rfc dosen 1

*Corresponding author. Tel.: #31-40-247-3673.E-mail address: [email protected] (J. G. Boelhouwer).

Chemical Engineering Science 56 (2001) 2605}2614

The induction of pulses in trickle-bed reactors bycycling the liquid feed

J. G. Boelhouwer*, H. W. Piepers, A. A. H. DrinkenburgDepartment of Chemical Engineering, Eindhoven University of Technology, Den Dolech 2, PO Box 513, 5600 MB Eindhoven, Netherlands

Received 28 January 2000; received in revised form 15 September 2000; accepted 7 November 2000

Abstract

The operation of a trickle-bed reactor in the pulsing #ow regime is well known for its advantages in terms of an increase in mass andheat transfer rates. However, fairly high gas and liquid #ow rates necessitate the operation in the pulsing #ow regime, resulting inrelatively short contact times between the phases. By means of the periodic operation of a trickle-bed reactor it is possible to obtainpulsing #ow at average throughputs of liquid usually associated with trickle #ow during steady-state operation. This feed strategy toforce pulse initiation is termed liquid-induced pulsing #ow. The advantages associated with pulsing #ow may then be utilized toimprove reactor performance in terms of an increase in capacity and the elimination of hot spots, while interfacial contact times arecomparable to trickle #ow. An additional advantage of liquid-induced pulsing #ow is the possibility to tune the pulse frequency andtherefore the time constant of the pulses. During the periodic operation of a trickle bed, continuity shock waves are initiated in thecolumn due to the step-change in liquid #ow rate. This results in the division of the column into a region of high liquid holdup anda region of low liquid holdup. At high enough gas #ow rates, the inception of pulses takes place in the liquid-rich region. Analysis ofthe performed experiments indicates that besides gas and liquid #ow rates, an additional criterion for pulse inception is the availablelength for disturbances to grow into pulses. For self-generated pulsing #ow this results in the upward movement of the position of thepoint of pulse inception with increasing gas #ow rate. With liquid-induced pulsing #ow this means that higher gas #ow rates arenecessary to induce pulses as the length of the liquid-rich region decreases. For both self-generated and liquid-induced pulsing #owthis relationship between the gas #ow rate and the available length for pulse formation is identical. � 2001 Elsevier Science Ltd.All rights reserved.

Keywords: Multi-phase reactors; Hydrodynamics; Cycled liquid feed; Continuity shock waves; Induced pulsing #ow; Pulse frequency

1. Introduction

A trickle-bed reactor is a commonly used type ofthree-phase catalytic reactors in which a gas and a liquidphase #ow cocurrently downward through a "xed bed ofcatalyst particles. A trickle-bed reactor is usually oper-ated in the trickle #ow regime, which means that theinteraction between the phases is rather poor. The overallreaction rate is often governed by mass transfer resist-ances. Changing the feed strategy may reduce mass trans-fer resistances and thus enhance the performance ofa trickle-bed reactor. One of most simple feed strategies iscycling the liquid feed. With this mode of operation,

signi"cant increases in conversion can be obtained(Haure, Hudgins, & Silveston, 1989; Lee, Hudgins, & Sil-veston 1995; Castellari & Haure, 1995). Performanceimprovement is due to reduction of mass transfer resist-ance, the formation of controlled hot spots and theappearance of a gas-phase reaction over an almost drycatalyst (Gabarain, Castellari, Cechini, Tobolski, &Haure, 1997).Pulsing #ow can be considered as a spontaneously

arising unsteady-state behavior of the reactor. Studiesof Wu, McCready, and Varma (1995, 1999) showed anincrease in selectivity for the hydrogenation ofphenylacetylene to styrene due to the change in #owregime from trickle to pulsing #ow. Boelhouwer, Piepers,and Drinkenburg (1999) used the concept of cycling theliquid feed to induce pulses at average liquid #ow ratesusually associated with trickle #ow. When the durationof the high liquid #ow rate decreased, higher gas #ow

0009-2509/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 5 2 7 - 3

Table 1Properties of the packed beds used in this investigation

Packing material Nominal diameter (mm) Packed height (m) Porosity Speci"c area (m��)

