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INFLUENCE OF THE DISTRIBUTOR PLATE AND OPERATING CONDITIONSON THE FLUIDIZATION QUALITY OF A GAS FLUIDIZED BEDJoão Monney Paiva a; Carlos Pinho b; Rui Figueiredo c

a Mechanical Engineering and Industrial Management Department, ESTV, Polytechnic of Viseu, Viseu,Portugal b CEFT-Mechanical Engineering and Industrial Management Department, Faculty of Engineering,University of Oporto, Porto, Portugal c Mechanical Engineering Department, Faculty of Science andTechnology, University of Coimbra, Coimbra, Portugal

Online Publication Date: 01 March 2009

To cite this Article Paiva, João Monney, Pinho, Carlos and Figueiredo, Rui(2009)'INFLUENCE OF THE DISTRIBUTOR PLATE ANDOPERATING CONDITIONS ON THE FLUIDIZATION QUALITY OF A GAS FLUIDIZED BED',Chemical EngineeringCommunications,196:3,342 — 361

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Influence of the Distributor Plate and OperatingConditions on the Fluidization Quality of a Gas

Fluidized Bed

JOAO MONNEY PAIVA,1 CARLOS PINHO,2 ANDRUI FIGUEIREDO3

1Mechanical Engineering and Industrial Management Department, ESTV,Polytechnic of Viseu, Viseu, Portugal2CEFT–Mechanical Engineering and Industrial Management Department,Faculty of Engineering, University of Oporto, Porto, Portugal3Mechanical Engineering Department, Faculty of Science and Technology,University of Coimbra, Coimbra, Portugal

Experiments were carried out to examine the influence of both the type and thepressure drop of distributor plates on the fluidization quality of an atmosphericfluidized bed. Three different distributor types were used, perforated Perspex,metallic mesh, and porous ceramic, with pressure drops ranging from 0.05 to350 kPa and superficial air velocities ranging from 0.1 to 2.3 m=s. Three sizes of sil-ica Ballotini beads, 355–425, 600–710, and 850–1000 mm, were used as bed material.The static bed height was set to 300 mm and was divided into six horizontal 50 mmhigh slices. For each slice, pressure drop values were recorded for U0=Umf ratiosfrom 20 to 1. In order to produce a reference for the pressure drop evolution, amodification of the two-phase theory was introduced, taking into consideration theincrease in the average global porosity as well as the change in the ratio offlow through the bubbles versus the flow through the dense phase. This allowedassessment of the influence of the different operating conditions and setups on thequality of fluidization, Q�.

Keywords Distributor plate; Fluidization; Quality; Pressure drop

Introduction

The concept of quality in fluidization has been broadly interpreted and has been usedin different environments as a way of evaluating the bed behavior, according to theexpectations of a specific situation. Most authors refer to the quality of fluidizationof a fluidized bed on a descriptive basis, making judgments based on ‘‘qualitative’’assumptions such as the level, perfection, or goodness of the mixture. Many seem-ingly assume an established, though unknown, definition based on the degree ofsome variables such as the pressure level, the pressure fluctuations themselves(Saxena and Waghmare, 2000) or the amplitude of standard deviation (Chen andBi, 2003), the level of gas-solid contact existing in a mixture (Fan and Zhu, 1998),

Address correspondence to Carlos Pinho, CEFT–Mechanical Engineering and IndustrialManagement Department, Faculty of Engineering, University of Oporto, 4200-465 Porto,Portugal. E-mail: [email protected]

Chem. Eng. Comm., 196:342–361, 2009Copyright # Taylor & Francis Group, LLCISSN: 0098-6445 print/1563-5201 onlineDOI: 10.1080/00986440802359451

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the level of interaction between the two phases of a bubbling bed (Nienow et al.,1978), or the maximum value of the segregated regions in a mixture that makesthem look as though they are imperfectly mixed (Danckwerts, 1953). Others inter-relate hydrodynamic behavior and fluidization quality and recognize that relativelylittle work has addressed this last question (Llop and Jand, 2003). Some definitionsalso arise from a negative standpoint, such as examples of slugging or channelingand of deterioration changes in the characteristics of particles (Geldart, 1986) orciting defluidization as the degradation of the quality of fluidization (McLaughlinand Rhodes, 2001). Fluidization quality is also defined as the fluid-dynamic con-ditions brought about by the fluidization process itself (Gallucci and Gibilaro,2005), and a fairly broad and general approach is taken by Kunii and Levenspiel(1991), who refer to the quality of fluidization as the ability of a set of particles tofluidize.

Bed Pressure Drop Criterion

One of the first attempts to produce an objective point of view on the degree of flui-dization quality was by Hiraki (1969). Hiraki stated that the measure of quality wasthe closeness between the value of the measured bed pressure drop and the calculatedweight of the existing particles per bed section, at all times, considered approximatelyconstant beyond the minimum fluidizing velocity, Umf. Other authors (Dutta andDullea, 1990) established a bed of Group C particles and compared the resultingpressure drop with an ideal value computed from the knowledge of the mass of par-ticles charged at the start of the operation.

In industrial environments, it is important to be able to detect changes of beha-vior in fluidized beds due to unexpected agglomerations or to changes in the stabilityof the phases (Zenz, 1957; Rowe et al., 1978; Yang et al., 1985; Geldart and Buczek,1989; Jean et al., 1992; Schouten and van den Bleek, 1998; van Ommen et al., 2000,2001a). The capacity to recognize and monitor changes in fluidization quality, as aresult of the gross hydrodynamic behavior of fluidizing beds, has been achievedeither through estimations of visible flow rate or by measurement of bed pressurefluctuations, the appeal of the latter being its ease of use, at both a laboratoryand an industrial scale (Song et al., 1984; Chong et al., 1987; Daw and Halow,1993; Briens et al., 1997; Schouten and van den Bleek, 1998; van Ommen et al.,1998, 1999, 2001b). Some used this method as a form of detection of what they called‘‘deterioration of fluidization quality,’’ defined as the deterioration arising from non-fluidized zones over the distributor plate, causing the appearance of hot spots in bedsworking at high temperatures, as a result of a sequence of particle sintering andagglomeration (Song et al., 1984). The grade of fluidization quality was also definedas a function of the proximity of the bed under observation compared to the incipi-ent fluidization condition, this state being established by means of gas extractionalong the column in order to avoid bubble formation (Chong et al., 1987). A quan-titative method for monitoring fluidization quality was described based on compara-tive measurements of successive time series of pressure values obtained during bedoperation in which a particular time series was defined as a reference of optimalquality (Schouten and van den Bleek, 1998). As a corollary, ‘‘quality of fluidization’’was defined as the state of a fluidized bed that leads to an optimal mixture of gas andparticles all over the bed, which allows easy handling of the bed material and stabi-lization of internal temperature distribution and of the average bed pressure drop.

