state of the art turbulent fluidization

*Corresponding author. Tel.: #1-604-822-3121; fax: #1-604-822-6003.

E-mail address: [email protected] (J. R. Grace).

Chemical Engineering Science 55 (2000) 4789}4825

Review

A state-of-the-art review of gas}solid turbulent #uidization

H. T. Bi, N. Ellis, I. A. Abba, J. R. Grace*Fluidization Research Centre, Department of Chemical and Biological Engineering, University of British Columbia, 2216 Main Mall, Vancouver, BC,

Canada, V6T 1Z4

Received 31 August 1999; accepted 27 March 2000

Abstract

Turbulent #uidization has only been widely recognized as a distinct #ow regime for the past two decades, even though it iscommonly utilized in industrial #uidized-bed reactors due to vigorous gas}solids contacting, favourable bed-to-surface heat transfer,high solids hold-ups (typically 25}35% by volume), and limited axial mixing of gas. Despite its practical importance, turbulent#uidization has received much less attention than the adjacent #ow regimes of bubbling, slugging and fast #uidization, due to thechallenges of experimental and theoretical work related to this #ow regime. However, recent years have seen an upsurge in interest inturbulent #uidization. Various methods } pressure #uctuations, visual observations, capacitance signals, optical "bre probes and bedexpansion } have been used to determine the transition velocity, usually denoted;

c, at which turbulent #uidization begins. Di!erent

methods tend to give di!erent results. There appear to be as many as three di!erent types of turbulent #uidization, depending on suchfactors as mean particle size, particle size distribution, column diameter and internal ba%es, if any. When turbulent #uidization ispreceded by bubbling, ;

cdenotes a change from closed laminar bubble wakes to open turbulent wakes. The upper boundary of

turbulent #uidization occurs when a distinct upper bed surface disappears due to substantial entrainment. Much of the literatureregarding the turbulent #uidization #ow regime adopts the terminology of the bubbling regime, ascribing such properties as bubblediameter and bubble rising velocity, despite the transitory and distorted nature of the voids. Turbulent beds exhibit non-uniformradial voidage distributions, with lower time-mean voidages near the wall than in the interior of the column. Axial mixing of both gasand solids is usually characterized by axial dispersion coe$cients and Peclet numbers which depend on the column dimensions, aswell as the gas and particle properties. Empirical equations are presented for prediction of these quantities for both gas and solids.Surface-to-bed convective heat transfer coe$cients tend to reach a maximum in the turbulent #uidization regime. When turbulentbeds are represented by two-phase models, interphase mass exchange is rapid. Reactor models vary widely, some treating theturbulent bed as a single phase homogeneous suspension subject to axial dispersion, while others assume two-phase behaviour.A probabilistic approach that merges these approaches as the gas velocity increases shows promise. While considerable progress hasbeen made, substantial challenges remain in understanding and characterizing the turbulent #uidization #ow regime. ( 2000Elsevier Science Ltd. All rights reserved.

Keywords: Fluidization; Turbulence; Multiphase #ow; Hydrodynamics; Mixing; Multiphase reactors

Contents

1. Historical development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4790

2. Existence of and transition to turbulent #uidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47912.1. Modes of turbulent #uidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47912.2. Existence of turbulent #uidization #ow regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47912.3. Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47922.4. Factors in#uencing transition velocity, ;

c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4793

2.5. Comparison for ;c

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47942.6. Transition mechanisms and modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4794

0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 1 0 7 - X

3. Transition from turbulent to fast #uidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47963.1. Transport velocity (;

53) based on phase diagram method . . . . . . . . . . . . . . . . . . . . . 4796

3.2. Critical velocity, ;se, based on solids entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . 4797

3.3. Transition velocity, ;k, based on pressure #uctuations . . . . . . . . . . . . . . . . . . . . . . . 4798

3.4. Comparison of ;53, ;

seand ;

k. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4799

3.5. Identi"cation of data pertaining to turbulent #uidization regime . . . . . . . . . . . . . . . 4799

4. Local #ow structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47994.1. Local voidage and void-phase fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47994.2. Local void size and rise velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48004.3. Radial and axial voidage distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48014.4. Turbulence characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4802

5. Gas and solids mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48035.1. Gas mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48035.2. Solids mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4807

6. Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48086.1. Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48086.2. Heat transfer in the freeboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48106.3. Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810

7. Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48117.1. Interphase transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48117.2. Gas/particle mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4811

8. Solids entrainment in turbulent #uidized beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48138.1. Entrainment #ux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48138.2. Transport disengagement height (TDH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4814

9. Modelling and reactor performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4814

10. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4819

Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4819

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4821

1. Historical development

The turbulent #uidization #ow regime is commonlyconsidered to lie between bubbling #uidization and thefast #uidization regime. It has been characterized by lowamplitude of pressure #uctuations, resulting from thedisappearance of large bubbles/voids. The "rst photo-graph of a turbulent #uidized bed, distinctly di!erentfrom bubbling #uidization, was published by Matheson,Herbst and Holt (1949). A turbulent #uidization regimewas introduced in the #ow regime diagram of Zenz(1949). The "rst quantitative study seems to have beenperformed by Lanneau (1960) who measured local void-age, voidage #uctuations and pierced void lengths ina 76 mm ID #uidized bed with "ne catalyst particles athigh gas velocities, although the transition from bubbl-ing/slugging to the turbulent regime was not quanti"ed.Kehoe and Davidson (1970) extended their work onslugging to higher velocity operation and identi"ed the

transition from bubbling to turbulent #uidization basedon visualization of a 2-D bed and bubble rise velocityand capacitance traces in a 3-D column. Later the turbu-lent #uidization regime was reported by Massimilla(1973), Thiel and Potter (1977) and Crescitelli, Donsi,Russo and Clift (1978). In these early studies, transition toturbulent #uidization was generally determined based onvisual observations and local voidage or pressure traces.

The "rst transition criterion was proposed byYerushalmi, Cankurt, Geldart and Liss (1978) to quantifythe transition from bubbling/slugging to turbulent #ui-dization. The gas velocity, ;

c, at which the standard

deviation of pressure #uctuations reached a maximumwas said to mark the beginning of the transition toturbulent #uidization, while;

k, where the standard devi-

ation of the pressure #uctuations levels o!, was said todenote the end of the transition. In recent years, ;

chas

been widely adopted to de"ne the transition to turbulent#uidization.

4790 H. T. Bi et al. / Chemical Engineering Science 55 (2000) 4789}4825

Table 1Some commercial turbulent #uidized bed reactors

Process Particleclassi"cation

Typical gasvelocity (m/s)

FCC regenerators Group A 0.5}1.5Mobil MTG reactors Group A &0.5Acrylonitrile Group A &0.5Maleic anhydride Group A &0.5Phthalic anhydride Group A &0.5Ethylene dichloride Group A &0.5Roasting of zinc sul"de Group B &1.5

There were only a few works on turbulent #uidizationbefore 1975 when most researchers focused on bubbling#uidization. From 1975 to 1985, there were about 10papers published on turbulent #uidization, indicatingsome growth in research interest. Since 1985, research onturbulent #uidization has gained momentum with anaverage of about four papers per year. Although moststudies have been focused on the transition from bubbl-ing/slugging to turbulent #uidization, papers have begunto deal with gas and solids backmixing, gas-to-solids andinterphase mass transfer and reactor performance.

Industrial application of turbulent #uidized beds in-cludes chemical and metallurgical processes, as listed inTable 1. Yerushalmi and Avidan (1985) reviewed theearly work on turbulent #uidization. Since then, signi"-cant progress has been made in improving understandingof turbulent #uidization and its applications. The objec-tive of this review is to summarize available informationon turbulent #uidization and to focus on aspects whichneed to be advanced in the future.

2. Existence of and transition to turbulent 6uidization

2.1. Modes of turbulent yuidization

Previous experimental work using a variety of tech-niques and indices indicates that there are at least threedi!erent types of transitions to turbulent #uidization:

Type I: A relatively sharp transition to a hydrodynamicregime which is physically distinct from other regimes(Kehoe & Davidson, 1970; Yerushalmi et al., 1978; Cres-citelli et al., 1978; Yang & Chitester, 1988; Tsukada,Nakanishi & Horio, 1993).

Type II: A gradual transition involving intermittentslug-like structures interspersed with periods of fast-#ui-dization-like behaviour, the latter becoming predomi-nant with increasing super"cial gas velocity (Crescitelli etal., 1978; Rowe & MacGillivray, 1980; Brereton & Grace,1992; Mchirgui, Tadrist & Radev, 1999).

Type III: A relatively gradual transition to distinctivebehaviour for shallow beds (H

mf/D

t(2) of large par-

ticles (Canada, McLaughlin & Staub, 1978; Chyang& Huang, 1988; Dunham, Mann & Grewal, 1993).

Type I transitions generally occur in non-slugging sys-tems of "ne (Geldart group A) particles, while Type IIcorresponds to slugging (i.e. group B and presumably D)systems. Type III transitions result from the penetrationof gas jets in shallow #uidized beds of large particleswhere fully developed slug #ow is never achieved due tothe limited bed depth. Type I and Type II transitions aredistinguished based on the ratio of maximum stablebubble diameter to the column diameter, i.e.dB.!9

/Dt(0.7 for Type I transition, while Types II and

III can be distinguished by the Hmf

/Dt

ratio. Type IIcorresponds to slugging systems where H

mf/D

tis larger

than about 2, while dB.!9

/Dtis larger than about 0.7.

2.2. Existence of turbulent yuidization yow regime

The bubbling, slugging and fast #uidization #ow re-gimes have been widely studied and accepted by #uidiz-ation researchers. However, the turbulent #uidization#ow regime has been controversial and not always accep-ted as a separate #ow regime (e.g. see discussion followingLanneau, 1960; Rowe & MacGillivray, 1980; Geldart& Rhodes, 1986; Rhodes & Geldart, 1986b; Rhodes,1996, 1997).

