Hydrodynamic Similarity in Bubbling Fluidized Beds: TheImportance of the Solid-to-Gas Density Ratio

P. John Sanderson,†,‡ K. Seng Lim,*,† Igor Sidorenko,‡,§ and Martin J. Rhodes§

CSIRO Minerals, Box 312 Clayton South, Victoria, Australia 3169, CRC for Clean Power from Lignite,8-677 Springvale Road, Mulgrave, Victoria, Australia 3170, and Department of Chemical Engineering,Monash University, P.O. Box 36, Victoria, Australia 3800

Since bubbling fluidized-bed scaling laws were first developed, there has been some debate abouttheir correct application and the relative importance of the various scaling parameters, inparticular, the solid-to-gas density ratio. In this paper, we highlight the differences in the existingliterature and present the results from experimental fluidized-bed systems where the solid-to-gas density ratio has been changed by varying degrees. From our results, we conclude that thereis some flexibility for altering the solid-to-gas density ratio when scaling bubbling beds of Geldartgroup B materials up to particle Reynolds numbers of at least 12, but further work is needed toclarify the range of particle Reynolds numbers over which the density ratio requirement can berelaxed. In contrast, when scaling group A materials, we find that the density ratio is animportant parameter even if the particle Reynolds number is small.

Introduction

Because of the commercial risks associated withscaling up of a fluidized-bed process, the effect of a scalechange on the bubbling bed behavior has received muchattention over the years. In the early 1980s, hydro-dynamic similarity criteria were recognized as onepossible way of predicting the physical behavior of alarge bubbling fluidized bed based on measurementsmade in a small one. These similarity criteria, or“scaling laws”, could be summarized by equations or aset of dimensionless groups that, when applied to twofluidized-bed units of different size, should ensure thatthe physical phenomena occurring in the beds werescaled with their size.

Fitzgerald et al.1,2 first suggested and tested thesimilarity approach on bubbling fluidized beds. Glicks-man3 proposed a similar set of dimensionless groups butconsidered the cases of inertial-dominated and viscous-dominated flow separately, so that simplifications couldbe made to the set of dimensionless groups under thoseconditions. Horio et al.4 suggested an alternative formof scaling relationship expressed as a pair of equationsthat were later shown5 to be equivalent to the viscous-dominated version of Glicksman’s scaling relationships.Foscolo et al.6 showed that scaling criteria derived fromtheir generalized particle-bed model of fluidization wereconsistent with the aforementioned scaling laws ofFitzgerald and Glicksman and, importantly, implied thesuccessful application of scaling criteria to systems ofgroup A materials from a fluid-dynamic basis (i.e.,without the need to include any additional criteria fornon-fluid-dynamic interparticle forces). This proposalwas soon verified by the work of Rapagna et al.7 and DiFelice et al.8

The solid-to-gas density ratio is of particular interestbecause its inclusion in the so-called “simplified” scaling

criteria is open to different interpretations in theliterature. While the scaling relationship of Horio et al.4does not explicitly require the solid-to-gas density ratioto be matched between the two scaled systems, it hasoften been experimentally evaluated in situations wherea constant solid-to-gas density ratio has been main-tained inadvertently (by virtue of using the samefluidization media at both scales), for example.4,9,10 Onthe other hand, Glicksman et al.11 specifically includethe solid-to-gas density ratio in their development of agenerally applicable simplified scaling law. Their rea-soning is that for fluidization conditions with particleReynolds numbers exceeding Rep ) 4 (the limit forviscous-dominated drag forces) the inertial drag termcan no longer be neglected in the Ergun12 equation andthus the density ratio should be included in the scalinglaw.

Note that eqs 1 and 2 are equivalent except for the solid-to-gas density ratio requirement in the latter. Note alsothat the additional particle-related requirements ofsimilar size distribution and sphericity should also beconsidered in practice.

Because the only difference between the scaling lawof Horio et al.4 and the simplified scaling law ofGlicksman et al.11 is the inclusion of the density ratioin the latter, further work is needed to clarify thesignificance of this parameter when applying scalinglaws in practice.