Glass spheres 6.0 1.20 0.36 640Glass spheres 3.0 1.04 0.40 1200

Fig. 1. Schematic view of the experimental equipment (1: packed col-umn; 2: liquid storage tank; 3: pump; 4: liquid rotameters primary feedline; 5: liquid rotameters secondary feed line 6: gas rotameters; 7: airbu!er tank; 8: compressor; 9: conductivity probes; 10: pressure taps; 11:magnetic valve and 12: electronic timer).

rates were necessary to induce pulses in the column. Thisstudy makes clear that not a combination of the gas andliquid #ow rate as such determines the existence of pulses,but at least one or the other parameter must beaccounted for.The physical mechanism responsible for pulse incep-

tion often encountered in literature is the occlusion ofpacking channels by the liquid and subsequently blowingo! the liquid slug by the gas #ow. Based on this conceptseveral models are proposed in literature to describe thetransition to pulsing #ow (Sicardi et al., 1979; Sicardi& Ho!mann 1980; Blok, Varkevisser, & Drinkenburg1983; Ng, 1986; Cheng & Yuan, 1999). These modelsattempt to explain the transition on the basis of a micro-scopic view of two-phase #ow in a individual packingchannel. It is not clear how these microscopic occlusionsof various packing channels lead to the macroscopicnon-uniform behavior of pulsing. The "rst to adapta macroscopic view to interpret the transition from trick-ling to pulsing #ow were Grosser, Carbonel, and Sun-daresan (1988). They demonstrated that a loss of stabilityof the uniform state occurs and identi"ed this loss ofstability as the transition boundary. According to Krieg,Helwick, Dillon, and McCready (1995), travellingwaves of high liquid holdup comparable to pulses arealready present in the trickle #ow regime. A sta-bility analysis predicts the conditions of onset of thesetravelling disturbances, which may or may not evolveinto pulses. These travelling wave instabilities groweventually into pulses only if su$cient column length isavailable.The objective of this study is essentially to improve

reactor performance in terms of an increase in capacity,selectivity and the elimination of initial hot spots. Thismay be achieved by altering the feed strategy froma steady into a cycled liquid feed. With this mode ofoperation it is possible to induce pulses at throughputs ofliquid that would only lead to trickle #ow during steady-state operation (Boelhouwer et al., 1999). The advantagesassociated with pulsing #ow may be utilized to increasereactor performance in terms of enhanced mass and heattransfer rates, while interfacial contact times remain com-parable to trickle #ow. The aim of this paper is toexamine the hydrodynamic e!ects concerning the peri-odic operation of a trickle bed and subsequently thecircumstances in which eventually pulses are generated inthe column.

2. Experimental setup and procedures

A schematic view of the experimental set-up ispresented in Fig. 1. The experiments were performed ina Plexiglas column of 0.11 m inner diameter. The packingmaterial consisted of 3.0 and 6.0 mm glass spheres ofwhich the packing characteristics are listed in Table 1.The packing was supported at the bottom of the columnby a stainless-steel screen. Air and water were uniformlyfed at the top of the column by means of distributors. Forthe air supply, a bu!er tank was kept on 7 bar by a com-pressor to minimize #uctuations in the gas #ow rate dueto pressure #uctuation in the column. The experimentswere carried out at room temperature and atmosphericpressure.For the liquid feed, two di!erent feed lines were ap-

plied. The primary feed line was used to introducea steady liquid feed to the column while the secondaryfeed line provided an additional liquid feed for a certaintime interval. In this manner a square-wave cycled liquidfeed was achieved. The cycled liquid feed is characterizedby four parameters, schematically shown in Fig. 2.A magnetic valve in the secondary feed line activated byan electronic timer was used to regulate the feed times of,respectively, the high and low liquid feed rates. High andlow liquid feed rates were controlled by calibratedrotameters.

2606 J. G. Boelhouwer et al. / Chemical Engineering Science 56 (2001) 2605}2614

Fig. 2. Schematic view of the characterization of the cycled liquid feed(t�: high-liquid-feed-time; t

�: low-liquid-feed time; ;

��: super"cial high

liquid feed velocity; ;��: super"cial low liquid feed velocity).

Fig. 3. Liquid holdup in the trickle #ow regime as a function ofsuper"cial gas and liquid velocities (packing material: 3.0 mm spheres).