The existence of a turbulent #uidization #ow regimeparallels the churn-turbulent #ow regime for gas}liquidtwo-phase #ows, and it is worth noting that this too hasbeen subject to controversy (Hewitt & Jayanti, 1993). Inboth cases, at lower super"cial gas velocities, one "ndseither bubbly #ow or, for tubes of relatively small dia-meters, slug #ow, with bubbles or slugs dispersed ina continuous phase comprised of liquid (for gas}liquid#ows) or particles and interstitial gas (for gas}solid#uidized beds). At high super"cial gas velocities, one"nds annular mist #ow (for gas}liquid systems) or fast#uidization (gas}solid systems). The churn-turbulent andturbulent #uidization #ow regimes then representtransitional regions between lower velocity #ow regimes(bubbling or slugging), where there is a dense continuousphase, and a higher velocity #ow regime (annular mist orfast #uidization), where gas forms the continuous phaseand there is a relatively dense annular region at the outerwall. The turbulent #uidization #ow regime may then bede"ned as the range in which there is no clear continuousphase, but instead, either via intermittency or by inter-spersing voids and dense regions, a competition betweendense and dilute phases in which neither gains theascendancy.

A complementary manner of explaining the existenceis to consider the population of bubbles as the gas #owrate increases in the bubbling #ow regime. As more gas#ow must be accommodated, the volume occupied bybubbles increases and a greater and greater fraction of

H. T. Bi et al. / Chemical Engineering Science 55 (2000) 4789}4825 4791

Fig. 1. De"nitions of transition velocities, ;c

and ;k, based on stan-

dard deviation of pressure #uctuations.

their time is spent in pursuit of other bubbles. Ultimately,when the bubbles occupy approximately half the volumeof the bed, it is no longer possible for them to maintainindividual identity, and bubbling breaks down intoa chaotic state.

Grace, Issangya, Bai and Bi (1999a) proposed severalcriteria to be satis"ed for any #ow regime:

f There must be distinctive features: The darting transi-tory voids viewed in Type I turbulent #uidizationdistinguish turbulent #uidization from the other #ui-dization #ow regimes.

f There must be distinctive trends. Such features as theradical improvement in gas}solid contacting (Mas-similla, 1973), reversal of the direction of the pressure#uctuation vs. gas velocity plots (Yerushalmi & Can-kurt, 1979), change in the tendency for gas mixing tovary with gas velocity (see Section 5.1), unique statist-ical and chaotic properties (Bai, Issangya & Grace,1999) and a decrease in the amplitude of the root meansquare force on immersed horizontal tubes (Grace& Hosny, 1985) are clear examples of distinctivetrends.

f A #ow regime should also be capable of being both fullydeveloped and statistically steady. This criterion alsoappears to be met by the turbulent #uidization #owregime as de"ned above.

The controversy over the existence (or non-existence)of the turbulent #uidization #ow regime appears to havelargely originated from the two transition velocities,;

cand ;

k, introduced by Yerushalmi and Cankurt

(1979) and shown schematically in Fig. 1. The confusionhas arisen because these authors proposed that;

kmarked the onset of turbulent #uidization, whereas

subsequent authors have found either that ;k

does notexist or that it marks the end of the turbulent #ow regime,i.e. the transition from turbulent #uidization to fast #ui-dization. Details are discussed below. Turbulent #uidiz-ation is now widely accepted as extending from;

cto the

onset of fast #uidization, and this is the range consideredin this review article.

2.3. Measurement techniques

Several measurement methods have been utilized todetermine the transition from bubbling or slugging toturbulent #uidization including visual observation, localcapacitance, pressure #uctuations and local and overallbed expansion. Based on signals from pressure trans-ducers, capacitance probes, optical "bre probes, X-rayfacilities, as well as manometers, several transition cri-teria have been proposed.

(a) Visual observations: Kehoe and Davidson (1970)de"ned turbulent #uidization as a state of continuouscoalescence } virtually a channeling state with tongues of#uid darting in zigzag fashion through the beda. Beyondthe point where this regime was initiated, it was impos-sible to detect slugs on traces from capacitance probes.This de"nition has been adopted in some subsequentstudies (e.g. Crescitelli et al., 1978; Thiel & Potter, 1977;Massimilla, 1973; Yang & Chitester, 1988). Thetransition in Geldart group A particle systems seems tobe sharp, but in slugging systems with group B andD particles it is gradual. As a result, the transition toturbulent #uidization could only be identi"ed based onvisual observations in non-slugging systems (Thiel& Potter, 1977).

(b) Heterogeneity index: Local voidage #uctuationsmeasured by capacitance and optical "bre probes havealso been used to deduce the transition to turbulent#uidization. Kehoe and Davidson (1970) and Crescitelliet al. (1978) de"ned the transition as the point where it isimpossible to detect slugs in capacitance traces. Thestandard deviation of the local voidage #uctuations in-creases with increasing super"cial gas velocity anddecreases slightly after reaching a maximum value(e.g. Abed, 1984; Chehbouni, Chaouki, Guy & Klvana,1994). It is thus di$cult to determine a transition pointbased on the standard deviation of local voidage #uctu-ations. Alternative approaches have been developed todetermine the transition based on local voidage signals.Lanneau (1960) de"ned a heterogeneity indexa as e!ec-tively half the average absolute deviation of the local beddensity from its mean value based on capacitance signals.This quantity increased with increasing ; before reach-ing a maximum, after which it decreased. Lancia, Nigro,Volpicelli and Santoro (1988) de"ned a similar index todetermine the transition. Transition velocities deter-mined in this manner appear to be lower than from thepressure #uctuation method.

(c) Bed expansion: Avidan and Yerushalmi (1982) iden-ti"ed an abrupt change in the bed expansion with in-creasing super"cial gas velocity, and ascribed this to thetransition from bubbling to turbulent #uidization.Lee and Kim (1990a), Yamazaki, Asai, Nakajima and


Fig. 2. Comparison of transition velocity,;c, from absolute and di!er-

ential pressure #uctuations (Bi & Grace, 1995).

Jimbo (1991) and Nakajima Harada, Asai, Yamazakiand Jimbo (1991) reported similar data. However,in #uidized beds where entrained particles are e$cientlyreturned to the bed at high gas velocities, such abruptchanges tend to disappear (Geldart & Rhodes, 1986;Grace & Sun, 1991; Bi & Grace, 1995). Hence, thismethod tends to be dependent on the solids collectionand return system.

(d) Pressure yuctuations: Most research groups,beginning with Yerushalmi and Cankurt (1979), haveutilized the velocity, ;

c, de"ned above, to demarcate

the transition to turbulent #uidization. Determination of;

cand ;

kare shown schematically in Fig. 1. Ex-

tensive studies have also been carried out to quantifythese two transition points. However,;

koften cannot be

identi"ed (e.g. Satija & Fan, 1985; Rhodes & Geldart,1986b) and depends on the system used to return par-ticles captured after being carried out of the bed (Bi& Grace, 1995) and measurement location (Chehbouni etal., 1994). Hence ;

chas become widely accepted as the

standard means of delineating the transition to turbulent#uidization.

Both absolute (single-point) and di!erential (two-point) pressure #uctuations have been measured to assessthe transition to turbulent #uidization. The recordedpressure signals have been interpreted in terms of averagepeak-to-peak amplitude, maximum peak-to-peak ampli-tude, peak-to-average amplitude, standard deviation,normalized standard deviation, skewness, etc. Some re-searchers (Avidan & Yerushalmi, 1982; Lee & Kim, 1988)have claimed that the same transition point can be ob-tained from alternative techniques. Others (Cai, 1989;Lee & Kim, 1988; Brereton & Grace, 1992) showed that;

c, evaluated from di!erent interpretations can di!er. Bi

and Grace (1995) showed that ;cvalues based on abso-

lute and di!erential pressure #uctuations di!er. The di-mensional standard deviation also gives a di!erent;

cvalue from the dimensionless standard deviation nor-

malized by the average absolute or di!erential pressuremeasurement. The maximum peak-to-average valuemethod appears to give more or less the same;

cvalue as

the dimensional standard deviation method. ;c

fromdi!erential pressure #uctuations varies with the measure-ment interval, while ;

cfrom absolute pressure #uctu-

ations is relatively insensitive to axial location. Thesephenomena can be explained (Bi & Grace, 1995) basedon the origin and transmission of pressure #uctuations ingas}solids #uidized beds.

Fig. 2 compares transition velocities determined fromabsolute and di!erential pressure #uctuations. It is seenthat ;

cfrom di!erential pressure #uctuations is system-

atically higher than from absolute pressure #uctuations.The transition velocities from visual observations andfrom the bed expansion method are consistent with;

cfrom absolute pressure #uctuations, because all three

re#ect global #uctuations of the #uidized bed. Since the

in#uence of di!erent measurement methods and dataanalysis methods is signi"cant, it is essential to standar-dize (Brereton & Grace, 1992) or to fully report allexperimental details so that experimental data from dif-ferent sources can be compared.

2.4. Factors inyuencing transition velocity, ;c

In measurements of pressure #uctuations, tubes ofvarious lengths are connected to a pressure transducer.To prevent particles from blocking the probe, the probeneeds to be either purged by gas or "tted with a "lter.When the probe is continuously purged, the issuing gasmay disturb the #ow "eld around the probe tip. On theother hand, a high resistance "lter can damp pressuresignals. While the intensity of pressure #uctuations de-creases with increasing probe resistance, the peak pointdoes not shift appreciably, indicating that ;

cis not

signi"cantly a!ected by the probe resistance, so long asthe probe has the same resistance in all experiments.

Grace and Sun (1990) and Bi and Grace (1995) foundthat the transition velocity ;

cdetermined from di!eren-

tial pressure signals over the same interval was almostindependent of the static bed height, which varied from0.4 to 1.0 m. Similar results were reported by Cai (1989)and Satija and Fan (1985) based on absolute pressure#uctuations with H

mf/D

t2. On the other hand, for

a shallow #uidized bed of Hmf

/Dt(2 with Group B and

D particles, Canada et al. (1978) and Dunham et al.(1993) found that ;

cincreased with static bed height.

This could be related to the undeveloped bubble #ow inshallow beds before transition to turbulent #uidizationcan occur.

Since column diameter may a!ect bubble size andbubble rise velocity, the transition velocity ;

cis in-

#uenced by the column diameter. As shown in Fig. 3 fromCai (1989),;

cdecreases with increasing column diameter

for small columns, becoming insensitive to column dia-meter for D

t0.2 m. Similar trends were observed by

Zhao and Yang (1991) in columns with internals.;

cincreases with increasing mean particle size and


Fig. 3. E!ect of column diameter on transition velocity, ;c

(adaptedfrom Cai, 1989).