Influence of Distributor Plate 343


This procedure was tested with different particle sizes (Song et al., 1984) and forseveral superficial velocities (van Ommen et al., 1999). Finally, measurements of dif-ferential pressure were found to be more sensitive to situations where segregationwas expected to happen quickly, suggesting that the single probe used should beplaced in the lower half of the bed, and not just above the distributor because ofthe presence of defluidized layers (van Ommen et al., 2001b).

Distributor Pressure Drop Influence

Concerning the influence of the gas distributor, most studies reported in the litera-ture were carried out at low fluidization velocities. One investigation examined theminimum required pressure drop across the distributor plate to ensure a uniformgas distribution over the bed (Kunii and Levenspiel, 1969). The influence of thetype of distributor was investigated at low velocities (U�Umf < 0.25 m=s) and thefollowing findings were observed:

1. When the plate pressure drop was changed by adding sheets of porous materials,bubble size increased with decreasing distributor pressure drop when the bedpressure drop was greater than 10 times the distributor pressure drop valueand remained the same when that value was smaller (Geldart and Kelsey, 1968);

2. Bubble size increases with a decrease in the distributor pressure drop when sev-eral slot screens were used to allow variation of the open area (Saxena et al.,1979) and perforated plates were used to change the diameter of the holes (Fanet al., 1981);

3. Bubble size was not influenced by the use of different distributors with the sameopen area, but by different numbers and sizes of holes (Hatate et al., 1991).

Other authors worked at higher gas velocities (U�Umf> 0.5 m=s) and, usingfive different perforated plate distributors with the same orifice diameters, foundthree bubbling regimes (multiple, single, and exploding) and related them to thepressure fluctuations in the air plenum (Svensson et al., 1996). These investigationshave shown that the pressure drop across the distributor is extremely important inthe bubble regime. Finally, several experiments were developed to ascertain the influ-ence of the distributor type, aspect ratio, and operating velocity on the quality offluidization of a 0.2 m ID, 1 m high fluidized bed column (Sathiyamoorthy andHorio, 2003). A critical aspect ratio was found and the marked influence of thedistributor on shallow beds was recognized.

Still, the importance of the distributor performance on the fluidization quality inthe lower internal layers of common non-shallow beds is relatively unknown.

In this work, fluidization quality is defined as the ratio between the experimen-tally measured bed pressure drop and the theoretical drop, calculated by integrat-ing bubble growth from the plate to the free surface of the bed using a simplemodification of the two-phase model. The fluidization quality indicator, Q�,a dimensionless pressure drop that is defined similarly to that presented bySathiyamoorthy and Horio (2003), is evaluated along the bed height, and theinfluence that the different types of distributor (porous ceramic, metallic mesh,and perforated Perspex) exert on a quality indicator is observed, particularly inconsidering the bed lower regions.

344 J. M. Paiva et al.


Experiment

The experimental work was carried out in a 100 mm internal diameter Perspex tube,using air at ambient conditions as the fluidizing medium. The pressure drop regis-tered by the gas flow passing through the distributor plates, for increasing valuesof the superficial air velocity within the tested flow range and for each distributorplate, was previously measured with pressure probes calibrated against U-tubemercury pressure manometers. To help achieve a uniform airflow distribution overthe cross section of the bed, two consecutive primary fixed beds were used in thewind box section (Figure 1). The first fixed bed was filled with 20 mm diameter silicaspheres and the second with 3 mm spheres.

Figure 1. Schematic of the experimental setup.



The fluidized bed under analysis was established by fluidizing three size rangesof silica Ballotini beads, 355–425, 600–710, and 850–1000 mm, previously screenedand statistically weighted with t tests using SPSS software as well as a Coulter LS230 Particle Size Analyser (size distributions in Figure 2). The airflow rate wasmeasured with orifice plate flow meters, equipped with a Furness Control FCO18differential pressure transducer, connected to a data acquisition system. The staticbed height was set to 300 mm and divided into six 50 mm high horizontal slices(Figure 1, enlarged at right). Each slice pressure drop, DPj, is the difference of

Figure 2. Particle size distribution (Coulter LS230) for size 355–425, 600–710, and 850–1000 mm particles; see Table I for average particle diameter.

Table I. Experimental conditions

Experimental conditions Value

Internal bed diameter, D (m) 0.10Height of the unit, L (m) 3.5Local atmospheric pressure, P (Pa) 97500Bed temperature, T (�C) 15Bed material Silica beadsBed material density, q (kg=m3) 2485Average particle diameter I (355–425 mm),

dpI¼ 1=(Rxi=dpi) (mm)387

Average particle diameter II (600–710 mm),dpII¼ 1=(Rxi=dpi) (mm)

651

Average particle diameter III (850–1000 mm),dpIII¼ 1=(Rxi=dpi) (mm)

941

Minimum fluidization velocity I, UmfI (m=s) 0.104Minimum fluidization velocity II, UmfII (m=s) 0.271Minimum fluidization velocity III, UmfIII (m=s) 0.448Fluidization velocities, U0 (m=s) 0.1 . . . 2.3Static bed height, H (m) 0.3



measured pressures between one level and the next. Pressure measurements con-sidered cumulative values of slices per layer, i.e., the first layer is slice 1, the secondlayer is slice 1 plus slice 2, and so on until the sixth layer, which corresponds to thesum of slices 1 to 6 (Figure 1, enlarged at right).

In this way, the effect of bubble growth and coalescence phenomena as they rosein the bed could be detected on the pressure drop evolution, unlike the considerationof the pressure drop through single slices, which ignores such phenomena.

