trickle bed hydrodynamics and flow regime transition at elevated temperature for a newtonian and a...

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Chemical Engineering Science 60 (2005) 6686–6700

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Trickle bed hydrodynamics and flow regime transition at elevatedtemperature for a Newtonian and a non-Newtonian liquid

Bora Aydina, Faïçal Larachia,∗,1aDepartment of Chemical Engineering, Laval University, Québec, Canada G1K 7P4

Received 27 March 2005; received in revised form 25 May 2005; accepted 28 May 2005

Abstract

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, tricklebed hydrodynamic behavior at elevated temperatures, on the contrary, largely remainsterra incognita. This study’s aim was to demonstrateexperimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdupand liquid axial dispersion coefficient. These parameters were determined for Newtonian (air–water) and non-Newtonian (air–0.25%Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlationsfor confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficialvelocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden thetrickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71,319–321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything elsebeing kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulsevelocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi,2002, Chemical Engineering Science 46, 1233–1246] predicted with very good accuracy both the pressure drops and the liquid holdupsregardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and EngineeringChemistry Research 43, 4511–4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulsevelocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (Dax) extractedfrom the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonianand power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Trickle bed; Elevated temperature; Hydrodynamics; Transition boundary; Pulsing flow; Non-Newtonian fluids

1. Introduction

Trickle-bed reactors (TBR) are perhaps the simplestand the most ubiquitous three-phase reactor configura-tions wherein gaseous and liquid streams are forced toflow co-currently downwards across a porous medium of

∗ Corresponding author.E-mail addresses:[email protected](B. Aydin),

[email protected](F. Larachi).1 Current address: ARKEMA/TOTAL - Centre Technique de Lyon,

Chemin de la Lône - BP32 69492 Pierre-Bénite, Cédex, France.

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.05.065

randomly packed catalytic grains. Though not being its ex-clusive user, the petroleum industry nowadays tremendouslyrelies on trickle bed for its hydrotreating and hydrocrackingoperations. This stems from the gradual reserve depletion ofthe so-called conventional oil which is forcing the oil sec-tor to exploitdirtier non-conventional hydrocarbon depositssuch as heavy crude oils, bitumen and residues (Speight,1999, 2001; Wauquier, 1994; Lepage et al., 1990).

Ongoing research on trickle bed efficiency demonstratesthe significance of spotting the optimal operational modesand of quantifying the incidence of its most influentialfactors. As several industrial applications require elevated

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pressure and temperature, understanding of TBR hydrody-namics at these conditions is imperative. A great deal of ex-perimental studies dealing with the effect of elevated pres-sures on TBR hydrodynamics concerned the trickle flowregime. Though the advantages of pulsing flow are welldocumented in the literature (Rao and Drinkenburg, 1985;Tsochatzidis and Karabelas, 1995; Boelhouwer et al., 2002)interest on pulse flow regime characteristics at elevated pres-sures is very recent (Burghardt et al., 2002, 2004). Sincethis flow regime takes place in several industrial applicationsoften at high temperature, it is necessary to unveil the tem-perature effects on basic characteristics, e.g., pulse velocity,that occur in this particular flow regime.

To the best of our knowledge, experimental studies onTBR hydrodynamics involving non-Newtonian systems con-cern friendly atmospheric pressure and ambient temperatureconditions. As TBR applications also touch the realm of bio-chemical processes, the effects of temperature and pressureought to be unveiled for the hydrodynamic parameters oftrickle-bed reactors traversed by the flow of non-Newtonianliquids.

Flow regime transitions at elevated pressure were firstinvestigated byHasseni et al. (1987)up to 10 MPa. Trickle-to-pulse flow regime transitions were determined bothvisually and from locating slope inflation using pressuredrop-flow rate curves obtained for different pressure valuesfor aqueous and organic liquids, and two particle sizes.Using the gas mass flux scale and the original Charpentierand Favier flow regime diagram (Charpentier and Favier,1975), Hasseni et al. (1987)noted a collapse with increas-ing pressures of the L/G�� versus G/� lines. Wammes etal. (1990a,b)determined visually the shift with pressure offlow regime transition for air-nitrogen system up to 1.5 MPa.They observed a shift in transition boundary to higher liq-uid velocities with increasingly pressures for a constant gassuperficial velocity.Larachi et al. (1993)derived a graphicalcorrelation based on elevated pressure experimental data bymodifying the Charpentier and Favier flow chart throughintroducing a new gas density sensitive correction function�, on top of the two traditional physical-property Baker�and� coordinates. The amended flow regime diagram em-braced most of the high-pressure flow regime transition datapublished in the 1990s.Burghardt et al. (2002)observed thegas continuous to pulsing flow regime for air–water systemup to 0.9 MPa and ambient temperature by means of elec-trical conductivity cells. They confirmed their predecessors’observations regarding the shift from trickle to pulse flowtransition to higher superficial velocities of the two phases.Experimental investigations on flow regimes in trickle bedsinvolving non-Newtonians liquids (mainly pseudo-plasticinelastic power-law aqueous solutions) were scanty andconcerned exclusively ambient temperature and pressure,e.g.,Sai and Varma (1988)visual observation of transitionfor air–0.25% carboxymethylcellulose (CMC) system, andIliuta et al. (1996)andIliuta and Thyrion (1997)studies fordifferent power-law aqueous CMC solutions. Their findings

were coherent with a trickle flow region that retracts withincreased liquid viscosity.

Experimental data on pulse flow characteristics in tricklebeds has begun to be reported in the early 1960s.Weekmanand Myers (1964)measured pulse frequency and velocityfor different particle sizes for the air–water system usingphoto-resistors. They reported an increase in pulse velocitywith gas and/or liquid flow rates.Sato et al. (1973)usedmotion pictures, pressure transducer and electrical conduc-tivity probes for the determination of pulse velocity, andpointed out to the negligible dependence of pulse velocityupon phase flow rates.Blok and Drinkenburg (1982), usingelectrical conductivity probes for the measurement of pulsevelocity and frequency for air–water system, found no in-fluence of liquid flow rate on pulse velocity. Similarly, ac-cording to experiments with different particle sizes,Rao andDrinkenburg (1983)also observed marginal effect of liquidflow rate and proposed a pulse velocity correlation function-alizing interstitial gas velocity and packing geometry. How-ever, at high liquid flow rate,Tsochatzidis and Karabelas(1995) observed significant influence of this parameter onpulse velocity for the air–water system. They suggested anempirical correlation functionalizing interstitial gas veloc-ity and superficial liquid velocity.Bartelmus et al. (1998)andBurghardt et al. (2002, 2004)implemented optical andelectrical conductivity techniques for measuring pulse ve-locity, pulse frequency and pulse length for different particlesizes, gas–liquid systems and pressures. Increasingly pres-sures were found to decrease pulse velocity and to increasepulse frequency, whereas pulse length was shortened. Theyproposed a pulse velocity correlation as a function of packingsize, and gas and liquid interstitial velocities.Boelhouwer etal. (2002)measured pulse frequency and pulse velocity fordifferent particle sizes using an electrical conductance tech-nique and observed an increase in pulse velocity with gasflow rate but indicated insignificant effects of liquid flowrate.