Fig. 4. E!ect of gas density on transition velocity ;c.

density. Sun and Grace (1990) and Ihara, Kayou andNatori (1996) showed that ;

calso depends on the par-

ticle size distribution, with wider distributions givinglower pressure #uctuations and lower ;

cthan particles

of narrow size distributions.Lanneau (1960) found that the transition velocity

based on the heterogeneity indexa decreased with in-creasing system pressure. Later experiments (Yang& Chitester, 1988; Cai, Chen, Jin & Wang, 1989; Tsukadaet al., 1993; Marzocchella & Salatino, 1996) con"rmedthis trend (see Fig. 4). Such an e!ect may be related toimproved #uidization quality due to the reduction inbubble size in pressurized #uidized beds.

Only a few studies have reported the e!ect of temper-ature (e.g. Peeler, Lim & Close, 1999). Cai et al. (1989)and Foka et al. (1996) discovered that;

cincreases as the

temperature is increased at constant pressure, although

the amplitude of pressure #uctuations was reduced athigher temperatures. The lower amplitude of pressure#uctuations at elevated temperature has been related tosmoother #uidization and smaller bubbles (Kai &Furusaki, 1985; Knowlton, 1992; Rapagna, Foscolo& Gibilaro, 1994), while the higher transition velocity;

cmay result from the lower gas phase density and

higher gas viscosity.Various types of internals have been widely used in

commercial #uidized-bed reactors for heat transfer, im-proved contacting, etc. Internals usually restrict bubblegrowth and promote bubble breakup. Transition to tur-bulent #uidization thus tends to occur at lower gas vel-ocities in the presence of internals. Zhao and Yang (1991)and Jin, Yu, Wang and Cai (1986) measured ;

cin beds

containing various types of internals and found that theygenerally reduced the transition velocity ;

c.

2.5. Comparison for ;c

A number of equations have been developed to predictthe transition velocity ;

c, as listed in Table 2. Bi and

Grace (1995) evaluated these correlations based on theavailable data. The AP (absolute pressure) equation of Biand Grace (1995) and that of Cai et al. (1989) appear togive the best predictions for absolute pressure #uctuationmeasurements. These two equations also give good pre-diction of the data from bed expansion measurements,con"rming that the transition velocity based on bedexpansion measurements are close to those from absolutepressure #uctuation measurements. The DP (di!erentialpressure) equation of Bi and Grace (1995) best predictsthe di!erential pressure data. For di!erential pressure#uctuation data, the root mean square deviation is gener-ally larger than 0.30 m/s, indicating considerable scatter.This is in part because ;

cvaries with axial location,

a factor neglected in all correlations. All equations showpoor agreement with data from visual observationmethods. In addition, recent data from Peeler et al. (1999)show that the in#uence of temperature is not well pre-dicted by the various correlations.

2.6. Transition mechanisms and modelling

To explain the transition from bubbling to turbulent#uidization, Yang (1984) proposed that clusters of par-ticles obey laws similar to those governing the behaviourof individual particles #uidized in a homogeneous man-ner. Based on the maximum velocity of continuity waves,he obtained:

;c";

iAm!1

m Bm

(1)

where ;iis the terminal velocity of particle clusters, and

m, the Richardson and Zaki (1954) index, is determinedbased on bed expansion tests.


Table 2Correlations for transition velocity, ;

c

Source Equations No.

Yerushalmi and Cankurt (1979) ;c"3.0(o

pdp)0.5!0.77 (a)

Yang (1984) ;c";

ieme

(b);

i";

tRe~0.485

tee"(m!1)/m

m"2.31 Re~0.0547t

Jin et al. (1986);

c

Jgdp

"AfD

tdp

op!o

gogB0.27 (c)

fDt"0.00367 (for bed without internals)

fDt"0.00232 (for bed with vertical tubes)

fDt"0.00032 (for bed with pagoda type ba%es)

Zhao & Yang (1991) ;c";

ienmfA

n#1n!1B

n (d)

;i"14.55;

tRe~0.6038

t Aop

1000ogB

~0.3738(for D

t0.3 m)

n"6.807Re~0.135t

;c";

cDDt/0.3 .

#0.833(0.3!Dt) (for D

t(0.3 m) (e)

Lee and Kim (1988) Rec"0.700Ar0.485 (f)

Cai et al. (1989);

c

Jgdp

"Akg20kgB

0.2

CA0.211

D0.27t

#0.00242

D1.27t

[email protected]

Aog20ogB A

op!o

gogB A

Dt

dpBD

0.27 (g)

Sun and Chen (1989) ;c"1.74d2

pAop!o

gogB

2

Aop/(o

p!o

g)!e

mf1!e

mfB

2g0.5

Z1.5c

#;mf

(h)

where

Zc"2.25S

0.6Dt

dB.!9

#0.6Dt

dB.!9

dB.!9

"1.32dpA

op!o

gogBA

op/(o

p!o

g)!e

mf1!e

mfB

2

Leu, Huang and Gua (1990) Rec"0.568Ar0.578 (i)

Horio (1991) Rec"0.936Ar0.472 ( j)

Nakajima et al. (1991) Rec"0.663Ar0.467 (k)

Dunham et al. (1993) Rec"1.201Ar0.386(H/D

t)0.128-/(opdp )0.264 (l)

for Group A and B articles, andRe

c"1.027Ar0.450(H/D

t)0.128-/(opdp )0.264 (m)

for Group D particles

Bi and Grace (1995) (DPF data) Rec"1.243Ar0.447 (n)

Bi and Grace (1995) (APF data) Rec"0.565Ar0.461 (o)

Chehbouni, Chaouki, Guy and Klvana (1995) ;c/JgD

t"0.463Ar0.145 (p)

Geldart and Rhodes (1986) accounted for ;cin terms

of transport of particulate material beyond the pressuretaps recording the #uctuations. With increasing gas #ow,the bed expands, while freeboard hold-up increases caus-

ing a decrease in bed height. ;c

was said to be reachedwhen the two opposing processes balance, i.e. where thebed height reaches a maximum. Such a mechanism,however, fails to explain the maximum in the pressure


#uctuations with two pressure taps always immersed inthe dense bed. Furthermore, Avidan and Yerushalmi(1982), Zhao and Yang (1991) and Svensson, Johnssonand Leckner (1993) showed that;

cbased on bed expan-

sion and standard deviation of both absolute and di!er-ential pressure #uctuations does not correspond to thepoint at which the bed height reaches a maximum be-cause the bed height continues to increase beyond ;

c.

Sun and Chen (1989) modelled the transition based onthe maximum stable bubble size. ;

cis assumed to be

reached when bubbles reach their maximum stable size ata certain height, causing bubble breakdown to becomepredominant. With the bubble size predicted by theequation of Rowe (1976), they obtained:

;c";

mf#d2

B.!9g0.5/z1.5

c(2)

with dB.!9

estimated (Harrison, Davidson & de Kock,1961) by

dB.!9

"1.32dpA

op!o

gog BA

op!o

gog

!emf

1!emf

B (3)and z

ccorrelated by

zc"2.25A

0.6Dt

dB.!9

#0.6DtB

0.5dB.!9

. (4)

Based on the coherence function of pressure signalsfrom two pressure transducers one above the other, Cai,Jin, Yu and Wang (1990) postulated that the bed under-goes a transition from bubbling to turbulent #uidizationwhen bubble break-up predominates over coalescence.Hence ;

cis said to be reached when:

L2NB

L;2 KU/Uc

"0 (5)

where NB

is the number of bubbles per unit bed volume.Cai et al. (1990) derived equations for;

cwith the bubble

rise velocity estimated by the Davidson and Harrison(1963) equation, and the bed voidage correlated(Cai et al., 1989) by

e"A0.796#0.00894

DtBA

Re3Ar2B

0.0653(6)

Li, Kwauk and Reh (1992) predicted ;c

based onenergy dissipation minimization. ;

cwas predicted to be

reached when the bubble phase volume fraction reached0.5, as proposed by Grace (1986b). However, Hyre andGlicksman (1997) discount the idea of energy or pressuredrop minimization. Yamazaki et al. (1991) considered theformation of vertically aligned bubbles connected bychannels at the transition from bubbling to turbulent#uidization. The channel fraction was found to be almostzero in the bubbling condition, increasing rapidlybeyond ;

c.

Based on an analogy to gas}liquid two-phase #ow, Bi,Grace and Lim (1995a) postulated that bubbles reach

maximum stable size when their wakes transform froma closed laminar to an open turbulent structure. Whena following bubble enters a turbulent wake of a leadingbubble, the trailing bubble tends to split. The onset ofmassive bubble break-up then transforms the #ow frombubbling to turbulent #uidization as bubble splittingbecomes dominant. The analysis led to:

;c";

mf#2.59Ar0.04l1@3d>!0.3Ar0.04 (7)

where >"0.8 for Group A particles, while ld

can beestimated by

ld"0.00374Ar0.0764 (8)

based on experimental data for spherical particles evalu-ated from a rotating cylinder viscometer (SchuK gerl, Merz& Fetting, 1961) and from bubble shapes (Grace, 1970).

All of these criteria relate the transition process toa change of void behaviour in non-slugging systems.Bubble behaviour at high gas velocities, however, is notwell understood due to severe distortion caused bybubble}bubble interactions. A key point in seeking thetransition mechanism is to understand void behaviour athigh gas velocities.

3. Transition from turbulent to fast 6uidization

The transition from turbulent #uidization to fast #ui-dization is characterized by signi"cant entrainment ofparticles, setting an upper limit on the gas velocity forbatch operation, and a lower limit for the disappearanceof the upper dense}dilute interface. There are two typesof transition criteria, one based on solids entrainmentbehaviour and the other on solids concentration pro"les.Table 3 classi"es existing criteria into these twocategories.

