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Chapter 7
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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
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Figure 3.1: Elements of a Fluidized Bed
Gasin
Windbox
Gasdistributor
Fluidbed
Disengagementspace
Solidfeed
Soliddischarge
Dustout
Gas
out
Dust separator
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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.
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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
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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
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C (
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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;
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150
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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
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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
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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
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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
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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
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- 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 .
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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
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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.
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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
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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.
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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
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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
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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.
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3.1 Bubbles
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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
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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.
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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
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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
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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
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Terminal velocity
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Terminal velocity Reynolds number, ReT
Terminal velocity determination
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Terminal velocity
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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
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•Region above the fluidized bed surface:
Freeboard
Splash zone
Disengagement zone
Dilute-phase transport zone
(Refer to page 112 – from text book)
Entrainment
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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
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Entrainment
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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
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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
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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
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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
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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
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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
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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
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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)
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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)
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Zig Ziglar: You don't have to be great to start,
but you have to start to be great.
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