8/3/2019 Kiel93mass

1/9

Chemical Enginewitig Science, Vol. 48, No. 1, pp. 117-125, 1993. ooo9-2509/93 55.00 + 0.00Rintcd in Great Britain. 0 1992 Per tcamn Pr ess Ltd

MASS TRANSFER BETWEEN GAS AND PARTICLES IN AGAS-SOLID TRICKLE FLOW REACTORJ. H. A. KIEL, W. PRINS and W. P. M. VAN SWAAIJDepartment of Chemical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede,The Netherlands

(First received 20 December 1991; accepted in revised form 26 May 1992)Abstract--Gas-solids mass transfer was studied for counter-current flow of gas and millimetre-sized solidparticles over an inert packing at dilute phase or trickle flow conditions. Experimental data were obtainedfrom the adsorption of water vapour on 640 and 2200 q diameter molecular sieve spheres at ambientconditions in a test column with a cross-sectional area of 0.06 x 0.06 m2 and a packing height of 0.27 or0.53 m. The packing consisted of a bank of regularly stacked, 0.01 m diameter bars made of stainless steel.Assuming the effective area for mass transfer to be. equal to the external surface area of the spheres, theexperimental values of the average gas-solids mass transfer coefficient were determined to amount toapproximately 40-80% of the values calculated from the well-known Ranz-Marshall correlation for asingle sphere in an undisturbed gas Row. These experimental values were identified as conservativeestimates of the actual average gas-solids mass transfer coefficient because the pore diffusion resistancecould not be eliminated completely. A comparison between experimental data on hydrodynamics(gas-solids momentum transfer) and gas-solids mass transfer indicated, furthermore, that the influence ofparticle shielding with interfering concentration boundary layers of different particles was small for themillimetre-sized particles and the experimental conditions investigated. Gas-solids mass transfer as well asgas-solids momentum transfer were mainly determined by single-particle flow bchaviour.

1. INTRODIJCITONIn a gas-solid trickle flow reactor (GSTFR), gas andsolids are contacted counter-currently over a packedcolumn under dilute phase or trickle flow conditions.The potential of this relatively new type of gas-solidscontactor for gas treating, adsorption and heatrecovery has been shown in several previous studies(Verver and van Swaaij, 1987; Kuczynski, 1986;Guigon et al,, 1986). As reported in earlier publi-cations (Kiel et al., 1990; Kiel, 1990), our research isfocused on the application of a gas-solid trickle flowreactor as the absorber in a continuous dry regener-ative process for the simultaneous removal of SO, andNO, from flue gases. A gas-solid trickle flow reactoris expected to be an efficient absorber because offavourable properties such as a low pressure drop,little axial mixing in both phases and high rates ofgas--solids heat and mass transfer. Relatively largesolid particles (millimetre-sized) are to be preferredbecause they allow a high superficial flue gas velocity(l-5 m s- I), which limits the required cross-sectionalarea of the absorber. Hydrodynamic properties, parti-cularly pressure drop and average solids hold-up, fortrickle flow of relatively large particles over severalspecially designed, regularly stacked packings havebeen described by Kiel and van Swaaij (1989) and Kiel(1990). In this paper, the results ofa subsequent studyof gas-solids mass transfer are presented.

Gas-solids mass transfer for small particles (aver-age particle diameter 70 pm) under trickle flow condi-tions was investigated by Roes and van Swaaij (1979b)

tPresent address: Netherlands Energy Research Founda-tion ECN, P.O. Box I, 1755 ZG Petten, The Netherlands.

for a packed column of Pall rings, and by Verver andvan Swaaij (1987) for a double-channel baffle column.In both studies, the experimentally obtained values ofthe mass transfer rate constant, &,a, were at least afactor of 100 lower than the values calculated fromexperimental solids hold-up data and the well-knowncorrelation of Ranz and Marshall (1952) for masstransfer between a single sphere and its surroundinggas phase. The low experimental k,a values wereattributed to particle shielding phenomena due to theformation of less dilute suspensions or trickles, as theywere called on the basis of visual observations of theirappearance. Formation of trickles is likely to occurbecause it reduces the friction force experienced by theparticles. The above-mentioned hydrodynamic study,and also the experimental data of Verver and vanSwaaij (1986a), however, clearly indicate that theinfluence of particle shielding phenomena decreasesconsiderably with increasing particle diameter. There-fore, a smaller difference between experimental andcalculated k,a values may be expected for largerparticles.

