Chapter 7 Fluidization Clean

8/20/2019 Chapter 7 Fluidization Clean

1/48

Chapter 7


2/48

3.0 FLUIDIZATION

3.1 Introduction

A fluidized bed is formed by passing a fluid

usually a gas upwards through a bed oparticles supported on a distributor.

As a fluid is passed upward through a bed oparticles, pressure loss due to frictionalresistance increases as fluid flow increases.

At a point, upward drag force exerted by thefluid on the particle equal to apparent weight oparticles in the bed.

W

F F F = drag forceW = apparent weight


3/48

Figure 3.1: Elements of a Fluidized Bed

Gasin

Windbox

Gasdistributor

Fluidbed

Disengagementspace

Solidfeed

Soliddischarge

Dustout

Gas

out

Dust separator


4/48

3.1 Characteristics of Gas Fluidized Bed

These can be roughly divided into two categories;

3.1.1 Primary Characteristics

Bed behaves like liquid of the same bulkdensity – can add or remove particles,pressure-depth relationship, wave motion,heavy objects sink, and light ones float.

Rapid particle motion – good solid mixing

Very large surface area available –

1m3 of 100m particles has a surface area of about30,000 m

2, and 1 m

3 of 50 m particles –

60,000 m2.

3.1.2 Secondary Characteristics

Good heat transfer from surface to bed, andgas to particles.

Isothermal conditions radially and axially.

Pressure drop through bed depends only on

bed depth and particle density –

does notincrease with gas velocity.


5/48

Particles motions usually streamline – some

erosion of surface or attrition of particles

where gas velocities are high.

3.1 Advantages of Fluidized Bed

High mobility

o Gives superb heat transfer, which usuall

always a problem to powders.

o Heavily used for drying eg: pharmaceutical

industry.o Excellent reactors

Good temperature control

o A perfect gas/liquid mixing equipment.

Very flexibleo Can carry out many processes in a single

vessel.

o Mix, dry, granule, separate etc. in one

vessel.

Less number of moving partso Easy to handle


6/48

3.1 Disadvantages of Fluidized Bed.

Costlyo Blowing air into the system.o Trap air to make it fluidized.o Cleaning processo Some powders

–

costly in operation thanothers.

Not all particles fluidizedo Cohesive and large particles are difficult to

fluidize.

Difficult distributor designo Maldistribution of fluidizing gas

o P across distributor = 30% of bed P.

3.2 Pressure Drop Flow Relationship

The force balance;

Pressuredrop

= Weight of particles - up thrust on particles

Bed cross - sectional area


7/48


8/48

C (


9/48

Based on Carmen-Kozeny (1927, 1933 and1937),

32

21180

pd

U

H

P

(3.7)

Carmen-Kozeny equation for laminarflow.

3.1.1 Turbulent Flow

3

2175.1

p

g

d

U

H

P

(3.8)

Burke – Plumme equation for turbulentflow through a randomly packed bed omonosized spheres of diameter, d p.

3.1.2 General equation for turbulent andlaminar flow.

Based on experimental data covering a widerange of size and shape of particles, Ergun(1952) suggested the following general

equation for any flow conditions;


10/48

150


11/48

75.1Re*

150* f (3.12)

with Re*

150* f for Re* < 10

and 75.1* f for Re* > 2000

For non-spherical particles; d p is replaced by

d sv, then,

3

2

32

2 175.11150

sv

g

sv d

U

d

U

H

P

(3.13)

The surface/volume size, d sv is used: if onlysieve sizes are available, depending on the

particle shape, an approximation can be used

for non-spherical particles;

Recalling, p sv d d 87.0

where d p is the mean sieve size.

Note also that: pv d d 13.1

And for Carmen – Kozeny equation for lamina

flow;

2


12/48

32

21180

svd

U

H

P

(3.14)

3.1 Minimum Fluidization Velocity, U mf .

A plot of pressure drop across the bed vs. fluid

velocity as below.

Figure 3.2: Plot of P vs. U o for fluidized bed

system

Line OA

packed bed region Solid particles do not move relative to one another and theirseparation is constant.

ABed pressure

drop, p

Gas velocity, U

B

O

C

Umf

ppp


13/48

P vs. Uo relationships in region OA: useCarmen-Kozeny equation for laminar flow andErgun equation in general.

Region BC: fluidized bed region. In here,equation 3.1, equation 3.2 and also Ergunequation in general applies.

Point A: P higher than predicted value fromequation 3.1 and 3.2.

This is due to powders, which have beencompacted to some extent before thefluidization process takes place.

Higher P is associated with the extra forcerequired to overcome inter particle attractiveforces.

Minimum fluidization velocity, U mf : superficialfluid velocity at packed bed becomes afluidized bed (as marked on graph above).