Starting just above the distributor plate, three pressure probes were used at eachslice, set 120� apart and in parallel (Figure 1, top left), to obtain the correspondingaverage value. The purpose of this particular setup was to obtain more representativepressure data from each section of the bed, as the visual observation of the fluidizingbehavior showed nonuniformities of the spatial flow distribution, particularly whenthe bubbling regimes were initiated. The measurement of pressure values between thebottom of the bed, or, more specifically, the upper plate surface, and the atmosphere,allowed whole bed pressure drop and standard deviation of whole bed pressure fluc-tuations to be registered. U0=Umf ratios were measured from 20 to 1, using orificeplate flow meters equipped with Furness Control differential pressure transducersFCO15 and 16, connected to a data acquisition system.

Table II. Data on the orifices of the distributors

No. of orifices Orifice diameterType Plate reference Nor dor (mm)

Perforated plate withtriangular pitch (p#x)

p3x 300 0.3p4x 386 0.3p9x 948 0.3

Metallic mesh (dyn) dyn O (0.3)Porous ceramic (ker) ker O (0.3)

Figure 3. Pressure drop (log values) versus superficial velocity for different distributor plates;see Table III for distributor reference.



The experimental conditions are summarized in Table I. To ensure sufficientaccuracy in the statistical analysis, each plotted experimental point corresponds tothe arithmetic average of eight defluidizing runs. For each run, a minimum of 50steady-state flow readings, corresponding to each position of the flow meter, wereacquired by the data acquisition system, which used a sampling frequency of50 Hz. The dubious points were eliminated according to Chauvenet’s criterion(Holman, 1994).

Five different distributors were used, three in perforated Perspex, with differentorifice layouts, one in metallic mesh, and another in porous ceramic (Figure 1,bottom left, and Table II), with pressure drops ranging from 0.05 to 300 kPa forsuperficial gas velocities ranging from 0.1 to 2.3 m=s, at standard pressure andtemperature (Figure 3).

The data corresponding to the maximum possible fluidization velocity (i.e., thevelocity corresponding to the maximum flow allowed by the restriction imposed byeach distributor plate and dependent upon the constant static pressure supplied bythe air compressor) as well as the respective percentage of open area are givenin Table III. The uncertainty calculations followed the systematic approach ofColeman and Steele (1999).

Analysis

As commonly stated in fluidization literature, the point of minimum fluidization ischaracterized by the following force balance (Kunii and Levenspiel, 1969):

DP ¼ ðqp � qf Þð1� emf ÞHmf g ð1Þ

in which Hmf is the height of the bed at minimum fluidization conditions. This equal-ity is usually considered the fundamental fluidization condition (Couderc, 1985).

Assuming that the dense phase remains at minimum fluidization conditions,according to the two-phase theory (Davidson and Harrison, 1963), any increase inflow rate beyond that point leads to:

DP ¼ ðqp � qf Þð1� emf ÞHf gð1� dÞ ð2Þ

where Hf is the bed height at any other fluidization regime and d is the fraction of thevolume of the bed now occupied by the bubbles.

Table III. Data on the open areas and velocities through distributors

Open area Maximum U0

Type Plate reference (%) (m=s)

Perforated plate with triangularpitch (p#x)

p3x 0.270 1.7p4x 0.347 2.0p9x 0.853 2.2

Metallic mesh dyn 0.675 2.2Porous ceramic ker 8.482 2.3



On the other hand, the absolute velocity of the rise of bubbles is commonlyestablished as (Davidson and Harrison, 1963):

Uba ¼ ðU0 �Umf Þ þUbr ð3Þ

where Ubr is the rise velocity of the bubbles relative to the dense phase. According tothe same authors, if the upward flow of gas in the dense phase is Umf, through thebubble phase it must be Ubaþ bUmf, and the total gas flow in the bed can beexpressed as:

U0 ¼ ð1� dÞUmf þ dðUba þ b Umf Þ ð4Þ

where b is a factor representing the number of times the bubbles are processingthe amount of gas passing an equivalent section of the dense phase (Kunii andLevenspiel, 1969).

Reviewing the literature for the various attempts to obtain a sustainable valuefor the bubble’s bypass factor (Lockett et al., 1967; Grace and Harrison, 1969; Kuniiand Levenspiel, 1969; Peters et al., 1978; Werther and Wein, 1994; Gallucci andGibilaro, 2005), it can be noted that none of the proposed values adequatelydescribed the experimental results (this disagreement had been noted previously byRowe et al. (1978) and Grace and Clift (1974)). Basically, the b factor is supposedto account for the ratio:

b ¼ Qbinv

Qdphð5Þ

where Qbinv is the invisible gas flow through the bubble phase and Qdph is the gasflow through the dense phase (Fan and Zhu, 1998). This factor should take into con-sideration both the influence of the average bed particle size (Davidson andHarrison, 1963; Kunii and Levenspiel, 1991), dp, through which gas will flow, andthe bed initial height, H, as it acts on the rate of growth, coalescence, and breakingof the bubbles. Therefore, one can write:

b / U0 �Umf

U0

� �c1 H

dp

� �c2

ð6Þ

where c1 and c2 are fitting exponents. One possible solution is (Paina et al., 2000):

b ¼ 10U0 �Umf

U0

� �0:5H

dp

� �0:3

ð7Þ

And, though based on the mentioned generic assumptions, it leads to b values ofthe same order of magnitude as those obtained experimentally by other authors(Grace and Clift, 1974).

Solving Equation (4) in order of d and then replacing Uba by means ofEquation (3), a general expression of the volume fraction of bubbles in a certainlayer of the bed is obtained:

di ¼Vb

Vl

� �i

ð8Þ



di ¼U0 �Umf

Ubr þU0 þ ðb� 2ÞUmf

� �i

ð9Þ

But, as the bubbles grow in height, an average value of the bubble volume fraction �ddi

should be used to account for the change from the distributor level to the freesurface. For that purpose, an average value for the bubble rise velocity Ubr can becalculated through integration:

Ubr ¼1

Hi

Z Hi

0

0:71ffiffiffiffiffiffigd

pb

� �dz ð10Þ

There are many equations that correlate db with the superficial velocities.Darton, LaNauze, Davidson, and Harrison’s equation (1977) is used here as itaccounts for the influence of the type of distributor plate and takes into consider-ation the existing number of holes. After integration, Ubr becomes

Ubr ¼ 0:373ðU0 �Umf Þ15g

25H�1

i ðHi þ 4ffiffiffiffiffiffiA0

pÞ

75 � ð4

ffiffiffiffiffiffiA0

pÞ

75

h ið11Þ

with A0 representing the ratio A=Nor, where A is the area and Nor the number oforifices of the distributor plate.

