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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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Characterizing breakage
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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Characterizing breakage
Particle breaks?(body)
Collision energy
YES NO
Energy-specific
surface breakage
function
WeakeningSurface breakage
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Characterizing breakage
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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Characterizing breakage
Particle breaks?(body)
Collision energy
YES NO
Energy-specific
surface breakage
function
Energy-specific bodybreakage function
WeakeningSurface breakage
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Characterizing breakage
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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Characterizing breakage
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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Characterizing breakage
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
.
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