trickle-bed reactor performance. part i. hold up and mass transfer effects

7/22/2019 Trickle-Bed Reactor Performance. Part I. Hold Up and Mass Transfer Effects

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Kutateladze, S. S., et a ., Hyd raulic resistance an d heat trans -fer in stabilized flow of non-New tonian fluids. Heat trans-fer-Sooiet Research 2(6), 114 (1970).Lyon, R. N., Liquid metal heat transfer coefficients, C h e m .Eng. Progr. Sym p. Ser. N o . 2, 47, 75 ( 1951).McComas, S. T., and E. R. G. Eckert, Combined free andforced convection in a horizontal circular tube, Trans. Am .SOC . Mech. Engrs., J. Heat Transfer, Ser. C, 88, 147 (1966).McKillop, A. A., Heat transfer for laminar flow of non-New-tonian fluids in entrance region of a tube, Intern. 1. HeatMass Transfer, 7, 853 ( 1964 ) .Matsuhisa, S., and R. B. Bird, Analytical and numericalsolutions for laminar flow of t he no n-Newton ian Ellis fluid,AIChE J. 11,588 ( 1965).Michiyoshi, I., Heat transfer of slurry flow with internal heatgeneration, Bull. Jap. SOC.Mech. Engrs., 5, 315 (1962).Michiyoshi, I., and R. Matsumoto, Heat transfer of slurry flowwith internal heat generation, ibid., 7, 376 ( 1964).., and M. Hozum i, He at transfer of slu rry flow wi thheat generation, ibid., 6,496 (1963).Mitsuishi, N., and 0. Miyatake, Laminar heat transfer to non-Newtonian Ellis model fluids in cylindrical tubes, Che m .Eng. Japan, 5 , 82 1967).., Heat transfer of nowNewtonian laminar flowin tubes with constant wall heat flux, Kagaku Kogaku, 32,1222 ( 1968).., Heat transfer with non-Newtonian laminarflow in a tube having a constant wall heat flux, Intern.Chem. Eng. , 9,352 ( 1969).Mizushina, T., et al., Laminar heat transfer to non-Newtonianfluids in a circular tube (constant heat flux), Kagaku Kogaku,31,250 (1967).Mori, Y., and K. Futaga mi, Fo rced convective heat transferin uniformly heated horizontal tubes, 2nd Report, theoreti-cal study, Intern. J. Heat Mass Transfer, 10, 1801 (1967).Mori, Y., et al., Forced convective heat transfer in uniformlyheated horizontal tubes, 1st report-experimental study onth e effect of buoyancy , ibid., 9,453 ( 1966).Morton, B. R., Laminar convection in uniformly heated hori-zontal pipes at low Rayleigh numbers, Quarterly J. Mech.Appl . Math. , 12,410 (1959).Newell, P. H., and A. E. Bergles, Analysis of combined freeand forced convection for fully developed laminar flow inhorizontal tubes, Trans. Am. SOC . Mech. Engrs., 1. HeatTransfer, Ser. C, 92, 83 19 70) .Oliver, D. R., a nd V. G. Jenson, Heat transfer to pseudo-plastic fluids in laminar flow in horizontal tubes, Che m .Eng. Sci. , 19, 115 (1964).Petukhov, B. S., a nd A. F. Polyakov, Experimental investiga-tion of heat transfer during viscous gravitational flow of

liquid in horizontal pipe, Teplofczika Vysokikh Temp., 5:87(1967). ., Effect of free convection on heat transferduring forced flow in a horizontal pipe, Teplofizika Vyso-kikh Temp. , 5 , 384 (1967).Pigford, R. L., Nonisothermal flow and heat transfer insidevertical tubes, Chem. Eng. Progr. Symp., Ser. N o . 17, 51 ,79 (1955).Schenk, J., and J . Van Laar, Heat transfer in non-Newtonianlaminar flow in tubes, Ap pl. Scientific Research, Sec. A ,7,449 (1958).Sellars, J. R., hl . Tribus, and S . J. Klein, Heat transfer tolaminar flow in a round tu be or flat conduit-the Graetzproblem extended, Trans. Am . SOC . Mech. Engrs., 78 , 441(1956).Sestak, J., and M. . Charles, Limiting values of Nusseltnumber for heat transfer to pipeline flow of non-Newtonianfluids with arbitrary internal heat generation, Chem. Eng.Progr. Sym p. Ser. No. 82 64, 212 ( 1968).Shannon, R. L., and C. A. Depew, Combined forced andfree laminar convection in horizontal tube with uniform heatflux, Trans. Am . S O C . Mech. Engrs., I . Heat Transfer, Ser.C, 90,353 1968).., Forced laminar flow convection in a horizontaltube with variable viscosity and free-convection effects,ib id . , 91,251 ( 1969).Siegel, R., E. M. Sparrow, and T. M. allman, Steady laminarheat transfer in a circular tube with prescribed wall heatflux, Ap pl. Scientific Research, Sec. A , 7, 386 (1958).Siegwarth, D. P., and T. J. Hanratty, Computational and ex-perimen tal stu dy of th e effect of sec ondary flow on the tem-perature field and primary flow in a heated horizontal tube,Intern. 1.Heat Mass Transfer, 13, 27 ( 1970).Siegwarth, D. P., et al., Effect of second ary flow on the tem-perature field and primary flow in a heated horizontal tube,Intern. J. Heat Mass Transfer, 12, 1535 (1969).Skelland, A. H. P., Non-Neutonian Flow and Heat Transfer,Wiley, New York (1967).Test, F. L., Laminar flow heat transfer and fluid flow for liq-uids with temperature dependent viscosity, Trans. Am. SOC.Mech. Engrs., J . Heat Transfer, Ser. C , 90, 385 (1968).Van Wazer, J . R., et a ., Viscosity and Flow Measurements: ALaboratory Handbook of Rheolog y, Interscience, New York(1963).Yang, K. T., Laminar forced convection of liquids in tub eswith variable viscosity, Trans. Am. SOC. Mech. Engrs., J .Heat Transfer, Ser. C, 84, 353 ( 1962).Manuscript receioed August 27, 1974; reoision received and accepted

