chapter 7 fluidization and entrainment 2

7/26/2019 Chapter 7 Fluidization and Entrainment 2

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Geldart classification

100

1000

10000

10 100 1000 10000

Particle size, (m)

p

-

g

(kg/m3

)

C

A

B

D


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Classification of Powders

Geldart (1973) (Figure 3.3) classified powdersinto four groups according to their fluidization

properties at ambient condition.

There are 4 stages of particles: Aerated (A),Bubble (B), Cohesive (C) and Dense (D).


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Group B

Bubbling at Umf, thus UmbUmf

Bubbles continue to grow,never achieving a maximumsize.

This makes poor fluidizationquality associated to largepressure fluctuation.

However, lots of bubbles

produced results in less P togenerate, thus lessentrainment.

Example: construction sand.


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Group A

For smaller particles structures where cohesivity becomessignificant.

Lies between group C and free flowing particles (B).

Existence of forces that holds particles togetherwhen gas is

supplied, bed expands but does not bubble. Non-bubbling fluidization at beginning of Umf, followed by

bubbling fluidization as Uoincreases (a.k.a. aeratable state).

Aeratable state = transformation from cohesive to free-

flowing particles type. The freeboard has to be increased to allow for bed

expansion.

Dangerif the powder is left in a drum high voidage and it

could cause blow-up


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Group C

Pressure loss across the bed is always less than

apparent weight of the bed cross sectional area due

to the particles not fully supported by fluidizing gas.

However, group C fluidization can be improved: Mechanical help: vibration, mixer

Binary mixtures: act as flow conditioner


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Many industrial processes use fine powders, e.g. pharmaceutical,cosmetics, paint industries, food industries etc.

Thus, many researches going on to improve and 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 to fluidize well and the pressuredrop across the bed is close to the theoretical pressure drop during

fluidization.

Theoretically, when vertical vibration is applied to a fluidized bed column,the effect of forces between the bed and the distributor cause the break-up of interparticle forces and this cause the particles to fluidize well.

According to Janssen et al. (1998), at a specific vibration frequency, theratio between distributors plate and the bed displacement increases withan increase in vibration intensity.


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Condition at where the powderstops behaving like solids butthey behave like liquidtwophase system.

Bubbles are extremely importantin supplying circulation as theyare major circulating mechanism

hence, lead to mixing.

As bubbles rise, it grows andexpand

If the bed is deep enough anddiameter of the column is small,

Then slugging could occur

This means problem becauseslugging will push the powder upand possibly out of the vessel.

Through bubbles, particles aretransported out of the bed.

Approximately, when Uo

,superficial gas velocity equals toparticle terminal velocity, Vt, thencarry over/entrainment couldoccur.


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Expansion of non-bubbling bed

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

Thus, in general;

Khan and Richardson (1989), suggested the correlation in theequation which permits the determination of the exponent natintermediate values of Re.

If the packed bed depth (H1) and voidage (1) are known, then ifthe mass remains constant, the depth at any voidage can bedetermined:

nTo VU

27.0

p57.0

Dd4.21Ar043.0

4.2nn8.4

1

2

1

2 H1

1

H


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For the optimization of a fluidization process, isessential for predicting the bedsbehavior, for bothhomogeneous and heterogeneous particles. Theprediction of the transport disengagement height

(TDH) is very important, which directly influencesthe column's dimensions and the determination ofthe appropriate placement of a cyclone, therecycling system and the recovery of elutriatedmaterials.

Origin of the entrainment of solid particles:

Lewis (1962), and Kunii and Levenspiel (1991)observed that the solid particles are released intothe freeboard because of bubbles burst up and

slugs. Figure 1 shows the three hypothesesexplaining this phenomenon.

Since the bubbles internal pressure is higher thanthe bed's surface, they burst when reaching thesurface, releasing the particles from their uppersurface into thefreeboard.(Figure 1a);

Because of the bubbles rapid growth, the solidmaterial present in its lower side (wake) is ejectedwhen it bursts (Fig. 1b);

When two bubbles coalesce at the moment itsreach the bed's surface, there is an energeticejection of the particles from the wake of bubble(Figure 1c).