The effect of pressure on two-phase pressure drop wasinvestigated by many previous researchers. Experimentaltwo-phase pressure drop data was first reported in the late1980s byHasseni et al. (1987)for the nitrogen-water sys-tem up to 10.1 MPa based upon whichEllman et al. (1988)proposed correlations for the calculation of pressure dropboth in low (trickle flow) and high interaction (mainly pulseflow) regimes.Wammes et al. (1990a,b), Wammes et al.,1991measured and correlated pressure drops up to 7.5 MPafor different aqueous and organic liquid systems under var-ious flow regimes, including trickle and pulse flow regimes.Larachi et al. (1991)andWild et al. (1991)provided pres-sure drop experiments up to 8.1 MPa for diverse systemsand a pressure drop correlation thereof. In their correla-tion, pressure drop is expressed by means of two-phase flowfriction factor and the modified Lockhart–Martinelli ratio.Al-Dahhan and Dudukovic (1994)conducted experimentsup to 5 MPa for different aqueous and non-aqueous systemsin trickle flow regime. Recently,Burghardt et al. (2004)

6688 B. Aydin, F. Larachi / Chemical Engineering Science 60 (2005) 6686–6700

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reported pressure drop data up to 0.9 MPa for air–waterand air–glycerin systems at elevated pressure; whereasGuoand Al-Dahhan (2004)studied pressure drop up to 0.8 MPafor air–water system. Pressure drop data for non-Newtonianliquids is much scantier and only concerned ambient con-ditions. Larkins et al. (1961)were the first who studiedthe behavior of pressure drops in trickle beds for differ-ent CMC systems.Iliuta and Thyrion (1997)investigatedthe pressure drop for different CMC concentrations andSai and Varma (1987)presented a correlation in terms ofLockhart–Martinelli parameters, flow variables and packingcharacteristics.

Liquid holdup plays a crucial role in several trickle bedprocesses such as control of catalyst wetting efficiency,radial heat transfer, gas–liquid mass transfer of gaseousreactant, solvent evaporation and exposure of bare drycatalytic surfaces thereof, etc. Ongoing research on thisparameter has mainly been concerned with the incidenceof elevated pressures as described in the pressure drop ref-erences above. Besides the reported experimental work atelevated pressure, to our knowledge there is at least only onestudy published for liquid holdup measurements at elevatedtemperature.Ring and Missen (1991)measured the liquidholdup between 330 and 370◦ C in trickle flow regime inthe conditions of dibenzothiophene catalytic hydrodesulfu-rization. According to the data obtained from pulse-tracerexperiments, no clear cut emerged regarding the effect oftemperature which was difficult to interpret.

As seen briefly from the above literature survey, evenif an adequate body of knowledge on TBR hydrodynam-ics has become available for the elevated pressures overthe past decade or so, the effect of temperature was largelyoverlooked by the existing systematic TBR hydrodynamicstudies. This situation is paradoxical considering that tem-perature affects virtually all the gas and liquid physicalproperties whereas pressure is known to influence almostexclusively density and molecular diffusivity for sub-criticalgases that are above atmospheric pressure. It is thereforefelt opportune to address this issue and supplement the lit-erature with a study fully devoted to the implications oftemperature on the macroscopic hydrodynamic properties oftrickle beds. As the hydrodynamic parameters are incumbentupon the prevailing flow regime, it is worthwhile to iden-tify the trickle to pulsing flow transition boundary for ele-vated temperature. Also the hydrodynamic parameters suchas pulse velocity, two-phase pressure drop, liquid holdupand axial dispersion coefficient, which is informative of thedegree of liquid backmixing, are also reported for elevatedtemperature.

2. Experimental setup and procedure

Experiments were carried out in a stainless steel reactorable to withstand temperatures up to 100◦ C and pressuresup to 5 MPa. Hydrodynamic measurements concerned flow

regime changeover from trickle to pulse flow, pulse veloc-ity, two-phase pressure drop, liquid holdup and liquid ax-ial dispersion coefficient. A systematic study was devotedto study the effect of temperature for Newtonian and non-Newtonian liquids between 25 and 75◦ C and up to a pres-sure of 0.7 MPa. The main elements of the experimentalsetup are schematically represented inFig. 1. The reactor(I.D.= 4.8 cm) was packed with 3 mm glass beads to com-plete a total bed height of 107 cm with an overall poros-ity 39%. The resulting column-to-particle diameter ratio of16 was not very far from the criterionDc/dp>20 recom-mended for avoiding wall flow maldistribution (Al-Dahhanet al., 1997). Though this ratio was not sufficiently high tocompletely get rid of such undesirable phenomena, an as-sessment of the quality of data and the marginal extent ofwall flow distribution will be revealed post facto from thematching quality with some literature models and correla-tions. The packing was maintained by means of a rigid stain-less steel screen placed at the column bottom, and had amesh openness large enough to prevent artifactual bed flood-ing but narrow enough to impede particles crossings. In allthe experiments, air was the process gas, whereas water oraqueous 0.25% w/w carboxymethylcellulose (CMC) solu-tion were the process liquids. The CMC solution, preparedby dissolving powdered CMC in water at ambient temper-ature, exhibited an inelastic pseudoplastic rheological be-havior which was well represented by means of a simplepower-law Ostwald-DeWaele model (Eqs. (1) and (2)). Theconsistency index,k, and the power-law index,n, were fittedfor each process temperature after measuring the solutionshear stress-shear rate responses on an Advanced Rheomet-ric Expansion System (ARES) rheometer in the 0–1000 s−1

shear-rate ranges. The rheological parameters for each pro-cess temperature are summarized inTable 1.

� = k(�)n, (1)

�eff = k(�)n−1. (2)

After the liquid was heated in the reservoir (up to max.60◦ C), it was pumped by means of a rotary valve pump(Procon model 1309XH) through a liquid preheater via cal-ibrated flowmeters then to the reactor. The gas was fed froma compressed air supply able to deliver a maximum pres-sure of 0.7 MPa. It passed through a gas preheater beforeencountering the liquid on the reactor top to be both fedcocurrently downwards through it. Once leaving the reactor,the outgoing stream was intercepted in a gas–liquid separa-tor. The gas was then expanded and its flow rate measuredthrough calibrated flowmeters before being vented to the at-mosphere. The liquid was circulated in a closed loop fromthe reservoir. Before starting the experiments the reactor wasoperated till the desired operating temperature was reached.Prior to performing any experiment, the reactor was preven-tively operated in the pulsing flow regime for 1 h to achieveperfect bed prewetting.