February 3, 1975.

T rickle-Bed Reactor Performa ncePart 1 Holdup and Mass Transfer Effects

Liquid holdup and mass t r ansfe r rates were m e a su r e d i n a 2.58-cm I.D.t ube , p i c ke d w i th g la ss be a ds a nd g r a nu lar C uO Z n O c at a ly s t or p n a p h -tho1 par t ic le s , and opera ted as a tr ickle bed. Gas- to- l iquid (water) transportcoefficients were de te r m ine d f r om a bso r p t ion a nd de so r p t ion e xpe r im e n t swi th oxygen at 25OC and 1 atm. Liquid- to-par tic le mass transfer was studiedusing ,&naphthol particles.Ho ldu p a nd b oth mass t r ansfe r coe ff icients were unaf fec ted by gas flowr a t e bu t i nc r e a se d w i th l i qu id rate. The da ta w e r e c o r r e l a t e d w i th e qua -t ions tha t could be used f or pred icting mass transfer coeff ic ients a t hightempera tures and pressures for use in the reac t ion s tudies r epor ted in Part 11.

SHIGEO GOT0 and J. M. SMITHDepartment of Chemical Engineering

University of CaliforniaDavis, California 95616

Correspondence concerning this paper should be addressed to J. M .Smith. S. Goto is on leave from University of Nagoya, Japan.Page 706 July, 1975 1 AlChE Journal Vol. 21, No. 4)


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Oxidation of organic pollutants in water with a solidcatalyst offers some potential as an alternative process forwater purification. Catalysts developed up to this time,which are usually metal oxides, require temperatures ofabout 200OC. This means that the reactor must be oper-ated under pressure in order to maintain the water in theliquid phase. Further, inadequate oxygen for completereaction can be dissolved in the water. Hence catalyticoxidation of pollutants in water is well suited for trickle-bed reactor operation where a continuous supply ofoxygen is introduced with the gas (air) stream. The twoparts of the paper describe studies in a laboratory-scaletrickle-bed reactor for oxidation of formic acid in waterat 40 atm pressure and 212O to 240OC. The purpose ofthe work is to develop data and procedures useful fordesign of this type of reactor system.

The design approach for a trickle-bed reactor may bedivided into two aspects. The first is a procedure to pre-dict the global rate, that is, the rate associated with asingle catalyst particle. Evaluation of this rate requiresintrinsic kinetics, intraparticle diffusion, and mass transferrates between gas, liquid, and solid (catalyst) phases. The

second aspect is a model to predict the conversion in thereactor as a whole. Such models must describe the natureof the mixing in the gas and liquid streams; that is,.plugflow, flow with axial dispersion, etc. It is here that liquidholdup is involved. In the work reported, experimentaland predicted results were obtained for both aspects.In Part I, holdup, and gas-to-liquid and liquid-to-solidmass transfer rates are presented for a trickle-bed ap-paratus of the same characteristics as used in Part I1 forthe reaction studies. Of necessity these measurementswere at 1 atm and room temperature. Correlations weresuggested for predicting the mass transfer rates at hightemperatures and pressures.Two types of data are given in Part 11: global ratesmeasured in a differential reactor with low conversionsof formic acid and oxygen, and high-conversion 60 to97y0 for formic acid) results obtained with deeper catalystbeds in the same reactor. The global rates were comparedwith predicted values using known intrinsic kinetics andthe mass transfer coefficients reported in Part I. Theintegral reactor data were compared with predictionsbased upon plug-flow and axial dispersion models.

CONCLUSIONS AND SIGNIFICANCEMost correlations for dynamic holdup and interphasemass transport are based upon data obtained in absorp-tion towers using special types of relatively large parti-cles (that is, Raschig rings, Berl saddles, etc.). However,Satterfield and Way (1972) reported holdup data for smallglass beads and for extruded catalyst particles. Our holdupdata did not agree with the correlations based upon theabsorption tower data, except for the largest particles

studied in our work (0.41-cm glass beads). The correlatingprocedure of Satterfield and Way fit well our data for thesmaller particles but not that for 0.41-cm glass beads.Apparently the effect of particle size on holdup changesat a particle size from 0.3 to 0.4 cm.For the oxygen transport system we found the masstransfer resistance from bulk gas to gas-liquid interfaceto be negligible. On the liquid side of this interface, thecorrelating procedure for the mass transfer coefficient kLaof Sherwood and Holloway (1940) fit our data well. Thiscorrelation is in terms of parameters characteristic of pack-ing size and shape. Experimental results for the mass trans-fer coefficient k,a from liquid to outer particle surface didnot agree with the correlation proposed by Van Krevelenand Krekels (1948) for trickle beds, possibly because theircorrelation was based upon data for larger particle sizes.An equation analogous to that of Sherwood and Hollowaywas developed for use in predicting kp at reaction condi-tions.Holdup and all mass transfer coefficients were un-affected by gas flow rate at the conditions of our experi-