Entrainment and Elutriation of Solids from Fluidized Beds

Figure 1: Mechanism of ejection of solidsfrom a fluidized bed in the freeboard (Kunii

and Levenspiel, 1991)


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Transport Disengangement heightIn the study by Wen and

Chen (1982), the TDH isconsidered to be thedistance between theend of the fluidized

region and the height atwhich the particles nolonger exist. It has alsobeen defined as the

region in which theentrainment ratebecomes constant(Figure 3).

Figure 3: Entrainment of

particles according to Wen

and Chen (1982).


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TDH-Geldart

Geldart (1986) defined the TDH as the region

where the fluidized solids fall back in the bottom

of the bed, and being specific to fine (F) and large

(C) particles:

(i) TDH (F): is the height at which the solidconcentration (especially fines), above the bed

surface, reaches a constant or a slight variation.

TDH (C): is the height where the large particles(or clusters) are released to the freeboard, and

return to the bed.


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TDH-Horio et al Horio et al., (1983) have

distinguishedcharacteristics of the

threefreeboardregions,

shown in Figure 5. From

it, the splash'sheight is

differentiated from the

TDH's: the TDH would

be the sum of

the splash'sand the

diffusion zone heights.


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Zenz and Weil (1958) concluded that theincrease of entrainment rate is related

to the instability of the gas velocitydistribution, due increase of bubblefrequency. The increase in TDH (F)results from the violent bursting of thelarge bubbles, which are less frequentin the bed.

Fournol et al., (1973) concluded thatthe entrainment rate decreases rapidlywith the declining of fluidizationvelocity and with the increasing heightabove the bed.Baron et al. (1988) e Geldart et al.(1995) established that the gas velocitystrongly influences the TDH (F) height.

Sciazko et al. (1988, 1991) based their TDH(C)study on the Pemberton and Davidson's(1984) ghost bubbles theory. The particles

movement in a moving state can bedescribed by force balances. The authorsproved that excess velocity is the mostimportant parameter for the TDH.

Pinto et al., (1999) analyzed theinfluence of three factors on theentrainment of particles: fraction ofopen area in the distributor, solidmass and superficial gas velocity.The material used was sand withmean diameters between 268 and711mm.Regarding the influence ofgas velocity on the homogeneous

particles, the authors observed anincrease in the TDH(C) only for thelow velocities.

Influence of Different Parameters on the TDH

Superficial Gas velocity


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Mass/height of solid Hamdullahpur et al., (1986) conducted their

experiments in a rectangular fluidized bed of0.319m 0.176m 4m. The entrainment gas wasat atmospheric pressure and room temperature.The material used was sand with mean diameterof 300mm (Geldart's group B). In addition to,the experiments were realized for six differentvelocities using the LDV (Laser DopplerVelocimeter) system.

The axial velocity and turbulence intensity

were measured by the central axis andcrossing thefreeboard. The experimentswere performed at 5.2 and 12 cm of fixed-bed, by applying velocities between 0.20and 0.40 m/s. The authors noted that at0.2 m/s, the gas velocity in the center ofthe bed increased with the bed height;however, for the other velocities, the

intensity was lower. The variation ofturbulent magnitude increased 35% withthe bed height. This confirms that thefreeboard turbulence is induced by thebubbles eruption in the center of the bed,and the level is highly dependent on thebubble size.

Fournol et al., (1973) used FCC with meandiameter of 58 mm as entrained materialand gas superficial velocity ranging from0.11 to 0.22 m/s. The authors concludedthat the entrainment rate rapidlydecreases with the rise in bed height;moreover, it depends on the reduction inthe fluidization velocity.

Pinto et al. (1999) worked

experimentaly using homogeneousparticles with mean diameterbetween 268 and 711mm, a solidmass from 1.0 to 3.0 kg, bed heightfrom 0.10 to 0.30, and both of aperforated plate (1.4, 3.4 and 5.9% offree area) and a Tuyere

distributor(1.4% of free area). Fromthe results, they observed that thesolid mass is the most influentialvariable to the TDH.