* To whom correspondence should be addressed. Tel.: +613 9545 8500. Fax: +61 3 9562 8919. E-mail: seng.lim@csiro.au.

† CSIRO Minerals.‡ CRC for Clean Power from Lignite.§ Monash University.

Scaling law of Horio et al.:4

Condition 1: U2 - Umf2 ) xm(U1 - Umf1)

Condition 2: Umf2 ) xmUmf1

similar bed geometry (1)

Simplified scaling law of Glicksman et al.:11

U2

gL, U

Umf,

L1

L2,

Fs

Ff(2)

5466 Ind. Eng. Chem. Res. 2004, 43, 5466-5473

10.1021/ie0341810 CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 03/05/2004

Literature Review

The issue of matching the solid-to-gas density ratiowas highlighted by Broadhurst and Becker13 in theirearly dimensional analysis study of bubbling fluidiza-tion. In their comparison of four different-sized columns,they found that the solid-to-gas density ratio wasimportant for phenomena such as the minimum bub-bling velocity. The question of matching the solid-to-gas density ratio with the simplified scaling parameterswas pointed out by Glicksman et al.,11 experimentallyreported on by Farrel et al.,14 and also highlighted byGlicksman.15

Glicksman et al.11 explained the reasoning behind theinclusion of the parameter in their simplified scalinglaws as follows: Because the minimum fluidizationvelocity is a function of the particle-to-gas density ratio,if the density ratio is altered in the small-scale model(scaled by the simplified parameters), the requiredparticle diameter must then be changed in order thatthe minimum fluidization velocity is still scaled correctlybetween the two units. Changing the particle diameterwill thus alter the particle Reynolds number, which maysignificantly increase the error in the drag coefficient inthe scale model. Thus, for scaling beds with intermediateor large Reynolds numbers, the solid-to-gas density ratioshould be included in the set of scaling parameters.

A number of experimental investigations have ex-plored the use of the simplified scaling laws withmismatched solid-to-gas density ratios. Roy and David-son16 conducted several runs with a density ratiomismatch in which it could be argued that the simplifiedcriteria were met and concluded that for particle Rey-nolds numbers of less than 30, the solid-to-gas densityratio was unimportant (i.e., Glicksman’s requirementfor Rep < 4 was conservative). Leu and Lan17 alsoinvestigated a density mismatch with the use of thesimplified scaling criteria. Contrary to Roy and David-son, they found that similarity was not achieved, eventhough their experiments were conducted at low particleReynolds numbers (6 < Rep < 14 and 2 < Rep < 8) andthey satisfied both requirements of the similarity rulein their first comparison and condition 2 alone in thesecond. van der Stappen18 also explored a densitymismatch for the range 10 < Rep < 35 and found thatsimilarity was not achieved for gas velocities exceeding2.5Umf (corresponding to Rep ) 13), although the particlesize distribution and sphericity were also mismatchedand the choice of the distributor may also have influ-enced the results. Farrel et al.14 carefully matched all

parameters except the density ratio in their study ofthe simplified scaling law and found that similarity wasnot achieved at all for 10 < Rep < 25. Finally, Stein etal.19,20 carried out runs in their study of the simplifiedcriteria in which the density ratio was mis-matched (for17 < Rep < 42), and they did claim to find similarbehavior, tentatively suggesting that the range for theviscous limit scaling criteria could be as high as Rep )100.

Given the somewhat contradictory evidence from theprevious studies and the differences in the approachesof Horio et al.4 and Glicksman et al.,11 it can only beconcluded from a review of the literature that furtherwork is needed to clarify situations when the gas-to-solid density ratio should be included and when it canbe safely ignored.

In the present work, experimental verification of thesimplified scaling laws is undertaken with the specificobjective of mismatching the solid-to-gas density ratiowhile maintaining the other parameters constant. Inthis way, we seek to determine the importance of thisparameter for scaling in both Geldart group A and Bmaterials at various particle Reynolds numbers.