The most common arrangement for a trickle-bed reactoris concurrent downflow of liquid and gas over a fixed bedof catalyst particles and such a configuration was used inthis work. In the reaction studies (Pa rt 11) one reactantwas introduced with the gas stream and the other with theliquid. Hence, the global reaction rate at any axial posi-tion in the reactor may bq retarded by gas-to-liquid andliquid-to-particle mass transfer. Also the conversion of theAlChE Journal Vol. 21, No. 4)

ments.Accurate calculations of global reaction rates from themeasured mass transfer results was somewhat hinderedby lack of experimental data for diffusivities of oxygen andformic acid in water at 212O to 24OOC and 40 atm pres-sure. Predicted global rates were from 0 to higherthan the measured rates. Gas flow rate did not influencethe global rate. Increases in liquid flow rate and in tem-perature increased the global rate, indicating that masstransfer and intrinsic kinetics were both important factorsin reactor performance.Integral reactor conversions of formic acid were cal-culated from intrinsic kinetics, effective intraparticlediffusivities, k,a, and l cLa as determined from the datagiven in Part I. Agreement between predicted and experi-mental results was within lvo.lug flow of both gasand liquid streams gave conversions 1 to 2y0 higherthan when axial dispersion was accounted for in the liquidphase. This difference was less than the effects of intra-particle diffusion, k,a, and of k ~ an the conversion. Theretardation of the rate and conversion due to gas-to-liquidmass transfer was the most important transport effect,followed by intraparticle diffusion, even for catalyst par-ticles of 0.0541 cm diameter. The relatively great signifi-cance of gas-to-liquid transport with respect to axial dis-persion means that reactor modeling questions, such asholdup and residence time distribution, were much lessimportant than accurate values for mass transport coeffi-cients.

reactant in the liquid is dependent upon the residencetime, which in turn is determined in part by the liquidholdup. Design of trickle-bed reactors should include theefFects of these factors, yet there is inadequate informa-tion available for both mass transfer rates and for holdup,particularly for small diameter particles and for low liquidflow rates.The objective in Part I was to obtain holdup and mass

July, 1975 Page 707


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TABLE .STATICHOLDUPND BEDPROPERTIES4 m PP,g/cm3 pS g/cm3 P EB at', cm2/cm3 H , His H e ,

Glass beads 0.413 2.15 2.15 0.0 0.371 9.14 0.0282 0.0 0.0282CuO .ZnO Catalyst 0.291 2.35 5.29 0.56 0.441 11.5 0.371 0.313 0.058CuO * ZnO Catalyst 0.0541 2.35 5.29 0.56 0.453 60.7 0.429 0.306 0.123p-naphthol 0.241 1.17 1.22 0.038 0.483 12.9p-naphthol 0.0541 1.17 1.22 0.038 0.520 53.26(1 - B

dn* Calculated by assuming that the particles have a spherical diameter of dp; that is, at = -transfer data for both porous and nonporous particles,Measurements were made at 25C and atmospheric pres-sure using water for the holdup studies, absorption anddesorption of oxygen for the gas-to-fluid mass transfer, anddissolution of &naphthol for particle-to-fluid mass transfer.LIQUID HOLDUP

The residence time of liquid in a trickle-bed reactor isdetermined by the dynamic lioldup H d which is the vol-ume of liquicl that drains from the bed, after gas andliquid flows are stopped, divided by the total volume ofthe bed. In addition to I g d , static holdups were also deter-mined. The Lotal static holdup IZ, is the volume fractionof liquid that remains afLer draining the bed. H , wasevaluated by weighing tlie bed after H d had been deter-mined and comparing this weight with that of the drybed. For porous particles tlie static holdup consists of theliquid in the intraparticle pores ,Hi,nd the liquid held inthe interparticle space If the internal pores are com-pletely filled with liquid, Hi s calculable from the bedand particle void fractions according to the equation

H i , = r p l B ) 1)Then N,, s obtained by subtracting H i , from H,.The same apparatus (Figure 1) was used for holdupand mass transfer sludies. 'I'he particles were held in aglass tube (I.D. = 2.58 cm, packed bed length = 15.2cm) by a stainless steel screen. The liquid entered thetop of the bed through a liquid distributor containing fivecapillary tubes ( 0.1 cm I.D., 0.5 cm long), Preliminary

1 Feed R e s e rv o i r2 Pump3 F l o w Meter4 F low C o n t ro l l e r5 V a l v e6 T r i c k l e - B e d

2 5 cn; 1.0 , g lass

0 2 N2 Ur A i rGas D i s c h a rg e

85L i q u i d D i s c h a r g eFi,g. 1. Apparatus for holdup and mass transfer data.