3.1. Transport velocity (;53) based on phase diagram

method

According to Yerushalmi and Cankurt (1979), a criti-cal solid circulation rate may exist where a sharp changein the pressure gradient occurs when the solids circula-tion rate is varied at a given gas velocity in the riser ofa circulating #uidized bed (see Fig. 5). As the gas velocityincreases beyond a certain point, the sharp change inpressure gradient disappears, with the gas velocity at thiscritical point de"ned as the transport velocity ;

53. This

method has been widely used to determine the transportvelocity. However, some researchers (Rhodes & Geldart,1986a; Schnitzlein & Weinstein, 1988; Bi, Grace & Zhu,1995b) reported that it was di$cult to identify sucha transition point in their systems, while a close examina-tion of the pressure gradient pro"les reported by


Table 3Methods for determining transition from turbulent to fast #uidization

Author Method Type

Lewis Gilliland and Bauer (1949) Bed expansion versus ; Solid concentrationYerushalmi Turner and Squires (1976)Schnitzlein and Weinstein (1988)Yerushalmi and Cankurt (1979) !dP/dz};}G

sphase diagram Solid concentration

Bi, Jang and Fan (1991)Horio et al. (1992)Adanez, de Diego and Gayan (1993)Chen, Li, Wang, Wang and Kwauk (1980) Voidage } ;}G

sphase diagram Solid concentration

Li and Kwauk (1980)Leu et al. (1990) Pressure #uctuations Solid concentrationYang, Rong, Chen and Chen (1990)Han, Lee and Kim (1985) Emptying-time versus ; EntrainmentPerales et al. (1991)Chehbouni et al. (1995)Schnitzlein and Weinstein (1988) Maximum G

sversus ; Entrainment

Le Palud and Zenz (1989) Elutriability versus dp

EntrainmentBi et al. (1995b) Saturated G

sversus ; Entrainment

Fig. 5. De"nition of transport velocity, ;53, by Yerushalmi and

Cankurt (1979).

Table 4Correlations for ;

53

Author Equation

Lee and Kim (1990b) Re53"2.916Ar0.354

Perales et al. (1991) Re53"1.415Ar0.483

Bi and Fan (1992) Re53"2.28Ar0.419

Adanez et al. (1993) Re53"2.078Ar0.458

Tsukada, Nakamishi and Horio (1994) Re53"1.806Ar0.458

Chehbouni et al. (1995) Re53"0.169Ar0.545(D

t/d

p)0.3

Yerushalmi and Cankurt (1979) reveals that ;53

varieswith axial location.

An analysis by Bi (1994) showed that the transportvelocity, ;

53, based on the phase diagram of Yerushalmi

and Cankurt (1979) may indicate a transition of axialvoidage pro"les in the riser, analogous to the criticalpointa in a phase diagram (Matsen, 1982; Klinzing, 1981).Below this velocity, a distinct interface exists between thetop dilute region and the bottom dense region whena su$cient solids circulation rate can be ensured. Beyondthis velocity, the interface becomes relatively di!use. Thevariation of voidage with height tends to be relativelysmooth. However, such a transition relies on themeasurement method and on interpretation of the data.

Li and Kwauk (1980) de"ned a transport velocity incirculating #uidized-bed systems, based on a plot of bed

voidage versus solids circulation rate at various super"-cial gas velocities. They de"ned the transport velocity asthe point below which the bed remained in a densecondition and above which the unit could be operated ina dilute phase transport state. This transport velocity isclearly lower than that de"ned by Yerushalmi andCankurt (1979).

To increase the accuracy of determining the transportvelocity, Horio, Ishii and Nishimuro (1992) calculatedthe maximum [L(!dP/dz)/LG

s]U

at di!erent gas vel-ocities and then plotted this derivative against the super-"cial gas velocity. The resulting curve allows ;

53to be

determined by extrapolation. Several correlations havebeen developed to predict the transport velocity, ;

53, as

listed in Table 4. In view of the scatter in the experimentaldata due to changes in measurement location, columndiameter, height, etc., it is di$cult to judge which correla-tion gives the best prediction.

3.2. Critical velocity, ;se

, based on solids entrainment

Solids entrainment in #uidized beds at low and inter-mediate gas velocities has been well documented (e.g. see


Fig. 6. De"nition of transition velocity, ;se

(Bi et al., 1995b).

Fig. 7. Reciprocal of bed emptying time as a function of ; based ondata of Perales et al. (1991) for FCC particles, d

p"80 lm,

op"1715 kg/m3.Geldart, 1986). Entrainment at higher ; has also been

reported in recent years (e.g. Yerushalmi et al., 1978; Gao,Zhao, Qiu & Ma, 1991). In gas}solids transport systems,solids #ux and gas velocity are related by

Gs"o

p(1!e)A

;e!;

4-*1B. (9)Since the apparent bed density at high gas velocities isnot sensitive to the gas velocity and solids circulationrate (Bi et al., 1995b), a linear relationship betweenG

sand; in the high gas velocity range with e constant in

Fig. 6 suggests that ;4-*1

approaches a constant value,which can be determined from the intercept and slope ofthe linear portion of the curve. ;

secan be considered to

correspond to the onset of signi"cant entrainment for anassembly of particles. Schnitzlein and Weinstein (1988)proposed that the maximum solids circulation attainableat a given gas velocity be plotted versus the super"cialgas velocity. The transport velocity determined by extra-polation of the linear section of the curve to G

s"0 is the

same as;se

de"ned by Bi et al. (1995b).;se

also appearsto be similar to the critical velocity de"ned in gas}liquidvertical transport systems demarcating the transitionfrom counter-current to co-current upward transport(Wallis, 1969).

The critical velocity ;se

can also be determined inbatch-operated #uidized beds by measuring solids en-trainment or the time required to empty the bed. In a tall#uidized bed with particle inventory, =

0, the time re-

quired to blow all the bed particles out of the column(so-called emptying time) is related to the entrainmentrate by:

e"=

0/G

sA (10)

where Gs

is the entrainment #ux, corresponding to thesolids circulation #ux in a circulating #uidized bedmeasured at the exit of the column, and A is the risercross-sectional area.;

secan then be determined, as dem-

onstrated in Fig. 7 for the data of Perales et al. (1991), byplotting 1/

eversus super"cial gas velocity.

Bi et al. (1995b) collected and analysed available;

sedata based on the entrainment and emptying-time

methods. It was found that;se

is independent of columndimensions (i.e. riser height, riser diameter), geometry(e.g. solids feed device) and solids inventory when largediameter, tall risers are used. ;

se, like ;

mf, can thus be

considered a property of the bed material and gasproperties alone. Available data were correlated byRe

se"1.53Ar0.5. For large particles where Re

sefrom this

equation is less than Ret, Bi et al. suggested that ;

sebe

taken as equal to the single particle terminal velocity,;t.

3.3. Transition velocity,;k, based on pressure yuctuations

The transition velocity ;k

has been found to bea strong function of the con"guration and the solidsreturn system (Rhodes & Geldart, 1986b; Schnitzlein& Weinstein, 1988; Bi & Grace, 1995). In units whereentrained particles are e$ciently captured and returnedto the bottom of the dense bed, the standard deviationdoes not level o! until transport is reached, i.e. whereparticles are carried over signi"cantly. Based on existingexperimental data, Bi and Fan (1992) showed that ;

kis

more or less the same as the transport velocity, ;53.

Chehbouni et al. (1994), on the other hand, found that


Fig. 8. Voidage and standard deviation of pressure #uctuationsas a function of super"cial gas velocity (adapted from Schnitzlein& Weinstein, 1988).

Table 6Comparison of ;

53, ;

seand ;

kbased on literature data

Author Particles ;k

(m/s) ;se

(m/s) ;53

(m/s)

Yerushalmi and Cankurt (1979) FCC 0.61 0.90 1.37HFZ-20 1.37 1.50 2.10

Chen et al. (1980) FCC NA 1.25 1.80Rhodes and Geldart (1986b) 9G Al 1.45 1.50 NA

Al 25 1.98 1.75 NACBZ-1 1.38 1.11 NA

Horio et al. (1992) FCC 0.60 0.55 1.10sand 3.50 NA 4.50

Bi et al. (1991) Polyethylene NA 1.60 2.25Bi et al. (1995b) Sand NA 2.50 5

Table 5Correlations for ;

k

Author Equation

Yerushalmi and Cankurt (1979) ;k"7.0(o

pdp)0.5!0.77

Horio (1991) Rek"1.41Ar0.56 for Ar(104

Rek"1.46Ar0.472 for Ar104

Bi and Fan (1992) Rek"0.601Ar0.695 for Ar(125

Rek"2.28Ar0.419 for Ar125

Tsukada et al. (1993) Rek"1.31Ar0.45

;kcould be determined from di!erential pressure #uctu-

ations, but not from absolute pressure #uctuations.The levelling-o! of the standard deviation of pressure#uctuations in Fig. 8 (Schnitzlein & Weinstein, 1988) ismainly caused by the levelling-o! of bed voidage (Bi,1994). Hence ;

kis not a well-de"ned criterion to quan-

tify the transition to turbulent #uidization and may in-stead correspond to the transition to fast #uidization.Several correlations have been developed for the predic-tion of ;

kas listed in Table 5.

3.4. Comparison of ;53, ;

seand ;

k

Table 6 compares experimental ;53, ;

seand ;

kdata

from di!erent sources. ;53

is generally higher than ;se

,indicating that the change in the upper interface of thebed occurs at higher gas velocities than that correspond-ing to signi"cant entrainment of particles. Also, ;

kis

close to ;se

, con"rming that the levelling-o! of pressure#uctuations is related to signi"cant entrainment.

3.5. Identixcation of data pertaining to turbulent yuidiz-ation regime

In the subsequent sections of this review, we considerhydrodynamics, heat and mass transfer, dispersion andchemical reaction in cases where some or all of the dataalmost certainly correspond to the turbulent #uidization#ow regime, as determined by having ;

c););

se,

where ;c

is based on Eq. (o) in Table 2, and ;se

onRe

se"1.53Ar0.5 as discussed in Section 3.2.