Preliminary experiments showed a slight increase inpressure at the top of the column when the additionalliquid feed was fed to the column. This increase in pres-sure drop somewhat lowers the super"cial gas #ow rateat the top of the column. This variation in gas #ow ratedue to pressure #uctuations is however very small. Thereported super"cial gas velocities in this study are cal-culated by using the pressure at the top of the column atthe moment the additional liquid feed is ended. It must bementioned that pressure #uctuations in non-steady stateoperated trickle-bed reactors are inherent to this mode ofoperation. Along the column axis, super"cial gas vel-ocities will vary due to #uctuations in liquid holdup andpressure drop.A conductance technique, successfully implemented by

Tsochatzidis, Karapantsios, Kostoglou, and Karabelas(1992) and Tsochatzidis and Karabelas (1995), was usedto provide instantaneous measurements of cross-section-ally averaged liquid holdup. The column was providedwith "ve sets of conductance probes, separated 0.2 mfrom each other, to measure liquid holdup at variousaxial positions. The conductivity probes were calibratedby salt-tracer injections and by the stop-#ow method.Both calibration methods proved to be very reproducibleand no signi"cant di!erence existed between the calib-ration outcome. Pressure drop was measured by pressuretransducers which could be connected to several pressuretaps separated by distances of 0.2 m. Both liquid holdupand pressure data were simultaneously recorded andstored in a computer. These data were collected witha sampling rate of 100 Hz for a period of at least 5 min.Before performing any experiments, the column was

operated in the pulsing #ow regime for at least 1 h inorder to ensure a perfectly prewetted bed. Liquid holdupduring trickle #ow was measured for six di!erent liquid#ow rates and a wide range of gas #ow rates. Thetransition to self-generated pulsing #ow was establishedat several axial positions in the bed to examine theupward movement of the point of pulse inception withincreasing gas #ow rate. This was accomplished by visualobservation and by monitoring of the signals from twoneighboring conductivity probes. Transition to pulsing#ow was acknowledged when the lower conductivity

probe clearly showed large #uctuations in liquid holdupwhile the upper probe showed an almost unvaryingliquid holdup.The e!ect of cycling the liquid feed on the liquid

holdup distribution in the column was examined fora broad range of "xed cycled feed characteristics. In theseexperiments, the gas #ow rate was gradually increaseduntil eventually pulses were observed. With this proced-ure, the e!ect of cycling the liquid feed on the hydrodyn-amics at gas #ow rates not high enough for pulseinception was examined and subsequently, the minimumgas #ow rate required for pulsing to occur was deter-mined. The pulse frequency was determined through ananalysis of the #uctuations in the liquid holdup data.

3. Steady-state hydrodynamics

As will be revealed later, accurate liquid holdup data inthe trickle #ow regime are essential to explain the phe-nomena observed during cycled liquid feed. In Fig. 3, theliquid holdup, de"ned as the fraction of the empty col-umn occupied with liquid, is plotted as a function ofsuper"cial gas and liquid velocities for 3.0 mm glassspheres as packing material. Liquid holdup increaseswith increasing liquid #ow rate and decreases with in-creasing gas #ow rate. Liquid holdup data regarding6.0 mm glass spheres as packing material are somewhatlower, since the liquid #ow is less supported by thepacking because of the smaller speci"c area of the pack-ing. A comparison of the measured liquid holdup versusa number of literature correlations proved to be in goodagreement.In Fig. 4, the transition boundary from trickling to

pulsing #ow is plotted for both packing materials. Theaxial position in the column at which this transition isestablished is located at approximately 0.1 m from thebottom of the column. There is no noticeable di!erencebetween the transition boundaries for 3.0 and 6.0 mmspheres.

J. G. Boelhouwer et al. / Chemical Engineering Science 56 (2001) 2605}2614 2607

Fig. 4. Transition boundary from trickle to self-generated pulsing #owlocated at approximately 0.1 m from the bottom of the column.

Fig. 5. In#uence of super"cial gas velocity on the axial position of thepoint of pulse inception (packing material: 6.0 mm spheres).

Fig. 6. Example of the measured liquid holdup during cycled liquidfeed (;

��"0.0035 m s��; ;

��"0.0102 m s��; ;

�"0.10 m s��; t

�"

20 s; t�"5 s; packing material"3.0 mm spheres).