experiments showed that a 0.5-cm length of capillary pro-vided enough flow resistance to ensure nearly equal flowof liquid from each lube. The five tubes were locatedvertically in the cross section of the glass tube so that the{luxof liquid was approximately uniform.Data were ob~aii iedor glass beads, porous, CuO * ZnOcatalyst particles (Cliemetron Corp. G-66B) and for non-porous, granular p-naphtliol particles. The catalyst parti-cles were the same as those employed for the reactionstudies (Part 11). Properties of tlie several particles andthe beds are given in Table 1. The original 1/4 in. x I/a in.cylindrical catalyst pellets were cut into equal pie-shapedquarters which liad an equivalent spherical diameter d= GV,/S, of 0.291 cm. For the smaller size, the pelletswere crushed and sieved, retaining the 28-32 mesh frac-tion (average dIl = 0.0541 cm). The p-naphthol particleswere crushed pellets with size ranges of 28-32 and 7-9mesh (average d, = 0.241 cm).For dynamic holdup measurements the inlet and out-let valves [Figure 1 5)] were simultaneously closed aftersteady state conditions were achieved. Then the volume ofliquid that would drain from the column was measured.After a maximum period of 30 min., the drainage essen-tiallv ceased. In the range of gas rates from 0 to 4.0 cm3/s(25'C, 1 atm), H,I was nearly constant for a fixed liquidrate. A masimum variation of 6 in H c l with F , wasobserved for the 0.291-cm catalyst particles.

The static holdups are listed in Table 1 . It was notpossible to measure static values for /%naphthol becausethe weight of the particles changed due to dissolution.The measured dynamic holdups are shown by the datapoints in Figure 2.The most frequently cited correlation for dynamicholdup is that of Otake and Okada (1953) which is basedupon data obtained in absorption columns packed withnonporou? particles of diameters from 1 to 5 cm. Theyproposed the following correlations:1. For spheres (10 < Re < 2000):

H d = 1.25 R e )76 (Ga) 0.44 a , 2 )2. For Rasching rings and broken solids:H d = 15.1 ( (Gu) 0 . 4 4 (a ,) -o.ao;

10 < Re < 2000 3 )H d = 21.1 ( R e ) .51 (Gu 0.44 (a ) --O. O;

0.01 < Re < 10 (4)where at is the total external surface area of the particlesper unit volume of the bed (see Table 1) .The dotted lines in Figure 2 represent Equation (2) forthe glass beads, and Equations 3 ) and (4) or the gran-ular catalyst and ,@naphthol particles. Only for the rela-tively large glass beads do these correlations fit the data.The deviations increase with decrease in particle size. Thesolid lines represent Equation (5) , as discussed in thefollowing paragraph.

AlChE Journal Vol. 21, No. 4)Page 708 July, 1975


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0 30

m 255z 0 2 0-

-,t 0 I 5

0 10

0 05

+ b 3 I G i i s s Beads 241 cm 8-Naphlhsl0 2 Y i i c io . Z n O A 0.0511 Cm B- Naph tho l0 C141 :F. u0 I Zi iO L = 1 5 2 c l i ( a i l Packingsi

Fg = 2 c m 3 sec 1 = 25C

I--- i o m E q s 1 2 ) 1 3 or 1 4

I I0 G I I 0 I 5 2 0 2 5 3 0 3 5

F~ cm3 sec

Fig. 2. Effect of liquid flow rate on dynamic holdup.Satterfield and Way (1 97 2) proposed that the dynam icholdup in a trickle-bed reactor was a function of thesuperficial velocity an d viscosity of t he liqu id:

H d = A (U L ) ( loop) * ( 5 )with the dimensional parameter A to be determined fromholdup data for each type of particle. Equation ( 5 ) wasbased upon ddta for 0.3-cm glass beads a nd 0.16 and 0.32-cm cylinders of Si02-A1203 catalyst. Our data are plo ttedaccording to Equation (5) in Figure 3. This method ofcorrelations appears to be adequate for the porous orsolid particles so long as d, is less than 0.3 to 0.4 cm.However, the deviation from a linear relationship is sig-nificant for 0.4-cm glass beads. Th e solid lines in Fig ure 3represent Equation (5) with the indicate d values of A.It is concluded from these comparisons with holdupdata that for downflow trickle-bed reactors the effect ofparticle size on H d changes at a d, of 0 .3 to 0.4 cm. Exist-ing correlations for Hd hould be used with caution for d,values bevond the range of data upon which the correla-tions are based. Figures 2 and 3 show that the holdupfor the nonporous &naphthol is slightly higher than forporous CuO . ZnO particles of the sam e particle size. Thisdifferenc e is du e primarily t o the larger bed porosity Q ,Table 1) for the ,&naphthol case rather tha n du e to differ-ences in surface characteristics. It should be noted thatthe packed bed depth and the ratio of tube-to-particlediameter were both relatively low for all the holdup mea-surements.GAS-TO-LIQUID MASS TRANSFER

Since the application of mass transfer data in Part 11is for an oxidation process, the tran spo rt of oxyge. A -tween the gas and liquid phase in a trickle bed wasstudied. For such a slightly soluble gas the interphasetransport is expected to be controlled bv the liquid phaseresistance a nd our results sub stantiated this conclusion.The ahsorption measurements were made by feedingoxvgen-free, distilled water and pure oxygen gas to thebed using the apparatus shown in Figure 1. The waterwas stripped of oxygen with a stream of nitrog en prior toAlChE Journal Vol. 21, No. 4)

0.0541 Cm 8 - aphtholi i \ r A = O . 6 6 l l

0 0 2 0 4 0 6 0 8 1 0 1 2

y i ~ 1 0 0 p 1 ( c m set)' 3 ( c p 11 4Fig. 3. Dynamic holdup vs. u ~ ' / ~ ( l W r ) ~ ' ~ .