3

1

2

T2

4

PTPT

5

6

7

8

9

Liquid Gas

P3

Gas

10

11

P1

T1

P2

12

Fig. 1. Experimental setup: (1) packed bed, (2) conductance probes, (3) conductimetric sensors, (4) preheater for the gas phase, (5) preheater for theliquid phase, (6) pressure transducer, (7) reservoir, (8) gas–liquid separator, (9) lock-in amplifiers, (10) gas flowmeter, (11) liquid flowmeter, (12) tracerinjection loop.

Table 1Rheological properties of 0.25% CMC at elevated temperatures

Temperature k n �(◦C) (kg/m s2−n) (kg/s2)

25 0.072 0.666 0.05650 0.041 0.707 0.05475 0.033 0.659 0.051

In order to measure the pulse properties, an electricalconductance technique was implemented using recommen-dations and design details provided byTsochatzidis andKarabelas (1995)andBoelhouwer et al. (2002). Two con-ductance probes were mounted in the middle of the reactor,a distance of 0.225 m apart from each another. Each probeconsisted of two ring electrodes 0.001 m in thickness and0.03 m separation distance between the two electrodes(Fig. 2). Each probe was connected to a lock-in amplifierto acquire the output signal. After amplification, the sig-nals were transmitted to a computer by means of a data

2 cm

4 cm

22.5

cm

Fig. 2. Ring electrical conductivity probes for measuring pulse velocity.

acquisition system. Identification of flow regime transitionwas carried out using a moment method (Rode, 1992).The coefficient of variationT was calculated from the


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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.002 0.008 0.014 0.02

uL (m/s)

T

Trickle Flow

Pulsing Flow

Transition

Fig. 3. Schematic illustration of the coefficient of variationT as a functionof uL, Tr = 50◦ C, Pr =0.7 MPa,uG=0.2088 m/s. Vertex correspondsto transition between trickle flow and pulse flow regimes.

second-order central moment (variance) and the first-ordermoment (arithmetic average) of the probability densityfunction of the fluctuating signals. The coefficient of varia-tion simply compares the amplitude of the fluctuations withrespect to the average signal value (Eqs. (3) and (4)):

xn =∫ ∞

−∞(X −X)np(X)dX, (3)

T =√x2

X, (4)

in which X is the mean value, andx2 is the variance ofthe conductivity signal.Fig. 3shows an example of locationof the coefficient of variationT corresponding to the occur-rence of trickle-to-pulse flow regime transition as a func-tion of superficial liquid flow velocity for a constant super-ficial gas velocity. The maximum in the curve at (uL, T )=(0.01 m/s,0.13) corresponds to the change of flow regimewhereof the critical values for superficial liquid and gas ve-locities can be picked up. The instability of the transitionalflow occurs due to low frequency pulsations leading to highercoefficient of variation values whereof a maximum emergeson the curve.

For the determination of the pulse velocity, the distancebetween the two ring probes was divided by the time delayof maximum cross-correlation between signals. The cross-correlation function peaks at a time delay equal to the timerequired for the pulses to travel between probes 1 and 2.An example for pulse time-of-flight determination from thecross-correlation of the fluctuating conductivity signals isshown inFigs. 4a and b for a sampling frequency of 50 Hzand a deduced time-of-flight of 2 s.

The two-phase pressure drop was measured with a dif-ferential pressure transducer (Endress+Hauser Model PMD235) connected to the packed bed top and bottom sections.

For liquid holdup measurements, the Aris’s double-detection tracer response method was implemented. Appro-priateness of this technique for elevated pressure trickle-bedreactors due to its capability of being performed with-

2.4E-03

2.8E-03

3.2E-03

0 10 20 30 40 50

Probe 1

Probe 2

Time (s)

Con

duct

ance

(a.

u.)

-1.0E-08

-5.0E-09

0.0E+00

5.0E-09

1.0E-08

1.5E-08

-80 -60 -40 -20 0 20 40 60 80

Time delay (s)

Cro

ss-c

orre

latio

n

Pulse time-of-flight

(a)

(b)

Fig. 4. An example for the electrical conductance recordings in pulseflow regime (a) and the corresponding cross-correlation function (b),Tr = 50◦C, Pr = 0.7 MPa,uG = 0.0522 m/s, uL = 0.00698 m/s. Arrowindicates time-of-flight of pulse from probe 1 to probe 2.

out interrupting the flow was already proven by previousinvestigators (Al-Dahhan and Highfill, 1999). Two elec-tric conductivity probes—one at the top and another atthe bottom of the column—were used. The output signalsfrom the probes were received by a conductivity controller(Omega model CDCN-91) and transmitted to a computerby a data acquisition system. Each conductivity probe con-sisted of three series of three stainless steel wires of whicheach series is connected by a transverse stainless steelwire. Each probe was separated by a Teflon lining fromthe (stainless steel) column wall to confine the electricalfield only to within the region of influence of the probes(Fig. 5). An aqueous sodium chloride solution was usedas a tracer and injected upstream of the column by meansof a specially designed injection loop similar to that pro-posed byLarachi et al. (1991). This system consists of fourthree-way pneumatic valves: two of them being used forinjecting the tracer while the other two valves are beingused for feeding the injection line from a tracer reservoirby means of a peristaltic pump (Omega model FPU112).Liquid residence time distribution (RTD) curves were cal-culated using the imperfect pulse Aris method in which


4 cm

2 cm

2 cm

RingElectrodes

Conductimetric Probes

Fig. 5. Schematic illustration of the electrical conductivity probes for RTD measurements and probes position in reactor.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 10 20 30 40 50 60

Measured inletMeasured outletPredicted outlet

Time (s)

Nor

mal

ized

sig

nal (

a.u.

)

Fig. 6. Example of experimental inlet and outlet conductance responsecurves along with the fit of the outlet response using a two-parameter PDRTD model,Tr=75◦C,Pr=0.7 MPa,uG=0.1044 m/s,uL=0.00349 m/s.

the inlet and outlet tracer response conductivity signalsare used to fit the two-parameter impulse response RTDmodel. The plug flow with axial dispersion (PD) modelwas used to describe the liquid backmixing state. The spacetime (�) and the axial dispersion Péclet number (Pe) weredetermined using a non-linear least-squares fitting wherethe convolution method was used for a time-domain anal-ysis of the non-ideal pulse tracer response data. (Wakaoand Kaguei, 1982). Fig. 6 gives an example of match be-tween measured and PD-model predicted outlet curves for arun at 75◦ C.