A general observation reported in literature is theupward movement of the point of pulse inception withincreasing gas #ow rate. In Fig. 5, the e!ect of increasinggas #ow rate on the axial position of the point of pulseinception is presented. In literature, this upward move-ment of the position at which pulses are initiated withincreasing gas #ow is explained by the higher volumetricgas #ow rate with increasing distance from the top of thecolumn due to the pressure drop over the bed. In Fig. 5, itis seen that a relatively large increase in gas #ow rate isneeded to shift the point of pulse inception upwards,much larger than pressure drop can account for. Visualobservations illustrate that even though pulses are gener-ated at the bottom of the column, traveling disturbancesare present above the point of pulse inception. These"ndings are in harmony with the observations of Krieget al. (1995) who claim that traveling disturbances arealso present in the trickle #ow regime. They consider thatthe transition to pulsing #ow corresponds to onlya quantitative change in the strength of these waves.Convective disturbances, if unstable, will grow with dis-tance until they become observable and thus recognizedas pulses, at a position that depends on #ow conditions.

Apparently, with increasing gas #ow rate, the requiredcolumn length for disturbances to grow into detectablepulses decreases. Hence the location of the point of pulseinception moves upward in the column. Available col-umn length may be identi"ed besides gas and liquid #owrates as a fundamental parameter for pulse generation.

4. Unsteady-state hydrodynamics

Before performing liquid-induced pulsing #ow experi-ments, it is meaningful to investigate the e!ect of cyclingthe liquid feed on the hydrodynamics at gas #ow ratesnot high enough for pulse initiation. Only then the condi-tions at which pulses are generated during cycled liquidfeed can be con"dentially examined. An example of theliquid holdup determined at two conductivity probesseparated by a distance of 0.2 m, during cycled liquid feedis shown in Fig. 6. The introduction of the additionalliquid feed results in an almost instantaneous increase inliquid holdup. The back of the liquid-rich region is char-acterized by a more gradual decrease in liquid holdup.The high liquid holdup endures for a period equal to thehigh liquid feed time, from now on abbreviated to hlf-time.

4.1. Liquid holdup

Due to cycling the liquid feed, the liquid holdup variesbetween a low and a high value. To examine whetherthere is an e!ect of the hlf-time on the liquid holduprealized as a consequence of the high liquid feed rate, therelative high liquid holdup is de"ned as follows:

��

"

��(t�(10 s)

��(t�"10 s)

. (1)

Regarding this de"nition, the high liquid holdup at a hlf-time of 10 s serves as a reference to examine the e!ect ofdecreasing hlf-time on the high liquid holdup. A plot of


Fig. 7. E!ect of the hlf-time on the relative high liquid holdup(;

��"0.0035}0.0077 m s��; ;

��"0.0059}0.0128 m s��; ;

�"0.03}

0.30 ms��; t�"20 s).

Fig. 8. Comparison of liquid holdup during high liquid feed rate withliquid holdup during trickle #ow (;

�"0.0059}0.0128 m s��; ;

�"

0.03}0.30 m s��; t�"2}10 s; t

�"20 s).

Fig. 9. Velocity of the moving liquid front (t�"20 s; t

�"1}10 s; pack-

ing material"6.0 mm spheres).

the relative liquid holdup as a response to decreasinghlf-times is provided in Fig. 7. In this "gure it is noticedthat, except for hlf-times of 1 s and less, no e!ect of thehlf-time is recognized. The liquid feed is probably notperfectly square-wave cycled since some delay in thesecondary feed line is inherently present due to the timeneeded for the acceleration of the liquid. For very shorthlf-times, the high liquid feed is ended before it is fullydeveloped. Hence for hlf-times of 1 s and less, the highliquid holdup which should be reached during cycledliquid feed is not entirely accomplished.As seen in the foregoing paragraph, a certain high

liquid holdup is reached as the result of the additionalliquid feed. This high liquid holdup is probably identicalto the liquid holdup during steady-state operation ata steady liquid #ow rate, equivalent to the high liquidfeed rate. A comparison of the high liquid holdup duringcycled liquid feed with the liquid holdup during constantliquid feed is made in Fig. 8. Due to cycling the liquidfeed, the liquid holdup varies between two values resem-bling the liquid holdup obtained during steady-state op-eration at comparable liquid feed rates.

