Luis Marcelo Tavares

7/30/2019 Luis Marcelo Tavares

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TOWARDS HIGH-FIDELITYSIMULATION OF SAG MILLS USING A

Rodrigo M. de Carvalho and Lus Marcelo TavaresDepartment of Metallurgical and Materials Engineering

Universidade Federal do Rio de JaneiroRio de Janeiro, Brazil


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Outline

Introduction

Objective

Characterizing breakage DEM simulation of charge motion

Results

Future developments

Conclusions

Acknowledgements


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IntroductionCurrent methods used to design and optimize the operation of SAG/AG mills can

answer some relevant questions:

How much power with a mill draw?

What is the industrial mill performance (provided good pilot data is available)? ...

... however, their application may be risky to respond to other questions (Greenfield

projects, unusual ores, ...):

s go ng o wor or a par cu ar ore

How will the mill respond to blends of hard-soft?

Will critical size material be accumulated in the mill?

What is the optimum ball load?

How will the mill respond to changes / fluctuations in ore grindability?

How will grinding change with liner wear?

To respond all these questions, significantly improved modeling and characterizationapproaches should become available to industry


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Objective

Develop a new model framework that:overcomes limitations of current methods used in AG and

SAG mill design and optimization

decouples contributions of ore and grinding environment

describes each breaka e mechanism in AG and SAG mills

over a wide range of sizes and collision energies

describes mechanistically the effect of mill design and

operating variables


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Characterizing breakage

Use testing methods that allow describing a

single event involving an ore particle in a mill

as a function of:

Breakage mechanism

body breakage surface breakage

particle weakening

Stressing energyParticle size


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Particle breaks?(body)

Collision energy

YES NO

Particle fracture energyminimum energy required to break a particle


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Characterizing breakage Distribution of particle fracture energies

Single particle: 2-120 mm

20

40

60

80

100

Force(N) Particle primary

fractureRebreakage of

the fragments

2.4 mm Copper ore

Impact Load CellTavares & King (1998), Int. J. Miner. Process. 54

10 100 1000 10000Mass-specific fracture energy - E

m(J/kg)

99.9

99

90

70

50

30

10

1

0.1

Cumulativedistr

ibution(%)

2.83-2.36 mm

5.60-4.75 mm

11.2-9.50 mm

22.4-19.5 mm

45.0-37.5 mm

63.0-53.0 mm

0 200 400 600 800 1000 1200 1400

Time (ms)

0


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Characterizing breakage Distribution of particle fracture energies

Single particle: 2-120 mm

1

10

energyEm50

(kWh/t)

Particle bed: 0.2-2 mm

... which approximately matches the size range of

interest in AG/SAG mills

Barrios, Carvalho & Tavares (2011), Trans. Instn. Min. Metall. 120

0.1 1 10 100Particle size (mm)

0.001

0.01

0.1

Me

dianmass-spec

ificfrac

ture

Model

Single particle breakage

Bed breakage test


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Collision energy

YES NO

Energy-specific

surface breakage

function

WeakeningSurface breakage


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Weakening and surface breakage

80

100

en

(%) 80

100

ution

(%)

Copper ore: 125-75 mm

0 10 20 30 40

Number of drops

0

20

40

Cumu

lativeb

ro

0.005 kWh/t

0.011 kWh/t

0.022 kWh/t

0.01 0.1 1 10

Particle weight loss (%/impact)

0

20

40

Cumu

lative

dis

trib

39.2 J/kg

19.6 J/kg

Both influenced by stressing energy! Low energynormal collision

Continuum damage model

Tavares & King (2002), Powder Technol.