Also known as incipient fluidization velocity.

ABed pressure

drop, p

Gas velocity, U

B

O

C

Umf

ppp

U i ith ti l i d ti l


14/48

U mf increases with particle size and particledensity and affected by fluid properties.

Recalling Ergun (1952) for any flow condition;

3

2

32

2 175.11150

sv

g

sv d

U

d

U

H

P (3.15)

and g H P f p 1 (3.2)

substituting (3.15) into (3.2),

3

2

32

2175.11150

1

sv

mf g

sv

mf

f pd

U

d

U g

(3.16)

Rearranging,

2

222

3

2

3

3

2

3

2

..175.1

..1150

1

f svmf

sv f

f svmf

sv f

f p

d U

d

d U

d g

ABed pressuredrop, p

Gas velocity, U

B

O

C

Umf

ppp


15/48

2,3

,3

2

2

3

.175.1

.1150

1

mf e

mf e

sv f

f p

R

Rd

g

(3.18)

or

2,3,3

2

.175.1

.1150

mf emf e R R Ar

(3.19)

where,

2

3

sv f p f

gd Ar

- Archimedes no. (3.20)

svmf f d U Re - Reynolds no. (3.21)

Wen and Yu (1966) correlation for U mf .

687.1

,, 1591060 mf emf e R R Ar (3.22)

or

11059.317.33 5.05, Ar R mf e (3.23)

- for spheres ranging 0.01 < R e,mf < 1000

d f ti l l th 100


16/48

- used for particles larger than 100 m- use d v instead of d sv for Wen and Yu

NB: Please check the Wen & Yu correlation indetermining U mf from Data Booklet.

Baeyens and Geldart

- for particles, d p < 100 m;

066 .0

f

87 .0

f

8.1

p

934.0934.0

f p

mf

1110

d g U

(3.24)

Example

A bed of angular sand of mean sieve size 778 mis fluidized by air. The particle density is 2540

kg/m3

, g (air) = 18.4 10-6

kg/ms, g = 1.2 kg/m3

and 24.75 kg of the sand are charged to the bed0.216 m in diameter. The bed height at incipientfluidization is 0.447 m. Find;

a) mf b) The pressure drop across the bubbling bed

in cm water gauge.c) The incipient fluidization velocity, U mf .


17/48

100

1000

10000

10 100 1000 10000

Particle size, ( m)

p

-

g ( k g / m 3 )

C

A

B D

Figure 3.3: Particles classification according to Geldart (1973)

Classification of powder

3 1 1 Group D


18/48

3.1.1 Group D

Large particles – able to produce deep spoutbed.

Need very large U mf and P to fluidize.

It is a costly operation since lots of air isneeded for blowing.

Quite similar to group B particles, i.e. U mb U mf .

Fluidization of group D and larger group Bparticles: jet circulation/spout bed – techniqueused to get circulation.

Example of operation: paddy drying.

For B and D particles:o No inter particle involve.o Bed collapses instantly when gas supply

interrupted.o Short residence time in bed.

Example: paddy, beans, soy etc.


19/48

3.1.1 Group B

Bubbling at U mf , thus U mb U mf

Bubbles continue to grow, never achieving a

maximum size.

This makes poor fluidization quality associated

to large pressure fluctuation.

However, lots of bubbles produced results in

less P to generate, thus less entrainment.

Example: construction sand.

3 1 1 G A


20/48

3.1.1 Group A

For smaller particles structures wherecohesivity becomes significant.

Lies between group C and free flowing

particles (B).

Existence of forces that holds particlestogether – when gas is supplied, bed expandsbut does not bubble.

Non-bubbling fluidization at beginning of Umf ,

followed by bubbling fluidization as Uo increases (a.k.a. aeratable state).

Aeratable state = transformation from cohesiveto free-flowing particles type.

The freeboard has to be increased to allow forbed expansion.

Danger – if the powder is left in a drum highvoidage and it could cause blow-up.

U mb > U mf , bubbles are constantly splitting and

coalescing, and maximum stale bubble size isachieved.


21/48

Take long time to de-aerate after gas supply iscut-off.

Inter particle forces?? – yes, but significantlysmaller than hydrodynamic forces.

Good quality and smooth fluidization.

Gas bubbles are in limited size, break down athigh velocity and it gives good gas/solidcontact

Example: Fluid bed catalytic cracking (FCC)catalyst.

GROUP A


22/48


23/48

Many industrial processes use fine powders,

e.g. pharmaceutical, cosmetics, paintindustries, food industries etc.

Thus, many researches going on to improveand predict the behaviour of group C particles.

Example: the application of vibrations to the

fluidized bed column.

With the aid of vibration, the bed is found tofluidize well and the pressure drop across thebed is close to the theoretical pressure dropduring fluidization.