4.2. Continuity shock waves

By evaluating the time lag between the two signalsfrom neighboring conductivity probes, it is possible toevaluate the velocity of the moving liquid front, resultingfrom the step-change in liquid feed rate. The experi-mentally determined linear velocity of the liquid front isplotted in Fig. 9 as a function of the super"cial gasvelocity for 6.0 mm spheres as packing material. Thevelocity of this moving liquid front increases both withincreasing gas #ow rate and with increasing di!erencebetween pulse and base liquid #ow rate. The velocities ofthe moving liquid front, altering roughly between 0.1 and0.2 m s��, are much higher than the linear liquid vel-ocities (super"cial liquid velocity divided by liquid hold-up) which vary between 0.02 and 0.08 m s��. Hence it canbe concluded that due to cycling the liquid feed somekind of waves are initiated in the column.To examine the e!ect of the hlf-time on the velocity of

the moving liquid front, similar to the relative high liquidholdup, the relative wave velocity can be de"ned as

<��

"

<�(t�(10 s)

<�(t�"10 s)

. (2)

A plot of the relative wave velocity versus the hlf-time isshown in Fig. 10. Analogous to liquid holdup during highliquid #ow rate, it is noticed that for hlf-times of 1 s andless, the velocity of these waves is somewhat less than thevalues corresponding to hlf-times above 1 s.It seems useful to investigate the possibility of the

formation of continuity shock waves resulting from thestep change in liquid #ow rate. Continuity waves occurwhenever the #ow rate of a substance depends on theamount of that substance which is present. Continuitywaves often emerge in systems where gravity and pres-sure drop are balanced against drag forces, as is the casewith liquid #ow in packed beds. One steady-state valuesimply propagates into another one and there are no


Fig. 10. E!ect of the hlf-time on the relative shock wave velocity(;

��"0.0035}0.0077 m s��; ;

��"0.0059}0.0128 m s��; ;

�"0.03

}0.30 m s��; t�"20 s).

Fig. 11. Comparison of the experimentally determined and calculatedshock wave velocity (;

��"0.0035}0.0077 m s��; ;

��"

0.0059}0.0128 m s��; ;�"0.03}0.30 m s��, t

�"20 s; t

�"2}15 s).

Fig. 12. Enlargement of the pulsing #ow regime by cycling the liquidfeed (t

�"20 s; t

�"0.5}15 s; packing material: 3.0 mm spheres).

dynamic e!ects of inertia or momentum (Wallis, 1969).Waves can either propagate continuous changes in somevariables or can involve a step change or "nite discon-tinuity. The later are called shock waves. According toWallis (1969), the velocity of a shock wave, derived fromcontinuity considerations obeys the following equation:

<�

"

;��

!;��

��!�

�

. (3)

According to Eq. (3), the shock wave velocity is directly,related to the di!erence between liquid feed rates and thedi!erence between the resulting values of the liquid hold-up.To calculate the shock wave velocity, the experi-

mentally determined liquid holdup data during trickle#ow are used. This is justi"ed by the fact that the liquidholdup varies between the values, which are obtainedfrom steady-state experiments, as shown in Fig. 8. Thesolid lines in Fig. 9 depict the calculated velocity of themoving liquid front conform Eq. (3). A good agreementexists between experimentally and calculated values, aswell qualitatively as quantitatively. A comparison of allthe experimental data with calculated values is shown inFig. 11. Shock wave velocities corresponding to hlf-timesof 1 s and less are not shown here for reasons presentedearlier. The overall agreement is satisfactory for thewhole range of shock wave velocities. The accuracy of thecalculated values increases with increasing di!erence be-tween high and low liquid holdup. Since this di!erencevaries in a narrow range between 0.03 and 0.1, it is veryimportant to use very accurate values of the liquid hold-up, because this has a large e!ect on the calculated shockwave velocity.In summary, due to the step-change in liquid feed rate,

continuity shock waves are initiated in the column. Asa result, the column can be split up into two regions ofdi!erent liquid holdup, both corresponding to steady-state conditions. In other words, at the same time two

di!erent steady-state conditions are present in the col-umn. These steady-state conditions are separated bya moving boundary of which the velocity can be cal-culated using accurate liquid holdup data obtained dur-ing steady-state operation at equivalent liquid feed rates.

5. Liquid-induced pulsing 6ow

5.1. Enlargement of the pulsing yow regime

Fig. 12 provides the results of the enlargement of thepulsing #ow regime by cycling the liquid feed for 3.0 mmglass spheres as packing material. Similar results arefound for the 6.0 mm glass spheres as packing material.The solid line, denoting the transition boundary to self-generated pulsing #ow, is taken at approximately 0.1 mfrom the bottom of the column. In Fig. 12, for each seriesof data, the hlf-time increases in the downward direction


Fig. 13. The for induced pulsing #ow necessary super"cial gas velocityas a function of the hlf-time (t

�"20 s; packing material: 3.0 mm

spheres).

