(2007) 187–193www.elsevier.com/locate/powtec

Powder Technology 178

Flow dynamics in a four-inch downer using solidsconcentration measurements

B. Wu, J.-X. Zhu ⁎, L. Briens, H. Zhang

Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9

Received 4 February 2007; accepted 7 May 2007Available online 13 May 2007

Abstract

Local solids concentration fluctuations were measured in a long downer reactor (0.1 m ID, 9.3 m tall) using an optical fiber probe. Axial flowdevelopment and radial flow dynamics were analyzed using both statistical and chaos methods. Core, transition and annulus regions wereidentified and each region showed different flow behavior. Cross-sectional averaged chaos parameters were correlated to cross-sectional averagedsolids holdup to develop relationships between non-linear flow dynamics and operating conditions.Crown Copyright © 2007 Published by Elsevier B.V. All rights reserved.

Keywords: Downer; Flow dynamics; Solids concentration; Chaos analysis

1. Introduction

Downer reactors have short residence times, less back-mixing, more uniform gas–solids flow, and less solidsaggregation compared to riser reactors [1]. These propertiesmeet the requirements of certain kind of reactions, such asfluid catalytic cracking (FCC). Due to the potential applica-tions and many advantages, numerous studies in the pastdecade have focused upon the hydrodynamics of downerreactors [2].

The axial flow development in a downer was studied byWang et al. [3] using pressure measurements. Three sectionsalong the axial direction were proposed: (1) the firstacceleration section is from the top entrance to the position atwhich the particle velocity and the gas velocity are equal; (2) thesecond acceleration section is further along the downer axiswhere the particles are accelerated only by gravity and resistedby the drag force between the gas and solids; (3) the thirdsection is the fully developed section where the drag force andgravity are equal, and therefore the particle velocity is constant.Axial profiles of solids holdup, particle velocity, pressure

⁎ Corresponding author. Tel.: +1 519 661 3807; fax: +1 519 850 2441.E-mail address: jzhu@uwo.ca (J.-X. Zhu).

0032-5910/$ - see front matter. Crown Copyright © 2007 Published by Elsevier Bdoi:10.1016/j.powtec.2007.05.006

gradients and solids flux were investigated by Zhang [2] in a9.3 m long downer. The acceleration zone and fully developedzone were consistently identified.

The radial flow structure was initially reported to have threeregions across the cross-section of the downer [4]: a dilute coreregion, where solids flow is normally very uniform; a denseannular region, where there exists maximum solids holdup,particle velocity and solids flux; a wall region, where solidsholdup, particle velocity and solids flux generally decrease.However, later studies showed that the annular regiondisappeared and the radial profiles of the variables becameparabolic in the developed zone [2].

Although many studies have investigated the hydrodynamicsof downer reactors, most have only calculated time-averagedparameters and thus have not considered the microscopic flowdynamics.

Time series of local solids concentration signals have beenused widely to study the flow dynamics in fluidized bedsystems. Local solids concentration fluctuations can reflect thetemporal flow dynamics, which are important for mass and heattransfer properties. Chaos methods can be used to study thetemporal fluctuations of the local solids concentration. Chaosanalysis of the flow dynamics in the downer reactor usingsolids concentration measurements has been performed by

.V. All rights reserved.

188 B. Wu et al. / Powder Technology 178 (2007) 187–193

Cheng et al. [5], but only under limited operating conditions(1.0bUgb7.0 m/s, 20bGsb50 kg/m2/s). Temporal flowdynamics under a wide range of operating conditions must bestudied to obtain more information on the flow behavior indowner reactors.

In this article, time series of solids concentration fluctuationsunder a wide range of operating conditions of a downer reactorwere extensively analyzed using both statistical and chaosmethods.