malcing a run. For desorption measurements, the distilledwater was first saturated with pure oxygen and the gasstream consisted of pure nitrogen.The oxygen concentration CL,02 in the water was mea-sured by stripping a sample with helium in a packedcolumn and passing the exit gases to a chromatograph foranalysis. Details of the procedure have been reported(Balcli el al., 19 74 ). Oxygen was determined in the feedand discharge water streams for runs with different liquidand gas flow rates. The oxygen concentration in the dis-cliarge stream was nearly indepe nde nt of gas flow rateover the range 1.0 to 4.0 cm3/s. For the bed of 0.291-cmCuO . ZnO particles CL,oz varied by 4 at a liquid flowrate of 1.03 cm3/s. This indicates that the effect of Fon the mass transfer coefficient k L was insignificant. Thevarialion in CL,02 with liquid flow rate is illustrated inFigure 4 for desorption runs with the column packed with

12 . / * I I I- . I

I 0

u 5 I 1 5 2 0 2 , 3 0 3 5Liquid F l o w R a t e F cm3 secFig. 4. Concentrations o f oxygen in desorption runs.

July, 1975 Page 709


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( k La ) tm

7T r i c k l e b e d

7-f2

FL

E m p t y b e dFig. 5. Modeling of end effects in trickle-bed reactor.

0.291-cm CuO ZnO particles. To test for mass transferin the end regions, between liquid distributor and top ofbed and between bottom of bed and liquid level in thetube, CL,02 was measured in the discharge stream whenthe packing was removed and the liquid distributor waslowered to just above the screen. This concentration,designated (CL,O~):, was 24 to 36% less than (CL,OZ)~,indicating that considerable mass transport was occurringin the end regions of the bed, Figure 4 shows (CL,O~);for one bed.To determine kLa for tlie bed itself, the mass transferat the top ( k L a ) t o p and bottom (kLa),,tmend regions wasaccounted for by the procedure depicted in Figure 5 . Ifaxial dispersion is neglected, mass balances for oxygen inthe two end regions and the bed itself, for tlie desoiptioncase, may be written

F L ~ C L , O ~ (1cLa)top (CL, O~0 ) sd~ (6)7 )L dC~,op= - I c L ~ )CL,O~ 0) S d

FL CL.02 = - (1cLa)btin ( c L , O 2 - dz ( 8 )At the gas rates used the concentration of oxygen in thegas was negligible. Boundary conditions for these equa-tions are

CL,oZ= ( CL,oz)f at z = 0 (9)= ( C L , 0 2 ) 1 at z = z1 (10)= ( C L , O ~ ) ~t z = 21 + Z B (11)= ( C L , O ~ ) ~t z = z1+ Z B + 2 2 (12)

where zl, B and zz are the lengths of the upper end sec-tion, bed, and lower end section, as shown in Figure 5.If Equations (6) to (8 ) are solved with the boundaryconditions, and the concentrations (CL,O~)are eliminated from the three integrated equations, anexpression involving only ( C L , O ~ ) ~nd ( C L , O ~ ) ~s ob-tained:

and (C L , O Z )

( CL OZ )~ ( C L , O ~ ) ~ -J (13)- ( k L a ) t o p z l - k L a ) z B - (kLa)btmZ2e* [ F L / SIn a similar way the expression for the exit concentrationin the empty bed isPage 710 July, 1975

(14)Dividing Equation (13) by 1 4 ) gives the following ex-pression for kLa for the bed in terms of the measured con-centrations ( C L , O ~ )and (CL,O~)

A similar derivation for the absorption case yields

where C'L,O2 is the concentration of oxygen in water inequilibrium with pure oxygen gas. For 1 atm and 25Cthis value is 12.6 x lo-' g mole/cm3 (Perry, 1963).The effect of axial dispersion was evaluated by estimat-ing a dispersion coefficient E from the correlation ofFurzer and Michell (1970) which is based on data forcountercurrent, two-phase fiow in a packed bed. Solutionof the mass balances using such dispersion coefficients gavek L ( i values no more than 3 higher than when axial dis-persion is neglected. This small increase justifies neglect-ing axial dispersion in the analysis of the mass transferdata. For k, i (see next section) the bed depth was lessso that the axial dispersion effect was larger, but less than10 . In terms of the overall effect of mass transfer onthe hickle-bed reactor performance discussed in Part 11,/;La is several times as important as k,a.

Values of k ~ uetermined from Equations (15) and(16) are shown in Figure 6 for beds of glass beads andof catalyst particles. Absorption and desoiption results forthe glass beads agree well with each other. This is evi-dence that the interphase mass transfer is controlled bythe resistance in (he liquid phase since in one case theoxygen mole fraction in the gas is nearly 100% and in theother case i t is low. In view of this agreement, only themore accurate desorption measurements were made forthe catalyst particles.Based upon a siudy of desorption of 0 2 Hz, and C02from water in countercurrent packed beds, Sherwood andHolloway (1940) found also that kLa was independentof gas flow rate. Their dimensional correlation is

2 5 , - 1 1 I I 1V 0 4 1 3 Cm Glass Beads A b s o r p t l o n i \ o o w cue. Zn0I A U 4 1 3 crr G l a s s Beads DesorDtion I