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Pinto et al., (1999) showed that thefraction of openarea in the distributor is not relevant to the TDH(C)determination. They used both types of distributor; aperforated plate one with 1.4, 3.4 and 5.9% open areaand a Tuyere with 1.4% open area, and the results weresubstantial for the homogeneous particles averaging

from 268 and 711mm. Cipolato et al., (2004) showed that the fraction of open

area in the distributor is not relevant to the TDH(C)determination. In this paper, the authors used

perforated plate distributor with fraction of open areasof 1.4 and 5.9%, obtaining a significant result for theheterogeneous particles of mean diameter of 4000mm.

Fraction of Open Area in the Distributor


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Empirical Correlation Fournol et al., (1973) describes the

TDH (F) - as inversely proportional to

the Froude number. Despite thisproposition, the authors note thatthis height is significantly higher thanpredicted by Zenz and Weil (1958):

Hamdullahpur et al., (1986)proposed an equation thatcharacterizes the TDH(C) asdependent on the bubble

diameter:

Baron et al., (1988)

suggested a newcorrelation to estimate

the TDH(F), in which the

maximum height reached

by the large clusters is

directly proportional to

the velocity square of the

particle (KUb) ejection,

which in turn would be

the gas velocity:


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Sciazko et al., (1988) haveshown though, that the ratiobetween both the splash-zone height and the bedheight is strongly influencedby the excess gas velocity (U-Umf). This volumetric fractionwould be the critical value ofthe bubbles fraction, which isrelated to the difference in theexcess gas velocities

Sciazko et al., (1991)determined a new correlation

for the TDH(C) depending onthe diameter of the bubble onthe bed surface:

Pinto et al., (1999) proposed acorrelation for the TDH(C)depending on the physicalcharacteristics of both theparticles (particle diameter),and the gas (density andviscosity) and the operatingconditions (solid mass and gasvelocity):

Cipolato et al., (2004stablished a new correlationfor the TDH(C) depending onthe solid mass through the

statistical analysis, for a firstorder model with twointeractions:


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The design of a fluidized bed reactor should be done as to minimizethe velocity of the entrainment of particles. Two solutions areusually adjusted: to increase the cross section above the bedsurface, and to predict the reactor's gas outlet from a height abovethe TDH. Devices can be added inside or above the bed to reducethe entrainment, e.g., stirrers, grids, vertical and horizontal bafflesand cyclones (Geldart, 1986).

The elutriation phenomenon can follow a first order process, i.e.,the elutriation velocity of the particle size (dpi) is proportional to themass fraction (xi) of the particles in the reactor:

Where is the elutriation constant velocity of particles


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There are several correlations in terms of proposed in theliterature and two of them are summarizing in Table 1:


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Entrainment rateThe determination of the entrainment requires

knowledge of concentrations of each particlesize in the bed. Figure 10 shows a generalcase and the various possible combinations

(Geldart, 1986). For example:Without feed, 100% efficient cyclone; totalrecycle of product on cyclone;

Continuous feed, cyclone's efficiency variesdepending on dpi; partial recycle of the fines.

No matter the arrangement, the mass balances ofeach component and global must bereached. As an illustration, it is assumed that

RE=RR=0, and F and Q are different from zero.The mass balance of the fraction consideringdpigiven by:

The global mass balance given by:

Now:

In addition, in a well-mixed bed: xQi =xBiSubstituting in the mass balance for eachparticle size and re-arranging:

Figure 9: Balance of the components around

a fluidized bed (Geldart, 1986)


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This equation cannot be directly solved

because RT depends on the values from xBiforeach fraction. In practice a rapid convergence

and an interaction error can be avoided by

using RT=0 in the first attempt.

If the freeboard height is greater than 2m, and

the column's diameter exceeds about 0.2 m,

then for the fraction sizes will have Ut/U 1000)

dp> 1500 m CD0.43

Transition region, 0.2 < Ret< 1000

or

18

2

,

vgp

STt

gdV

t

DCRe

24

g

vgp

t

gdNV

43.0.

3

4,

32

3

4

Re vgpgtD gdC

3

t

g

2

g

gp

t

D

V

g

3

4

Re

C

chapter 7 fluidization and entrainment 2

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