2. Experimental setup

The riser–downer unit consisted of a 9.3 m high downer anda 15.1 m high riser of the same ID of 0.1 m (Fig. 1). Thecolumns were made of plexiglass. Solids from the storage tankwere first carried up through the 15.1 m tall riser by the air to theriser primary cyclone installed at the top of the downer. Afterthe separation of gas and solids, the remaining solids werefurther captured in the secondary and tertiary cyclones. Fineparticles were finally retained in a baghouse filter, and the gaswas exhausted. There was a distributor at the downer top andbelow the dipleg of the riser primary cyclone. The solids abovethe distributor were maintained at minimum fluidization by thedowner distributor auxiliary air. Solids then fell down into the

Fig. 1. Schematic diagram of the dow

downer column through solids feed tubes. More details aboutthe riser–downer system can be found in Zhang et al. [6]

FCC catalyst with a mean diameter of 67 μm and particledensity of 1500 kg/m3 was used in this study. Electrostaticswere minimized by introducing a small stream of steam intothe main air pipeline to obtain a relative humidity of 70–80%.Solids concentration was measured using an optical fiberprobe at eight axial positions from the top of the downer(h=0.02, 0.51, 1.20, 2.11, 4.40, 6.23, 8.06, 9.15 m) and at 11radial positions (r /R=0.0, 0.158, 0.382, 0.498, 0.59, 0.67,0.741, 0.806, 0.866, 0.922, 0.975). The measurement volumeof the optical probe was very small, so that the flow dynamicswere microscopic and local. The solids circulating rate wascontrolled by a butterfly valve and measured by diverting thesolids from the downer to a measurement tank. The amount ofsolids lost through the secondary and tertiary cyclones wereless than 0.5% of the total solid flux. Therefore this amountwas not included in the measurement of solids circulatingrate. The true solids holdup was converted from the originalvoltage time series using a calibration equation [7]. Solidsconcentration fluctuations were measured at a frequency of970 Hz and a time length of 30 s. The data were filtered at alow-pass frequency of 250 Hz based on power spectrumanalysis.

ner reactor and its accessories.

Fig. 2. Time series of solids concentration at different radial positions.

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3. Chaos methods

Kolmogorov entropy (K) reflects the information loss rateand predictability into the future and was estimated using themaximum likelihood method [8]. The correlation dimension (D)is another frequently used chaos parameter, reflecting thecomplexity of the attractor in the phase space and the dynamicaldegree of freedom. The correlation dimension was estimatedusing the method proposed by Grassberger and Procaccia [9].An embedding window was used in this method with the lengthof the window estimated from the dominant cycle time using theV statistic [10]. Hurst [11] developed a rescaled range analysisto study the reservoir storage in the Great Lakes of the NileRiver Basin. The Hurst exponent (H) characterizes thefluctuation of the time series from the system: 0≤Hb0.5indicates anti-persistence, H=0.5 indicates random behavior,and 0.5bH≤1 indicates persistence. The three chaos para-meters were estimated from each time series of local solidsconcentration measurements in the downer reactor to charac-terize the solids flow behavior.

4. Results and discussion

The axial flow development inside the downer has beenexamined from axial profiles of pressure gradient, cross-sectional averaged solids holdup and particle velocity, andlocal solids flux [6,12]. The length of acceleration (LOA)was found to be mostly within 1–4 m from the downerentrance. In order to avoid the distributor effect, only flowdynamics in the fully developed region will be discussed inthis article.

Examples of time series of instantaneous solids concentrationfluctuations in the fully developed region are shown in Fig. 2.The fluctuations differed with radial position. At r /R of 0.0and 0.382, in the core region as reviewed by Zhu et al. [4], thefluctuations were generally small and rapid. At r /R of 0.59,0.741 and 0.866, there were more large fluctuations possiblydue to the passage of clusters. Near the wall (r /R=0.975), therewere almost no small fluctuations possibly due to the reducedsolids holdup and particle velocity and wall effects.

Fig. 3 shows the radial profiles of time-averaged solidsholdup (εs). Gs were 49 and 194 kg/m2/s, and Ug was 3.7 m/s.At positions close to the top entrance of the downer, profiles ofεs fluctuated along the radius due to the strong “distributoreffect” and solids acceleration. Further along the downer axis, atGs=194 kg/m2/s, there was a peak at r /R of around 0.86 in theannular region. The peak moved toward the center and finallydisappeared toward the bottom of the downer column. Radialdistribution of solids at Gs=49 kg/m2/s was very uniform andthere was no clear peaks in the annular region. In the developedzone, there was a flat core and a wall region with εs generallydecreasing toward the wall. At Gs=49 kg/m2/s, the radialdistribution of solids holdup developed faster compared to highsolids flux of 194 kg/m2/s. There was little radial variation ofsolids holdup for h≥0.512 m. Increasing superficial gasvelocities also generally affected the flow development asdecreasing solids flux. To avoid the distributor effect, only the

flow behavior in the fully developed region was furtherexamined.