0 5 I 0 I 5 2 0 2 5 3 0 3 5F~ cm3 sec

Fig. 6. Effect of liquid f l o w rate on kLo ( F , = 2.0 cm3/s; ZB =15.2 cm).AlChE Journal Vol. 21, No. 4)


6/8

where the proper units are those shown in the Notation,and nL and 0 1 ~re related to the mass transfer surface andgeometry of the particles and are specific for each bed.This form of correlation for kLa agreed well with our dataas indicated by the straight lines obtained in Figure 7where l cLa/D)/ ( p / p D ) is plotted versus GJp. Thesolid curves in Figure 6 represent Equation (17) with thefollowing values of CYLand nL:Particles w cm) L-2 nLGlass beads (0.413 cm) 2.8 0.40CuO * ZnO (0.291 cm) 6.0 0.41CuO ZnO (0.0541 cm) 7.8 0.39

The dimensionless correlation of Onda et al. (1959)for kLa for absorption columns packed specifically withRaschig rings does not agree with our data for tricklebeds containing glass beads or granular particles. Theeffect of liquid rate on kLa predicted from this correlationis greater than observed experimentally, as shown by thedotted lines in Figure 6. ?'he data in Figure 6 will beused in Part 11for caIculating the gas-to-liquid mass trans-fer resistance under reaction conditions.

I

LIQUID-TO -PARTICL E MASS TRANSFERMass transfer rates from particle-to-liquid were mea-sured by flowing distilled water (a t 25C and 1 atm)

down through short beds of &naphthol particles. Bedlengths ZB are given in Figure 8. Runs were made withconcurrent air flow for trickle-bed operation and with thebed full of liquid (no gas phase). Concentrations of @-naphthol in the liquid were measured using a BeckmanDK-2A spectrophotometer at a wavelength of 315 milli-microns where &naphthol has a large absorptivity. Themeasured solubility in water at 25C was 0.0748 g/ (lOOgH20 ) which agrees well with the reported (Perry, 1963)value of 0.074 g / ( lOOg HzO) . End effects were not in-volved for these runs so that lc,a can be calculated froma mass balance for &naphthol in the bed. Neglecting axialdispersion, this expression is

F L d CL,N= ( h a ) C * L,N- C L , N ) S z (18)Integrating with the appropriate boundary conditionsand solving for k,a gives

I

Here z B is the average length of packed bed. Because ofdissolution, the length decreases during the run. Thisdecrease was not large, ranging from 1 o 7 .The values of k,a evaluated from Equation (1 9) fortrickle-bed operation were nearly insensitive to the gasrate for F, from 0 to 4.0 cm3/s. For example, k,a changedby 7 7 ; between zero gas flow and 4.0 cm3/s for 0.241-cmparticles, at a liquid flow rate of 1.03 cm3/s. Note thateven for F , = 0, a gas phase existed in the bed. Hence,the conditions are different than for the liquid-full runs.

The results are displayed in Figure 8 for both trickle-bed and liquid-full conditions. Several correlations havebeen presented fo r fluid-particle mass transfer in liquid-full packed beds and these agree, in general, with ourdata. F o r example, the dotted curves in Figure 8 repre-sent the correlation of Evans and Gerald ( 1953 ). Thiscorrelation, which permits calculation of k may bewritten

Equat ion 1 1 7 )

33 5 7 10 2 30 50 70 100

GL p cm-'Fig. 7. Correlation of kLa.

A 0 241 crn T r i c k l e B e d i z B = 2 60 cm 10 0541 c m . Tiickle Bed l r B = l 9 8 c m )

0 541 c m , LIqdld Ful l i z g = 1 54 cm

2 0

5

.O

0.5

an K r e v e l e n and K r e k e l s (1 9 4 8 )

0 0 5 1 0 1 5 2 0 2 5 3 0 3 5F~ cm3 rec

Fig. 8. Effect of liquid flow rate on ksu ( F , = 2.0 cm3/s).The effective mass transfer surface used to obtain theproduct lc,a is based upon the total external surface of theparticles per unit volume of bed; that is, a = at =

Figure 8 shows that lc,a is greater in the trickle bedthan in the liquid-full bed, at the same flow rate, for thelarger particles. This is probably due to the larger linearvelocities in trickle beds where part of the volume isoccupied by gas. Correlations such as that of Van Krevelenand Krekels (1948) for trickle beds and Evans andGerald (1953) for liquid-full beds indicate similar results.In contrast, our experimental data for the smaller parti-cles (0.0541 cm) show k,a to be larger for liquid-fulloperation. Possibly the entire external surface is not effec-tive for mass transfer in trickle beds containing very smallparticles. If this effect predominates over the velocityfactor, lc,n would be greater for liquid-full operation.The dot-dash curves in Figure 8 represent the VanKrevelen and Krekels correlation, which may be written

6 (1 E B ) / C .

AlChE Journal Vol. 27, No. 4) July, 7975 Page 777


7/8

10

7

5

3

2

-'Y

N 1ax-mY) 0 7

0 5x

m_1

Or?