Finally, reference values for the pressure drop beyond the point of minimumfluidization can be defined for each layer i in the bed:

DPtheor ¼ ðqp � qf Þð1� emf Þ 1� U0 �Umf

Ubr þU0 þ ðb� 2ÞUmf

" #i

" #gHi ð12Þ

This represents a more accurate value than just the overall bed pressure loss, asit incorporates the possibility of monitoring the pressure drop evolution from thebottom to the free surface, using a correction that accounts for the reduction ofthe mass of particles in each of the layers due to the presence of rising bubbles.

The quality of fluidization, Q�, can now be obtained through the ratio betweenthe experimentally measured value for each specific layer of the bed, DPi, and thecorresponding theoretically calculated pressure drop, DPtheor:

Q� ¼Pi

j¼1 DPslice j

DPtheorð13Þ

Results and Discussion

Distributor Pressure Drop

The first part of the experiments related to the pressure drop in the distributors.Each plate was tested three times nonconsecutively; the evolution of pressure dropmeasurements versus the superficial velocity is presented in Figure 3, where the rela-tive performance of the tested distributors is shown.

Perforated distributor plates demonstrate higher pressure drops, whereas themetallic mesh stays in the mid range and the ceramic porous plate remains in thelower range. The ‘‘p9x’’ (see Table II) perforated plate distributor was designed tohave a pressure drop evolution with U0 superficial velocity close to that of the



metallic mesh plate, ‘‘dyn.’’ With these two distinct distributors having similarpressure drop curves, differences in bed hydrodynamics dependent upon conditionsat the gas entry region of the bed, clearly influenced by the type of distributor, couldbe detected. The other perforated plates have 386 and 300 0.3 mm holes, whichmeans that the number of jets leaving the surface decreases at the same time thatthe space between orifices increases. The range extends from the case of the ceramicplate, ‘‘ker,’’ which has a space between orifices of the same order as the orificesthemselves, i.e., 0.3 mm, to the 5.4 mm of the ‘‘p3x’’ perforated plate with 300 holes.This implies that, for the higher pressure drop plates, the amount of particles poten-tially undisturbed by the jets increases with the increase in distance between theiroriginating holes, as well as with the angles formed between adjacent jets, as thoseangles decrease with increasing superficial velocity (Hong et al., 2003).

Stability criteria have had different approaches over the past decades. Wen andKing (1980) defined the condition for stability based on an even gas distributionabove the distributor plate; Gibilaro (2001), recovering a statement from Wallis(1969), defined a stability criterion as the transition between homogeneous and bub-bling fluidization. Both the criteria were tested. All but the ‘‘ker’’ plate presentd(DP)=dU values higher than 800 Ns=m3 and give stable distribution for superficialvelocities above Umf, using the Wen and King criterion, on the one hand; for allsituations, on the other hand, the dynamic-wave velocity, UD, is always smaller thanUK, the velocity of the kinematic wave, hence indicating that the bed should presentunstable fluidization. The visualization of the experiments showed, nonetheless, thatthe bed started bubbling at the minimum fluidization condition for all the plates andoperating conditions tested and, therefore, must be considered unstable (i.e., bub-bling, aggregative, or heterogeneous) at all times, using the Gibilaro’s criterion.The ceramic distributor plate did not demonstrate a particularly uneven gas distri-bution when compared with the other plates tested.

Fluidization Quality and Bed Height

The main set of experiments dealt with the measurement of the pressure drop pereach slice j of the bed, made with consecutive probe sets (Figure 1, main and enlargedright). The data were then treated according to the procedure of accumulated slicesexplained above and are presented in Figure 4 for the case of the 355–425 mmparticles.

In these figures, experimental results of the quality of fluidization, Q�, as definedin Equation (13), are plotted for each of the considered layers.

This dimensionless pressure drop is evaluated with U0=Umf ratios along the bedheight and is the basis for the assessment of the hydrodynamic behavior experiencedby the bed. Figure 4 represents the evolution of Q�for each layer of the bed of355–425 mm particles (from the first to the sixth), as well as the performance ofthe various types of distributor plates with U0=Umf ratios.

As fluidizing gas flows through the distributor, jets are formed creating a thinlow pressure region as a result of the high velocity jets. This initial region shows highbed voidage, especially close to the upper face of the distributor. At a certain dis-tance away from the distributor, there is a jet impaction against bed particles,depending on the number of orifices of each plate for equivalent mass flow rates.This action results in gas velocity reduction and a consequent pressure rise associatedwith the conversion of jet gas momentum (Guo et al., 2001; Hong et al., 2003). Inside



this region of jet flow degradation and bubble creation, the real pressure is higherthan predicted theoretically, as this usually concerns the overall bed as a wholeand does not take into account local flow particularities or the existence of the undis-turbed regions mentioned in the next section.

The higher value registered for the fluidization quality ratio, Q�, in the first,second, and third layers after the distributor, which can be observed in Figure 4for the 355–425 mm particle size (which is similar to the other sizes used in the experi-ments), is a result of these factors. Moving from the lower layers towards the higherlayers, the subsequent reduction of Q� is connected to the gas-solid flow regulariza-tion that takes place as the gas, in either the particulate phase or the bubble phase,moves upwards.

In the fourth and fifth layers, inside which the flow proceeds as expected, thefluidization quality ratio approaches 1, while, in the sixth layer, the ratio dropsbelow 1. Once again, flow abnormalities are responsible for such a result. In thiscase, it is the behavior of the gas-solid flow at the top of the bed that causes the

Figure 4. Evolution of fluidization quality from the first to the sixth layer, 355–425 mmparticles. (�: ker, �: p9x, þ : dyn, *: p4x, �: p3x).



degradation of fluidization quality. At the top, at the bed free surface, bubbleeruption takes place and particles are thrown off the bed. This creates a lean regionwhere the bed boundary and hydrodynamic conditions are not as well defined as atmid-bed. Consequently, the bed is not as dense as before and the pressure drop islower than what would be expected because of these local peculiarities.