Radial flow development was significantly affected byoperating conditions. Radial profiles of εs in the developedsection (8.06 m) are shown in Fig. 4. An increase in Gs at aconstant Ug (10 m/s) increased εs in the core region, but notobviously near the wall (r /RN0.9). The reasons for thisphenomenon are not clear at this moment, but seems to bedue to less significant contribution of gas phase momentum tothe system according to Zhang et al. [6]; at a lowerUg of 3.7 m/sεs increased in both the core and the wall region with an increasein Gs. An increase in Ug generally decreased εs for Gs of 50 and100 kg/m2/s. A higher gas velocity allow a higher solidsvelocity in the fully developed section, therefore a lower εs atconstant Gs according to the equation:ρpε̄sVp=Gs. At Gs of200 kg/m2/s, solids holdup was high in the core region butlower at the wall region at high Ug of 10 m/s compared tothose at 3.7 m/s. As addressed above, the reasons for thisphenomenon were not clear. More details about the radialprofiles of εs can be found in Zhang [2] and Zhang et al. [6].

Clustering and multi-scale behavior in the gas fluidizationhas been studied from experimental, theoretical and simulation[13–16]. Where there were general observations for clusters anddispersed particles, synchronized observation with the dataacquisition was not available with optical probe. However, theoptical probe does give enough information in the signals toreveal certain information about the flow pattern including adistinction between clusters and dispersed particles as shown in

Fig. 3. Radial profiles of time-averaged solids holdup (data from Zhang, 1999).

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Fig. 2. Based on this fact, the terms, dispersed particles andclusters, were adopted in this paper to explain the chaotic flowof solids in the downer.

Radial profiles of chaos parameters estimated from timeseries of solids concentration in the fully developed region(8.06 m) are shown in Fig. 5. Although the time-averaged solidsholdup indicated an almost flat radial profile, the chaosparameters show that the flow behavior is complex and thatthere appear to be three radial regions: core, transition, andannulus regions, as shown in Fig. 6. In the core region, K and D

Fig. 4. Effect of Gs and Ug on radial profiles of εs at h=8.06 m (data fromZhang, 1999).

were relatively high and H low due to the intermittent and anti-persistent (Hb0.5) flow behavior of dispersed particles andvery small clusters. In the transition region, K and D decreasedandH increased towards the wall, as the solids holdup increasedand cluster size increased. At the boundary between thetransition and annulus regions, D reached a local minimumdue to the relatively regular passage of large clusters. At thisradial position, there was more organized flow behavior. In thewall region, solids holdup started to decrease and clusteringbehavior was less significant. The slow and weak flow behaviorof small clusters and dispersed particles caused the flow to bepersistent (HN0.5) and less intermittent, thus low K and high H,but the noisy small fluctuations caused relatively high D. Rightat the wall, due to the wall effect and very dilute flow, the flowwas very complex due to noisy small fluctuations (Fig. 2).Therefore H decreased and D increased. However, underrelatively dense flow (Ug=3.7 m/s and Gs=100 kg/m2/s,Ug=7.2 m/s and Gs=200 kg/m2/s), H remained very high dueto the slow and persistent flow.

