The evolution of hpgr modelling final
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Transcript of The evolution of hpgr modelling final
The evolution of HPGR
Modelling
Roberto Carlos Medrano Nina
From Napier-Munn et al., 1996.
HPGR Schema
TAGGART (1954) Spring Roll Crusher
aC
d100/2
xg/2
D/2
D/2
108cos
100
C
g
CdD
xDaa
First equation to describe a compression angle
EARLY MODELS
The Guevara & Menacho model (1987)
The Fuerstenau, Shukla & Kapur model (1991)
The Austin, Weller & Lim model (1993)
Guevara & Menacho (1987) First HPGR model
pDLuP
Power model
ESPP E
ii exp11 0
Product size distribution model
5.0
025.0
80402
p
pF
Relationship between power, pressure and roll speed.
Link between specific energy and first order grinding kinetics
equation
Fuerstenau, Shukla & Kapur (1991) HPGR model
Laboratory scale tests with several materials
HPGR PSD are similar to Ball Mills PSD after long grinding times
PSD are self-similar: Modified tumbling mills grinding equations
could be used for HPGRs
Fuerstenau, Shukla & Kapur (1991) HPGR model
EMkEMbk
dE
EdMii
i
j
jjiji
1
1
Product size distribution model
32
11 1
aa
aa
j
i
j
iij
x
x
x
xB
Functional expression for breakage (Austin & Luckie)
Functional expression for rate of breakage (Fuerstenau et al)
q
j
a
j
ixQ
xAk
1
First to use functional expressions for breakage and breakage rate
Austin, Weller & Lim (1993) HPGR model
gCC
CS
DLuG
a
a
1
1
cos1
1
cos1
Throughput model
84.056.1 pDLuP
Power draw model
Product size distribution model
g
i
i
x
x
a
1
11
Evolved from Menacho model for throughput and power draw
Modifies Whiten crusher model
Rate of breakage
32
11 1
aa
j
iB
j
iB
ijx
xpA
x
xpAB
Breakage
BREAKTHROUGH STUDIES
Peripheral and axial pressure distribution
Power draw models
Pressure distribution and shear forces in the gap
Johanson (1965) defined a “nip angle” during the roller compaction
process.
Katashinski (1966) was the first to measure, with a sensor pin,
compressive and shear forces during the compression of metal powders.
Feige (1989) used the sensor-pin method for the measurement of
peripheral and axial pressure distributions in a roller crusher.
Schwarz and von Seebach (1990) discovered the “edge effect” in an
industrial HPGR.
Lubjuhn (1992) characterized the peripheral pressure distribution in a
lab-scale HPGR using quartz and limestone.
Both Guevara (1991) and Schönert (2000) calculated a force balance in
the gap.
Klymowsky Power draw equations
Relationship between average pressure and grinding force
IPaveDLFp a
21000
sin30 FDnP
Total HPGR motor power
Grinding force, F, is applied to the rolls in a specific point
defined by angle .
Klymowsky recommends using half the value of the
compression angle (later confirmed by Torres).
RECENT MODELS
The Morrell, Lim, Shi & Tondo Model (1997)
The Schneider, Alves & Austin Model (2009)
The Torres & Casali Model (2009)
Morrell, Lim, Shi & Tondo (1997) HPGR model
Evolved from Austin model after exhaustive laboratory tests at
JKMRC
Uses Andersen cone crusher model for pre-crusher, edge effect
and compressive bed breakage zones.
Bundled with JKSimMet since Version 5.3
Schneider, Alves & Austin (2009) HPGR model
ni
ni
x
xa
g
ii
0
1
1
1
“Estorcego”
ij
xxij xxnitB ij
111 1
9
10
k
Px
k
Px
k
Px
a
i
ii
i
1
'
a
ij
xxij xxnitB ij
111 1
9
10
Compression
Evolved from Austin model
Uses Austin’s functional
expressions for breakage and
rate of breakage for two
comminution mechanisms.
Bundled with ModSim 3.6.17.Product
Feed
i
j
jjii fdp1
,
Torres & Casali (2009) HPGR Model
Evolved from Morrell and Fuerstenau model and Klymowsky power
equations
Uses Herbst & Fuerstenau functions for rate of breakage and
specific rate of breakage scale-up.
Uses a pressure profile function to model edge and centre
products.
xc
aIPPressure
xg
u
C
u
Moveable Roll
D x L
uLxG gCS 3600
HPGR Throughput
Single particle
Compression
x > xC
Particle bed
compression
f
Cg
ggIP
DxDxDx
D
a
4
2
1cos
2
Compression angle uLDpP IP
2sin100
aPower draw
Torres & Casali (2009) HPGR Model
Parabolic pressure profile
Centre productEdge
product
Edge
product
NB “comminution boxes”
1 2 NBNB-13 NB-2… …
Torres & Casali (2009) Comminution Model
Torres & Casali (2009) Comminution in the kth box
i
jz
kj
kijki zv
SAp
1
*,
,, exp
iki ff ,
IP
Dz asin
2
*
kip ,
zmSzmbSzmdz
dv kiki
i
j
kjijkjkiz ,,
1
1
,,,
Solve N x NB system of ODEs
border conditions:
kikiiki pzzmfzm ,
*
,, 0
BN
j j
kIPk
yL
yLuDLpP
1
22
22
4
4
2sin100
a
E
i
k
kki S
H
PS
,
Scale up of the specific rate of breakage for each
block (Herbst & Fuerstenau)
Power in each block (parabolic pressure profile)
Uses functional expressions for breakage (Austin
& Luckie) and rate of breakage (Herbst &
Fuerstenau)
Torres & Casali (2009) Model Validation
Specific energy (predicted vs experimental)
Damp sample
Laboratory (a) and full scale (b) product size distribution model
Inherited and shared properties of each model
Steady-state condition.
Plug-flow hypothesis.
Use of functional expressions for breakage and breakage rate.
Two comminution mechanisms: Nipping and particle bed compression.
Main comminution zone defined between compression angle and gap.
Main breakage mechanism: compression of multiple particles.
Enough maturity to be included in plant simulation software.
Schönert
Taggart
Austin et al
Schneider et alMorrell et alTorres &
Casali
Fuerstenau et al
Klymowsky
Lubjuhn
Schwarz & von Seebach
Katashinskii
Johanson
Feige
Guevara &
Menacho
HPGR Evolution Tree