4. Local 6ow structure

4.1. Local voidage and void-phase fraction

As the gas velocity is increased from the bubblingregime into the turbulent regime, di!erent behaviour isobserved, in particular a di!use bed surface, turbulentmotion of solids clusters, and voids of irregular shapes(Venderbosch, 1998). Many of those who have studiedturbulent #uidized beds, beginning with Lanneau (1960)have assumed two distinct phases as in bubblingbeds } a dilute (or void) phase largely empty of particlesand a dense phase containing most of the particles andinterstitial gas. If this approach is adopted, a volume


Fig. 9. Radial distributions of void fraction for spent FCC catalysts:0.2 m diameter bed, 0.85 m static bed height, ;: 0.13}0.93 m/s, axialposition above distributor: z"0.1 and 0.7 m (adapted from Nakajimaet al., 1991).

balance on the solids gives

1!e"dv(1!e

v)#(1!d

v)(1!e

d) (11)

where e is the overall voidage, dvis the void phase volume

fraction, ev

is the void phase voidage and ed

is the dense-phase voidage.

As the gas velocity is increased in the turbulent regime,the volume fraction of voids increases, while the dense-phase voidage increases above e

mf. The dense-phase

voidage is important in inventory control, process mod-elling and determination of pressure balances in #uidizedbeds (King, 1989). The measured average void fractionhas been used to estimate the dense-phase voidage(Yamazaki et al., 1991), suggesting expansion of the densephase when there is a transition from the bubbling to theturbulent #ow regime. Similarly, Werther and Wein(1994), using Geldarts Group B particles, observed a sig-ni"cant increase of dense-phase voidage, obtained fromthe probability density distribution of the capacitanceprobe signals, with increasing gas velocity. There was noclear in#uence of radial position on the dense-phasevoidage. In both of these studies, point density measure-ments were analysed to deduce the phase fractions fromprobability density functions. However, in such measure-ments the threshold value in the probability distributionfunction strongly in#uences the derived phase fraction, sothat this method is questionable.

Lee and Kim (1989b) indirectly measured the dilute-phase fraction, and the interstitial gas rise velocity fromtracer gas measurements in the dense and the dilute phasesusing Geldart group B particles. No direct measurementsof dense-phase voidage were reported for ;0.5 m/s,possibly due to the di$culty of conducting collapse testsfor high velocity #uidized beds. Wang, Wang, Jin and Yu(1997) conducted collapse tests in a column which phys-ically separated the bed and freeboard, thereby eliminatingaccumulation of entrained particles on top of the bedsurface as it collapsed. The dense phase voidage did notvary with gas velocity between 0.1 and 0.5 m/s, in agree-ment with Yamazaki et al. (1991).

Local void fractions have also been deduced fromprobes which can di!erentiate between the phases. Op-tical "bre probes have revealed an increase in the non-uniformity of radial pro"les of local voidage for turbulent#uidized beds with increasing height (Nakajima et al.,1991; Farag, Ege, Grislinga> s & deLasa, 1997; Zhang,Qian, Guo & Zhang, 1997) and increasing gas velocity(Zhang et al., 1997; Nakajima et al., 1991). Representativetrends appear in Fig. 9.

The work of Nakajima et al. (1991) suggests the possi-bility of di!erent circulation #ow patterns for di!erentstatic bed heights, i.e. 4D

tversus 6.5D

t. The shallower bed

revealed a gross circulation pattern, in line with other"ndings (Avidan & Yerushalmi, 1982; Abed, 1984;Zhang, Guo, Li & Zhang, 1996). With voids risingthrough the centre of the column and dense phase de-

scending near the wall, a di!erent circulation pattern wasobserved for the deeper bed. The radial non-uniformitydecreased for the higher static bed height due to smallervoids near the wall at higher axial positions. Farag et al.(1997) found two circulation cells in a column of diameter0.3 m, and a more homogeneous #ow structure fora 0.5 m diameter column in the turbulent regime. Thegreater homogeneity for the larger column could resultfrom a lesser wall e!ect and from turbulent eddies dis-rupting gulf streaming (Ege, 1995).

Due to the #uctuating and di!use bed surface in turbu-lent #uidized beds, it is not possible to determine bedexpansion solely by visual observation. Pressure pro"lesare commonly used to characterize the bed expansionand overall voidage. However, this method has beencriticized (Werther & Wein, 1994) as yielding valueswhich are too high due to the acceleration of particles inthe region close to the distributor.

A modi"ed Richardson}Zaki equation has been ap-plied to both Group A particles (Avidan & Yerushalmi,1982) and Group B particles (Lee & Kim, 1990b) forcorrelating the average voidage with the super"cial gasvelocity within the turbulent #uidization regime. Avidan(1980) introduced an e!ective terminal cluster velocity,;H

t, such that

;/;Ht"en. (12)

A recent summary of;Ht

and the index na was providedby Venderbosch (1998).

4.2. Local void size and rise velocity

In the previous section, voids were treated as distinctentities as in bubbling beds. Local void size and rise


Fig. 10. Mean bubble size and bubble rise velocity for spent FCCcatalysts: 0.2 m diameter bed, 0.85 m static bed height (adapted fromYamazaki et al., 1991).

velocity have been investigated in the turbulent #uidizedregime as analogous to the bubbling regime (Lanneau,1960; Yamazaki et al., 1991; Lu, Xu, Shi and Shen (1997);Farag et al., 1997; Taxil, Guigon, Archimbault &Gauthier, 1998). However, voids in turbulent #uidizedbeds tend to be small and transient, with indistinct orirregular boundaries (Rowe & MacGillivray, 1980; Lee& Kim, 1989a). Lanneau (1960) concluded that voidswere small, rapid and losing their identity for;0.6 m/s. The void sizes depend on the mechanisms ofcoalescence and splitting as voids rise. Wall proximityclearly a!ects these factors. Local void sizes inferred fromprobes provide little information on their behaviour.Werther and Wein (1994) claim that for Geldart groupB particles, both void dimensions and their rising vel-ocities can be predicted with reasonable accuracy fromresults obtained in bubbling beds. For Group A particles,however, the void rise velocity showed considerable devi-ation from the Davidson and Harrison correlation (1963)for ;;

c(Yamazaki et al., 1991).

Lu et al. (1997) extended a bubble diameter correlationof bubbling beds to a turbulent #uidized bed, usingGroup A particles. Experimental studies indicated thatthe coalescence and splitting mechanisms di!ered in thecentral core (r/R)0.4), an intermediate region(0.4(r/R(0.8) and near the wall (r/R*0.8). There wasfavourable agreement with the model of Horio andNonaka (1987) which considers both bubble splitting andcoalescence, as well as a modi"ed two-phase model indetermining bubble frequencies. Voids grew in the dis-tributor region, and decreased in size in the centre of thecolumn. In contrast, Zhang et al. (1997) found a uniformdistribution of void size and rise velocity along both theaxial and the radial directions in a 0.19 m column. Thebubble size was correlated by

dB"(1.34#0.8;)]10~2 (m). (13)

The local #ow structure seems to be greatly in#uenced bythe equipment, so that caution must be exercised inapplying such correlations to other columns.

The most common method of obtaining the void risevelocity is to cross-correlate the signals from two sensorswhich are aligned vertically and a known distance apart(Bendat & Piersol, 1971). The optimum distance betweenthe probes depends on the frequency and the waveformunder investigation.

Yamazaki et al. (1991) and Lee and Kim (1989a) haveshown for "ne and coarse particles, respectively, thatthe mean void rise velocity increases with; up to aroundthe transition velocity,;

c, and then tapers o! or remains

constant (see Fig. 10). Lee and Kim (1989a) also notedvariations of void rise velocity from the centre to the wall.Farag et al. (1997) reported negative rise velocities in thecentre of a column of diameter 0.3 m, indicating a circula-tion pattern where gas travels downwards near the axisand upwards near the wall. Taxil et al. (1998) found little

correlation between the void chord length and rise velo-city. Reported void properties in turbulent #uidized bedsare summarized in Table 7.

4.3. Radial and axial voidage distribution

The inhomogeneity of the solids hold-up in a turbulent#uidized bed was investigated by Abed (1984) usingcapacitance probes. Downward #ow was found along thewall coupled with accelerated upward #ow at highervoidage in the interior of the column. Hydrodynamicparameters such as void phase fraction and dense-phasevoidage (emulsion void fraction) were derived from theprobability density function of local signals. Even beyondthe transition to the turbulent #ow regime, the gas con-tinued to #ow preferentially up the centre of the bed.Using Geldart group B particles and a capacitanceprobe, Werther and Wein (1994) reported a shift to high-er voidage in the central region as the gas velocity in-creased from 0.38 to 2.05 m/s.

Lu et al. (1996) correlated the local voidage with respectto radial position based on optical "bre probe measure-ments without including any in#uence of axial position:

e"a0#a

1ArRB#a2A

rRB

2#a3A

rRB

3#a4A

rRB

4(14)

where for ;"0.954 m/s, a0"0.868, a

1"!0.891,

a2"0.383, a

3"1.308, and a

4"!1.218. An alterna-

tive expression due to Wang and Wei (1997) is

1!e1!e6 "0.908#0.276A

rRB

4. (15)

Comparison of data from larger (Lu et al., 1996; Wang& Wei, 1997) and smaller (Abed, 1984; Li, Reh, Tung


Table 7Summary of hydrodynamic parameters determined in turbulent #uidized beds

Investigators Parameters studied Method Dt

dp

; ;c

Static bed zp

(m) (lm) (m/s) (m/s) height (m) (m)

Lanneau (1960) Void size Capacitance probe 0.76 40}80 0.03}1.5 N/A 4.6 2.3Lee and Kim (1989a) Void rise velocity Pressure transducer 0.1 362 0.3}1.3 1.1! 1.0 0.35

0.55Nakajima et al. (1991) Void phase fraction Optical "bre probe 0.2 64 0.13}1.33 0.50! 0.85 0.1

0.764 0.16}0.80 0.50! 1.30 0.1

1.387 0.27}1.59 0.65! 0.85 0.1

0.7Yamazaki et al. (1991) Void rise velocity Optical "bre probe 0.2 64 0.45}1.1 0.55 0.85 0.5

Void sizeFarag et al. (1997) Void phase fraction Optical "bre probe 0.3 65 0.34 0.45! 0.6, 0.9 0.21, 0.60

0.400.52

Void rise Velocity Optical "bre probe 0.5 65 0.4 0.45! 1.6 0.1, 0.4,Void size 0.55 0.8,

0.7 1.2

Zhang et al. (1997) Void phase fraction Optical "bre probe 0.20 77.6 0.39 N/A 0.88 0.15Void rise velocity 0.59 1.15 0.35Void size 0.78 0.55

0.98 0.750.85

Lu et al. (1997) Void size Optical "bre probe 0.71 69.2 0.44}0.86 0.43! 0.6 0.23, 0.36,0.85

75.0 0.44}0.99 0.48! 0.6 0.23, 0.36,0.85

Taxil et al. (1998) Void rise Velocity Optical "bre probe 0.2 95 0.2}1.7 0.52! 1.3 0.386

!;c

calculated based on Eq. (o) in Table 2.