Operating conditions affected the value of chaos parametersand the length of the radial regions. At Gs of 100 kg/m2/s andUg of 3.7 m/s, flow in the core was very regular with relativelylow K, low D and high H as solids holdup was very high.Chaos parameters were close to each other under otheroperating conditions due to similar flow dynamics in the coreregion under relatively high superficial gas velocities. Thecombination effects of Gs and Ug on the value of chaosparameters in the transition and annulus region were morecomplex due to different clustering behavior under differentoperating conditions. The core region was relatively wide at

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100 kg/m2/s and Ug of 3.7 m/s as well as at 200 kg/m2/s and Ug

of 7.2 m/s due to relatively dense and uniform flow.Operating conditions significantly affected the distribution

of solids and their flow behavior inside the downer, and thusalso affected the values of chaos parameters. There should thusbe a relationship between chaos parameters (K, D, H) and time-

Fig. 6. Different radial regions in the downer, shown using K, atGs=100 kg/m2/s,

Ug=10.0 m/s and h=8.06 m.

Fig. 5. Radial profiles of chaos parameters in the downer at h=8.06 m.

averaged solids holdup, εs. Since cross-sectional average solidsholdup was generally constant in the fully development regionand directly related to the operating conditions, cross-sectionalaveraged chaos parameters were correlated to cross-sectionalaveraged solids holdup in the lower section of the downer(≥4.4 m) and are shown in Fig. 7. K and D first decreased withincreasing εs under dilute flow (b0.008). The relatively high Kand D were due to the intermittent and dilute flow of dispersedparticles and small clusters. K and D decreased due toincreasing more regular flow of clusters. However, K began toincrease gradually with increasing solids holdup beyondεs=0.008, while D fluctuated. With increasing solids holdup,more clusters were formed and some of the clusters becamevery large. The large clusters caused stronger and slower cyclicbehavior in the time series of solids concentration measure-ments. The competing behavior of large and slow fluctuationsof clusters and small and rapid fluctuations of dispersedparticles resulted in fluctuating D under denser flow, which alsoindicated more complex effect of operating conditions on Dthan K. Since the overall intermittent behavior was enhancedunder denser flow regardless the flow of increasing largeclusters, K increased. The value of H was normally below 0.5,indicating very “random” and anti-persistent flow behaviorinside the downer. A high K generally corresponds to a low H.However, no obvious trends could be found in the profiles of Hversus cross-sectional solids holdup. Therefore, K is likely to bethe best chaos parameters among the three to characterize thedynamics flow behavior of solids.

It should be pointed out that the relationships in Fig. 7 wereexamined from the cross-sectional averaged values; some of thelocal flow behavior near the wall may not follow theserelationships. Therefore, these relationships only qualitativelycharacterized the effect of solids holdup on the overall flowdynamics in the fully developed region of the downer.

5. Conclusion

In the top entrance section of the downer, radial profiles oftime-averaged solids holdup fluctuated significantly across the

Fig. 7. Relationships between chaos parameters and εs in the lower section of thedowner.

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radius of the downer. Further along the downer axis in thedevelopment zone, radial profiles of chaos parametersgenerally had a flat core and varying transition, and annulusregions. K and D were relatively high and H was low in thecore region due to strong and intermittent flow behavior ofdispersed particles and small clusters. In the fully developedregion, a minimum D at the boundary of transition and annulus

regions existed due to the regular flow of clusters. Relativelyhigh D and H closer to the wall (r /RN0.85) were due to verypersistent but small fluctuations of small clusters and dispersedparticles.

Cross-sectional averaged K and D were very high underrelatively dilute flow (εsb0.008) due to flow of dispersedparticles and small clusters. K slightly increased under moredense flow (εsN0.008) due to enhanced overall intermittentflow behavior of particles and clusters, while D fluctuated dueto competing cyclic flow behavior of large clusters and smallfluctuations of dispersed particles. A high K normallycorresponded to a low H.

NomenclatureCFB Circulating fluidized bedD Correlation dimension (–)dp Particle diameter (μm)FCC Fluid catalytic crackingGs Solid flux (kg/m2/s)h Height from the top of the downer (m)H Hurst exponent (–)ID Inner diameter (meter)K Kolmogorov entropy (bits/s)LOA Length of acceleration (m)r /R Reduced radial position (–)Ug Superficial gas velocities (m/s)εs Time-averaged local solids volume concentration (–)ε̄s Cross-sectional average solids holdup (–)ρp Particle density (kg/m3)Vp Particle velocity (m/s)

Acknowledgements

The authors are grateful to the Natural Sciences andEngineering Research Council of Canada for their financialsupport.

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