Effect of Distributor on Fluidization Quality

Clift (in Geldart, 1986) considers that there is little harm in calling ‘‘jets’’ the regionsresulting from gas entering a bed of solids, from an orifice or hole, forming a seriesof bubbles or a permanent void with low solids concentration. Also, the gas can leavethe orifices in a plate distributor or can be directly injected through nozzles inside abed, held close to minimum fluidization by means of a background gas flow. Experi-mental results that predict the size of the jet penetration originating directly from theplate’s orifices are scarce, and the vast majority of the work presented since then hasaddressed jets from nozzles: single, multiple, vertical, horizontal, and inclined.Nevertheless, data obtained in experiments with those idealized conditions, suchas openings in the distribution plates forming jets and eventually bubbles, whilethe bed is maintained in the state of incipient fluidization, are useful for calculationsin real fluidized beds and evaluation of the bottom zone hydrodynamics.

Methods from the literature predicting the length of established jets when a gasenters an established fluidized gas-solid bed vertically (Basov et al., 1969; Yang andKeairns, 1979; Wu and Whiting, 1988; Blake et al., 1990; Yates et al., 1995; Honget al., 2003) indicate height values that range from 4 to 40 mm, for multiple jet pen-etration. These results are obtained for orifice velocities that are deduced from thesuperficial velocity values used in these experiments, namely from minimum orincipient conditions up to the higher values attained (see Table III). Some of the cor-relations referenced (Wu and Whiting, 1988; Yates et al., 1995) take the distancebetween jet locations into consideration, a factor that affects the jet penetrationheight, considered as the distance from the bed bottom to the point where adjacentjets begin to combine. Again, if these particular correlations were used with the high-est pressure drop plate (‘‘p3x’’), the values obtained would be 3.4, 3.0, and 2.8 mm,for average diameters of 387, 651, and 941 mm, respectively, using the Wu andWhiting (1988) empirical equation, and 25, 23, and 22 mm using the Hong et al.(2003) equation, for the same particle sizes.

If these correlations were used with the ceramic plate, ‘‘ker,’’ the length of the jetwould be almost nonexistent, as the orifice diameter is of the same order as the sizeof the space between the centers of two consecutive orifices. In this case, the multiplecombined very small jets penetrating inside the bed result in a sort of pneumaticcushion supporting the bed of particles, as if they were a lengthening of the distribu-tor plate itself. This zone of multiple spouts and voids that spread horizontallyto form lenticular cavities eventually forms so-called bubbles (Clift et al., 1978;Cranfield, 1978) and was visually observable during the experiments.

The results also show that in adjacent layers next to the distributor plates(Figures 4 and 5, first, second, and third layers), the high velocity jets produce flui-dizing conditions that reflect the level of disturbance that particles are experiencingin those initial regions. Pressure buildup takes place near the distributors as thenumerous and contiguous small gas jets impinge against solid particles, pushing



them upwards and promoting a region of higher solid concentration that acts like abarrier against the gas flow (Cranfield, 1978; van der Schaaf et al., 1999).

The behavior of Q� reflects these effects. In fact, for those low pressure dropplates, Q� is greater than 1 for the lower layers as the pressure difference increasesbetween the buildup and the recovered regions above, when plates with a highernumber of orifices are tested. This is the case for the ‘‘ker,’’ ‘‘p9x,’’ and ‘‘dyn’’ plates,which have higher open area values.

For corresponding flow rates of the same magnitude, decreasing the number oforifices produces stronger and longer but fewer jets. This leaves a certain amount ofunsupported particles in between, resulting in low quality fluidization of the bottom.Also, as those higher velocity outgoing jets passing through the distributor platesthat have fewer open areas maintain a greater integrity, a gas buildup such as thatregistered for the plates with the higher number of orifices will not take place.

From the third layer onwards, the bubbles become bigger and scarcer and themixture becomes more impoverished. The pressure drop evolution of the fourth,fifth, and sixth layers (Figures 4 and 6) is all very much alike, with the quality of flui-dization, Q�, moving back closer to unity for all the tested plates.

The ‘‘dyn’’ distributor, a metallic mesh plate that produces an oblique preferen-tial direction for the outgoing jets, shows high Q� values that are the result of astrong level of mixture in the bottom of this 10 cm ID bed. In Figure 4, the first layershows a distinguishable evolution of the bed behavior when using the ‘‘dyn’’ dis-tributor with 355–425 mm particles for U0=Umf values over 12, especially when com-pared with its counterpart pressure drop plate, ‘‘p9x.’’ Larger sizes, 600–710 and

Figure 5. Evolution of fluidization quality from the first to the third layer, 600–710 and850–1000 mm particles. (�: ker, �: p9x, þ: dyn, *: p4x, �: p3x).



850–1000 mm, present the same overall behavior using the same distributor, forU0=Umf values over 6 and 3, respectively. The effect of directing the gas jets comingout of the metallic mesh in an oblique direction has not been sufficiently studied toallow a quantitative assessment of its influence. Nonetheless, from a qualitativepoint of view, there is probably an extra level of turbulence due to the considerableamount of particles that are hitting the bed wall.

Overall, plates with a higher pressure drop reveal decreased ability to disperseflow, particularly in the first regions of the bed, as reflected by lower values ofQ�. The lower number of jets and the increase in the distance between their originsstress the spouting behavior in the bottom of the bed. Particles in their zone of influ-ence are vigorously dragged upwards, but a considerable number of particles remainundisturbed within the jet half-angle region (Merry, 1971).

Effect of Superficial Velocity on Fluidization Quality

For equivalent superficial velocities, plates with a lower number of orifices (namely,‘‘p3x’’ and ‘‘p4x’’) register a correspondingly higher velocity through those orifices.

The effect of superficial velocity is not completely elucidated, as a number ofinvestigators report contradictory conclusions on this subject. A small collectionof related work in the literature (Yang and Keairns, 1979; Blake et al., 1990; Guoet al., 2001; Hong et al., 2003) reports that the jet penetration height increases asthe jet gas velocity increases, while other studies (Wu and Whiting, 1988; Yateset al., 1995) found that the jet penetration height decreases when increasing thesuperficial fluidizing gas velocity.

