Principle of Size Reduction

8/11/2019 Principle of Size Reduction

1/37

Particle Science and

Technology Laboratory

Pricinples of size reduction

Prof. B. Pitchumani

Department of Chemical Engineering

Indian Institute of Technology,

Delhi , INDIA


2/37



Overview

Single particle breakage

Energy requirements

Design considerations

Equipment types


3/37



Introduction

5% of ALL electricity generated is used for

grinding

Efficiency of grinding processes 1-5%

Unfortunately models available too empirical


4/37



Introduction

There are many ways to break a particle:

Main mechanisms tension and shear


5/37



Single Particle Breakage

Two ways in which a particle can break:

Brittle:

Strain

Stress

elasticfailure


6/37




Two ways in which a particle can break:

Ductile:

Strain

Stre

ss

yield

failure


7/37



Predicting Energy Requirements

Three postulates for predicting energy

requirements: Rittinger, Kick, Bond

Highly empirical

Quite old, but still widely used

Varying levels of success


8/37




Hookes Law:

Stress:

Strain:

Work per unit volume:

Y

A

F

0L

x


9/37




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


10/37




Kick (1885)

Energy requirement is related to ratio feed

size/product size:

Usually under predicts for fine grinding

2

1lnx

xCE K


11/37




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


12/37




Rittinger, Kick and Bond combined:


13/37



Grinding equipment- Selection

Selection depends upon

Feed size

Desired product sizeFeed composition/chemical structure

Desired production rate


14/37



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


15/37




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


16/37




Special materials

Explosive material- sulfur-jet mill

Heat sensitive materials- jet mill

Metal powders- spray technique

Plastic powders- cryogenic grinding


17/37




Flammable/explosive materials:

Use inert medium (e.g. nitrogen)

Specifically design equipment to withstand

extremely high pressures

Operate outside of explosion-risk conditions


18/37



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


19/37



n

dX

XXQ

exp3

Rosin Rammler Equation

DISTRIBUTION EQUATIONS

Ball milled product follows Rosin Rammler

equation


20/37



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%


21/37



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


22/37



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




23/37



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




24/37



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


MECHANISM OF PULVERIZATION


25/37



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



26/37



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.


Specific rate of grinding/ selection function


27/37



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


28/37



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.




29/37



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


SELECTION & BREAKAGE FUNCTION


30/37



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



31/37



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


MASS BALANCE EQUATION


32/37



Mass balance equation is made from mass of

particles got reduced and mass produced.

Q

MASS BALANCE EQUATIONS


33/37



tWSbtWS

dt

tdWjjjiii

i ,



34/37



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



35/37



Breakage distribution Bi,jwith with four parameters

model (,,)

j

i

j

iji

xx

xxB 11, 1

MASS BALANCE EQUATIONS


36/37



tWSbtWSdt

tdW

jjjiii

i ,

i

i

i

x

x

x

S

1

1

j

i

j

iji

x

x

x

xB 11, 1


37/37



Last slide

Documents

Principle of Size Reduction