yyzzzz SolidsNotes5 Fluidization

7/29/2019 yyzzzz SolidsNotes5 Fluidization

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SOLIDS NOTES 5, George G. Chase, The University of Akron

5. FLUIDIZATION

5.1 The Phenomenon of Fluidization

When a fluid is pumped upward through a bed of fine solid particles at a very low flow

rate the fluid percolates through the void spaces (pores) without disturbing the bed. Thisis a fixed bed process.

If the upward flow rate is very large the bed mobilizes pneumatically and may be swept

out of the process vessel. At an intermediate flow rate the bed expands and is in what we

call an expandedstate. In the fixed bed the particles are in direct contact with each other,

supporting each others weight. In the expanded bed the particles have a mean free

distance between particles and the particles are supported by the drag force of the fluid.

The expanded bed has some of the properties of a fluid and is also called afluidizedbed.

As shown in Figure 5-1, the velocity of the fluid through the bed opposite to the direction

of gravity determines whether the bed is fixed, expanded, or is swept out. There is a

minimum fluidization velocity, Vom, at which the bed just begins to fluidize. When the

(c) Intermediate

Flow Rate, Fixed

Bed, V tOOm uV

(b) High Flow

Rate, Mobilized

Bed, Ot Vu <

Figure 5-1. Fixed, mobilized, and expanded beds. The fixed bed (a) occurs when

the approach velocity, Vo, is much smaller than the minimized fluidization

velocity, Vom. The pneumatically mobilized bed (b) occurs when the approach

velocity is much greater than the particle terminal velocity, ut, and the expanded

bed (c) occurs when the approach velocity is intermediate between the minimum

fluidization velocity and the terminal velocity.

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approach velocity, Vo (otherwise known as the empty tank velocity, given by the fluid

volumetric flow rate divided by the cross-sectional area of the vessel), is greater than or

equal to the minimum fluidization velocity andit is less than the terminal velocity of the

particles then the bed forms a fluidized bed. When Vtoom uVV


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SOLIDSIN

GAS OUT

COUNTERCURRENTCOLUMN

GAS OUT

OUT

CROSS FLOW

GAS IN

SOLIDS OUT GAS IN

SOLIDSIN

Figure 5-2. Counter current and cross flow methods of continuous contacting in fluidized

bed designs.

5.2 Comparison of Contacting Methods

Kunii and Levenspiel (ibid, Figure 7) provide a table comparing different types of

fluidized beds to the fixed bed. Beds include:

Fixed bed Moving bed Bubbling/turbulent bed Fast fluidized bed Rotary cylinder Flat hearth

The advantages of fluidized beds include:

Liquid like behavior, easy to control and automate, Rapid mixing, uniform temperature and concentrations, Resists rapid temperature changes, hence responds slowly to changes

in operating conditions and avoids temperature runaway with

exothermic reactions,

Circulate solids between fluidized beds for heat exchange, Applicable for large or small scale operations, Heat and mass transfer rates are high, requiring smaller surfaces.

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The disadvantages of fluidized beds include:

Bubbling beds of fine particles are difficult to predict and are lessefficient,

Rapid mixing of solids causes non-uniform residence times forcontinuous flow reactors,

Particle comminution (breakup) is common, Pipe and vessel walls erode due to collisions by particles.

5.3 Uses of Fluid ization

The uses for fluidized beds are limited to our imaginations. Typical uses include

Reactors Cracking hydrocarbons coal gasification carbonization calcination

heat exchange Drying operations Coating (example, metals with polymer) Solidification/Granulation Growth of particles Adsorption/desorption Bio fluidization others

5.4 Geldart Classi fication of Particles

Geldart (Powder Technology, 7, 285-292, 1973) observed the nature of particles

fluidizing. He categorized his observations by particle diameter versus the relative

density difference between the fluid phase and the solid particles. (HANDOUT 5.1).

Geldart identified four regions in which the fluidization character can be distinctly

defined.