Experimental Section

Two small-scale bubbling bed models were used in theexperimental tests. Both were cylindrical in cross sec-tion and had vessel internal diameters of 146 mm.Henceforth, they shall be referred to as systems 1 and2 for clarity.

System 1 was designed to operate at ambient pressureand consisted of an acrylic column and bubble capdistributor with bed materials fluidized by ambient air.Figure 1a shows the overall arrangement. Measure-ments of fluidization properties were undertaken usingeither a single pressure probe located 103 mm abovethe distributor or a single-plane 12-electrode electricalcapacitance tomography (ECT) system with electrodeaxial centers located 150 mm above the distributor. Themeasurement electrodes were 50 mm high and locatedbetween pairs of driven shield electrodes. The pressureprobe, designed according to the guidelines of vanOmmen et al.,21 was used to generate absolute pressurefluctuation signals detected by a Data InstrumentsXCX01DNQ pressure transducer. For each condition,over 16 000 data points were sampled to a personalcomputer at a rate of approximately 250 Hz. ECT datawere sampled at approximately 80 Hz, and 16 000

Figure 1. (a) Physical arrangement of the ambient-air fluidized bed used in system 1. Note that pressure probe and ECT measurementswere carried out in separate runs. (b) Comparison of the cumulative particle size distributions for silica and garnet sands.

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5467

frames were recorded for each condition. Both ECT andpressure measurement runs were repeated three timesfor each operating condition to get an indication of theextent of random error. As may be seen in Figure 1b,the two bed materials used in this system (garnet sandand silica sand) had similarly shaped particle sizedistributions, although the particle size distributionswere somewhat wide, which may be the reason themeasured minimum fluidization velocities were lowerthan those predicted by the Wen and Yu correlation.An examination under an optical microscope showedthat both of the materials consisted of rounded sandlikeparticles with similar shape. Further details of theequipment and procedure may be found in work bySanderson.22

System 1 was used to compare situations in whichthe solid density was changed while the gas densityremained the same.

System 2 was designed to operate at ambient as wellas elevated pressures, up to 2500 kPa (25 bar). Itconsisted of an acrylic column and sintered bronzedistributor (nominal pore size 12 µm) housed within apressure vessel. The bed was fluidized by compressedair for pressures of up to 6 bar and by compressednitrogen for pressures above this. Figure 2 shows theprocess and instrumentation diagram. For experimentsreported here, measurements in the pressurized bedwere undertaken using the single-plane 12-electrodeECT system with an electrode axial center located 250mm above the distributor plate and electrode dimen-sions identical with those in system 1. Full details ofthe pressurized fluidized-bed equipment may be foundin work by Sidorenko.23

System 2 was used to compare situations in whichthe gas density was altered by changing the systempressure while the solid density remained the same. Thetests were carried out for both Geldart group A and Bmaterials (henceforth referred to as systems 2A and 2B,respectively).

Note that when the gas density is altered in this way,it is important to consider the impact of any inadvertentchanges to the gas viscosity and minimum fluidizationvelocity that result from altering the gas pressure. Whilethere is negligible change in the air viscosity at thepressures involved, the measured minimum fluidizationvelocity (Umf) is altered (see Table 2) for both bedmaterials.23 To account for this, the variation in theminimum fluidization velocity has been incorporatedinto our calculation of the dimensionless gas velocity(U/Umf) for proper comparison of dimensionless results.

The fluidization parameters for the two separateexperimental setups are shown in Tables 1 and 2. Notethat a complete verification test was conducted in eachof systems 1, 2A, and 2B; there is no attempt to matchthe parameters or achieve similarity between thesesystems.

Results from System 1: Change in the SolidDensity for Geldart Group B Materials

As can be seen from Table 1, the comparison under-taken in system 1 involved two Geldart group Bpowders, well matched in terms of the simplified scalingcriteria but with a mismatched solid-to-gas density ratioas a consequence different particle densities.