Fig. 14. Example of the measured liquid holdup during liquid-inducedpulsing #ow (;

��"0.0035 m s��; ;

��"0.0077 m s��; ;

�"

0.29 m s��; t�"20 s; t

�"3 s; packing material"6.0 mm spheres).

denoted by the arrow. This means that with decreasinghlf-time, higher gas velocities are necessary to obtainpulsing. It is possible to induce pulses at average liquid#ow rates, generally associated with trickle #ow duringsteady-state operation. Hence, it can be concluded thatalthough throughputs of liquid are equal, the prevailing#ow regime is pulsing instead of trickle #ow. The advant-ages associated with pulsing #ow may be utilized toenhance mass and heat transfer rates resulting in im-proved reactor performance. Moreover, with liquid-in-duced pulsing #ow longer contact times can be achievedcompared to self-generated pulsing #ow, while averageliquid #ow rates are reduced.The observation that higher gas #ow rates are required

to induce pulses when hlf-times decrease, is presentedmore pronounced in Fig. 13. In this "gure, the necessarygas velocity is plotted as a function of the pulse feed timefor some of the results presented in Fig. 12. At relativelong hlf-times, the required gas velocity equals the velo-city needed for transition to self-generated pulsing #ow atthe bottom of the column. However for relatively shorthlf-times, a higher gas velocity is necessary to initiatepulsing #ow. This gas #ow rate increases with decreasinghlf-times, although the cycled liquid feed rates remainconstant. These results indicate that not a combination ofgas and liquid #ow rates as such determines whetherpulses are initiated or not, but some other parameter hasto be included.

5.2. The process of liquid-induced pulsing yow

Due to the step-change in liquid feed rate, continuityshock waves are initiated in the column. This results inthe appearance and downwardmovement of a liquid-richregion. In Fig. 14, an example of the liquid holdup duringliquid-induced pulsing #ow at two neighboring conduct-ivity probes is plotted. In the signal taken at 0.5 m fromthe top of the column no pulse is present, while in the

signal taken at 0.7 m from the top evidently a pulse isvisible. Hence it can be concluded that pulses are in-itiated in the liquid-rich region.The length of the liquid-rich region can readily be

calculated by

l�

"<�t�. (4)

For relatively long hlf-times, the column will eventuallybe "lled entirely with the liquid-rich region, as schemati-cally shown in Fig. 15a. In this case the necessary gasvelocity for pulse formation equals the velocity needed toobtain self-generated pulsing #ow at the bottom of thecolumn. For short enough hlf-times, the length of theliquid-rich region is less than the column height. Asa result the column can now be divided into two zones ofdi!erent liquid holdup. With decreasing hlf-time, thelength of the liquid-rich region decreases, as schemati-cally shown in Fig. 15b}d. With decreasing hlf-times andhence decreasing length of the liquid-rich region, increas-ing gas #ow rates are necessary to obtain pulsing #ow.A similar phenomenon was observed for self-generatedpulsing #ow where the point of pulse inception was foundto move upwards with increasing gas #ow rate. As wellfor self-generated pulsing #ow as for liquid-inducedpulsing #ow, there seems to be a relationship betweennecessary gas #ow rate and available length for pulseformation.It is also noticed in Fig. 14, pulses are initiated at the

front of the liquid-rich region. This is a general observa-tion during liquid-induced pulsing #ow. In Fig. 15 thepoint of pulse inception during liquid-induced pulsing#ow is visualized. At relative large hlf-times, just as soonas the column is entirely "lled with the liquid-rich region,pulses are initiated at the bottom of the column. Forrelative short hlf-times, the point of pulse inceptionmoves upwards in the column with decreasing length ofthe liquid-rich region. Pulses are observable just as soonas the entire liquid-rich region is present in the column.


Fig. 15. Schematic representation of the in#uence of the hlf-time on theliquid distribution in the packed bed and the point of pulse inceptionduring liquid-induced pulsing #ow.

Fig. 16. Example of the measured liquid holdup during liquid-inducedpulsing #ow (;

��"0.0035 m s��; ;

��"0.0128 m s��; ;

�"

0.26 m s��; t�"20 s; t

�"2 s; packing material"6.0 mm spheres).