& Kwauk, 1990; Issangya, 1998; Chaouki, Gonzalez,Guy & Klvana, 1999a) columns suggest that the formershow #atter pro"les in the interior of the column due toa reduced wall e!ect. Table 8 summarizes the publishedwork on radial voidage distributions in turbulent#uidized beds.

Axial voidage distributions in turbulent beds arecharacterized by a smooth increase of gas volume con-centration with height in the freeboard, with the voidageremaining &0.65 to 0.75 in the bed. As the gas velocityincreases, the average solids concentration in the bedcalculated from pressure drop measurement decreases(Fig. 11). Both Horio et al. (1992) and Venderbosch (1998)reported that the decrease in hold-up moved higher withincreasing static bed height. A summary of data on theaxial distribution of voidage in turbulent #uidized beds ispresented in Table 9.

4.4. Turbulence characteristics

Despite the inclusion of the word turbulenta in thetitle of the #ow regime under consideration, there havebeen only limited attempts to determine the turbulence

characteristics of #uidized beds operated in the turbulent#uidization #ow regime. The standard deviation of void-age #uctuations, widely used to determine the onset of theregime as described in Section 2, can itself be consideredto be a measure of the intensity of turbulence. The macro-scale of turbulence is clearly related to the size of thetransient voids which appear and disappear, whilethe dominant frequency is determined by the frequencyof these voids. Probability distributions, power spectraldistributions, intermittency characteristics and cyclefrequencies have also been reported for Type 1 andType II (see Section 2.1) turbulent #uidized beds, respec-tively (Bai et al., 1999; Mchirgui et al., 1999; Lin, Wei& Jin, 2000).

SterneH us, Johnsson, Leckner and Palchonok (1999)speculate that much of the gas-phase turbulence encoun-tered in circulating #uidized beds originates in voids risingand bursting in the dense lower region of the riser. Theseauthors ascribe bubbling and slugging to this bottomregion, but the lower dense region is often found to besubject to turbulent bed hydrodynamics. Palchonok,Johnsson and Leckner (1997) operated CFB boilerswith and without dense bottom regions and estimated


Table 8Summary of literature data on radial voidage distribution in turbulent #uidized beds

Investigators Method Dt

dp

; ;c

Static bedheight

zp

(m) (lm) (m/s) (m/s) (m) (m)

Morooka, Kawazuishiand Kato (1980)

Capacitance probe 0.12 65}68 (0.5 0.4! 1.0 0.875

Abed (1984) Capacitance probe 0.152 54.8 0.03}0.55 N/A * 1.48Li et al. (1990) Optical "bre probe 0.09 54 * 0.34! * *Werther and Wein (1994) Capacitance probe 0.6 120 0.38, 2.05 0.77! 0.65 0.14}2.75

7 levelsLu et al. (1996) Optical "bre probe 0.71 75 0.41}0.95 0.48! 0.60 0.6Wang and Wei (1997) Optical "bre probe 0.47 54 0.38}0.95 0.41! 0.58 0.36}1.09Issangya (1998) Optical "bre probe 0.076 70 0.43}0.70 0.48! 0.46 0.38Xu, Sun, Nomura, Liand Kato (1999)

Optical "bre probe 0.09 54 0.11}3.15 0.34! * 3.0

!;c


Table 9Summary of literature data on axial voidage distribution in turbulent #uidized beds

Investigators Method Dt

dp

; ;c

Static bed zp

(m) (lm) (m/s) (m/s) height (m) (m)

Horio et al. (1992) Optical "bre probe 0.05 60 0.3}5.5 0.5 Hmf

0.7 m 0.98G

s"25.6 kg/m2s

Werther and Wein (1994) Capacitance probe 0.6 120 0.38}2.05 0.77! 0.65 0.14}2.75Wang and Wei (1997) Optical "bre probe 0.47 54 0.38}0.95 0.41! 0.58 0.36}1.09Venderbosch (1998) Pressure transducer 0.05 90 0.6, 0.8, 1.0 0.58 0.06}0.16 As indicated in

Fig. 11

!;c


Fig. 11. Axial solids concentration pro"le: 0.05 m diameter bed, 0.12 mstatic bed height (adapted from Venderbosch, 1998).

dominant frequencies and other gas-phase turbulentcharacteristics in both cases. The (commonly turbulent)dense bottom region appears to play a major role indetermining the overall riser turbulence characteristics.

Fluidized beds in general, de"nitely including thoseoperated in the turbulent #ow regime, have been found tobe chaotic (e.g. see van der Stappen, 1996). The turbulent

#uidization #ow regime has been found to exhibit uniquechaotic properties (Bai et al., 1999).

5. Gas and solids mixing

5.1. Gas mixing

The gas #ow pattern becomes di$cult to analyse in theturbulent #ow regime as it develops into intermittentcontinuous and discontinuous phases. Information onthe mixing behaviour of gas is vital for predicting reactorperformance.

The axial dispersion model is commonly applied tocharacterize the dispersion of #uid in #uidized beds. Axialmixing of gas in a turbulent #uidized bed can be character-ized by three coe$cients: the axial dispersion coe$cient,a backmixing coe$cient; and the radial gas mixing coe$c-ient. These coe$cients are related (SchuK gerl, 1967) by

Dz,g

;Dt

"Db,g;D

t

#b;DtD

r,g(16)

where b characterizes the nature of the velocity pro"le inthe tube (van Deemter, 1980). For turbulent #uidized


Fig. 12. Gas axial dispersion coe$cient versus super"cial gas velocityfor FCC particles: 0.1 m diameter bed (adapted from Foka et al., 1996).

beds, 5]10~3(b(5]10~4 based on radial concen-tration pro"les (Cankurt & Yerushalmi, 1978). The smallmagnitude of b has been used to justify eliminating theradial dispersion term, especially for Group A particles(Yerushalmi & Avidan, 1985; Li & Wu, 1991).

A number of studies have investigated axial gas disper-sion in turbulent #uidized beds as summarized in Table10. A pulse of injected tracer was detected at two di!erentlocations in the bed, one above the other, by Foka et al.(1996) and Li and Wu (1991). The residence time distribu-tion between these locations was then obtained by nu-merical deconvolution. The measurements obtainedthrough this method yield a transient response func-tiona (Nauman & Bu!ham, 1983), since one or both ofthe boundaries was open. It is necessary to obtain addi-tional information on the #ow structure to deduce thetruea RTD.

Li and Wu (1991) introduced hydrogen as a tracer tostudy the gas RTD in a #uidized bed of FCC particles.The axial solids concentration measurement from thesectional pressure drops ensured that the two probeswere subject to the same #ow regime. The gas dispersioncoe$cient was computed to "t RTD curves from a one-dimensional pseudo-homogeneous di!usion model andwas correlated by

Dz,g

"0.1835e~4.4453 (17)

suggesting that the dispersion coe$cient decreasesstrongly with increasing bed voidage. Tracer injection0.3 m above the distributor cannot ensure uniform intro-duction of tracer across the bed. With no explicit inclu-sion of operating conditions, the above correlation islikely limited to small columns.

Foka et al. (1996) injected radioactive argon toobtain RTD data, which were then "tted to both disper-sive and two-phase models. The dispersion coe$cientagain decreased with increasing voidage and velocityonce in the turbulent regime (Fig. 12). A correlation wasgiven as

Peg";Ht

Dz,g

"4.4]10~3Ar0.32Adp

DtB

~0.4. (18)

The same experimental data were also "tted to the two-phase model of van Deemter (1980).

Ege (1995) injected pulses of helium into the mainair#ow upstream of the wind chamber. Two thermalconductivity detectors were aligned vertically, one abovethe other in the bed. Pulse injection into the 0.3 m dia-meter column with 1.4 m static bed height led to a doublepeak for a detector 0.4 m above the distributor. This wasattributed to a decrease in the ratio of distributor pres-sure drop to bed pressure drop, causing #uctuation in thetracer #ow. Further analysis of the measurements re-sulted in a core-annulus model (see Section 9). Publishedgas mixing data from larger columns is lacking.

The one-dimensional axial dispersion model was ap-plied successfully to Mobils MTG process in scaling upfrom 0.04 m diameter reactor, through 0.1 m, to a ba%ed0.6 m diameter demonstration plant (Edwards & Avidan,1986). Sulfur hexa#uoride, an absorbing tracer, was injec-ted upstream of the distributor ensuring plug #ow tracerinjection. The detector was located 1.8 m above the bed.Measurements were obtained for di!erent average bedand freeboard voidages (Krambeck, Avidan, Lee & Lo,1987). The axial dispersion coe$cient increased withincreasing column diameter.

Guo (1987) employed hydrogen gas and a thermo-conductivity cell to analyse gas mixing in a two-dimen-sional bed. The axial dispersion coe$cient increased lin-early with static bed height. A similar trend was found byCankurt and Yerushalmi (1978). Wei, Lin and Yang(1993), on the other hand, studied the gas mixing ina 5.8 m diameter commercial FCC regenerator andfound that the gas axial dispersion coe$cient was pro-portional to the square root of the column diameter.

Gas dispersion in a turbulent #uidized bed is caused byturbulent mixing and molecular di!usion in addition tonon-uniform velocity pro"les. Van Deemter (1980) distin-guished smaller-scale mixing, related to turbulent eddies,from mixing induced by di!erences in vertical velocities.In order to understand the dispersion behaviour, it maybe necessary to investigate the void/bubble breakdownmechanisms. Guo (1987) concluded that void breakdownis caused by turbulent eddies. Such macro-scale eddiesclearly provide an important mixing mechanism in tur-bulent #uidized beds.