Figure 3 shows a comparison of the dimensionlessaverage pressure and dimensionless average absolutedeviation of pressure recorded by the pressure probesystem for the full range of gas velocities investigated.Pressure measurements were nondimensionalized via

where P is the measured pressure (Pa), Fb is the packed-bed bulk density (kg/m3), g is the acceleration due togravity (m/s2), and Hs is the settled bed height (m). Theresults indicate similar bed expansion and pressurefluctuation amplitude characteristics for both materials.Figures 4 and 5 show comparisons of the probabilitydensity function and amplitude spectrum, respectively,from the pressure fluctuation signals corresponding toa midrange gas velocity. The distributions were normal-ized to ensure that the area under each was the same,and for consistency with the simplified criteria, fre-quency was nondimensionalized via

where f is the measured frequency (Hz) and D is thebed diameter (m). These results are typical of thoseobtained throughout the velocity range investigated.21

Figure 2. Process instrumentation diagram for the pressurizedcold fluidized-bed model used in system 2: V1, V3, V5-V7, V10-V13, isolation valves; V2, V9, flow control valves; V4, nonreturnvalve; V8, safety relief valve; P1-P4, pressure gauges; T1, tem-perature indicator; F1, line filter; PVC1, line service unit consistingof a pressure regulator, air filter, and moisture trap; R1-R3,rotameters Krohne H250; R4, rotameter with flow controllerKrohne DK32; PVC2, manifold pressure regulator; PVC3, back-pressure control valve Samson 3510 with an integral positioner;BD1, safety bursting disk; DP1, bed differential pressure trans-mitter Honeywell STD-924; PC, universal digital controllerHoneywell UDC300.

Table 1. Specifics of System 1 (Ambient Conditions,Group B Materials)

system 1

bed diameter D (mm) 146 146bed material silica sand garnet sandstatic bed height Hs (mm) 295 295Sauter mean particle diameter

dsv (µm)337 300

minimum fluidization velocityUmf (m/s)

0.085 0.082

particle density Fs (kg/m3) 2650 4100gas velocity U (m/s) 0.101-0.327 0.101-0.402Froude number Fr 0.0071-0.075 0.0071-0.113particle Reynolds number Rep 2.2-7.2 2.0-7.9density ratio Fs/Ff 2190 3390

P* ) P/FbgHs (3)

f* ) fD/Umf (4)

5468 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

ECT results were compared by calculating the aver-age voidage across the measured cross section (i.e., acylinder of 146 mm diameter and 50 mm height) foreach frame of data and using these data to generate aspatially averaged bed voidage time sequence. Thechosen ECT measurement provides a means of compar-ing the ensemble-averaged property of the fluidizationhydrodynamics across a section of the bed. From thissequence, data were compared in a number of ways.

Figure 6 shows the time average and average absolutedeviation of the overall average bed voidage for the fullrange of gas velocities investigated. The trends in theresults are entirely consistent with those recorded bythe pressure probe in Figure 3. Figure 7 shows theaverage cycle frequency (calculated as half the numberof times the signal crosses its own average per unit time)for the voidage fluctuation time sequence, indicatingthat the two systems have similar time scales (although

there is some indication that at higher velocities thetrends may be starting to diverge). The similarity ofboth the magnitude and time scale of voidage fluctua-tions for the two materials is further confirmed bynormalized probability density functions (e.g., Figure 8)and amplitude spectra (e.g., Figure 9), both of which aretypical of the agreement seen across the velocity rangestudied.

Results from System 2A: Changes in the GasDensity for Geldart Group A Materials

In the system 2 tests, ECT results were used as themain method of comparing hydrodynamic phenomenaand were processed in the same way as that describedfor system 1. In system 2, spatially averaged ECT dataare taken from a measurement volume of 146 mm in

Table 2. Specifics of System 2 (High Pressure, Tests on Both Group A and B Materials)

system 2A system 2B

bed diameter D (mm) 146 146bed material FCC powder silica sandSauter mean particle diameter dsv (µm) 77 203particle density Fs (kg/m3) 1330 2650superficial gas velocity U (m/s) 0.005-0.059 0.033-0.15Froude number Fr 1.7 × 10-5-2.4 × 10-3 8.6 × 10-4-1.6 × 10-2

operating pressure (bar, abs.) 3-19 1-21gas density (kg/m3) 3.6-22.8 1.2-25.2minimum fluidization velocitya Umf (m/s) 0.0028-0.0021 0.033-0.028particle Reynolds number Rep 0.13-2.3 0.5-12density ratio Fs/Ff 370-58 2190-105

a Note that the minimum fluidization velocity is weakly affected by pressure and decreases with increasing pressure.