Theoretically, when vertical vibration is appliedto a fluidized bed column, the effect of forcesbetween the bed and the distributor cause thebreak-up of interparticle forces and this causethe particles to fluidize well.

GROUP C

G O C


24/48

GROUP C According to Janssen et al. (1998), at a

specific vibration frequency, the ratio betweendistributor ’s plate and the bed displacement

increases with an increase in vibrationintensity.

This phenomenon caused the resultant forcebecomes bigger and hence used to break theinterparticle forces between the particles.

Hence, these results in better fluidizationquality and smaller U mf values obtainedcompared to fluidization without vibration.

Vibration also is predicted to be able to reducethe distance between particles and thisreduces the voidage in the bed.

This is due to small compaction duringnegative displacement or due to the downwardmovement during half cycle of vibration.


25/48

3.1 Bubbles


26/48

d b

+

r Bubble

volume, V b

Cusp

3.1 Bubbles

The shape of bubble is a hemispherical

capped bubble.

The upper surface of the bubble isapproximately spherical, and it’s radius ofcurvature is denoted by r .

Since r is not readily determinable, it is usuallymore convenient to express the bubble size asits ‘volume-equivalent diameter’, i.e. thediameter of the sphere whose volume is equalto the bubble.

31

beq

V 6 d

(3.25)

Bubbling fluidization also known as lean


27/48

Bubbling fluidization also known as leanphase.

Condition at where the powder stops behavinglike solids but they behave like liquid – twophase system.

Bubbles are extremely important in supplyingcirculation as they are major circulatingmechanism – hence, lead to mixing.

As bubbles rise, it grows and expand

If the bed is deep enough and diameter of thecolumn is small,

o Then slugging could occuro This means problem because slugging will

push the powder up and possibly out o

the vessel.

Through bubbles, particles are transported outof the bed.

Approximately, when U o, superficial gas

velocity equals to particle terminal velocity, V t ,then carry over/entrainment could occur.


28/48

Bubbling and Non-Bubbling Fluidization

At U o above the U mf , fluidization may be

generally either bubbling or non-bubbling.

Most liquid fluidized bed system, except thoseinvolving very dense particles, does notbubble.

Gas fluidized bed system give either onlybubbling fluidization or non-bubblingfluidization beginning at U mf , followed bybubbling fluidization as U o increases.

Non-bubbling fluidization is also known as

particulate or homogenous fluidization is oftenreferred to as aggregative or heterogeneousfluidization.

3.1 Expansion of non-bubbling bed


29/48

p g

Richardson and Zaki (1954) found the functionf( ) which applied to both hindered settling andto non-bubbling fluidization.

Thus, in general;

n

T o V U (3.26)

Khan and Richardson (1989), suggested the

correlation in Equation (3.27) which permitsthe determination of the exponent n atintermediate values of Re.

27 .0

p57 .0

D

d 4.21 Ar 043.0

4.2n

n8.4 (3.27)

If the packed bed depth (H 1) and voidage ( 1)are known, then if the mass remains constant,the depth at any voidage can be determined:

12

1

2 H 1

1

H

(3.28)

3.1 Entrainment


30/48

Ejection of particles from the surface ofbubbling bed.

Also term as ‘carry over’ and ‘elutriation’.

Amongst the factors influencing rate ofentrainment are:o gas velocityo particle densityo particle sizeo fines fractiono vessel diametero Increasing gas temperatureo Increasing gas pressure

Discuss these factors …

Ejection of particles from fluidized beddepends on the characteristics of the bed: i.e.bubble size and velocity at surface.

If terminal velocity, Vt > Uo – entrained

If Vt < Uo – particle will fall back to the bed.

Increasingdrag

Terminal velocity


31/48

Terminal velocity


32/48

Terminal velocity Reynolds number, ReT

Terminal velocity determination


33/48

Terminal velocity


34/48

Alternatively, the following equations can be used to form acomputer program (Clift, Grace & Weber, Bubbles, Drops andParticles, Academic Press.

Range Correlation

C DReT 2 73; ReT 2.37

4210

327

224

2

1030272

1092526

1075691

24

T D

T D

T D

T DT

ReC x .

ReC x .

ReC x .

ReC Re

73


35/48

•Region above the fluidized bed surface:

Freeboard

Splash zone

Disengagement zone

Dilute-phase transport zone

(Refer to page 112 – from text book)

Entrainment


36/48

Generally: fine particles – entrainedCoarse particles – stay in the bed.

Practically: fine particles could stay in the bedand coarse particles being entrained.

TDH = Transport Disengagement heighto Height from bed surface to the top of the

disengagement height.o Entrainment flux and concentration o

particles are constant.