3. Results and discussion

3.1. Transition boundary

The interaction between phases in a trickle bed causesdifferent flow regimes which depend, among other things,on flow rate and physical properties of the fluids as well asparticle size. In order to better understand the effect of oper-ating conditions on the system’s hydrodynamics, it is alwaysuseful to portray the type of flow regime prevailing insidethe reactor. As the trickle flow and the pulse flow regimesare most commonly encountered in industrial applications,accurate fingerprinting of their demarcating line as a func-tion of temperature is a key issue in this work. InFigs. 7and8, the transition boundary from trickle flow to pulse flow isplotted as a function of the superficial gas and liquid veloc-ities, reactor pressure and temperature for the air–water andthe air–0.25% CMC systems.

Figs. 7and8 clearly show that the transition depends onboth reactor pressure and temperature regardless whetherthe liquid is Newtonian or non-Newtonian power law fluid.At constant superficial gas velocity and ambient tempera-ture, there is a shift towards higher liquid velocities with anincrease in reactor pressure. This effect is coherent with lit-erature observations (Wammes et al. (1990a,b); Burghardtet al., 2002). The flow regimes encountered in the reactorare established as a result of a balance between the drivingforces (inertia and gravity) and the shear-stress and surfacetension resisting forces. It is well known from the literature(and also confirmed in this study, see later) that increasinglygas densities (via increased reactor pressures) lead to in-creased pressure drops, everything else being kept constant.


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0

0.05

0.1

0.15

0.2

0.25

0 0.005 0.01 0.015 0.02 0.025 0.03

uL (m/s)

u G (

m/s

)

T=25C,P=0.3MPa T=50C,P=0.3MPaT=75C,P=0.3MPa T=25C,P=0.7MPaT=50C,P=0.7MPa T=75C,P=0.7MPa

Trickle Flow

Pulsing Flow

Fig. 7. Effect of pressure and temperature on the transition boundarybetween trickle and pulse flow regimes for the air–water system.

0

0.05

0.1

0.15

0.2

0.25

0 0.002 0.004 0.006 0.008

Trickle Flow

Pulsing Flow

uL (m/s)

u G (

m/s

)

T=25C,P=0.3MPa T=50C,P=0.3MPaT=75C,P=0.3MPa T=25C,P=0.7MPaT=50C,P=0.7MPa T=75C,P=0.7MPa

Fig. 8. Effect of pressure and temperature on the transition boundarybetween trickle and pulse flow regimes for the air–0.25% CMC system.

Besides gravity, the pressure drop driving force acts on theliquid phase causing its dynamic holdup to decrease. Like-wise, the liquid films get thinner preventing pulse phenom-ena to be initiated in the bed. Pulse flow regime is charac-terized by alternate traveling pockets in the form of gas richplugs and liquid rich slugs. Therefore, a higher liquid flowrate is required at elevated pressure to enhance the chancesof pulse formation linked to increased liquid holdup. Simi-lar to the effect of pressure, broadening of the trickle flowregime region in theuG versusuL diagram (Figs. 7and8)was observed with an increase in reactor temperature at con-stant pressure. The effect of temperature on the transitionboundary shift can be explained qualitatively using the samemechanism with regard to a decrease in liquid holdup withtemperature as will be explained in detail in the followingparagraph.

One of the resisting forces acting on the liquid phase is theshear stress. As temperature increases, the liquid dynamic

viscosity decreases whereas gas dynamic viscosity slightlyincreases. The liquid-side shear stress at the gas–liquid andliquid–solid interfaces weakens, accordingly, with temper-ature. This causes a decrease in the amount of liquid heldwithin the bed. Therefore, a higher liquid flow rate is re-quired to give a chance to the liquid films to collapse for theemergence of pulses. The decrease of liquid surface tensionwith increased temperature, albeit less dramatic than for thedynamic liquid viscosity, facilitates gas penetrability in theliquid films causing unlikelihood of liquid films to collapseon the solid surface, in addition to the aggravated liquid filmthinning brought about by decreasing viscosities with ele-vated temperatures. Both reductions in liquid viscosity andsurface tension with temperature lead to decreasing liquidholdups. This effect may also be given an explanation forthe necessity of higher liquid throughput to achieve suffi-cient liquid holdup for pulse formation to occur at increas-ingly temperatures. As can be seen fromFig. 7, the transitionboundary for 25◦ C at 0.7 MPa nearly collides with that of50◦ C and 0.3 MPa. This may be ascribed to the conflictingeffects of pressure and temperature on gas phase density.For the air–0.25% CMC system the same effect of temper-ature and pressure was observed. The consistency index de-crease with temperature leads the liquid-side shear stress todecrease at the gas–liquid and liquid–solid interfaces. Notethat the shift in the transition boundary is more distinctivehere than that for the air–water system.

The experimental data obtained in this study for theair–water system are plotted inFig. 9 along with those ofWammes et al. (1990a,b)for ambient temperature condi-tions and moderate pressure levels. A comparison of theexperimentally obtained data for the transition line of theair–water system for all the temperature and pressure levelsexplored in this study indicates good agreement with thecorrelation of Larachi et al. (1993)(Fig. 9). Recall thatthis correlation is an extension of Charpentier and Favierdiagram for the trickle-pulse flow regime portion to thehigh pressure conditions via inclusion of the function�.The fact that no additional fitting was required indicatesthat the natural Baker coordinates� and � as well as thegas density correction function� are sufficient to handlethe temperature dependence of the gas and liquid physicalproperties intervening in these property functions. However,no attempt was directed at rationalizing the transition datafor the power-law non-Newtonian fluids at elevated tem-peratures and moderate pressures as these systems requirespecial treatment (seeTable 2).

3.2. Pulse velocity

One of the important basic characteristics of pulsing flowis the pulse velocity which was determined at elevated pres-sure and temperature. The pulse velocity decreases withincreasing pressures thereby confirmingBurghardt et al.(2002)experimental findings (Figs. 10and11). The effect


1.E+00

1.E+01

1.E+02

1.E+03

0.01 0.1 1G/λ

L/G

λψϕ

P=0.3MPa,T=25C P=0.3MPa,T=50C

P=0.3MPa,T=75C P=0.7MPa,T=25C

P=0.7MPa,T=50C P=0.7MPa,T=75CWammes et al.(1990), P=0.2 MPaWammes et al.(1990), P=0.5 MPaLarachi et al.(1993)

Fig. 9. Comparison between measured transitions, experimental data ofWammes et al. (1990a,b)and predictions by theLarachi et al. (1993)trickle-to-pulse flow regime transition correlation at elevated pressure andtemperature for the air–water system.

Table 2Properties of water and air at elevated temperatures

Temperature water �water× 104 �water air �air × 105

(◦C) (kg/m3) (kg/m s) (kg/s2) (kg/m3) (kg/m s)

25 997.1 8.86 0.0720 1.184 1.8450 988.2 5.36 0.0679 1.092 1.9675 974.9 3.77 0.0635 1.012 2.07

of pressure was more pronounced at higher superficial gasvelocities. For the air–0.25% CMC system at a given super-ficial gas velocity, the augmentation of pulse velocity as afunction of superficial liquid velocity was less spectacularcomparatively with that for the air–water system. Also forthe air–water system, larger values of pulse velocities werereached.