Considering the fact that su$cient length for pulseformation must be available, pulses are always initiatedin the lower part of the liquid-rich region, at the momentthe entire liquid-rich region is present in the column. Thisis also observed visually. Once the liquid-rich regionenters the column disturbances are present in the liquid-rich region. However these disturbances do not grow intodetectable pulses. This occurs only as the high liquid feedis ended, when the liquid-rich region is completely pres-ent in the column.Because the velocity of the initiated pulses is much

higher than the shock wave velocity, pulses will eventual-ly move out of the liquid-rich region. Occasionally theinitiated pulses fade away when moving out of theliquid-rich region, but in most cases the pulses remainstable. An example of the later case is shown in Fig. 16, inwhich the liquid holdup during liquid-induced pulsing#ow at the two neighboring conductivity probes is plot-ted. It is clearly seen that the initiated pulses have movedout of the liquid-rich region, but remain stable. Howeverwhile the length of the column is rather short, it cannotbe assured at this moment if pulses remain stable incolumns of longer length.

5.3. Necessary gas yow rate

As described previously, as well for self-generated puls-ing #ow as for liquid-induced pulsing #ow, there is a rela-tionship between necessary gas #ow rate and availablelength for pulse formation. For self-generated pulsing#ow this results in the upward movement of the point ofpulse inception with increasing gas #ow rate. Neverthe-less, this point of pulse inception never reaches entirelythe top of the column. The upper part of the column doesnot actively participate in the process of pulse formation.It is likely to expect that this part of the column is neededto reach the necessary distribution of the phases. How-ever, to accomplish a relationship between availablelength for pulse formation and gas #ow rate, it is required

to know the length of this distribution zone. With liquid-induced pulsing #ow, the available length for pulseformation is externally controlled by the hlf-time. Thisprovides the possibility to determine the length of thedistribution zone. Referring back to Fig. 13, we canidentify a certain critical hlf-time. The critical hlf-time isde"ned as the hlf-time at which higher gas velocitiescompared to those needed to obtain self-generated puls-ing #ow at the bottom of the column, are required forpulse induction. The length of the liquid-rich regioncorresponding to the critical hlf-time can be readily cal-culated by multiplying the critical hlf-time with the shockwave velocity. A plot of this critical length of the liquid-rich region is given in Fig. 17. The critical lengths areroughly constant and 0.15 m less compared to the heightof the packed bed for both packing materials. It seemsthat the upper 0.15 m of the packed column is not active-ly participating in the process of pulse formation.Keeping in mind, that the "rst 0.15 m do not partici-

pate in the process of pulse formation, it is possible toestablish the interdependence between gas #ow rate andavailable length for pulse formation for self-generatedpulsing #ow. The data in Fig. 5, simply have to be shifted0.15 m towards lower distances from the top of the col-umn. Additionally, the x-coordinate from Fig. 13 can betransferred from hlf-times to length of liquid-rich regionsby multiplying the hlf-time with the calculated shockwave velocity. Subsequently, the relationship between thenecessary gas velocity and available length for pulseformation for both self-generated and liquid-inducedpulsing #ow is established. A comparison of these rela-tionships for 3.0 mm glass spheres as packing material ispresented in Fig. 18. The data of self-generated andliquid-induced pulsing #ow coincide. Note that inthe legend of Fig. 18, only high liquid #ow rates arementioned because pulses are initiated in the liquid-richregion. Low liquid #ow rates solely participate in theresulting shock wave velocity and thus in the length ofthe liquid-rich region.


Fig. 17. Critical length of the liquid-rich region.

Fig. 18. Comparison of the relationships between necessary gas velo-city and available length for pulse formation for self-generated andliquid-induced pulsing (solid points: self-generated pulsing #ow; openpoints: liquid-induced pulsing #ow).

Fig. 19. Comparison between necessary super"cial gas velocity forself-generated and liquid-induced pulsing #ow at equivalent availablelengths for pulse formation (;

��"0.0035}0.0077 m s��; ;

��"

0.0059}0.0128 m s��; t�"20 s; t

�"2}8 s).

Fig. 20. Number of pulses generated during one liquid feed cycle asa function of the length of the liquid-rich region (packing mater-ial"3.0 mm spheres).