Entrainment


37/48

Entrainment


38/48

For continuous operation, x Bi and M B areconstant, and so,

Bi*ihi Ax K R (3.30)

and total rate of entrainment,

Bi*ihiT Ax K R R (3.31)

Total solids loading leaving the freeboard,

AU / R oiiT (3.32)

The elutriation rate constant,*

ih K : predicted

value based on experiment.

Correlations are usually in terms of the carry

over rate above TDH,

*

i K

Entrainment

Entrainment


39/48

Examples of some widely acceptedcorrelations are as below:

(i) Geldart et al (1979); for particles > 100 mand Uo > 1.2 m/s.

o

ti

o g

*

i

U

V 4.5exp7 .23

U

K

(ii) Zenz and Weil (1958) – for particles < 100 mand Uo < 1.2 m/s.

88.1

2

27

*

1026.1

p pi

o

o g

i

gd

U

U

K

when4

2

2

103

p pi

o

gd

U

and

18.1

2

24

*

1031.4

p pi

o

o g

i

gd

U

U

K

when4

2

2

103

p pi

o

gd

U

Entrainment

Entrainment


40/48

3.10.1 Calculation of carryover rate

For continuous operation

General case:

Assumption: R E = R R = 0 and F and Q 0.

Mass balance on the size fraction

d pi gives:

T PiQi Fi R xQ x F x (3.33)

Overall mass balance:

F = RT + Q (3.34)

Bi

*

ihT Piih Ax K R x A E (3.35)

R T , x Pi

F, x Fi

Q, x Qi

x Bi

R E , x Ei

R C , xR i

R R , x Ri R R , x Ri

Entrainment


41/48

Recalling Bi*ihiT Ax K R R (3.36)

In a well mixed bed; xQi = x Bi (3.37)

Substituting and rearranging from equation(3.33);

T

*

ih

Fi Bi

R F A K

F x x

(3.38)

This equation cannot be solved directly

because from equation (3.36), R T depends onthe value of xBi for each size fraction.

In practice, a converging trial and error loopcan be set up, with R T = 0 for the first trial.

Entrainment


42/48

Worked example 7.2

A powder having size distribution given below and a particle

density of 2500 kg/m3 is fed into a fluidized bed of cross

sectional area 4 m2 at a rate of 1.0 kg/s.

Size range (i) sixe range (mm) Mass fraction in feed

1 10-30 0.20

2 30-50 0.65

3 50-70 0.15

The bed is fluidized using air of density 1.2kg/m3 at a

superficial velocity of 0.25 m/s. Processed solids are

continuously withdrawn from the base of the fluidized bed in

order to maintain a constant bed mass. Solids carried over

with the gas leaving the vessel are collected by a bag filter

operating at 100% total efficiency. None of the solids caughtby the filter are returned to the bed. Assuming that the

fluidized bed is well mixed and that the freeboard height is

greater than the TDH under these conditions, calculate at

equilibrium


43/48

Terminal velocity of each size range

Flowrate of solids entering the filter bag

The size distribution of the solids in the bed

The size distribution of the solids entering the filter bag

The rate of withdrawal of processed solids from the base of the bed

The solids loading in the gas entering the filter

For batch operation


44/48

For batch operation, the rates of entrainmentof each size range, the total entrainment rateand the particle size distribution of bed change

with time.

Thus, the formula,

t Ax K M x Bi*

ih B Bi (3.39)

where B Bi M x is the mass of solids insize range, i entrained in time increment,

t .

By assuming that the mass of bed, M Bi doesnot change significantly with time, t thus:

B

*

i

Bio Bi M

At K exp x x (3.40)

3 10 1 T t l t i t fl ( ll


45/48

3.10.1 Total entrainment flux (overallcarryover flux), E ih .

Large, Martini and Bergougnau (1976) picturethe total entrainment flux, E ih, for a given sizematerial, d pi consist of two partial fluxes:

o Continuous flux flowing upwards from bed

to outlet, E i .

o Flux of agglomerates ejected by burstingbubbles, which decreases exponentially asa function of freeboard height.

Expressed algebraically;

ha

ioiihie E E E

(3.41)

where E io is the component ejection flux =

E o x Bi and

Bi

*

ii x K E (3.42)

and

Bi*ihih x K E (3.43)


46/48

The total solids carryover flux when gasofftake is at any height, h above the bedsurface:

ah E E E oh exp (3.44)

Wen and Chen (1982) developed the ideafurther and proposed:

ahexp E E E E oh (3.45)


47/48

Zig Ziglar: You don't have to be great to start,

but you have to start to be great.


48/48

Date post:	07-Aug-2018
Category:	Documents
Upload:	mohamad-syahmie
View:	246 times
Download:	2 times

Chapter 7 Fluidization Clean

Documents