This is supported by a study of Verver and vanSwaaij (1986b), in which gas-solids heat transfer wasinvestigated under trickle flow conditions in a column(cross-sectional area 0.15 x 0.15 mZ) containing aregularly stacked packing of bars with a square cross-sectional area of 0.02 x 0.02 m, while using 370 pmsand particles for the solids phase. The obtainedexperimental values of the heat transfer rate constant,aa, were only about a factor of three smaller than theones calculated from the Ranz-Marshall correlationfor heat transfer (Ranz and Marshall, 1952).

Kato et aI. (1983) also report relatively high rates ofgas-solids heat transfer for counter-current flow of

117

8/3/2019 Kiel93mass

2/9

118 J. H. A. KIEL et a l .w et activated alumina spheres (3 17-832 pm diameter)and hot air in a bed of open-end cylindrical screenpackings (equivalent diameter 3.61 cm). The heattransfer coefficient a was determined from the inletand outlet gas temperature, assuming (i) the evap-oration rate of water from the spheres to be deter-mined by gas-solids mass and heat transfer only(constant drying rate period), (ii ) the solids temper-ature to be equal to the wet-bulb temperature of theinlet gas, and (iii ) the effective area for heat transfer tobe equal to the external surface area of the spheres.They found a to increase with increasing particleReynolds number, and also with decreasing averagesolids hold-up, 8_ For very low values of fl(< 0.00 l),the a values approximately agreed with the valuescalculated from the Ranz-Marshall correlation (seealso Fig. 7).Probably, the actual mass transfer rates for coun-ter-current flow of gas and mill imetre-sized particlesin a GSTFR can be estimated more accurately fromthese heat transfer data, while making use of theChiIton-Calbutn analogy [Chilton and Colburn,1934), than from an extrapolation of the mass transferdata for small particles. However, in case of a differentpacking configuration and different particle proper-ties (density, diameter) this estimation may still berather rough. Moreover, radiation and heat transferbetween gas and solids via the packing may haveinfluenced the gas-solids heat transfer measurements,and do not have a counterpart in case of mass transferexperiments. Therefore, the present study was carriedout to determine the gas-solids mass transfer for thespecific conditions of the gas-solid trickle flow ab-sorber in the bench-scale plant which was buil t toinvestigate the overall performance of the flue gastreating process. Gas-solids mass transfer rate con-stants were evaluated f rom adsorption experiments, inwhich previously dried 4 .& molecular sieve particleswere contacted in the absorber of the bench-scaleplant at ambient temperature, with a nitrogen flowcontaining 0.6-1.5 vol% water vaponr.

2. THEORYIn a gas-solid trickle flow reactor, the interactionbetween the upwards flowing gas and the downwardsflowing solid particles is very complex and diff icult todescribe. Some of the flow phenomena causing thiscomplexity have been discussed previously (Kiel andvan Swaaij, 1989), e.g. the turbulent flow pattern of thegas phase in the presence of large wakes beyond thepacking elements and the previously mentionedformation of trickles. In a simple approach, however,the overall gassolids mass transfer can be describedmaking the following assumptions for the gas and thedilute solids flow:(a) The solid particles are spherical and flow down-wards with the time-averaged solids velocity

u, = P, = $#

(b) The particles are considered to flow indi-vidually without any mutual interference oftheir concentration boundary layers.(c) The gas Aow is independent of the presence ofsolid particles.(d) The upward gas velocity is constant and equaltoGug=--.&P&3

With these assumptions, the total interfacial area isequal to the total external surface area of the solidparticles and the gas-solids mass transfer coefficient,kg, is constant throughout fhe column. k, can becalculated from the correlation of Ranz and Marshall(1952) for a single sphere in an undisturbed gas flowaccording to