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Collision energy

YES NO

Energy-specific

surface breakage

function

Energy-specific bodybreakage function

WeakeningSurface breakage


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Body breakage distribution

20

40

60

80

100

tn(

%)

t1.2

t1.5t2

t4

t25t50

t75

10

100

1 10 100Stressing impact en ergy / Specific median fracture energy - Em

/ Em50

63.0-53.0 mm45.0-37.5 mm31.5-26.5 mm22.4-19.2 mm16.0-13.2 mm5.60-4.75 mm2.83-2.36 mm

1

10

100

t10

(%)

0 10 20 30 40 50 60

t10 (%)

0

0.01 0.1 1 10 100Particle size (mm)

0.1

1

Passing

(%)

22.4-19.2 mm (2.50 kWh/t)

22.4-19.2 mm (1.00 kWh/t)

22.4-19.2 mm (0.25 kWh/t)

16.0-13.2 mm (2.52 kWh/t)

16.0-13.2 mm (1.00 kWh/t)

5.60-4.75 mm (2.50 kWh/t)

5.60-4.75 mm (2.50 kWh/t)

2.83-2.36 mm (5.00 kWh/t)

2.83-2.36 mm (2.50 kWh/t)

Tavares (2009), Powder Technol.


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Model predictions: single particle breakage

100

)

63-53 mm

100

)

0.600-0.425 mm

Fine Coarse

0.1 1 10 100

Particle size (mm)

1

10

Passing

(

0.10 kWh/t

0.25 kWh/t

0.80 kWh/t

0.01 0.1 1

Particle size (mm)

1

10

Passing

(

1.0 kWh/t

2.5 kWh/t

7.0 kWh/t


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utions

Collision energy is sufficient to break

all particles Collision energy is insufficient to

break any particles

For particles contained in a size class:

Body breakage

Collision energies

Fracture energies

100%

0%

100%

Energy

Cumu

lativedistr

i

Collision energy is sufficient to

break some of the particles

Surface breakage

Damage

Bodybreakage

ur ace rea age

Damage

Distribution of collision energies

0%

Energy

100%

0%

Energy

Energy

100%

0%


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DEM simulation of charge motion

Comercial software (EDEM) used

Calibration of contact parameters is requiredfor realistic simulations


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DEM simulation of charge motion6 (1.8 m) 38 (11.6 m)

Balls and particles coarser than grate size (DEM particles)

Particles finer than grate size (sub DEM particles)

Barrios, Carvalho & Carvalho (2011), Minerals Eng.


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DEM simulation of charge motion

Contact class Elements in contact Diameter of particles in collision

k Dp (mm) Dq (mm)

1 Ball-ball 160 160

4 Ball-particle 160 14010 Ball-liner 160

28 Particle-particle 140 140

34 Particle-liner 140

53 Particle-particle 14 14

-

Extracting distributions of collision energies (6 mill)

-


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Mechanistic model framework

0.01 0.1 1 10 100

Particle size (mm)

0.00

0.01

0.02

Dischargerate(s-1)

Power

Model can describe breakage of multi-component (hard-soft, heavy-light, ... ) blends

Model is dynamic in nature


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Results

Literature: size-dependent breakage rates in

AG/SAG mills

Morrell et al. (1996), Int. J. Miner. Process. 44-45


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Results

Predictions: Apparent breakage rates of a

copper ore in a 6 SAG mill

100

101

te(1/s)

1 10 100

Particle size (mm)

10-4

10-3

10-2

10-1

Relativebreakag

er

Total (body+surface)

Surface breakage

Body breakage


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Future developments

Modeling

Validate in multiple scales (lab, pilot & industrial)

Incorporate SPH/CFD to describe discharge

Characterization

Standardize surface breakage testing

Simplify body breakage characterization


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Conclusions

A mechanistic model framework has been

proposed for AG/SAG mills

Apparent breakage rates for grinding in a 6

mill have been estimated

After maturity, method will be used as a lowercost alternative or complement to pilot scale

studies


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Acknowledgements


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Contact

Prof. Lus Marcelo Tavares

Gracias

Obrigado

Thank you

.

Luis Marcelo Tavares

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