Figure 3. Variation in dimensionless average pressure (Av.) andaverage absolute deviation in dimensionless pressure (AAD) withdimensionless gas velocity for system 1 using silica and garnetsands.

Figure 4. Comparison of the normalized probability distributionof pressure fluctuations for system 1 (silica and garnet sands) atsimilar dimensionless superficial gas velocities.

Figure 5. Comparison of dimensionless amplitude spectra ofpressure fluctuations for system 1 (silica and garnet sands) atsimilar dimensionless superficial gas velocities.

Figure 6. Variation in the overall average voidage (Av.) andaverage absolute deviation in voidage (AAD) from ECT measure-ments for system 1 (silica and garnet sands) at a range ofdimensionless superficial gas velocities.

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5469

diameter and 50 mm height, located 250 mm above thedistributor plate. Results presented in Figure 10 showthe variation in the average bed voidage with gasvelocity for the FCC powder at a range of solid-to-gasdensity ratios, clearly indicating that an increase in thegas density results in a reduction of the average bedvoidage. Interestingly, it was shown elsewhere23 thatthe bed voidage at minimum bubbling conditions forsystem 2A remains virtually constant across the rangeof gas pressures used, varying only from 0.47 to 0.50 atpressures from 1 to 21 bar, respectively (a result verysimilar to that of Rapagna et al.7). Figure 11 shows the

variation in the average absolute deviation of the bedvoidage with gas velocity at a range of solid-to-gasdensity ratios. The increasing gas density results in adecrease in the average absolute deviation correspond-ing to more uniform bubbling. Figure 12 shows thevariation in the average cycle frequency with gasvelocity and solid-to-gas density ratio. The frequencydecreases with a large increase in the gas density. Inthe intermediate region between minimum fluidization

Figure 7. Comparison of the dimensionless average cycle fre-quency from ECT voidage fluctuations for system 1 (silica andgarnet sands) as a function of the gas velocity.

Figure 8. Comparison of the normalized probability distributionof measured ECT voidage fluctuations for system 1 (silica andgarnet sands) at similar dimensionless superficial gas velocities.

Figure 9. Comparison of the dimensionless amplitude spectraof ECT voidage fluctuations for system 1 (silica and garnet sands)at similar dimensionless superficial gas velocities.

Figure 10. Variation in the average bed voidage (from ECTmeasurement) with dimensionless superficial gas velocity forsystem 2A (FCC powder) for a range of solid-to-gas density ratios(DR). Lines are used to guide the eye.

Figure 11. Variation in the average absolute deviation of bedvoidage (from ECT measurement) with dimensionless superficialgas velocities for system 2A (FCC powder) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.

Figure 12. Variation in the dimensionless average cycle fre-quency of bed voidage fluctuations (from ECT measurement) withdimensionless superficial gas velocities for system 2A (FCCpowder) for a range of solid-to-gas density ratios (DR). Lines areused to guide the eye.