However, pulse velocities increased with increasinglytemperatures. This decrease can be rationalized, as will bediscussed later, in terms of decreasing liquid holdups whentemperature is increased. It is very plausible to anticipatea profound effect of liquid holdup on the control of pulsepropagation velocity. Said otherwise, the pulse velocity in-crease with increasingly temperatures (Figs. 10and11) is aconsequence of a decrease in dynamic liquid viscosity andan increase in interstitial liquid velocity. The monotonic in-crease of pulse velocity with temperature was qualitatively

0

0.2

0.4

0.6

0.8

1

0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.026uL (m/s)

Vp

(m/s

)

uG=0.104m/s,P=0.7MPa,T=25C

uG=0.104m/s,P=0.7MPa,T=50C

uG=0.104m/s,P=0.7MPa,T=75CuG=0.026m/s,T=75C,P=0.3MPa

uG=0.209m/s,T=75C,P=0.3MPa

uG=0.026m/s,T=75C,P=0.7MPa

uG=0.209m/s,T=75C,P=0.7MPaBurghardt etal.(2004),T=25C

Burghardt etal.(2004),T=50C

Burghardt etal.(2004),T=75C

Tsochatzidis and Karabelas(1995),T=25CTsochatzidis and Karabelas(1995),T=50C

Tsochatzidis and Karabelas(1995),T=75C

Fig. 10. Influence of temperature, pressure, gas and liquid superficialvelocities on pulse velocity for air–water system. Comparison with someliterature pulse velocity correlations.

0

0.2

0.4

0.6

0.001 0.003 0.005 0.007 0.009

uL (m/s)

Vp

(m/s

)

uG=0.104m/s,P=0.7MPa,T=25CuG=0.104m/s,P=0.7MPa,T=50CuG=0.104m/s,P=0.7MPa,T=75CuG=0.026m/s,T=75C,P=0.3MPauG=0.209m/s,T=75C,P=0.3MPauG=0.026m/s,T=75C,P=0.7MPauG=0.209m/s,T=75C,P=0.7MPaBurghardt et al.(2004)-25CBurghardt et al.(2004)-50CBurghardt et al.(2004)-75C

Fig. 11. Effect of temperature, pressure, gas and liquid superficial veloc-ities on pulse velocity, experimental and calculated values for air–0.25%CMC system.


ARTICLE IN PRESS

Table 3Correlations predicting the liquid axial dispersion coefficient in trickle beds

Author Correlation

Michell and Furzer (1972)uLdp

LDax=(dpLuL�LL

)0.70(d3pg

2L

�2L

)−0.32

for 80<dpLuL�LL

<8000

Liles and Geankoplis (1960) Dax = 0.261d0.73p

(uL

L

)0.93for 2<

dpLuL�LL

<500

S =log

(BoL

5.91× 10−4

)2.495

, BoL = uL

aPDax, S = 1

1 + exp(−∑10

j=1�jHj)

Piché et al. (2002)a Hj = 1

1 + exp(−∑8

i=1�ij Ui) , U1 =

log

(ReL

2.17× 10−4

)6.025

, U2 =log

(EoL

9.71× 10−6

)4.799

U3 =log

(GaL

6.02× 10−3

)7.199

, U4 =log

(GaG

2.65× 10−5

)7.272

,U5 =log

(Sa

1.44× 10−5

)7.320

U6 = K − 0.823

0.173, U7 = RTD− 1

2

aSee reference for meaning of the different symbols and variables.

similar regardless whether Newtonian or non-Newtonian liq-uids were tested.

The pulse velocity correlations ofTsochatzidis and Kara-belas (1995)and Burghardt et al. (2004)were chosen forperforming comparisons with our measured pulse velocitiesfor the air–water system (Fig. 10). These correlations weresummarized inTable 3. The correlation ofBurghardt et al.(2004) gave the same qualitative tendency as the experi-mental pulse velocity data regarding the effect of tempera-ture. This was not the case for theTsochatzidis and Kara-belas (1995)correlation which exhibited poor temperaturesensitivity. This mismatch could be a consequence of an in-sufficient correlating power of the chosen velocities sincethe interstitial gas velocity and the superficial liquid veloc-ity intervened in their correlation. Whereas, theBurghardtet al. (2004)correlation involved both liquid and gas in-sterstitial velocities via the corresponding Reynolds num-bers. Temperature indeed had a remarkable effect on liq-uid holdup which was taken into account in the calculationof the Reynolds number and the corresponding interstitialliquid velocity. TheTsochatzidis and Karabelas (1995)cor-relation predictions were higher in comparison to those byBurghardt et al. (2004)correlation. This latter one provided,however, close estimations of the pulse velocity which canbe recommended for approximate estimation of this parame-ter for aqueous systems at high temperature in addition to itscapability to capture high pressure pulse velocity data. TheBurghardt et al. (2004)correlation can also be recommendedfor the case of non-Newtonian liquids at elevated tempera-ture as shown in the plot ofFig. 11for the air–0.25% CMCsystem.

3.3. Two-phase pressure drop

Two-phase pressure drop is one of the driving forces act-ing on the liquid phase which has an effect on energy dis-sipation in the packed-bed reactor. Pressure drop is a func-tion of the fluids’ physical properties as well as of the oper-ating conditions, and bed and particle geometries. Thus, itis important to understand the effect of temperature on thepressure drop via the system characteristics.

Fig. 12shows the effect of temperature on the two-phasepressure drop for different values of superficial liquid andgas velocities for Newtonian and non-Newtonian power lawfluid. As expected, two-phase pressure drop increased withsuperficial liquid and gas velocities regardless of the tem-perature level and whether the liquid is Newtonian or not.As can be seen from the figures, two-phase pressure dropdecreased with increased temperatures. In the present con-ditions, pressure drop mainly depends on viscosity, densityand velocity of the fluids. As the liquid viscosity decreasesthough the gas viscosity follows an opposite trend with re-spect to temperature, the net effect of shear stress at thegas–liquid and liquid–solid interfaces is not obvious. Sincethe effect of temperature on gas viscosity is less pronouncedin comparison to that on liquid viscosity, increased tem-peratures are likely to weaken the frictional forces at thegas–liquid and liquid–solid interfaces. The global outcomewould be a reduction in two-phase pressure drop with in-creasing temperature. It can be seen that at high superficialgas and liquid velocities, the effect of temperature on pres-sure drop is more significant. Moreover, at constant pres-sure, both gas and liquid densities decrease as temperature