Sh = g = 2.0 + 0.6Re2Sc3Awith the Reynolds number defined as

In fact, both the local gas and solids velocity and,therefore, the local sl ip velocity, lu, - u,), will differfrom the constant values defined above. In a hydro-dynamic model presented earlier (Kiel and vanSwaaij, 1989), the overall effect of these different localvelocities and of particle shielding on the gas-solidsmomentum transfer is accounted for by defining aneffective gas velocity according to

in which 5, the hydrodynamic effectiveness factor, isan empirical parameter. Values of r were determinedfor various conditions by a comparison of experi-mental and calculated values (using the hydrodyn-amic model) of the average solids hold-up, B, atrelatively high values of the gas mass flux, G. In thecase of a packing type as applied in this study, andwith glass beads for the solids phase, < was found tobe 1.2-1.5 for a particle diameter of 200-750 pm and asolids mass flux of l-2 kgm- z s-r. Obviously, theactual momentum transfer was larger than the onecalculated using the gas velocity, u, = G &pa. Basedon these results, the average mass transfer coefficient,k,, may be expected to be slightly higher than the onecalculated according to the simple approach pre-sented above [eqs (l)-(4)]. On the other hand, how-ever, a possible mutual interference of the concentra-tion boundary layers of different particles will lead tolower values of k,.In conclusion, it is unlikely that the simple modelbased on the Ranz-Marshall correlation will give anaccurate description of gas-solids mass transfer in agas-solid trickle flow reactor. However, a generalmass transfer correlation more tailored to the specialcase of gas-solid trickle f low is not available yet.

8/3/2019 Kiel93mass

3/9

Mass transfer between gas and particles in a gassolid trickle flow reactor 119Furthermore, a comparison of the experimental masstransfer data with the values calculated from thissimple model can be very fruitful, because it enables adiscussion on the influence of phenomena like particleshielding and mutual interference of concentrationboundary layers.To determine the actual average gas-solids masstransfer coeffi cients from the adsorption experimentsin the gas-solid trickle flow reactor (GS TFR), asimple one-dimensional two-phase model was used.The trickle-phase model, introduced by Verver andvan Swaaij (1987) to account for the formation oftrickles, was not applied because the influence ofparticle shielding phenomena was expected to besmall for the millimetre-sized particles investigated.Radial eff ects such as segregation over the columndiameter and solids-wall interactions are lik ely to benegligib le due to the good radial (re-)distributionproperties of the regularly stacked packing applied.The amount of axial dispersion in the gas phasemay be estimated from experimental data presentedby Roes and van Swaaij (1979a) and Noordergraafet al. (1980) f or counter-current flow of air and 70 pmfluid cracking catalyst particles in a packed column of0.015 m Pall rings and in a baffle column, respectively.Based on their experimental results, it seems reason-able to assume that the height of a gas-phase mixingunit will approximately be equal to the height of 1 to 2packing layers at the high superficial gas velocitiesapplied (2 0.35 m s-l). This assumption results in agas-phase Ptclet number of 27-54 for the 27 cm col-umn and 53-106 for the 53 cm column appl ied in thepresent study, i.e. a distinct plug flow behaviour of thegas phase. Axial dispersion in the solids phase hardlyaffects the reactor performance if the change in watervapour loading of the particles during their fallthrough the GS TFR remains relatively small.In the case of plug flow for both phases, the watervapour concentration in the gas phase is given by thefollowing differential equation:

u$ + &C - ci) = 0.I ts boundary condition is: C = Cj, at z = 0. The axialcoordinate z is taken to be positive in upward direc-tion. k ,a is the average rate constant for the gas-solidsmass transfer and Ci the water vapour concentrationat the gas-solids interface. The specific interfacialarea, a, is supposed to be equal to the specific externalsurface area of the particles, which is calculated fromthe experimentally determined average solids hold-up, p, according to 68Uy-.Therefore, ef fects of particle shielding phenomena ongas-solids mass transfer will appear in the values ofthe average mass transfer coefficient, k ,. Using eq. (6)and calculating a according to eq. (7), k , can be evalu-ated from the experimental values of the inlet andoutlet concentrations of water vapour in the gas phase