0 2

0 10 2 0 3 u 5 0 7 1 2 3

FL 0 3 secFig. 9. Overall mass transfer rate in trickle bed 0.291-cm CuO.Zn0

particles).In addition to not predicting the relative values of k,a fortrickle-bed and liquid-full operation for the smaller parti-cles, Equation (2 1) does not well represent the trickle-beddata for either particle size. The correlation was developedfrom data for larger (0.29 to 1.4 cm) particles. I t is con-cluded that the effect of particle size on k , ~n trickle bedscan change for particles smaller than about 0.2 cm.In order 10 obtain a suitable correlation of k,a for usein Part 11, dimensional Equation (17) was modified to theform

where (Y and nL have values which are specific for a par-ticular particle size and shape and bed packing. Equation(2 2) agrees well (solid curves in Figure 8) with the ex-perimental data for the following values of (Y, and n,:

f f S,%Naphthol particle sizes, p (cm)na-2 n,

0.2410.054145. 0.56153. 0.67

OVERALL MASS TRANSFER IN A TRICKLE BEDEquations (17) and (22) provide correlations that maybe used to predict the overall mass transfer rate from gasto particle for the specific trickle beds used in this work. If

the two concentration boundary layers near the gas-liquidand Iiquid-solid interfaces do not overlap during the flowof liquid over one particle, the overall mass transfer coeffi-cient is given by (Satterfield, 1970)

Figure (9 ) shows the curve of kLsa versus liquid flow ratecalculated from Equations (1 7) , ( 22 ), and (23) for thetransfer of oxygen in a bed of 0.291-cm CuO * ZnO par-ticles. Since k ~ us several times smaller than k,a, the linefor the overall coefficient closely parallels that for kLa. Incalculating k,a from Equation (2 2) , the molecular diffu-sivity of oxygen in water was used. The diffusivities ofoxygen and @-naphthol at 25C were estimated to be2.26 x cm2/s and 0.774 x 10-5, respectively, fromthe Othmer and Thaker equation (Reid and Shenvood,1966). The values of as nd n, determined for the 0.241-cm particles of &naphthol were assumed to apply eventhough the particle size was somewhat less than the 0.291cm for the CuO ZnO particles.Experimental values of k ~ and k,a are necessary forpredicting the overall coefficient. For example, in the ab-sence of such information, it has been proposed (Satter -field and Way, 1972) that kLsa could be calculated fromthe dynamic holdup using the expression

or

Equation (2 5) is based upon two assumptions: completewetting of tlie particles so that the total external surfaceIt may be employed, and molecular diffusion through aiilm of thickness I j d / a t . The values of kLsa calculated fromEquation (2 5) using the H,i data in Figure 2 for 0.291-cmparticles of CuO ZnO are also shown in Figure 9. Thiscurve is higher than that based upon the experimentallydetermined coeficients [Equation ( 23 ) and shows adifferent trend witli liquid flow rate. This is significantsince the curve based upon Equation (2 5) is sometimesused as a conservative estimate for k ~ , a . n the basis thatthe error in tliis estimation method is due to at not repre-senting tlie eflective interfacial area, at in Equation (25)can be replaced with atGThe relation between a, and atlor 0.291-cm granular particles is not known. However,we can approximate this relation by employing the corre-lation cited by Onda et al. (1959) for a, for columnspaclced with Rascliig rings:

Using this expression for a, in the following form ofEquation (25)(27)

gives the lower line in Figure 9. This result shows theI - - .it11 liquid rate as the experimental data;.dqk>L I , i but the values are much too low.Neither Equation ( 2 5 ) or ( 2 7 ) are reliable for predictingkLsa for the trickle beds used in our studies,ACKNOWLEDGMENT

The financial assistance of the Water Resources Center,University of California, Grant \\'-392, is gratefully acknowl-edged. The Chemetron Corporation kindly supplied theZnO.CuO catalyst.N O T A T I O NA = parameters in Equation (5), (cm/s) (g/cm

= effective external surface area for mass transfer,s ) -114Cm2/ (cm3 of empty tube)

Page 712 July, 1975 AlChE Journal Vol. 21, No. 4)


8/8

ata,

= total external surface area of particles, cm2/ (cm3= wetted external surface area of particles, cm2/of empty tube)

(cm3 of empty tube)B = ~ D , , O Z C S , O ~ / D ~ , F A C S . F AC = concentration, g-mole/cm3C L o = concentration in liquid in equilibrium with gas,D = molecular diffusivity in liquid, cm2/sDe = effective intraparticle diffusivity, cm2/sd,, = particle diameter, cmE = axial dispersion coefficient, cm2/sE f = effectiveness fac tor of catalyst particleF , = volumetric flow rate of gas at 1 atm, 2 5 C , cm3/sF L = volumetric flow ra te of liquid at 1 atm, 25C,Ga = Gallileo number, 4 3 g p2/,u2GL = superficial liquid flow rate, g/ (cm2)sg = acceleration of gravity, cm/s2H = Henrys Law constant, (cm3 of li qu id )/ (cm3 ofH d = dynamic holdup, (cm3 of liq ui d) /( cm 3 of bed)H e , = external static holdupH i , = internal static holdupH , = static holdupk L = mass transfer coefficient from gas to liquid, cm/sk L , = overall mass transfer coefficient from gas to par-lc, = mass transfer coefficient from liquid to particle,ko02 = intrinsic second-order rate constant for O2 con-m = generalized Thiele modulusn~ = parameter in Equation 17)n, = parameter in Equation ( 2 2 )P = pressure, atmPe = Peclet number, ~ u L / ER = reaction rate, g-mole/ (g ) sRe = Reynolds number, G L / FS = cross sectional area of tube, cm2 5 .23 cm2 forSC = Schmidt number, p/pDS,t = temperature, CULV,Wx F A

g-mole/cm3

cm3/s

gas )

ticle, through a liquid layer, cm/scm/ssumption, cma/ (g mole) ( g ) ( s )