0

5000

10000

15000

20000

25000

0 0.05 0.1 0.15 0.2 0.25uG (m/s)

∆P

(P

a/m

)

Air-Water,uL=0.00349 m/s,T=25CAir-Water,uL=0.00349 m/s,T=75CAir-Water,uL=0.02094 m/s,T=25CAir-Water,uL=0.02094 m/s,T=75CAir-CMC,uL=0.00349 m/s, T=25CAir-CMC,uL=0.00349 m/s,T=75CAir-CMC,uL=0.00698 m/s,T=25CAir-CMC,uL=0.00698 m/s,T=75CIliuta and Larachi(2002),T=25CIliuta and Larachi(2002),T=75C

Fig. 12. Effect of temperature on two-phase pressure drop at varioussuperficial gas and liquid velocities for air–water and air–0.25% CMCsystems.Pr=0.7 MPa. Lines show predictions using theIliuta and Larachi(2002) slit model for Newtonian and non-Newtonian fluids.

increases resulting in a decrease in pressure drops. Theseresults illustrate how pressure drop evolves as a function ofshear stresses and inertial forces. For comparison with liter-ature work carried out at ambient temperature in agreementwith observations made by previous researchers (Larachiet al., 1991; Wild et al., 1991; Al-Dahhan and Dudukovic,1994), the two-phase pressure drop also increases with bothflow rates at higher temperature.

For the air–0.25% CMC system, the two-phase pressuredrop increases monotonically with the superficial gas andliquid velocities. The pressure drop values are obviouslylarger than those measured for the air–water system at thesame fluid fluxes, pressure and temperature. This is easilyunderstandable in light of the liquid-side shear stress at thegas–liquid and liquid–solid interfaces which are much largerin this case. In a similar manner than the air–water system,the two-phase pressure drop decreases as temperature is in-creased (Fig. 12) as a result of a decrease in apparent viscos-ity of the non-Newtonian CMC aqueous solutions. Due tothe decrease in gas phase inertia with temperature (via gasdensity), the two-phase pressure drop decreases at a givenparticular pressure and fluid superficial velocities. The sur-face tension of CMC also decreases with temperature result-ing in less gas resistance to push the liquid outwards fromthe reactor. This may also be advanced as an additional con-tributing factor in favor of an explanation for the pressuredrop to decrease with elevated temperatures.

Iliuta and Larachi (2002)generalized the slit modelof Holub et al. (1992)for the determination of pressuredrop and liquid holdup for non-Newtonian power-law flu-

ids. Their approach extended the double-slit representation(Iliuta et al., 2000) (dry slit + wet slit) of Newtonian flu-ids to the non-Newtonian case. The generalized bed-scaletwo-fluid model for pressure drop and liquid holdup wasobtained by mapping from slits- to bed-scale the momen-tum balance equations for the gas phase in the dry andwet slits, and the liquid phase in the wet slit. This modelcan be further reduced assuming first that non-Newtonianviscous liquids behave similarly to Newtonian viscous liq-uids so that full bed wetting is virtually achieved at thetypical gas and liquid superficial velocities encounteredin this work as a result of larger liquid holdups. In addi-tion, for moderate pressures and low to high superficialgas velocities corresponding to cases 2 and 3 according toAl-Dahhan and Dudukovic interaction classification (1994),the correction required for enhanced gas–liquid interactionsis not required. Under those circumstances, the hydrody-namic model after dimensionless transformations becomesfor power law fluids and spherical particles (refer to thenomenclature for the different variables):

Liquid phase pressure drop:

�" = − �P"gH

+ 1

= 3

3"

[E

n+12

1 2n−1

2Re"

Ga"Frn−1

"

(1 − )n−1

2n−2"

+E2Re2

"

Ga"F rn−1

"

]− �g

g"

− ""

. (5)

Gas phase pressure drop:

�g = − �PggH

+ 1

= 3

( − ")3

{E1Reg − ( − ")Rei

Gag

+E2[Reg − ( − ")Rei]2

Gag

}. (6)

Interfacial gas and liquid velocity:

Rei =gdp

(1 − )�g

(72

E1

) n+12n n

n+ 1

k− 1n

�""g

×

[�""g

"as

+ �ggg − "as

] n+1n

−�ggg

− "as

n+1n

. (7)

Note that this model is completely predictive providedthe Ergun constantsE1 andE2, the consistency index (k)and the power-law index (n) are known. The bed Ergun con-stants determined from the measured single-phase pressure


ARTICLE IN PRESS

drops for the 3 mm glass beads bed were, respectively, 215and 1.4. Puttingn= 1 in Eqs. (5)–(7) restores the model inits Newtonian version.Stricto sensu, the founding hypoth-esis of the slit model is the existence of a liquid film-likestructure reminiscent of trickle flow regime necessary for thederivation of the drag forces resulting from the gas–liquid,gas–solid and liquid–solid interactions. Notwithstanding, inwhat follows no distinction will be made between the trickleflow and the pulse flow regime hydrodynamic data duringmodel confrontation. As shown inFig. 12, the lines representthe slit model predictions by Eqs. (5)–(7) for the air–waterand the air–0.25% CMC systems for the trickle flow andpulse flow pressure drops alike. The effect of temperaturewas well captured by the model, although at the highest liq-uid superficial velocities, the predictions tended to be un-derestimated for the air–water system and over-estimatedfor the air–0.25% CMC system at the lowest temperature.These discrepancies could likely be ascribed to the choiceof negligible gas–liquid interaction function and full wettinghypothesized in the simplified slit model. Nonetheless, themean relative error was equal to 15% for the air–water sys-tem and 9% for the air–0.25% CMC system for all the inves-tigated temperature and pressure values, and flow regimes.These levels of errors remained compatible with the order ofmagnitude of experimental errors. Note also, that extensionof the slit-based drag force closures inherent to trickle flowhypothesis towards the pulse flow regime did not degradedramatically the model predictions. Therefore, although thischoice is open to criticism from a physical standpoint, it doesprovide good engineering estimates of the pressure drops inthe pulse flow regime.

3.4. Liquid holdup

Knowledge of the liquid holdup is a key in reactor designmodel calculations of reaction performances. For exother-mic reactions, higher liquid holdup enables better pellet-scale temperature and wetting efficiency control thus con-tributing to the prevention of hot spots formation. From thispoint of view, investigation of the liquid holdup at elevatedtemperature in trickle beds arises as a natural justification.