In Fig. 19 a comparison of the super"cial gas velocitiesrequired for self-generated respectively liquid-inducedpulsing #ow at equal available lengths for pulse forma-tion is presented for all the performed experiments. Thesolid line denoting the necessary gas velocity for self-generated pulsing #ow is obtained by intrapolation of themodi"ed results of Fig. 5, considering the fact that thepoint of pulse inception during self-generated pulsing#ow could only be measured at "xed points along thecolumn axis. From the data of Fig. 19, it is concludedthat the interdependence between necessary length forpulse formation and super"cial gas velocity is equivalentfor both self-generated and liquid-induced pulsing #ow.

5.4. Pulse frequency

Another feature of liquid-induced pulsing #ow is thepossibility to tune the pulse frequency and therefore thetime constant of the pulses. In Fig. 20, the number ofpulses generated during one liquid feed cycle is plotted asa function of the length of the liquid-rich region for3.0 mm glass spheres as packing material. Apparently,only one pulse is generated when the length of the liquid-

rich region is less than approximately 0.5 m. For lengthsof the liquid-rich region above 0.5 m, the number ofpulses increases linearly with increasing length. A compa-rable plot is encountered for 6.0 mm spheres as packingmaterial. In this case, the critical length beneath whichonly one pulse is generated during a liquid feed cycle isapproximately 0.6 m.

6. Concluding remarks

In this contribution it is made clear that by means ofthe periodic operation of a trickle-bed reactor it is pos-sible to obtain pulsing #ow at throughputs of liquidassociated with trickle #ow during steady-state opera-tion. Enhanced mass and heat transfer rates are thenconsidered to be due to the change in #ow regime. More-over, the fairly high #ow rates required to achieve naturalpulsing #ow are generally considered to be a drawbacksince they are associated with rather short contact timesbetween the phases. Thus applicability of self-generatedpulsing #ow appears to be restricted to chemical


reactions with fast kinetics. By means of liquid-inducedpulsing #ow, longer contact times can be achieved. Anadditional advantage of liquid-induced pulsing #ow isthe opportunity to control the pulse frequency. Thistuning of the pulses is an important issue in the optimiza-tion of selectivity in catalytic reactions. Higher selectiv-ity's can be achieved when the time constant of pulsing iscomparable to the time constant of important physicaland chemical processes (Wu et al., 1995, 1999).The formation of detectable pulses is the result of the

growth of convective instabilities, which grow with dis-tance into pulses. With increasing gas #ow rate, thenecessary length for pulse formation decreases. This phe-nomenon is responsible for the upward movement of thepoint of pulse inception for self-generated pulsing #ow.This same phenomenon is found to control the process ofliquid-induced pulsing #ow. By cycling the liquid feed,continuity shock waves are initiated in the column. Asa result, for relatively short hlf-times two regions ofdi!erent liquid holdup are present in the column. At highenough gas #ow rates, pulses are initiated in the liquid-rich region of which the length is a linear function ofthe hlf-time. With decreasing length of the liquid-rich region, higher gas velocities necessitate the inductionof pulses. For both self-generated and liquid-inducedpulsing #ow, the relationship between the availablelength for pulse formation and the required gas #ow rateis equivalent.Because the velocity of the initiated pulses is much

higher than the shock wave velocity, pulses will eventual-ly move out of the liquid-rich region. In most cases thepulses remain stable and move to the bottom of thecolumn. However in some cases, the pulses fade away. Atthe present, it is not possible to assure that the inducedpulses remain stable in columns of longer length whenthey have moved out of the liquid-rich region. Further-more, the stability of the initiated continuity shock wavesmay be a!ected by the distance these waves travel, al-though no evidence is found these shock waves are unsta-ble. In conclusion, it will be worth investigating theprocess of liquid-induced pulsing #ow in columns of largelengths. In the near future, experiments in a column of3 m in height will be performed in our laboratory.

Notation

f�

pulse frequency, s��

l�

length of liquid-rich region, mn�

number of pulses during one feed cycle, dimen-sionless

t�

low-liquid-feed time, st�

high-liquid-feed-time, s;

�super"cial gas velocity, m s��

;��

super"cial low liquid feed velocity, m s��

;��

super"cial high liquid feed velocity, m s��

<�

shock wave velocity, m s��

<��

relative shock wave velocity, dimensionless

Greek letters

��

liquid holdup corresponding to low liquid #owrate, dimensionless

��

liquid holdup corresponding to high liquid #owrate, dimensionless

��

relative liquid holdup during high liquid #owrate, dimensionless

References

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