Group A particles are characterized by

Bubbling bed fluidization, The bed expands considerably before bubbling occurs,

Gas bubbles rise more rapidly than the rest of the gas, Bubbles spit and coalesce frequently through the bed, Maximum bubble size is less than 10 cm, Internal flow deflectors do not improve fluidization,

Gross circulation of solids occurs.

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0.1

1

10

10 100 1000 10000

D

SPOUTABLEBED

B

SAND-LIKE

(BUBBLING

BED)

(EASY TO

FLUIDIZE)

A

AERATABLE

BED

(EASIEST TO

FLUIDIZE)

C

COHESIVE

(DIFFICULT TO

FLUIDIZE)

( )3/ cmg

gs

( )mdp

Figure 5-3. Geldart classification of fluidized beds. Particle properties are related to the

type of fluidized beds. (Geldart, Powder Technology, 7, 258-292,1973).

Group B particle beds are the most common. These beds

Are made of coarser particles than group A particles and more dense, Form bubbles as soon as the gas velocity exceeds Vom, Form small bubbles at the distributor which grow in size throughout the bed, Have bubble sizes independent of the particle size, and Have gross circulation.

Group C particles

Are difficult to fluidize and tend to rise as a slug of solids, Form channels in large beds with no fluidization, and Tend to be cohesive.

Group D particles

Are very large, dense particles, Form bubbles which coalesce rapidly and grow large, Form bubbles which rise slower than the rest of the gas phase, Form beds whose dense phase surrounding the bubbles has low voidage, Cause slugs to form in beds when the bubble size approaches the bed

diameter, and

Spout from the top of the bed easily.

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Kunii and Levenspeil present a more generalized diagram (ibid, Figure 16) for

classifying fluidization regimes. They plot a dimensionless particle diameter,

versus a dimensionless velocity where

dp *

u *

( ) ( )d d

gC Rp p

p

D ep* =

=

2

13

34

21

3(5-1)

and

( )u u

g

R

Cp

ep

D

* =

=

2

13 1

34

3. (5-2)

With the data arranged this way they identify several interesting features including:

Geldarts classification, Terminal velocity, ,ut Minimum fluidization velocity, , andumf Types of fluidization (spouted beds, bubbling, fast fluidized beds and

pneumatic transport).

5.5 Prediction of Minimum Fluidization

A minimum velocity is needed to fluidized a bed. If the velocity is too small the bedstays fixed and operates as a packed bed.

Recall the Ergun Equation is presented in dimensionless form in Eq.(4-25) which relates

the pressure drop to the flow rate through a packed bed. At the onset of fluidization the

particles are still close enough together that the pressure drop is related to the velocity by

the Ergun Equation. Also, a free body diagram tells us that the force due to pressure drop

is also related to the net weight of the solids in the bed

( )( )( )P A A L gg

p f f

c

= 1 (5-3)

where the right side of Eq.(5-3) is the weight of the solids minus the buoyant force due tothe displaced fluid. The subscriptsfmean that the quantity is for a fluidized bed.

If we consider a total mass balance on the solids, assuming that no solids are entrained

and carried out of the bed, then the total mass of solids is constant given by

( )M ALsolids p f f = = 1 constant (5-4)

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At different fluidization rates the porosity, , and the bed height, , vary but the rest of

the terms in Eq.(5-4) are constants. This means that at the porosities and bed heights at

flow rates 1 and 2 are related by

L

( ) ( )1 11 1 2 2 = L L . (5-5)

For liquids and for gases, as long as the pressure drop is small, the fluid phase density isconstant. Hence, the right hand side of Eq.(5-3) is constant and thus the pressure drop in

a fluidized bed is constant independent of the velocity.

Experimental data show this to be true. A typical plot of the pressure drop versus the

velocity is shown in Figure 5-4.

