TOWARDS HIGH-FIDELITY
SIMULATION OF SAG MILLS USING A
MECHANISTIC MODEL
Rodrigo M. de Carvalho and Luís Marcelo Tavares
Department of Metallurgical and Materials Engineering
Universidade Federal do Rio de Janeiro
Rio de Janeiro, Brazil
Outline
•
•
•
•
•
•
•
•
•
Introduction
Objective
Characterizing breakage
DEM simulation of charge motion
Mechanistic model framework
Results
Future developments
Conclusions
Acknowledgements
Introduction
Current 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, ...):
– Is AG going to work for a particular 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?
To respond all these questions, significantly improved modeling and characterization
– How will grinding change with liner wear?
approaches should become available to industry
•
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 breakage 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
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 energy
– Particle size
Characterizing breakage
Collision energy
YES
Particle breaks?
(body)
NO
• Particle fracture energy
– minimum energy required to break a particle
Characterizing breakage
• Distribution of particle fracture energies
100
Single particle: 2-120 mm
2.4 mm Copper ore
Force (N)
80
Particle primary
60
Rebreakage of
fracture
the fragments
40
20
0
0
200
400
600
800
1000
1200
1400
Time (ms)
99.9
Impact Load Cell
Tavares & King (1998), Int. J. Miner. Process. 54
Cumulative distribution (%)
99
90
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
70
50
30
10
1
0.1
10
100
1000
Mass-specific fracture energy - Em (J/kg)
10000
Characterizing breakage
• Distribution of particle fracture energies
Particle bed: 0.2-2 mm
Median mass-specific fracture energy Em50 (kWh/t)
Single particle: 2-120 mm
10
1
0.1
0.01
Model
Single particle breakage
Bed breakage test
0.001
0.1
1
10
Particle size (mm)
100
... which approximately matches the size range of
interest in AG/SAG mills
Barrios, Carvalho & Tavares (2011), Trans. Instn. Min. Metall. 120
Characterizing breakage
Collision energy
YES
Particle breaks?
(body)
NO
Weakening
Surface breakage
Energy-specific
surface breakage
function
Characterizing breakage
• Weakening and surface breakage
Copper ore: 125-75 mm
100
Cumulative distribution (%)
Cumulative broken (%)
100
80
60
60
Both influenced by stressing energy!
40
0.005 kWh/t
0.011 kWh/t
0.022 kWh/t
20
0
80
0
10
20
Number of drops
30
40
Continuum damage model
Tavares & King (2002), Powder Technol.
40
Low energy
normal collision
39.2 J/kg
19.6 J/kg
20
0
0.01
0.1
1
Particle weight loss (%/impact)
10
Characterizing breakage
Collision energy
YES
Energy-specific body
breakage function
Particle breaks?
(body)
NO
Weakening
Surface breakage
Energy-specific
surface breakage
function
Characterizing breakage
• Body breakage distribution
100
80
t1.2
t1.5
t2
t4
t25
t50
t75
t n (%)
60
100
40
20
Passing (%)
10
0
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)
0.1
0.01
0.1
1
Particle size (mm)
10
10
20
30
t10 (%)
40
50
60
100
63.0-53.0 mm
45.0-37.5 mm
31.5-26.5 mm
22.4-19.2 mm
16.0-13.2 mm
5.60-4.75 mm
2.83-2.36 mm
100
t10 (%)
1
0
10
Tavares (2009), Powder Technol.
1
1
10
100
Stressing impact energy / Specific median fracture energy - Em / Em50
Characterizing breakage
• Model predictions: single particle breakage
100
100
Fine
Coarse
63-53 mm
Passing (%)
Passing (%)
0.600-0.425 mm
10
10
1.0 kWh/t
2.5 kWh/t
7.0 kWh/t
1
0.01
0.1
Particle size (mm)
0.10 kWh/t
0.25 kWh/t
0.80 kWh/t
1
1
0.1
1
10
Particle size (mm)
100
Characterizing breakage
For particles contained in a size class:
Collision energies
Fracture energies
• Collision energy is sufficient to break
all particles
Cumulative distributions
100%
Body breakage
• Collision energy is insufficient to
break any particles
100%
0%
Energy
0%
• Collision energy is sufficient to
break some of the particles
Surface breakage
Damage
Energy
100%
0%
Body
breakage
Surface breakage
Damage
• Distribution of collision energies
100%
Energy
0%
Energy
DEM simulation of charge motion
• Comercial software (EDEM®) used
• Calibration of contact parameters is required
for realistic simulations
DEM simulation of charge motion
6’ (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.
DEM simulation of charge motion
Extracting distributions of collision energies (6’ mill)
Contact class
k
1
4
10
28
34
53
54
Elements in contact
Ball-ball
Ball-particle
Ball-liner
Particle-particle
Particle-liner
Particle-particle
Particle-liner
Diameter of particles in collision
Dp (mm)
Dq (mm)
160
160
160
140
160
∞
140
140
140
∞
14
14
14
∞
Mechanistic model framework
Discharge rate (s-1)
0.02
0.01
0.00
0.01
0.1
1
Particle size (mm)
10
100
Power
• Model can describe breakage of multi-component (hard-soft, heavy-light, ... ) blends
• Model is dynamic in nature
Results
• Literature: size-dependent breakage rates in
AG/SAG mills
Morrell et al. (1996), Int. J. Miner. Process. 44-45
Results
• Predictions: Apparent breakage rates of a
copper ore in a 6’ SAG mill
Relative breakage rate (1/s)
101
100
10-1
10-2
Total (body+surface)
Surface breakage
Body breakage
10-3
10-4
1
10
Particle size (mm)
100
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
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 lower
cost alternative or complement to pilot scale
studies
Acknowledgements
Gracias
Obrigado
Thank you
Contact
Prof. Luís Marcelo Tavares
[email protected]