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