For equivalent superficial velocities, plates with a lower number of orifices(namely, ‘‘p3x’’ and ‘‘p4x’’) register a necessarily higher velocity through those ori-fices, thereby increasing jet penetration depth. Bubbles form further up the bedand far from the distributor, thereby leaving the initial layers comparatively moreundisturbed.

Also, for all the distributor plates, the bed pressure drop in the lower layersincreases initially with the overall gas flow rate due to reasons presented in the pre-vious section. The evolution of the fluidization quality with the superficial velocityU0 shows how the collapsing of the jets affects fluidization quality as U0 initiallyrises. However, for very high values of gas superficial velocity, the influence of therarefaction of solids reducing the overall bed density supersedes the influence ofjet collapse and the fluidization quality diminishes, with Q� progressively approach-ing unity.

It is also noted that the evolution of the fluidization quality with the superficialvelocity, U0, presents a change in slope for all three sizes of particles tested, within allthe layers considered (Figures 4, 5, and 6, mainly third and fourth layers). The velo-city value at which it occurs seems to be consistent with the onset transition valuesfrom bubbling to turbulent regimes (Chen and Bi, 2003; Paiva et al., 2004). However,this subject requires further considerations and extends beyond the scope of thepresent study.

Summarizing the results from Figures 4, 5, and 6:

1. A higher superficial velocity equals better fluidization quality, Q�, for a similarnumber of orifices, in the first layers of the bed, for bubbling beds that operateunder 12 Umf with group B particles and under 4=5 Umf with group D.



2. Again in the first layers of the bed, for equal superficial velocities, distributorswith higher open area tend to promote a better fluidization quality.

Effect of Bed Material Size

Though belonging to two different Geldart groups and to the boundary betweenthem (B and D, for the 355–425 and 850–1000 mm particles, respectively, B=Dboundary for the 600–710 mm particles), if Q� values are compared for the sameratios of U0=Umf there are no significant differences between smaller particles anddiameters.

Jets formed from perforated distributor plates create a stream of fast-movingbubbles. This permanent gas void in the region of the hole causes a region of signifi-cantly higher gas and particle velocity and a much lower average concentration ofsolids in this region than in the rest of the bed. When the particle diameter increases,the jet penetration height decreases (Hong et al., 2003). For the particular case ofgroup D particles (Figures 5 and 6, 850–1000 mm), Cranfield and Geldart (1974)report the formation of consistent horizontal voids close to the distributor. Thisreduction of jet penetration height, according to what was discussed in the sectiondealing with the influence of distributors on the quality of fluidization, appears tocontradict the results obtained in this study. They show no such change in the beha-vior of Q� between 355–425 mm (group A) and 850–1000 mm (group D) particles,even looking only at the first layers of Figures 4 and 5, and for the lower pressuredrop plates (namely, ‘‘ker’’ and ‘‘dyn’’).

Figure 6. Evolution of fluidization quality from the fourth to the sixth layer, 600–710 and850–1000 mm particles. (�: ker, �: p9x, þ: dyn, *: p4x, �: p3x).



Conclusions

The present study defines the quality of fluidization, Q�, a criterion based on adimensionless pressure drop that allows an assessment of the influence of severaltypes of distributor plates and operating conditions on fluidization quality,especially influencing the lower regions of the bed.

As for the influence of the superficial velocity, Q� increases until the transitionvalue from bubbling to turbulent regimes is reached, if low pressure drop distributorplates are used. For higher flow resistance plates, Q� lowers beyond that transitionalpoint. Briefly, one could say that beyond certain U0=Umf values (typically around 10,5, and 3, respectively for particle sizes 355–425, 600–710, and 850–1000 mm) there isan indication that the fluidization quality in the lower bed layers decreases withincreasing distributor plate pressure drop. That reduction is softened as the bed pro-gressively encompasses the upper slices. Inversely, a high quality of fluidization of thegas-solid mixture in the lower bed layers seems to be assured when the lower flowresistance plates are used: typically, for the ‘‘p9x’’ and ‘‘dyn’’ plates and group A par-ticles, a distributor pressure drop of 10 kPa for superficial velocities around 0.5 m=sand of 100 kPa for superficial velocities around 2 m=s; beds made of group B or Dparticles will demonstrate a similar fluidization quality if the ‘‘ker’’ distributor plateis used between the same superficial velocities, in the 0.1 to 1 kPa pressure drop range.

Hence, although a certain value of distributor pressure drop is recommended toensure proper fluidizing conditions, distributor pressure drops that are too high cancause gas flow misdistributions in the lower layers of the bed because they lead to veryhigh momentum gas jets that drag particles upwards in the bed and later collapse vio-lently against such particles. High pressure drop plates produce a comparativelypoorer flow distribution and mixture with the particles at the bottom of the bed, thusdecreasing Q� when comparing the same order of gas flow passing through the samefluidized bed. Increasing the average size of bed particles used, for the same distribu-tor plate pressure drop, seems to have no significant influence on the values of Q�.

Furthermore, an oblique preferential direction of the flow leaving the surfacefrom the ‘‘dyn’’ metallic mesh distributor, having the same plate pressure drop asa conventional perforated Perspex distributor, ‘‘p9x,’’ was found to produce a com-parative increase in the quality of fluidization in the same first layers. This effect hasnot been sufficiently studied at this point to allow the quantitative assessment of howsuch a mechanism influences the reported pressure evolution.

Beyond the bottom zone, and for all the plates and particle size distributionstested, the hydrodynamics of the bed behaves as traditionally expected.

