebound Pendulum Impact Pendulum Rock Particle

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**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

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**Bond Impact Crushing Test – Wi(C)**

Values measured are: 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, "Crushing Tests by Pressure and Impact", Transactions of AIME, 169, A. Doll, R. Phillips, and D. Barratt, "Effect of Core Diameter on Bond Impact Crushing Work Index", 5th International Conference on Autogenous and Semiautogenous Grinding Technology, Paper No. 75, pp.19.

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**Bond Impact Crushing Test – Wi(C)**

Some example results: A. Doll, R. Phillips, and D. Barratt, "Effect of Core Diameter on Bond Impact Crushing Work Index", 5th International Conference on Autogenous and Semiautogenous Grinding Technology, Paper No. 75, pp.19.

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**Bond Mill – to determine Wi(RM)**

For a Wi(RM) test, the standard Closing screen size should be closing sieve size is 1180μm close to desired P80 Multiply desired P80 by √2 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 m) Wave liners Mill speed = 40 rpm Charge = 8 rods (33.38 kg)

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**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)**

For a Wi(BM) test, the standard Closing screen size should be closing sieve size is 150μm close to desired P80 Multiply desired P80 by √2 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 m) Smooth liners / rounded corners Mill speed = 70 rpm Charge = 285 balls ( kg)

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**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.

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**Effect of Circulating Load on Wi(BM)**

From S. Morrell, "A method for predicting the specific energy requirement of comminution circuits and assessing their energy utilization efficiency", Minerals Engineering, 21(3),

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**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) > 20

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**Table of Materials Reported by Fred Bond1**

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 1.31 16.73 Copper ore 204 3.02 14.03 Diorite 2.82 23.04 Dolomite 5 2.74 12.42 Emery 3.48 62.50 Feldspar 8 2.59 11.90 Ferro-chrome 9 6.66 8.42 Ferro-manganese 9.15 1 adjusted from short tons to metric tonnes

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**Hematite-specularite**

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 3.01 9.82 Gabbro 4 2.83 20.34 Glass 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 17.70 Gypsum rock 2.69 7.42 Iron ore – hematite 56 3.55 14.25 Hematite-specularite 3.28 15.26 1 adjusted from short tons to metric tonnes

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**Table of Materials Reported by Fred Bond1**

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 11.65 Limestone 72 2.65 13.82 Manganese ore 3.53 13.45 Magnesite 9 3.06 12.27 Molybdenum ore 2.70 14.11 Nickel ore 3.28 15.05 Oilshale 1.84 17.46 Phosphate rock 17 2.74 10.93 Potash ore 2.40 8.87 Pyrite ore 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**

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 2.10 14.88 Spodumene ore 2.79 11.43 Syenite 2.73 14.47 Tin ore 3.95 12.02 Titanium ore 14 4.01 13.59 Trap rock 17 2.87 21.30 Zinc ore 3.64 12.74 1 adjusted from short tons to metric tonnes

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**Histogram of Wi Values Reported by Fred Bond1**

Average for 1055 tests = kWh/t F.C. Bond, "Work Indexes Tabulated", Trans. AIME, March, 194, F.C. Bond, "The Third Theory of Comminution", Trans. AIME, May, 193,

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Wi versus S.G. Average Wi for 1055 tests = kWh/t and 3.10 for S.G. F.C. Bond, "Work Indexes Tabulated", Trans. AIME, March, 194, F.C. Bond, "The Third Theory of Comminution", Trans. AIME, May, 193,

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**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 = for Dm < 3.81 m

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**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 = (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 = (P ) / (1.145 P80) where P80 is in microns Wi (RM) Fo (mm) for a BM

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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 = /(Rr ) if Rr < 6.0

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**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

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**Other Energy Indices MacPherson Autogeneous Mill Work Index Test**

SMC Test JK Rotary Breaker Test JK Drop Weight Test

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**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 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 Magnetite 0.250 Quartzite 0.690 Taconite Does not account for wear by corrosion in milling circuits

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**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

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**Nc =42.3(D-0.5) 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

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Grinding Mills Ball Mills

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Grinding Mills Ball Mills – grate-discharge

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Grinding Mills Ball Mills – rubber-lined

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Grinding Mills Ball Mills – conical mill (Hardinge mill)

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Grinding Mills Ball Mills

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Grinding Mills Ball Mills – Mufulira Mine Grinding Aisle

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Grinding Mills Rod Mills

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Grinding Mills Semi-Autogenous Mills

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**Grinding Mills Semi-Autogenous Mills**

End-plate Liners in an overflow SAG Mill

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**Grinding Mills Semi-Autogenous Mills**

Elements in a Grate-Discharge SAG Mill

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Grinding Mills Semi-Autogenous Mills

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Grinding Mills SAG Mill – Ball Mill Circuit (Lac des Iles)

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Grinding Mills Grinding Control Diagram

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**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.

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Grinding Mills Stirred Mills

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Grinding Mills Horizontal Stirred Mill with Pin Stirrers

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Grinding Mills Vertical Stirred Mill (ultra-fine grinding)

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Grinding Mills Micronizer Jet Mill (ultra-fine grinding)

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Grinding Circuits One Stage Ball Mill Circuit

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Grinding Circuits Two Stage Ball Mill Circuit

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Grinding Circuits Rod Mill / Ball Mill Circuit

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

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