Given the lack of a widely applicable approach forpredicting gas mixing in turbulent beds, we proposea new and improved correlation covering existing data,the "rst seven papers tabulated in Table 10, over a widerange of bed voidage and column diameters for axial gas


Table 10Sources of literature data on axial gas dispersion in turbulent #uidized beds

Investigators Model Tracer injection dp

(lm) Dt

; ;c

Dz,g

(gas}tracer) (m) (m/s) (m/s) (m2/s)

Cankurt and Yerushalmi One dimensional Steady state 55 0.152 0.21 0.36! 0.38(1978) dispersion 0.81 0.50(Air}CH

4) 1.17 0.57

1.50 0.32

Edwards and Avidan(1986)

1-D axial dispersion Pulse Group A with(15%

0.10.6

0.60.6

N/A 0.5870.838

(Air}SF6) 40 lm "nes

Lee and Kim (1989b) Di!usion process with Steady state 362 0.1 0.8 0.85 0.220(Air}CO

2) axial and radial 0.88 0.235

dispersion coe$cients 1.00 0.2301.08 0.2451.20 0.215

Li and Weinstein (1989) One dimensional Steady state 59 0.152 0.1 0.43! 0.1(Air}He) dispersion 0.5 0.55

1.3 0.60

Li and Wu (1991) 1D pseudo-homogeneous Non-ideal pulse 58 0.09 1.0 0.44! 0.45(Air}H

2) di!usion 1.0 0.51

1.0 0.56

Foka et al. (1994) One dimensionaldispersion

Pulse 75 0.1 0.417 0.47! 0.080

(Air}Ar) 0.516 0.1020.614 0.1100.691 0.1950.792 0.1300.892 0.1670.977 0.0971.051 0.0601.142 0.075

Foka et al. (1996) Two-phase model of van Pulse (less than 0.5 s) 75 0.1 0.21}0.94 0.55 Plotted in Fig. 12(Air}Ar) Deemter (1980)

Zhang et al. (1996) Pseudo-homogeneous Steady state 77.6 0.19 0.392 0.50! 0.374(Air}O

2) model with axial and 0.588 0.514

radial dispersion 0.784 0.6191.078 0.783

Wei et al. (1993) One dimensional Steady state 58 5.76 1.26 0.41! 3.05(Air}#ue gas) dispersion 1.41 3.4

!;c


mixing in the turbulent #uidization #ow regime:

Peg";Ht

Dz,g

"3.47Ar0.149 Re0.0234 Sc~0.231AH

tD

tB

0.285.

(19)

This equation is recommended in the absence of speci"cdata for the unit in question.

A general problem associated with the axial dispersionmodel is that it cannot di!erentiate between the spread inlongitudinal velocity and contributions from backmixing

(Briens, Margaritis & Wild, 1995). Continuous tracerinjection yields the steady-state component of di!usionwhile eliminating time variations (Louge, 1997). An at-tempt has been made to quantify radial mixing andbackmixing using Group B particles (Lee & Kim, 1989b).Tracer gas injected steadily at the column axis wasmonitored at four positions, both upstream and down-stream. The downstream radial concentration pro"le wasalmost uniform. Analysis of variations in the radial dis-persion coe$cient indicated that vigorous gas radial


Fig. 13. In#uence of gas velocity on gas backmixing: Gs"15.4 kg/m2s

(Li & Wu, 1991).

Table 11Summary of literature data on gas backmixing in turbulent #uidized beds!

Investigators Tracer injection Dt(m) ; (m/s) ;

c(m/s) e (m)! G

s(kg/m2s) eD

b,g(m2/s)

Cankurt and Steady-state injection from 0.15 0.81 0.36" 0.752 0.05, 0.3, 0.53,Yerushalmi (1978) centre 1.17 0.801 0.84, 1.75(Air}CH

4) 1.5 0.824

Weinstein et al.(1989)

Steady-state injection fromr/R"2/3

0.152 1.31.3

0.43" 0.770.97

0.13, 0.28, 0.61 6943

(Air}He)

Lee and Kim(1989b)

Steady-state upward injectionfrom centre (z"0.53 m)

0.1 1.21 0.85 * 0.1, 0.2, 0.3, 0.4

(Air}CO2)

Li and Wu (1991) Pulse injection 0.09 1.0 0.44! 0.774 0.04 15.4(Air}H

2) (z"1.5 m) 1.5 0.834

Zhang et al. (1996) Steady-state injection from 0.19 0.392 0.50! 0.632 0.09,0.19,(Air}O

2) centre (z"1.03 m) 0.588 0.673 0.29,0.49,

0.784 0.715 0.791.078 0.776

Venderbosch (1998) Steady-state injection from 0.05 0.4 0.58 * * 0.03(N

2}CO) centre 0.6 0.04

0.7

!Note: : axial distance between injection and sampling points.";

ccalculated based on Eq. (o) in Table 2.0.

exchange was present between the dilute and densephases. This was attributed to breakdown of slugs intosmaller voids. If the void phase where the tracer is injec-ted into the bed is indeed intermittent, steady-state pointinjection of tracer into the bed must be time dependent,as well as position dependent. The study may providesome explanations of the mechanism of gas mixing; how-ever, whether the reported values represent the actualdispersion coe$cients is questionable due to the experi-mental technique.

The same steady-state technique can be applied withgas backmixing evaluated from tracer monitored up-stream. Down#ow of gas can occur when the downwardvelocity of solids exceeds the relative interstitial gas velo-city in the dense phase (Stephens, Sinclair & Potter,1967). As shown in Fig. 13 (Li & Wu, 1991), a consider-able radial gradient of tracer concentration exists in theturbulent #uidization regime. In all backmixing studiesreported, summarized in Table 11, increased tracer con-centration was observed near the wall. Tracer was com-monly injected at the centre of the column, except for theCity College group (Cankurt & Yerushalmi, 1978; Wein-stein, Li, Bandlamudi, Feindt & Gra!, 1989; Li & Wein-stein, 1989) who argued that axial injection resulted inconcentrations too low to be detected in the turbulent#uidization #ow regime. Their study showed that theinjection position greatly a!ected measured gas backmix-ing. When injecting tracer gases into #uidized beds, theoutcome is signi"cantly a!ected by whether the gas isinjected into voids or the dense phase. They attributedthe detection of tracer on the side of the column oppositeto the injection point as indicating considerable circum-ferential mixing.

Venderbosch (1998) conducted gas backmixing experi-ments and interpreted the results using a pseudo-homo-geneous model:

lnCC

zp~ziC

zi D";

eDb,g

(zp!z

i). (20)


Table 12Summary of literature data on solids mixing in turbulent #uidized regime!

Investigators ; Particles Dt

;c

Model Observations(m/s) (m) (m/s)

Yerushalmi andAvidan (1985)

0.075}1.10 Catalysts 0.152 N/A One-dimensionaldispersion model

Dz,s

proportional to the square root of beddiameter

Lee and Kim(1990b)

0.3}1.3 Coarse particles 0.1 0.85 Mixed tanks in seriesconnected by perfectlymixed and plug #ows

Dz,s

lower for coarser particles, fraction ofperfectly mixed #ow in dense phaseincreases with increasing ;

Wei et al. (1993) 1.26}1.41 FCC 5.76 0.41 One-dimensional pseudo-dispersion model

Dz,s

proportional to square root of beddiameter

!;c


When this model was applied to other published back-mixing data, the backmixing coe$cient gradually in-creased with ; until it reached a maximum (at ;+;

c),

beyond which it decreased.Cankurt and Yerushalmi (1978) concluded that gas

backmixing diminishes when the turbulent #ow regimeis achieved. This trend is supported by Li and Wu (1991)and Bai, Yi, Jin and Yu (1992). As the gas velocityincreased, a higher tracer concentration was detectedby Zhang et al. (1996). Li and Weinstein (1989) reasonedthat as the gas velocity increased, the dilute coreregion expanded outwards, resulting in a higher radialconcentration gradient. Gas backmixing graduallyincreased with increasing radial position, coincidingwith increasing radial solids concentration (Li & Wu,1991).

Gas backmixing studies provide information related tothe #ow behaviour of gas in turbulent #uidized beds.Because of the wide variations of the results, dependingon such factors as injection location, injection technique,and model applied, care must be exercised when compar-ing dispersion coe$cients from di!erent studies in theliterature and in applying the results to modelling andscale-up.

Almost all gas mixing studies have concentrated onaxial mixing. Only Lee and Kim (1990a) provide data onradial mixing. These data suggest that radial dispersion isabout an order of magnitude less than axial dispersion, asin bubbling beds. However, the results were only forgroup B solids. More work is clearly needed, especiallyfor group A solids.

5.2. Solids mixing

Solid mixing in#uences gas}solid contacting, heattransfer, temperature uniformity and gas backmixingin #uidized-bed reactors. While many solid mixingstudies have been conducted in the bubbling and fast#uidization regimes applying various experimental tech-niques, very few pertain to the turbulent regime (seeTable 12).

May (1959) investigated the e!ect of column diameteron solids mixing, but only up to ;"0.24 m/s. Mixingwas found to be much faster in larger columns, withsmaller-scale mixing superimposed on a gross circulationpattern. Yerushalmi and Avidan (1985) investigated solidmixing using a ferromagnetic tracer. Noting the relativelyhomogeneous nature of a turbulent #uidized bed, theyapplied the one-dimensional dispersion model to obtainan apparent axial dispersion coe$cient related to a tur-bulent eddy size and frequency.

One of the few mixing studies on a commercial scaleunit was by Wei et al. (1993) using FCC particles ina 5.8 m diameter column. The data suggest that the solidsaxial dispersion coe$cient is proportional to the squareroot of D

twhen compared with the Yerushalmi and

Avidan (1985) data.Lee and Kim (1990a) studied axial mixing of solids in

a turbulent #uidized bed from steady-state axial trans-port of heat. Using Group B particles, they correlated theaxial Peclet number as

Pes"4.22]10~3Ar. (21)

In the turbulent #uidization regime, the e!ective axialdispersion coe$cient of solids increased as the gas velo-city increased. Fine particles exhibited higher dispersioncoe$cients than coarser ones. This was attributed todi!erent wake fractions, the in#uence of turbulence,and vigourous movement of clusters in "ne particlebeds. The authors also found that there was a strongcorrelation between the axial solid dispersion coe$cientsand radial gas dispersion coe$cients, as indicated inFig. 14, both increasing in a similar manner withincreasing gas velocity in the turbulent #uidization #owregime.