provided that the interface concentration Ci is knownas a function of the column height.For the case of H,O loadings of the porous molecu-lar sieve particles close to zero, the equilibrium watervapour concentration will be negligible comparedto inlet vapour concentrations of Cl, = O&1.5 ~01%and outlet vapour concentrations of C,,, > 0.2Ci,, asapplied in this study (see the adsorption isotherms ofthe applied molecular sieves presented in Fig. 1).Therefore, initially all the water vapour transportedfrom the bulk of the gas phase to the particles will bereadily adsorbed close to the particle outer surface.The adsorption rate will be completely determined bygas-solids mass transfer and the interface concentra-tion Ci may be taken equal to zero. Solution of eq. (6)then yields

k, = - 2 In Wo,t/G,). (8)Due to a limited pore diffusion rate, however, the

amount of water vapour adsorbed will not be homo-geneously distributed over the relatively large-sizedparticles. A radial concentration gradient of adsorbedH,O will develop, with the concentration increasingat increasing radial distance from the particle centre.This will cause the interface concentration Ci to behigher than that calculated from the average H,Oloading according to the adsorption isotherm. As aresult, the value of Ci may already start becomingimportant at low average H,O loadings, for which theaverage equil ibrium concentration is. still negligiblecompared to the concentration in the bulk of the gasphase. Basically, it is possible to determine the inter-face concentration Ci as a function of the columnheight if the diffusion coefficients for gas phase dif-fusion and for surface diffusion inside the molecularsieve particles are known. This is not the case for themolecular sieve particles applied, however, and deter-mination of these diffusion coefficients was outside thescope of this study.If the actual value of Ci is not negligibly small underthe experimental conditions chosen, then calculationof k , from the experimental inlet and outlet vapourconcentrations according to eq. (8) will result in aconservative estimate because of an overestimation ofthe driving force, C - Ci. Equation (8) then yields anapparent gas-solids mass transfer coeff icient, kt , withk; < k,. The lower the initial HZ0 loading and theincrease of the loading in the column, the closer willk: approximate k ,.

3. EXPERIMENTAL3.1. Adsorbent properties

Tw o different size fractions of 4 A molecular sievespheres manufactured by Grace (type MS 511 andMSS14) were used as the water-adsorbing solidsphase. The particle size distribution (for the small-sizefraction only), the average particle diameter and theaverage particle density (on a dry basis) of both sizefractions are presented in Table 1. Typical adsorptionisotherms for water are given in Fig. 1. Before the

8/3/2019 Kiel93mass

4/9

120 J.H. A. KIEL erai.Table 1. Properties of th e two molecular sieve size fractions a pplied

Pore diameter (A) 4Interna l surface area (m2 g-r) *sOlI640 pm s ize-fraction (Grace MS51 1)Pa rticle size distribut ion (from sieve ana lysis)

Cumulatived (low6 m) wt % wt%< 420 0.2 0.2420-500 2.7 2.9

500-600 37.1 40.0600-707 26.2 66.2707-850 33.0 99.2850-900 0.7 99.9>900 0.1 109.0

Average particle diameter (10e6 m) 640Average appar ent density (kg rnm 3) 1533Termin al velocity in N, at 25C1 at m (ms-) 3.42200 pm size-fra ction (Grace MS514)Particle diameter range (lo- 6 m) 2000-2360Average particle diameter (10e6 m) 2200Average appa rent density (kg m -s) 1270Termin al velocity in N, at 25C,1 at m (ms-) 8.6

molecula r sieves were applied in th e adsorpt ion ex-periments, they were first dried for approximately 3 hin a separate fluid&d bed operated with dry air at300-350C. Then the heating as well as the air supplywere switched off , and the molecular sieves werecooled to 100-150C. Subsequently, they were col-lected in an air-tight vessel and allowed to cool furtherto ambient temperature. From thi s air-tight vessel,they were finally fed into the upper storage vessel ofthe experimental set-up (see Fig. 2). After each pass ofthe molecular sieves through the packed column dur-ing an adsorption experiment, this drying procedurewas repeated to ensure the same low level of initialHz0 loading in all experiments.3.2. Experimental set-upThe experimental set-up is shown in Fig. 2. TheGS TF section (5) contained a packing configurationconsisting of regularly stacked, 0.01 m diameter cylin-

Fig. 1. Typical adsorpt ion isotherm s for water on GraceMS511 and Gra ce MS514 molecular sieves.