Nomenclature

A bed cross-sectional area, m2

A0 bed cross-sectional area per orifice of the distributor plate, m2=orificedb bubble diameter, mdor orifice diameter, mdp average particle diameter, mD bed internal diameter, mg gravitational acceleration, m=s2

H bed height, mHf bed height at flow conditions beyond minimum fluidization, m



Hi bed height corresponding to the ith layer, mNor number of orifices of the distributor plateP ambient pressure, PaQb volumetric gas flow rate through the bubble phase, m3=sQ� fluidization quality, DPexperimental=DPtheortical, Equation (13)U0 superficial velocity, m=sUba mean bubble absolute rise velocity, m=sUbr relative rise velocity of an isolated bubble, m=sUD dynamic wave velocity, m=sUmf minimum fluidization velocity, m=sUK kinematic wave velocity, m=sVb bubble volume, m3

Vl bed volume, m3

Greek Letters

b bubble bypass factor, Equation (5)c exponents in Equation (6)d bubble volume fraction, Equation (8)DP pressure drop, PaDPd distributor plate pressure drop, PaDPi layer pressure drop, PaDPj slice pressure drop, Pae void fractionemf void fraction at minimum fluidization conditionsq bed material density, kg=m3

Subscripts

0 relative to the bed free surfaceb bubbleexp experimentalf fluidi layerj slicel bedmf frelative to minimum fluidization conditionsor relative to the number of orifices on the distributor platep relative to the particlestheor theoretical

References

Basov, V. A., Markhevka, V. I., Melik-Akhnazarov, T. Kh., and Orochko, D. I. (1969). Inves-tigation of the structure of a nonuniform fluidized bed, Int. Chem. Eng., 9, 263.

Blake, T. R., Webb, H., and Sunderland, P. B. (1990). The nondimensionalization of equa-tions describing fluidization with application to the correlation of jet penetration height,Chem. Eng. Sci., 45, 365.

Briens, C. L., Briens, L. A., Hay, J., Hudson, C., and Margaritis, A. (1997). Application ofHurst analysis to the detection of minimum fluidization and gas maldistribution ingas-liquid-solid fluidized beds, AIChE J., 43, 1904.



Chen, A. and Bi, H. T. (2003). Pressure fluctuations and transition from bubbling to turbulentfluidization, Powder Technol., 133, 237.

Chong, Y. O., O’Dea, D. P., White, E. T., Lee, P. L., and Leung, L. S. (1987). Control of thequality of fluidization in a tall bed using the variance of pressure fluctuations, PowderTechnol., 53, 237.

Clift, R., Grace, J. R., and Weber, M. E. (1978). Bubbles, Drops and Particles, Academic Press,London.

Coleman, H. W. and Steele, W. G. (1999). Experimentation and Uncertainty Analysis forEngineers, John Wiley, New York.

Couderc, J. P. (1985). Incipient fluidization and particulate systems, in: Fluidization, 2nd ed.,eds. J. F. Davidson, R. Clift, and D. Harrison, 1, Academic Press, London.

Cranfield, R. (1978). Solids mixing in fluidized beds of large particles, AIChE Symp. Ser., 176,54.

Cranfield, R. R. and Geldart, D. (1974). Large particle fluidization, Chem. Eng. Sci., 29, 935.Danckwerts, P. V. (1953). Research 6, 355, quoted by M. J. Rhodes (1998), Introduction to

Particle Technology, John Wiley, New York.Darton, R. C., LaNauze, R. D., Davidson, J. F., and Harrison, D. (1977). Bubble growth due

to coalescence in fluidized beds, Trans. Inst. Chem. Eng., 55, 274.Davidson, J. F. and Harrison, D. (1963). Fluidised Particles, Cambridge University Press,

Cambridge.Daw, C. S. and Halow, J. S. (1993). Evaluation and control of fluidization quality through

chaotic time series analysis of pressure-drop measurements, AIChE Symp. Ser., 89, 103.Dutta, A. and Dullea, L. V. (1990). A comparative evaluation of negatively and positively

charged submicron particles as flow conditioners for a cohesive powder, AIChE Symp.Ser., 86, 26.

Fan, L.-S. and Zhu, C. (1998). Principles of Gas-Solids Flows, Cambridge University Press,Cambridge.

Fan, L. T., Ho, T.-C., Hiraoka, S., and Walawender, W. P. (1981). Pressure fluctuations in afluidized bed, AIChE J., 27, 388.

Gallucci, K. and Gibilaro, L. G. (2005). Dimensional cold-modeling criteria for fluidizationquality, Ind. Eng. Chem. Res., 44, (14), 5152–5158.

Geldart, D. (1986). Gas Fluidization Technology, John Wiley, New York.Geldart, D. and Buczek, B. (1989). The effect of the size of the fines on the fluidization

behavior of equilibrium cracking catalyst, in Fluidization VI: Proceedings of the SixthEngineering Foundation Conference on Fluidization, eds. J. R. Grace, L. W. Shemilt,and M. A. Bergougnou, 179, Engineering Foundation, New York.

Geldart, D. and Kelsey, J. (1968). The influence of the gas distributor on bed expansion,bubble size and bubble frequency in fluidised beds, Inst. Chem. Eng. Symp. Ser., 30, 114.

Gibilaro, L. G. (2001). Fluidization-Dynamics: The Formulation and Applications of a Predic-tive Theory for the Fluidized State, Butterworth-Heinemann, Oxford.

Grace, J. R. and Clift, R. (1974). On the two-phase theory of fluidization, Chem. Eng. Sci., 29,327.

Grace, J. R. and Harrison, D. (1969). The behaviour of freely bubbling fluidised beds, Chem.Eng. Sci., 24, 497.

Guo, Q. J., Yue, G. X., Zhang, J. Y., and Liu, Z. Y. (2001). Hydrodynamic characteristics of atwo-dimensional jetting fluidized bed with binary mixtures, Chem. Eng. Sci., 56, 4685.

Hatate, Y., Uemura, Y., Migita, M. S., Kawano, Y., Tanaka, K., Ijichi, K., and King, D. F.(1991). Chem. Eng. Commun., 101, 39.

Hiraki, I. (1969). Personal communication in D. Kunii and O. Levenspiel (1969), FluidizationEngineering, p. 75, Robert E. Krieger, Huntington, N.Y.

Holman, J. P. (1994). Experimental Methods for Engineers, 6th ed., McGraw-Hill, New York.Hong, R. Y., Guo, Q. J., Luo, G. H., Zhang, J.-Y., and Ding, J. (2003). On the jet penetration

height in fluidized beds with two vertical jets, Powder Technol., 133, 216.



Jean, R.-H., Eubanks, R. J., Hang, P., and Fan, L.-S. (1992). Fluidization behavior ofpolymeric particles in gas-solid fluidized beds, Chem. Eng. Sci., 47, 325.

Kunii, D. and Levenspiel, O. (1969). Fluidization Engineering, Robert E. Krieger, Huntington,N.Y.