Based on the analogy between bubble columns andgas-#uidized beds, Baird and Rice (1975) applied theeddy di!usivity concept, based on the isotropic turbu-lence model, to solids mixing at high gas #ow rates in theform:

Ea"KD4@3

tPm

(22)


Fig. 14. Axial dispersion coe$cient of the solids and radial dispersioncoe$cient of the gas phase as a function of gas velocity: 0.1 m diameterbed, 362 lm particles (adapted from Lee & Kim, 1990a).

Fig. 15. E!ects of particle size and temperature on modes of heattransfer (from Fan & Zhu, 1998).

where Pm

is the energy dissipation rate per unit mass ofsolids, de"ned by

Pm"(;!;

mf)g. (23)

Although the agreement was poor with respect to data ofMay (1959) and de Groot (1967), the clear physical basisof the correlation represents a useful starting point forcorrelating solids mixing. Lee, Kim and Baird (1991)extended this approach and correlated solid mixing ofGroups A particles by

Ez,s

Mg(;!;mf

)N1@3D4@3t

"0.365Re~0.368t

. (24)

Given the dearth of data on solids mixing in turbulent#uidized beds, it may be useful to pursue the analogywith liquid mixing in bubble columns operated at highsuper"cial gas velocities. Such mechanisms as globalconvective recirculation, turbulent di!usion due to ed-dies caused by rising bubbles, and molecular di!usion(Degaleesan & Dudukovic, 1998) may also explain solidsmixing in turbulent #uidized beds.

6. Heat transfer

Three types of heat transfer * gas}particle, par-ticle}particle and suspension}surface heat transfer } canbe considered in #uidized beds. Thermal gradients be-tween the voids and dense phase tend to be very smalldue to the large surface area of the particles, with typicalparticle}gas heat transfer coe$cients of order6}23 W/m2 K (Botterill, 1986). Thermal equilibrium inthe bed is normally attained within about 25 mm of thegrid, although somewhat greater distances may be re-quired for high-velocity jets entering through nozzles andperforated plates. Conductive particle}particle heat

transfer due to particle collisions is usually negligible.Thus, particle}gas and particle}particle heat transfers arerarely limiting factors in the overall heat transfer analy-sis. Hence, subsequent discussion is limited to suspen-sion}surface heat transfer.

Suspension-to-surface heat transfer is caused by par-ticle convection due to the convective #ow of particlesfrom the bulk to the heat transfer surface and conductionthrough the gas between the particle and wall, gas con-vection due to gas percolation through the bed contact-ing the heat transfer surface, and radiation. Although notstrictly valid, these three components are commonly as-sumed to be independent of one another and additive sothat

h"hpc#h

gc#h

r. (25)

The importance of each component depends on par-ticle properties and operating conditions. Several mapshave been proposed to indicate where each of thesecomponents is important (Decker & Glicksman, 1981;Saxena & Ganzha, 1984; Flamant, Fatah & Filtris, 1992).Flamant et al. (1992) extended the scheme of Saxena andGanzha (1984) to incorporate temperature, thus e!ec-tively delineating regions in which contributions fromeach of these components are signi"cant. Their proposedheat transfer diagram } enhanced by Fan and Zhu (1998)} is shown in Fig. 15. Radiation is insigni"cant below5003C; gas convective transfer becomes increasingly im-portant with increasing particle size, while the particleconvective component decreases in importance with in-creasing particle size.

6.1. Convection

While many studies have been conducted on heattransfer in bubbling #uidized beds (see Wiman &Almstedt, 1997; Molerus & Wirth, 1997 for recentreviews), there are only a few studies explicitly for


h"jgll C

0.125(1!emf

)[1#33.3M 3J[(;!;mf

)/;mf

](opcp/j

gg)](;!;

mf)N~1]~1

1#(jg/2c

pk)M1#0.28(1!e

mf)2[o

g/(o

p!o

g)]0.5[ 3J[o

pcp/j

gg](;!;

mf)]2;

mf/(;!;

mf)N

#0.165Pr1@3Aog

op!o

gB

1@3

C1#0.05A;!;

mf;

mfB

~1

D~1

for Ar)108.

D (26)

Fig. 16. Comparison of heat transfer prediction using Eq. (26) withexperimental data of Wunder (1980) for single immersed tube measuredat ambient conditions for mullite particles (adapted from Molerus et al.,1995).

turbulent #uidized beds (Staub & Canada, 1978;Canada & McLaughlin, 1978; Staub, 1979; Wood,Kuwata & Staub, 1980; Hashimoto et al., 1990; Basu,Halder & Nag, 1986; Leu, Hsia & Chen, 1997).

Basu et al. (1986) investigated bed-to-wall heat transferin a 102 mm diameter, 4.5 m high column operated overa wide range of gas velocities (0.01}3.8 m/s). Using sandparticles of average sizes 122 and 348 lm (Group B par-ticles) and ambient air as the #uidizing gas, they foundthat h reached a maximum with increasing; at a super"-cial gas velocity close to the transition velocity, ;

c.

A similar "nding was reported by Leu et al. (1997). Inboth cases the maximum decreased with increasing par-ticle diameter. However, as illustrated in Fig. 16, thesuper"cial velocity corresponding to the maximum heattransfer coe$cient is often lower than ;

c. Lacking a

reliable turbulent bed correlation, Basu et al. (1986)compared their experimental heat transfer data withpredictions from the bubbling bed correlation ofGlicksman (1984) and reported large deviations.

Staub and co-workers (Staub & Canada, 1978; Canada& McLaughlin, 1978; Staub, 1979; Wood et al., 1980)extensively studied heat transfer in a column of squarecross-section with immersed horizontal tubes at di!erentpressures and particle sizes (large particles) coveringa wide range of super"cial gas velocities. Staub (1979)

developed a heat transfer model based on the dense-#owsolid suspension concept (incorporating upward anddownward #ow of gas and solids). His model (see Table13) includes a dependency on super"cial gas velocity.Using a combination of the #ow model of Staub (1979)and the correlation for local solid hold-up, Wood et al.(1980) correlated splash zone experimental data for dif-ferent static bed heights. Canada and McLaughlin (1978)investigated heat transfer to immersed horizontal surfa-ces at pressures up to 10 bar for large particles(650}2600 lm) and showed that the heat transfer coe$-cient increases appreciably with increasing pressure (seealso Molerus, Burschka & Dietz, 1995). Molerus andMattmann (1992a, b), Molerus et al. (1995) and Molerusand Wirth (1997), though mainly concerned with bub-bling #uidization, covered super"cial gas velocitiesbeyond ;

cas determined based on Eq. (o) in Table 2.

Heat transfer to the containing wall was determined fora wide range of Archimedes numbers in terms of thecharacteristic laminar and turbulent length scales, gasvelocity and e!ective thermal conductivities. Molerus

et al. (1995) presented a single uni"ed correlation, consis-tent with experimental data covering a wide range ofphysical properties and operating conditions(

b&290}1050 K; P

b&0.03}2 MPa; ;};

mfup to

2.5 m/s; dp&74}4000 lm; o

p26}11 800 kg/m3):

Eq. (26) predicts experimental data well over a range ofconditions as shown in Fig. 16. Although the character-istic length scale, l

l, is used instead of the particle size, d

p,

the equation accounts for the particle size through theminimum #uidization velocity, ;

mf. For Group D par-

ticles (Ar108), the equation of Molerus and Mattmann(1992b), independent of gas velocity, is suggested for theturbulent #uidization #ow regime, where transfer is dom-inated by gas convection:

h"0.0247jgd1@4p

l3@4tCA

dpltB

3@2PrD

1@3. (27)

Here ll

and lt

are characteristic laminar and turbulentlength scales given by

ll"A

k

Jg(op!o

g)B

2@3, (28)

lt"A

k2g(o

p!o

g)o

gB

1@3. (29)


Table 13Summary of correlations for convective bed-to-surface heat transfer coe$cients applicable to turbulent #uidized beds

Author Correlation Range Remark

Staub (1979) Nu"Nu!4

]C1#A

150

dp]106B

0.73

]A0.42o

p(1!e6 )DZ0.4

mog

BD0.45

20 lm )dp)1000 lm For 1000 lm(d

p(3000 lm, use d

p"10~3 m

N!4

is for empty column (no particles)Investigation in square columns with immersed horizontal tube banks(bare tubes). Study focused on e!ect of tube bank and gas density.Showed e!ect of tube spacingh lies between 100 and 250 W/m2K for ; in the range 0.1}4.5 m/s forglass beads of sizes 650}2600 lm

Bak et al. (1989) Nu"0.4Ar0.303 Re~0.059p

107(Ar(698 High temperature combustion experiments(Tube at centre of bed) Measurements made in both expanded bed section and freeboard with

immersed vertical tubesNu"0.41Ar0.304Re~0.064

p107(Ar(698 Showed e!ects of gas velocity, tube position, bed temperature and

particle size(Tube at r/R"0.5)h lies between 40 and 370 W/m2 K for ; in the range 0.6}1.9 m/s andparticle size in the range 330}780 lm

Nu"0.4Ar0.015Re0.179p

149(Ar(28900.47(Re

p(4.0

(Freeboard overall heattransfer coe$cient)

Hashimotoet al. (1990)

Eq. (30) ;/;t1.2 Measurements made in freeboard region with immersed vertical tubes

Correlation not applicable for ;/;t(1.2

h lies between 20 and 700 W/m2 K for; in the range 0.07}0.97 m/s anddp"48 lm

Molerus et al.(1995)

Eq. (26) Ar)108 Overall heat transfer coe$cient to containing wallEq. (27) Ar108 Developed for bubbling beds, but also covers turbulent regime

Covers a wide range of physical properties and operating conditions(

b&290}1050 K; P

b&0.03}2 MPa; ;!;

mfup to 2.5 m/s;

dp&74}4000 lm; o

p&26}11 800 kg/m3)

state of the art turbulent fluidization

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