Fig. 2. Experime nt al set -up. Pa cked colum n: cross-sectionalar ea 0.06 x0.06 m*, packing length 0.53 or 0.27 m.

drical bars made of stainless steel. The applied totalpacking height was 0.53 or 0.27 m.The solids were supplied bat chwiae to allow int er-mediate regenerat ion in a separat e fluidised bed asdescribed in Section 3.1. A specially designed solids

8/3/2019 Kiel93mass

5/9

Mass transfer between gas and particles in a -lid trickle flow reactor 121feed unit (2), similar to the one described by Horsleyand Rothwell (1972), provided a constant solids flowrate. The solids feed pipe (3) ended just above thepacking to minimise the initial water vapour loadingof the sorbent particles. Despite the presence of onlyone feed point for the solids, a good radial distribu-tion of the solids phase was achieved within approx-imately five packing layers due to the good radialdistribution properties of the packing itself. The solidsmass flow rate was measured by collecting the solidsflow below the GSTF section in a sample bottle (8)during a certain time interval, and subsequentlyweighing the obtained sample. The average solidshold-up in the packed section could be determined bysimultaneously closing two guillotine valves (4), onejust above and the other just below the packing.The gas phase consisted of 0.6-M ~01% watervapour in nitrogen. Water was supplied by acalibrated tubing pump to an evaporation vesselplaced on a stove. The resulting water vapour wassubsequently mixed with technical grade nitrogen(UCAR) by means of a sprayer. A gas distributor (6),consisting of two horizontal pipes with a closed endand a regular pattern of 1 mm holes on the top side,was used to achieve a good initial gas distribution inthe column.The outlet water vapour concentration was deter-mined by withdrawing a small gas sample (about50 ml min) from just above the packing and leading itto a hygrometer (Test0 6400). This instrument meas-ures the relative humidity and the temperature of thesample simultaneously. The relative humidity (RH) ismeasured with an accuracy of t_ 0.02 for RH= 0.05-0.98 and the accuracy of the temperaturemeasurement is + O.lYC. Experiments with RHvalues outside the range of 0.05-0.95 were not takeninto account. The inlet water vapour concentrationwas always determined by measuring the outlet con-centration at zero solids flow rate.

4. RESULTS AND DJS CUSSION4.1. HydrodynamicsIn Fig. 3, experimental values of the average solidshold-up, B are presented for both size fractions anddifferent solids mass fluxes. Also indicated is the gasmass flux, for which the gas velocity in the minimalopen cross-sectional area of the packing (which is50% of the total cross-sectional area of the column) isequal to the terminal or free-falling velocity of thesolid particles (G = p,u,/2). It appears that the load-ing regime, characterised by a sharp increase of theaverage solids hold-up, 8, at increasing gas mass fluxG, starts at relatively low G values (approximately atG = p,u,/4). This is probably caused by a combina-tion of limited particle shielding and relatively highsolids hold-up values. Verver and van Swaaij (1986a)obtained $ vs G curves for 70 pm diameter fluidcracking catalyst particles flowing over a regularlystacked packing of bars with a 1.4 x 1.4 cm cross-sectional area. For solids mass fluxes ranging from0.21 to 0.75 kgm~zs-, they found the loading