The effect of temperature, superficial gas and liquid ve-locities and reactor pressure on the liquid holdup for the twogas–liquid systems is illustrated inFigs. 13and14. At thehighest temperature, the liquid holdup increases with super-ficial liquid velocity for the air–water system. As discussedabove, the trickle-to-pulse flow regime transition is repelledtowards larger superficial liquid velocities at a given super-ficial gas velocity. Thus, the increase in holdup with liquidthroughput is first through film thickening in trickle flow fol-lowed by more frequent liquid-rich slug events in the pulseflow regime. The decrease of liquid holdup with increas-ingly superficial gas velocities and/or with reactor pressurewas also persistent for the elevated temperatures confirmingmaintenance of this behavior as in the previous literatureworks regarding ambient temperature and elevated pressure

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03

uL (m/s)

ε L

uG=0.0261 m/s,T=75C,P=0.3 MPauG=0.2088 m/s,T=75C,P=0.3 MPauG=0.0261 m/s,T=75C,P=0.7 MPauG=0.2088 m/s,T=75C,P=0.7 MPauG=0.2088 m/s,T=50C,P=0.7MPaIliuta andLarachi(2002),T=75C,P=0.3MPaIliuta andLarachi(2002),T=75C,P=0.7MPaIliuta andLarachi(2002),T=50C,P=0.7MPa

Fig. 13. Effect of temperature, pressure, gas and liquid velocities on liquidholdup for air–water system. Lines show prediction using the Iliuta andLarachi (2002) slit model for Newtonian and non-Newtonian fluids.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.002 0.004 0.006 0.008uL (m/s)

ε L

uG=0.0261 m/s,T=75C,P=0.3 MPauG=0.2088 m/s,T=75C,P=0.3 MPauG=0.0261 m/s,T=75C,P=0.7 MPauG=0.2088 m/s,T=75C,P=0.7 MPauG=0.2088 m/s,T=25C,P=0.7MPaIliuta and Larachi(2002),T=75C,P=0.3 MPaIliuta and Larachi(2002),T=75C,P=0.7 MPaIliuta and Larachi(2002),T=25C,P=0.7 MPa

Fig. 14. Effect of temperature, pressure, gas and liquid velocities on liquidholdup for air–0.25% CMC system. Lines show prediction using theIliutaand Larachi (2002)slit model for Newtonian and non-Newtonian fluids.


conditions. The drag force at the gas–liquid interface, whichis a driving force for the liquid flow, depends on gas veloc-ity and density. Hence since the drag force increases withgas velocity and density, shorter liquid mean residence timearise occasioning a reduction in liquid holdup.

The air–0.25% CMC system, at constant gas and liquidsuperficial velocities and the highest temperature, exhibitsliquid holdups decreasing with increasingly pressure simi-larly to the air–water system. However, the effect of pressurefor this system is more visible at high superficial gas ve-locity. As expected, the liquid holdup values are larger thanthose for the air–water system due to higher viscosity.

For air–water system, the liquid holdup decreases withincreasing temperature at constant superficial liquid and gasvelocities. This can be explained by a decrease in liquid vis-cosity as temperature is increased (Table 2). The shear stressat the gas–liquid and liquid–solid interfaces decreases re-sulting in lower liquid holdup. One of the resisting factorsto gas flow, i.e., surface tension, decreases with temperaturethereby reducing the number of events corresponding to filmcollapse around and between particles. The effect of tem-perature on liquid holdup is more remarkable at high liquidthroughputs. Thus, gas-side and liquid-side shear stressesplay an important role on the liquid holdup in the high in-teraction regime.

For the air–0.25% CMC system, the liquid holdup de-creases also with temperature as the flow consistency indexdecreases with temperature (Table 1). The increase of liq-uid holdup with superficial liquid velocity is however lesssubstantial in comparison with the air–water system due tothe propensity of the bed to operate at already large holdupvalues for viscous liquids.

In a similar manner to pressure drops, the liquid holdupvalues for both systems were analyzed in the light of theIliuta and Larachi (2002)slit model described in the previoussection. As shown inFigs. 13and14, the lines represent theslit model predictions using Eqs. (5)–(7) for the air–waterand the air–0.25% CMC systems for the trickle flow andpulse flow liquid holdups alike. The model captures properlythe temperature and pressure dependencies observed exper-imentally. Quantitatively, the model is in good agreementwith experimental data with a mean relative error of 9.6%and 9.5% for the air–water and the air–0.25% CMC sys-tems, respectively. Despite occasional overestimations espe-cially at the highest temperatures (Figs. 13and 14), theseerrors remained acceptable and compared pretty well withthe level of experimental accuracy. Note that although themechanistic role of surface tension can be understood as animpeding phenomenon against inception of pulse flow, andtherefore as being a potential factor affecting liquid holdup,surface tension phenomena were not described in the sim-ple Poiseuille flow type of flows based upon which the slitmodel was derived. Moreover, extension of the slit-baseddrag force closures inherent to trickle flow hypothesis to-wards the pulse flow regime did not appear to degrade dra-matically the liquid holdup model predictions. For engineer-

0.E+00

3.E-04

6.E-04

9.E-04

0.001 0.01 0.1uL (m/s)

Dax

(m

2 /s)

uG=0.1044 m/s,P=0.3 MPa,T=25CuG=0.1044 m/s,P=0.3 MPa,T=50CuG=0.1044m/s,P=0.3 MPa,T=75CuG=0.2088 m/s,P=0.3 MPa, T=75CuG=0.2088 m/s,P=0.7 MPa,T=75CuG=0.0261 m/s,P=0.3 MPa,T=75CuG=0.0261 m/s,P=0.7 MPa,T=75CLiles and Geankoplis(1960),T=25CLiles and Geankoplis(1960),T=50CLiles and Geankoplis(1960),T=75CMichell and Furzer(1972),T=25CMichell and Furzer(1972),T=50CMichell and Furzer(1972),T=75CPiche etal.(2002),T=25CPiche etal.(2002),T=50CPiche etal.(2002),T=75C

Fig. 15. Liquid axial dispersion coefficient as a function of superficialliquid velocity for various superficial gas velocities for air–water sys-tem. Effect of reactor temperature and pressure. Comparison with someliterature liquid axial dispersion coefficient correlations.

ing accuracy computations therefore, the slit model can alsobe recommended for predictions of holdup even in the pulseflow regime.