Kunii, D. and Levenspiel, O. (1991). Fluidization Engineering, 2d ed., Butterworth-Heinemann, Boston.

Llop, M. F. and Jand, N. (2003). The influence of low pressure operation on fluidizationquality, Chem. Eng. J., 95, 25.

Lockett, M. J., Davidson, J. F., and Harrison, D. (1967). On the two-phase theory of fluidiza-tion, Chem. Eng. Sci., 22, 1059.

McLaughlin, L. J. and Rhodes, M. J. (2001). Prediction of fluidized bed behaviour in thepresence of liquid bridges, Powder Technol., 114, 213.

Merry, J. M. D. (1971). Penetration of a horizontal jet in a fluidized bed, Trans. Inst. Chem.Eng., 49, 189.

Nienow, A., Rowe, P., and Chiba, T. (1978). Mixing and segregation of a small proportion oflarge particles in gas fluidized beds of considerably smaller ones, AIChE Symp. Ser., 176, 45.

Paiva, J. M., Pinho, C., and Figueiredo, R. (2000). Distributor plate influence on fluidizationquality, measuring pressure drop evolution in adjacent slices through the bed, in:Proceedings of the FEDSM2000-ASME Fluids Engineering Division Summer Meeting,June, Boston, Massachussets, paper FEDSM2000-11026.ps.

Paiva, J. M., Pinho, C., and Figueiredo, R. (2004). The influence of the distributor plate on thebottom zone of a fluidized bed approaching the transition from bubbling to circulatingregimes, Trans. Inst. Chem. Eng., 81, Part A, 25.

Peters, M. H., Fan, L.-S., and Sweeney, T. L. (1978). Reactant dynamics in catalytic fluidizedbed reactors with flow reversal of gas in the emulsion phase, Chem. Eng. Sci., 37, 553.

Rowe, P. N., Santoro, L., and Yates, J. G. (1978). The division of gas between bubble andinterstitial phases in fluidized beds of fine powders, Chem. Eng. Sci., 33, 133.

Sathiyamoorthy, D. and Horio, M. (2003). On the influence of aspect ratio and distributor ingas fluidized beds, Chem. Eng. J., 93, 151.

Saxena, A., Chatterjee, A., and Patel, R. C. (1979). Effect of distributors on gas-solid fluidiza-tion, Powder Technol., 22, 191.

Saxena, S. C. and Waghmare, B. (2000). Investigation of pressure fluctuation history recordsof gas-solid fluidized beds, Int. J. Energy Res., 24, 495.

Schouten, J. C. and van den Bleek, C. M. (1998). Monitoring the quality of fluidization usingthe short-term predictability of pressure fluctuations, AIChE J., 44, 48.

Song, J. C., Fan, L. T., and Yutani, N. (1984). Fault detection of the fluidized bed distributorby pressure fluctuation signal, Chem. Eng. Commun., 25, 105.

Svensson, A., Johnsson, F., and Leckner, B. (1996). Fluidization regimes in non-sluggingfluidized beds: The influence of pressure drop across the air distributor, Powder Technol.,86, 299.

van der Schaaf, J., Schouten, J. C., Johnsson, F., and van den Bleek, C. M. (1999). Bypassingof gas through bubble chains and jets in circulating fluidized beds, in: Proceedings of the6th International Conference on Circulating Fluidized Beds, ed. J. Werther, 47,DECHEMA, Frankfurt am Main.

van Ommen, J. R., Coppens, M.-O., van den Bleek, C. M., and Schouten, J. C. (2000). Earlywarning of agglomeration in fluidized beds by attractor comparison, AIChE J., 46, 2183.

van Ommen, J. R., Schouten, J. C., Coppens, M.-O., and van den Bleek, C. M. (2001a).Monitoring fluidized bed hydrodynamics to detect changes in particle size distribution,paper presented at Fluidization X, May, Beijing.

van Ommen, J. R., Schouten, J. C., Lin, W., Coppens, M.-O., Dam-Johansen, K., and van denBleek, C. M. (2001b). Timely detection of agglomeration in biomass fired fluidized beds,paper #131 presented at the16th International Conference on Fluidized Bed Combustion,May, Reno, Nevada.



van Ommen, J. R., Schouten, J. C., and van den Bleek, C. M. (1998). Monitoring fluidizationdynamics for detection of changes in fluidized bed composition and operating conditions,in: Proceedings of the ASME Heat Transfer Division—1998: Presented at the 1998 ASMEInternational Mechanical Engineering Congress and Exposition, November 15–20, 1998,Anaheim, California, ed. R. A. Nelson, Jr., T. Chopin, and S. T. Thynell, vol. 5, 395,American Society of Mechanical Engineers, New York.

van Ommen, J. R., Schouten, J. C., and van den Bleek, C. M. (1999). Monitoring fluidizationdynamics for detection of changes in fluidized bed composition and operating conditions,J. Fluids Eng., 121, 887.

Wallis, G. B. (1969). One-Dimensional Two-Phase Flow, McGraw-Hill, New York.Wen, C. Y. and King, D. F. (1980). Distributor design, in Proceedings of the DOE=WVU

Conference on Fluidized-Bed Combustion System Design and Operation, 164.Werther, J. and Wein, J. (1994). Expansion behavior of gas fluidized beds in the turbulent

regime, AIChE Symp. Ser., 301, 31.Wu, C. S. and Whiting, W. B. (1988). Interacting jets in a fluidized bed, Chem. Eng. Commun.,

73, 1.Yang, W. C. and Keairns, D. (1979). Estimating the jet penetration depth of multiple vertical

grid jets, Ind. Eng. Chem. Fundam., 18, 317.Yang, Z., Tung, Y., and Kwauk, M. (1985). Characterizing fluidization by the bed collapsing

method, Chem. Eng. Commun., 39, 217.Yates, J. G., Wu, K. T., and Cheesman, D. J. (1995). Bubble coalescence from multiple entry

nozzles, in Fluidization VIII: Proceedings of the Eighth Engineering Foundation Conferenceon Fluidization, May 14–19, 1995, Tours, France, 335, Engineering Foundation,New York.

Zenz, F. A. (1957). Fluid catalyst design data: VI. Particle size affects initial fluidization, Pet.Refiner., 36, 305.



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