A

glass tube, 5.07 cm2 for stainless steel reac tor)= external surface area of particle, cm2= superficial velocity of liquid, cm/s= volume of particle, cm3= mass of catalyst particles, g= conversion of formic acid in liquid at the exit of

the reactorY,,oz = C~,02/ CL7.02)f= C O L , o z / ( C * L , 0 2 ) fY L . 0 2 = C L ,O Z / ( C * L , 0 2 ) fY d . 0 2 = C s , o z / ( C * L , o 2 ) fy L , F A = C L , F A / ( c L , F A ) fY.Y.FA = C s , F A / ( c L , F A )zZB

Greek LettersP LaE BE ,pPB

= axial coordinate in reactor tube, L ~= total length of packed bed, cm= parameter in Equation (17), cm)nL-2= parameter in Equation ( 2 2 ) , (cm) a - - 2= void friction in the bed= porosity in the particle= density of water, g/cm3= bulk density of particles in bed, g/cm3

AlChE Journal Vol. 21, No. 4)

ppp,p

= apparent density of particle, g/cm3= solid-phase density of particle, g/cm3= fluid viscosity, g/cm sSubscriptse = exitf =feedFA = formic acidg = gas phaseL = liquid phaseN = /%naphtholS = external surface of catalystLITERATURE CITEDBaldi, G., S. Goto, C. K. Chow, and J. M. Smith, TatalyticOxidation of Formic Acid in Water, Ind. Chem. Eng. Proc-ess Design Deuelop, 13,447 ( 1974).Bischoff, K. B., Effectiveness Factors for General ReactionRate Forms, A l C h E J., 11, 351 (1965).Evans, G. C., and C. F. Gerald, Mass Transfer from BenzoicAcid Granules to Water in Fixed and Fluidized Beds at LowReynolds Numbers, Che m. En g. Progr., 49( 3) , 135 ( 1953).Furzer, I. A., and R. W. Michell, Liquid-Phase Dispersion inPacked Beds with Two-Phase Flow, AIChE I., 16, 380

(1970).Hartman, M., and R. W. Coughlin, Oxidation of SO2 in aTrickle-Bed Reactor Packed with Carbon, Chem. Eng. Sci.,27,867 ( 1972).Himmelblau, D. M., Solubility of Inert Gases in Water, 0Cto near the Critical Point of Water, J . Chem. Eng. Data,5,lO (1960).Hoog, H., H. G. Klinkert, and A. Schaafsma, New Shell Hy-drodesulfurization Process Shows these Features, PetroleumRefiner, 32,137 (1953).Hougen, 0 . A., and K. M. Watson, Chemical Process Princi-ples, Part 111, p. 873, Wiley, New York ( 1947).Onda, K., E. Sada, and Y. Murase, Liquid-Side Mass TransferCoefficients in Packed Towers, A l C h E I.,5,235 ( 1959).Otake, T., and K. Okada, Liquid Holdup in Packed Towers,Kaguku Kogaku Che m. Eng. Jap an) ,17,176 (1953).Perry, J. H., Chemical Engineers Handbook, Fourth Edit.,pp. 3-37, 70, 14-4, 14-6, McGraw-Hill, New York (1963).

Ralston, A., and H. S. Wilf, Mathematical Meth ods for DigitalComputers, p. 110, Wiley, New York (1960).Reid, R. C., and T. K. Sherwood, Th e Properties of Gases andLiquids, Second Edit., p. 559, McGraw-Hill, New York(1966).Ross, L. D., Performance of Trickle Bed Reactors, C h e m .Eng . Progr., 61( o , 77 (1965).Sadana, A., and J. R. Katzer, Catalytic Oxidation of Phenol inAqueous Solution over Copper Oxide, Ind . Eng. Chem.Fundamentals, 13, 127 (1974).

p. 96, M.I.T. Press, Cambridge ( 1970)., and P. F. Way, The Role of Liquid Phase in the Per-formance of a Trickle Bed Reactor, A l C h E J., 18, 305( 1972).Sedriks, W., and C. N. Kenney, Partial Wetting in TrickleBed Reactors-The Reduction of Crotonaldenyde over aPalladium Catalyst, Chem. E ng. Sci. , 28, 559 (1973).

Sherwood, T. K., and F. A. L. Holloway, Performance ofPacked Towers-Liquid Film Data for Several Packings,Trans. Am. lns t . C hem. Eng. , 36, 39 (1940).Van Krevelen, D. W., and J . T. C. Krekels, Rate of Dissolu-tion of Solid Substances, Rec. Trau. Chim., 67, 512 1948).Washburn, E. W., (E d. ), International Critical Tables, FirstEdit., Vol. 5, p. 10, McGraw-Hill, New York ( 1929).Weekman, V. W., and J. E. Myers, Fluid-Flow Characteristicsof Concurrent Gas-Liquid Flow in Packed Beds, A l C h E J.10,951 (1964).

Satterfield, C. N., Mass Transfer i n Heterog Catalysis,

Manuscript received December 2 , 1974; revision received February3 and accepted February 14, 1975.

July, 1975 Page 713

trickle-bed reactor performance. part i. hold up and mass transfer effects

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