5470 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

and minimum bubbling conditions, the average cyclefrequency is very sensitive to small disturbances ap-parently caused by experimental noise and typicallyshows a decrease and then an increase with increasinggas velocity, a trend that has also been reported by otherworkers.24,25

Results from System 2B: Changes in the GasDensity for Geldart Group B Materials

In these tests, ECT results were again used as themain method of comparing hydrodynamic phenomenabut this time in the evaluation of Geldart group Bmaterial behavior as shown in Table 2. Figure 13 showsthe variation in the average bed voidage with gasvelocity and density ratio for the silica sand andindicates that the decreasing solid-to-gas density ratioresults in an increase in the average bed voidage, whichis small for small changes in the density ratio but moredramatic for larger changes in the density ratio. Figure14 shows the variation in the average absolute deviationof bed voidage with gas velocity for the same materialand, importantly, indicates that the change in thedensity ratio has a relatively minor effect on themagnitude of the fluctuations. Figure 15 shows thevariation in the average cycle frequency with gasvelocity for the same experiments and indicates that thechange in the density ratio has a relatively small effecton the time scale of the fluctuations.

Discussion

For system 1, the comprehensive analysis of bothpressure and voidage fluctuation signals indicates closelymatched bubbling bed hydrodynamics, in terms of boththe time scale and magnitude of the observed fluctua-tions. The results also serve to reinforce the validity ofconclusions drawn from the ECT data in this situationbecause they correspond well with the more conven-tional pressure fluctuation measurements. Although inthis work we do not present a deliberately mis-scaledscenario to test the measurement techniques, our previ-ous work22,26 demonstrates that both the pressure andvoidage fluctuation measurements we have undertakencan correctly distinguish between scaled and mis-scaledsystems. In the system 1 time-scale comparisons, thenondimensionalization of the frequency is carried outfor completeness rather than necessity because neitherthe bed diameter nor the minimum fluidization velocityis significantly altered between the two cases. Theparticle Reynolds numbers over which the system 1comparison has been evaluated are in the range 2 <Rep < 7, thus spanning the viscous limit (Rep ) 4)suggested by Glicksman.3 We find that the density ratiomismatch in this system (2190 for silica sand and 3390for garnet sand) does not cause any significant differ-ence in the hydrodynamics for this range of particleReynolds numbers. However, the voidage fluctuationaverage cycle frequencies in Figure 7 tend to suggestthat the time scales for the two systems may be juststarting to diverge at higher velocities, an observationalso made by Farrel et al.14 and something to beevaluated in future work at higher velocities.

For system 2B, also involving a Geldart B material,we find some differences in the measured bed expansionat different solid-to-gas density ratios that are moredramatic for a large change in the density ratio thanfor a small one. The magnitudes of the voidage fluctua-tions show a reasonable agreement and no clear trendwith changing density ratio. The frequencies of thevoidage fluctuations also show reasonable agreement;at low velocities, there is no clear trend with the densityratio, but at higher gas velocities, the frequency in-creases slightly with a 3-fold increase in the densityratio. So, in the pressurized group B system, we findthat it is only for significant differences in the solid-to-gas density ratio and/or higher gas velocities that thereis a measurable difference in the hydrodynamics.

Figure 13. Variation in the average bed voidage (from ECTmeasurement) with dimensionless superficial gas velocity forsystem 2B (silica sand) for a range of solid-to-gas density ratios(DR). Lines are used to guide the eye.

Figure 14. Variation in the average absolute deviation of bedvoidage (from ECT measurement) with dimensionless superficialgas velocities for system 2B (silica sand) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.

Figure 15. Variation in the dimensionless average cycle fre-quency of bed voidage fluctuations (from ECT measurement) withdimensionless superficial gas velocities for system 2B (silica sand)for a range of solid-to-gas density ratios (DR). Lines are used toguide the eye.

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5471

Note that both Farrel et al.14 and van der Stappen,18

who observed a mismatch in systems scaled by thesimplified scaling criteria and incorporating a mis-matched density ratio, did so at particle Reynoldsnumbers generally higher than those considered in thiswork (roughly above Rep ) 10), although other work-ers16,20 claim to have found well-matched behavior atstill higher particle Reynolds numbers (suggesting upto 30 and 100, respectively).

