Principle of Size Reduction
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Transcript of Principle of Size Reduction
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Particle Science and
Technology Laboratory
Pricinples of size reduction
Prof. B. Pitchumani
Department of Chemical Engineering
Indian Institute of Technology,
Delhi , INDIA
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Overview
Single particle breakage
Energy requirements
Design considerations
Equipment types
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Introduction
5% of ALL electricity generated is used for
grinding
Efficiency of grinding processes 1-5%
Unfortunately models available too empirical
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Introduction
There are many ways to break a particle:
Main mechanisms tension and shear
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Single Particle Breakage
Two ways in which a particle can break:
Brittle:
Strain
Stress
elasticfailure
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Single Particle Breakage
Two ways in which a particle can break:
Ductile:
Strain
Stre
ss
yield
failure
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Predicting Energy Requirements
Three postulates for predicting energy
requirements: Rittinger, Kick, Bond
Highly empirical
Quite old, but still widely used
Varying levels of success
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Single Particle Breakage
Hookes Law:
Stress:
Strain:
Work per unit volume:
Y
A
F
0L
x
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Predicting Energy Requirements
Rittinger (1867): Energy required is proportional to amount of new
surface created.
Feed particles of size x1, product particles of size x
2.
Amount of surface created per unit mass?
1212
1111
xx
CE
xxk
kR
pv
s
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Predicting Energy Requirements
Kick (1885)
Energy requirement is related to ratio feed
size/product size:
Usually under predicts for fine grinding
2
1lnx
xCE K
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Predicting Energy Requirements
Bond (1952) Based on large amount of experimental data
X1, X2: sieve size through which 80% product andfeed passes (in m)
WIis known as work index
12
1010
XX
WE IB
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Predicting Energy Requirements
Rittinger, Kick and Bond combined:
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Grinding equipment- Selection
Selection depends upon
Feed size
Desired product sizeFeed composition/chemical structure
Desired production rate
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Selection of Grinding equipment
particle properties
Brittle- Compressive, impact force
Soft: Sometimes they deform than break .This property is used for food processing likecorn flake production- compressive force
Some material become brittle at lowtemperature.- Polymer material is super
cooledit is known as cryogenic grinding
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Selection of Grinding equipment
Explosive material- Cooling during grindingor jet mill is used
Production of very small mill; wet grinding
is preferred to dry grinding
Moist material is difficult to grind- foodmaterial are roasted before ground
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Selection of Grinding equipment
Special materials
Explosive material- sulfur-jet mill
Heat sensitive materials- jet mill
Metal powders- spray technique
Plastic powders- cryogenic grinding
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Selection of Grinding equipment
Flammable/explosive materials:
Use inert medium (e.g. nitrogen)
Specifically design equipment to withstand
extremely high pressures
Operate outside of explosion-risk conditions
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Time of grinding is more than 4 hrs
The viscosity of the final slurry is high
The slurry concentration is low
The Ball loading is not knownBall size is not known
Ball size distribution is not known
Silica pebbles is used for economy
OBSERVATIONS DURING MILLING
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n
dX
XXQ
exp3
Rosin Rammler Equation
DISTRIBUTION EQUATIONS
Ball milled product follows Rosin Rammler
equation
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Limitations of grinding equation
The size taken is average size or 80% below thatsize. However it is possible to have different size
distribution for the similar size. Fig.1
When more fines are produced more energy will beconsumed and less energy consumed when coarse
are produced.
Fig 1 Significance of Size Distribution (product size 2%
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Fig.1 Significance of Size Distribution (product size 2%
cumulative over 20 m)
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
Particle Size [m icrons]
Cumulative
Undersize[wt%]
Sample-1
Sample-2
Sample-3
Effect of distribution on grinding
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The feed size distribution is important
Particles break when the particles are selected by
hammers or grinding balls
Amount of each size selected is important
Selected particle break into the smaller sizes
The distribution of particles formed from single
feed size
Effect of distribution on grinding
Effect of distribution on grinding
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Particles break when the particles are
selected by hammers or grinding balls.
Amount of each size selected is important is
known as selction function and it is denoted
by S function as S(x) of particle size x.
It is also termed as specific rate of grinding
Effect of distribution on grinding
Effect of distribution on grinding
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Selected particle break into the smaller sizes.
The distribution of particles formed from single
feed size is termed as breakage distribution
function bi,j
(x) indicate fraction of material
produced from size i to j
Effect of distribution on grinding
MECHANISM OF PULVERIZATION
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SELECTION DISTRIBUTION FUNCTION /
SPECIFIC RATE OF RATE OF GRINDING , S (i)
The fraction of size i selected by the system per unit
operation
BREAKAGE DISTRIBUTION, bi,j
The fraction of material of size j formed from theoriginal size i
MECHANISM OF PULVERIZATION
Effect of distribution on grinding
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Let f1, f2is fraction of material
of size d1and d2present in the
feed of the material. Then S1
and S2are the specific rate of
grinding values for size d1and
d2.
Effect of distribution on grinding
Specific rate of grinding/ selection function
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Specific rate of grinding/ selection function
f I feed
fraction inthe size i
diameter Selection
functionSi
f1 d1 S1
f2 d2 S2
f3 d3 S3
f4 d4 S4fn dn Sn
BREAKAGE DISTRIBUTION VALUES
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The fraction of size d1selected S1breaks and
fraction formed of sizes d2and d3are b1,2andb1,3etc.
The b1,1
refers to the fraction of size d1
though
selected by grinding media particles did not break.
BREAKAGE DISTRIBUTION VALUES
BREAKAGE DISTRIBUTION VALUES
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For the size d2selected will not become size d1
and hence 0 is written in the matrix for S2. Theparticles of size d2selected and fraction breaks to
sizes d3
and d4
are b2,3
and b2,4
etc.
b22refers to unbroken particles of d2remained.
The complete Matrix is shown in next slide
BREAKAGE DISTRIBUTION VALUES
SELECTION & BREAKAGE FUNCTION
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S C ON & G UNC ON
S1 S2 S3 S4 S5
b1,1 0 0 0 0
b2,1
b2,2
0 0 0
b,31 b3,2 b3,3 0 0
b4,1 b4,2 b,4,3 b4,4 0
SELECTION & BREAKAGE FUNCTION
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S1 S
2 S
3
b1,1 0 0b1,2 b2,2 0b1,3 b2,3 b3,3b1,4 b2,4 b3,4
b1,5 b2,5 b3,5.
.
.
.
.
.
.
.
.
b1,n
b2,n
b3,n
SELECTION & BREAKAGE FUNCTION
MASS BALANCE EQUATION
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Mass balance equation is made from mass of
particles got reduced and mass produced.
Q
MASS BALANCE EQUATIONS
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tWSbtWS
dt
tdWjjjiii
i ,
BREAKAGE DISTRIBUTION VALUES
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Many equations were developed to relate brekage
distribution with particles. Pitchumani and Mangal hasdeveloped for industrial ball mill selection function Si,
with three parameter model (,,)
i
i
i
x
x
x
S
1
1
BREAKAGE DISTRIBUTION VALUES
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Breakage distribution Bi,jwith with four parameters
model (,,)
j
i
j
iji
xx
xxB 11, 1
MASS BALANCE EQUATIONS
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Particle Science and
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tWSbtWSdt
tdW
jjjiii
i ,
i
i
i
x
x
x
S
1
1
j
i
j
iji
x
x
x
xB 11, 1
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Last slide