Substitution of Eq.(5-3) into Eq.(4-25) gives the modified Ergun Equation for fluidized

beds

GAfep

f

f

fep

f

NRR =

+

232

3

118080.1

(5-6)

where

RV d

ep f

of p=

(5-7)

and( )

Nd g

GA

p p

=3

2

. (5-8)

LOOSE PACKED

DENSE PACKED(FIRST TIME BED IS FLUIDIZED)

V

FLUIDIZED BEDOPERATION

P

PACKED BEDOPERATION

V m

Figure 5-4. Typical pressure drop versus velocity plot for fluidized beds. Initially if the

bed is densely packed the pressure drop overshoots the fluidization pressure until the

particles separate and fluidize.

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For small , such as with very small particles, we can neglect the term and

get the Blake-Kozeny expression

Repf< 1 Repf

2

GAfepf

f

NR =

23

1180

forRepf < 1 (5-9)

or( )

( )f

fpp

of

gdV

=

1180

232

(5-10)

which relates the fluidization velocity to the void volume fraction of the expanded bed.

To estimate the onset of fluidization, we can estimate the minimum fluidization

conditions. The minimum fluidization porosity, m , can be estimated from Figure 4-1 for

loose packing and known sphericity, . Using this value for m we can solve the Ergun

Equation, Eq.(5-6) for the minimum fluidization velocity, .moV

When m and are not known, we can still estimate the minimum fluidization velocity.

The modified Ergun Equation, Eq.(5-6) is rewritten as

(5-11)GAmepmep NRKRK =+ 12

2

where( )

231

1180

=

m

mK

and

=

32

8.1

m

K

Wen and Yu (AIChE J, 12(3), 610-612, 1966) noted that and stay nearly constant

over a wide range of particles and for

K1 K2

4000001.0


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Table 5-1. Values for constants in Wen and Yus correlation, Eq.(5-12).

PARTICLES K

K

1

22

1

2K

SOURCE

Fine 33.7 0.0408 Wen and Yu,AIChE J, 12(3), 610-612, 1966.

Coarse 28.7 0.0494 Chitesteret.al.,Chem. Eng. Sci., 39,253,1984.

5.6 Wide Size Distribut ions of Particles

The previous discussion applies predominately to beds of narrow size distribution of

particles. Now lets consider what happens when there is a large size distribution of

particles in a fluidized bed.

In such a bed the minimum fluidization velocity, , must be determined for the

particular size distribution in actually in the bed. This may differ significantly from thesize distribution in the fresh feed due to elutriation of fines, attrition, oragglomeration of

particles.

moV

One can estimate by using the average particle size (a permeability average is most

appropriate). However, as fluid flows upward and the flow is increased, the fine particles

in the voids between the larger particles will fluidize before the larger particles. This

partial fluidization will occur at a smaller velocity than the average .

moV

moV

Estimating for a wide size range of particles is analogous to measuring the boiling

point of a liquid mixture. The boiling point is not fixed, but varies with the composition.mo

V

To obtain a conservative estimate, to fluidize the whole bed, should be estimated forthe largest particle. You must also check the terminal velocity of the smallest particles to

make sure that you do not entrain fines and carry them out of the top of the bed.

moV

If a bed of particles has a bimodal distribution, it has two size ranges as for example

given in Figure 5-5. Several fluidization conditions can exist for fluidized beds with

bimodal size distributions. These conditions are shown in Figure 5-6. (HANDOUT 5.2)

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Particle Size

Number

BimodalDistribution

Figure 5-5. Bimodal distribution of particle sizes showing two peaks (modes) in the

number of particles of each size.

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d large

dp avg

p

d smallp

d large

FLOW

d small

p

p

(a) Complete segregation of particles into a region of predominately

small particles and a region of predominately large particles. The

segregation may also be characterized by an abrupt change in bed

porosity.

d large

dp avg

p

d smallp

d mixedp

d large

FLOW

p

d small

d mixed

p

p

(b) Partial segregation into two regions with different particle sizesseparated by a layer of mixed particle sizes.

dp avg

d mixedp

FLOW

d mixed.p

(c) No segregation of particles. The average particle size may gradually

vary throughout the depth of the bed.

Figure 5-6. Fluidized beds with bimodal size distribution.

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