Interestingly, we note that our results for both theambient and pressurized systems are in direct contra-diction to the results presented by Leu and Lan,17 whoexplored a density ratio mismatch with Geldart Bpowders in a Reynolds number range similar to that ofthis work, albeit with one system at elevated temper-ature. Leu and Lan observed a mismatch in the fluctua-tion frequency for the ambient-temperature systems inwhich they mismatched the density ratio, and theyobserved a mismatch in the fluctuation amplitudebetween hot- and cold-scaled models (also involving amismatched density ratio), although the fluctuationfrequencies coincided. We do not observe these differ-ences in our results, and at present we can offer nodefinitive explanation for the difference but acknowl-edge that the study was conducted in a two-dimensionalbed as opposed to our three-dimensional system. Wetherefore consider an experimental evaluation of fluid-particle systems similar to those used by Leu and Lan(e.g., involving elevated temperature) as grounds forfuture work.

In contrast to the observations of Geldart group Bmaterials, the results from the pressurized experimentsof system 2A demonstrate that matching the solid-to-gas density ratio is an important requirement whenscaling systems of Geldart group A powders, even if theparticle Reynolds number is very low. Our ECT-basedmeasurements indicate that differences in the bedexpansion, magnitude, and frequency of voidage fluc-tuations occur if the density ratio is mismatched, withthe most significant differences occurring for largechanges in the density ratio. (For comparison, we planfurther evaluation with pressure measurements infuture work.) Although the maximum change in the bedexpansion for the group A case is of magnitude similarto that observed in the group B case (comparing Figure10 with Figure 13), the density ratios have not beenaltered as dramatically to achieve it. Note that ourobservations for the group A system cover a range oflow particle Reynolds numbers of 0.1 < Rep < 3,implying that the criteria for viscous limit scaling mayrequire further evaluation. These findings are also inagreement with the recommendations of Rapagna etal.,7 who advised “extreme caution” when consideringneglect of the density ratio in group A systems due toits strong influence on the minimum bubbling voidage.

Conclusions

An evaluation of the effect of mismatch of the solid-to-gas density ratio in bubbling bed systems scaled bythe simplified scaling parameters was carried out insmall-scale cold models. Measurements of pressurefluctuations (from the pressure probe) and voidagefluctuations (from the ECT) were carried out. Weinvestigated both Geldart group A and B systems andmanipulated the density ratio via either choice of solidsor alteration of the system gas pressure. For Geldart

group B systems, we found that for the range of particleReynolds numbers considered (up to Rep ) 12), the effectof mismatch of the solid-to-gas density ratio was smalland only identifiable at higher gas velocities or wherethe change in the density ratio was large. This suggeststhat there is more flexibility with group B materialsthan the “traditional” viscous limit value of Rep ) 4would imply. However, further work on group B materi-als is required to better define the range in which thedensity ratio can be neglected. In contrast, we foundthat the solid-to-gas density ratio is an importantparameter when scaling systems with Geldart group Apowders and attempts should be made to match it evenwhen the particle Reynolds numbers are small andwithin the range of the viscous limit. Further study isrequired to address these issues in order to develop moredefinitive scaling procedures.

Acknowledgment

The authors gratefully acknowledge the financial andother support received for this research from the CRCfor Clean Power from Lignite, which is establishedunder the Australian Government’s Cooperative Re-search Centres Scheme.

Nomenclature

D ) bed diameter (m)dsv ) Sauter mean particle diameter (µm)f ) frequency (Hz)g ) acceleration due to gravity (m/s2)L ) length dimension (m)m ) scaling factor; ratio of length dimensionsHs ) settled bed height (m)P ) pressure (Pa)Umf ) minimum fluidization velocity (m/s)U ) superficial gas velocity (m/s)

Greek Letters

µ ) fluid viscosity (kg/ms)Fb ) bed bulk density (kg/m3)Ff ) fluid density (kg/m3)Fs ) particle density (kg/m3)

Dimensionless Groups

Rep ) particle Reynolds number, Rep ) dsvUFf/µFr ) simplified Froude number, Fr ) U2/gD

Superscript

* ) nondimensional form

Subscript

1, 2 ) parameters from different scaled systems

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Received for review October 14, 2003Revised manuscript received January 7, 2004

Accepted January 13, 2004

IE0341810

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5473