3.5. Axial dispersion

Besides liquid holdup, applying the PD model to ourRTD experimental data enabled extraction of the liquid ax-ial dispersion coefficients (Dax) for various temperatures,pressures, and gas and liquid superficial velocities for theair–water and the air–0.25% CMC systems. At constant tem-perature,Dax was found to slightly decrease with reactorpressure for both systems though for the air–0.25% CMCsystem the effect of pressure was the most remarkable es-pecially at the lowest superficial gas velocity (Figs. 15and16). For the air–water system, an abrupt increase ofDaxwas noticed for low superficial liquid flow velocities with atendency of leveling off as liquid velocities get larger. Suchan increase in liquid backmixing is to be mirrored qualita-tively with the trend exhibited by the liquid holdup versusliquid velocity plots. For the air–0.25% CMC system, the in-crease inDax with liquid flow rate is less pronounced. Thismay be ascribed to the early emergence of trickle-to-pulseflow regime transition at lower superficial liquid velocities.Larger liquid throughputs yield largerDax values due toincreased backmixing. The effect of temperature onDax val-ues is also illustrated inFigs. 15and16, respectively, for theair–water and the air–0.25% CMC systems. The temperature


ARTICLE IN PRESS

1.E-04

3.E-04

5.E-04

7.E-04

9.E-04

0 0.002 0.004 0.006 0.008 0.01uL (m/s)

Dax

(m

2 /s)

uG=0.1044 m/s,P=0.3MPa,T=25CuG=0.1044 m/s,P=0.3MPa,T=50CuG=0.1044 m/s,P=0.3 MPa,T=75CuG=0.1044 m/s,P=0.7 MPa,T=75CuG=0.0261 m/s,P=0.3MPa,T=75CuG=0.0261 m/s,P=0.7MPa,T=75CLiles and Geankoplis(1960),T=25CLiles and Geankoplis(1960),T=50CLiles and Geankoplis(1960),T=75CMichell and Furzer(1972),T=25CMichell and Furzer(1972),T=50CMichell and Furzer(1972),T=75CPiche et al.(2002),T=25CPiche et al.(2002),T=50CPiche et al.(2002),T=75C

Fig. 16. Influence of operating temperature and pressure on liquid axialdispersion coefficient for air–0.25% CMC system, experimental and cal-culated values. Comparison with some literature liquid axial dispersioncoefficient correlations.

effect was more notable for the air–0.25% CMC system. Thedecrease ofDax especially at 75◦ C is the most significant.This may be explained by a lowering in backmixing due toa decrease in liquid holdup with temperature.

ExperimentalDax data is plotted along with the val-ues calculated from the correlation ofMichell and Furzer(1972), Liles and Geankoplis (1960)andPiché et al. (2002)(Table 3). The correlation ofLiles and Geankoplis (1960)shows thatDax increases with temperature for both sys-tems. The correlation ofMichell and Furzer (1972)showsno significant effect of temperature onDax. The correlationof Piché et al. (2002)shows also no systematic effect oftemperature onDax, in agreement with experimental data.The values ofDax found with these correlations are sys-tematically lower than our experimental data. Especiallyfor the non-Newtonian liquid where the difference betweenexperimental data andPiché et al. (2002)predictions wasdramatically high pointing to a violation of the validityrange of the correlation. It seems that even if this correla-tion has been developed using a broadDax database, it willnecessitate parameters recalibration for moderate-to-highpressures and non-ambient temperatures for Newtonianand non-Newtonian liquids. The average absolute meanerrors for the air–water system were equal to 49%, 46%and 59%, respectively for the correlations ofMichell andFurzer (1972), Liles and Geankoplis (1960)andPiché et al.(2002). For the air–water system, the effect of superficial

liquid velocity on the axial dispersion coefficient is morepronounced than for the air–0.25% CMC system. This isalso in agreement with literature correlations. The effectof temperature on 0.25% CMC viscosity is relatively high.This considerable decrease in viscosity can be advancedas an explanation for the decrease of axial dispersion withtemperature.

One possible cause for the observed mismatch betweencorrelation predictions and PD-fittedDax coefficients couldthat wall flow that could be responsible for a maldistributionin the radial direction. It is however rather surprising thatthis effect is more visible on the axial dispersion data ratherthan on the liquid and pressure drop data since these aregenerally well accounted for by the slit model which ignoresper se any wall maldistribution phenomena. This mismatchwill be examined more thoroughly in a future study wheremore Dax data using several particle-to-column diameterratios are planned to be obtained. Eventually the usefulnesswill be evaluated of an amended version of thePiché et al.(2002)correlation to be recalibrated taking into account allthe axial dispersion coefficient data including those of thepresent study along with the ones that served for elaboratingthe original Piché et al. correlation.

4. Conclusion

In this study, the effects of temperature and moderatepressure on the hydrodynamics of trickle-bed reactors werediscussed for Newtonian and non-Newtonian liquids. Previ-ous works on trickle bed hydrodynamics dealt mainly withthe effects of elevated pressures. This work attempted to fillthe gap by adjoining new data on the temperature effect onflow regime transition, pulse velocity, two-phase pressuredrop, liquid holdup and liquid axial dispersion coefficient.The following conclusions can be drawn (Table 4):

• The trickle-to-pulse flow regime transition boundaryshifts to higher fluid velocities with increasingly temper-atures.

• Pulse velocity was an increasing function of temperature.• A decline of two-phase pressure drop was observed with

climbing temperatures.• So did the liquid holdup regarding its response with re-

spect to temperature due likely to a decrease in liquidviscosity and gas density.

Table 4Correlations for the prediction of pulse velocity in trickle beds

Author Correlation

Tsochatzidis andKarabelas (1995)

Vp = 1.03v0.79G

1 + 0.76v1.27G

(1+25.4uL)

for 0.4<vG <1.5and 0.011<uL <0.025

Burghardt et al.(2004)

Vp

vG= 3.445

(GaN

)0.352Re−0.464G,r

Re0.177L,r


Notation

as bed-specific surface area, m2/m3

dp particle diameter, mDax axial dispersion coefficient, m2/sE1, E2 Ergun constants

Frl liquid phase Froude number

(u2L

gdp

)g gravitational acceleration, m/s2

Gag gas phase Galileo number

(d3pg

2G3

(1−)3�2G

)

Gal liquid phase Galileo number

(d2+np g2−n2

L3

(1−)3k2

)k flow consistency index, kg/m s2−nn flow behavior indexP pressure, MPa�P/H two-phase pressure drop, Pa/m

Pe Péclet number(uLdpLDax

)Reg gas phase Reynolds number

(uGdpG(1−)�G

)Rel liquid phase Reynolds number

(u2−nL dnpL(1−)k

)Re ,r Reynolds number based on the real velocity of

the phase(vr dp

�

)T temperature,◦ Cu superficial velocity, m/sv real velocity, m/sVp pulse velocity, m/s

Greek letters

� shear rate, s−1

� shear stress, Pa bed void fractionL liquid holdup

� Baker coordinate,(

Ga

)0.5( Lw

)0.5

� viscosity, kg/m s�eff effective viscosity, kg/m s density, kg/m3

� surface tension, kg/s2

� gas density correction function, 1(4.76+0.5

Ga

)� Baker coordinate,

(�w�L

) (�L�w

)0.33(wL

)0.66

� dimensionless body force of the phase

Subscripts

a airG gasi gas–liquid interfaceL liquid

N normal conditionsr reactorw water

Acknowledgements

Financial support from the Natural Sciences and Engi-neering Research Council of Canada (NSERC) is gratefullyacknowledged.

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trickle bed hydrodynamics and flow regime transition at elevated temperature for a newtonian and a...

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