1.5 o 2.07kgm s

2.0Qy$y3s r 1.5

Fig. 3. Average solids hold-up vs gas mass flux at ambientconditions for both molecular sieve size fractions. The sym-bols rcpr eacnt ex perimenta l values, while the lines are caku-lated from the hydrodynamic model present ed by Kiel andvan Swaaij (1989). Best-fit values of the two empirical para -meters are given in Table 2. Also indicated is the gas msssflux, for which the gas velocity in the minimum open cross-sectional area of the packing (which is 50% of the total cross-sectional area of the column) is equal to the terminal velocityor the solid prticles (G = pou1/2).

regime to start at a much higher G value of about1.5~~~~. Apparently, the influence of particle shieldingand agglomeration is considerably larger for thesesmall particles than for the millimetre-sized particlesinvestigated in the present study. Figure 3 shows, inaddition, that the start of the loading regime shiftsslightly to lower G values at increasing S. This may becaused by the corresponding increase of fiThe experimentally obtained B-values were used toobtain best-fit values for the two empirical parametersof the one-dimensional hydrodynamic model, viz. thepreviously mentioned hydrodynamic effectiveness fac-tor,

8/3/2019 Kiel93mass

6/9

122 J. H. A. KIEL e t a l .Tabl e 2. Best-fi t values of the two empirical parameters of the hydrodyn-amic model f or the two molecular sieve size fractions at different solidsmass f luxes (us,, is positive in downward direction)

(lcgmSzs-) (m?) c [see eq.(5)]640 diameter fractionrn

2200 hrn diameter fraction

0.11 - 0.08 1.60.41 - 0.06 1.60.92 - 0.03 1.60.43 - 0.20 1.80.90 - 0.17 1.8I .43 - 0.15 1.8

solids mass fluxes shows similar trends as reported byKiel and van Swaaij (1989). First, the initial solidsvelocity, u.e, increases at increasing S, which isatt ributed to an increasing part icle-par ticle inter-action when th e par ticles are bouncing on the packingelemen ts. Second ly, t he 2200 pm size fraction yields alower value for y,, a nd a higher value for c than th e640 pm size fra ction at t he sam e S. This is related toth e lower nu mber of part icles flowing t hrough thecolumn for th e large-size fraction, which results in lesspar ticle-part icle intera ction during the bouncing ofpart icles on packing elements a nd less part icleshielding during t heir fall from one packing elementto another.

In summary, th ese hydrodynamic measurementsar e clearly in agreement with the conclusions dra wnabove from the literatu re. The millimetre-sizedmolecula r sieve pa rt icles show only a limited degr ee ofpart icle sh ielding, resulting in relatively lar ge negativevalues of the initial solids velocity, us0 (the pa rt iclesbouncing) an d high values of th e hydr odynam ic effect-iveness factor, 5. The values of 5 = 1.6 for th e 640 pmsize fraction an d e = 1.8 for th e 2200 @rn size fra ctionindicate that the average mass transfer coefficient mayeven be higher than t ha t calculated according to thesimple ap proach rep res ent ed by eqs (l)-(4).

4.2. Gas-solids mas s tr an sferThe first series of adsorption experiments was

carried out with a packing length of 0.53 m u sing th e640 m molecula r sieve size fraction for th e solidsphase. Experimen tal ran ges for th e gas and solidsma ss flux wer e set by th ree condit ions, viz. (i) a signi-ficant decrease of the water vapour concentr at ion inth e gas pha se (CoUt /Ci. < 0.9), (ii) at leas t 5% rela tivehum idity at th e gas outlet, and (iii) stable counter -curr ent opera tion (no loadin g, s ee Fig. 3). By app lyingeq. (8) an d, th us, neglecting th e possible influence ofpore diffusion, the appa rent gas-solids mass tra nsfercoefficient, k:, was determined from the measuredinlet an d outlet water vapour concentr at ions. Fr omexperiments with different inlet concentr at ions, viz.C, = 0.6, 1.0 an d 1.5 vol%, it was found th at th e ktvalue increased with a decreasing CI,. This indicatedthat it was not justified to neglect the pore diffusionresistance and to take th e interface concentr at ion Ciequal to zero.

To illustrate the influence of the pore diffusionresistan ce, the experimental k: values are shown inFig. 4 as a function of the am oun t of water adsorbedon t he molecular sieve part icles, or th e increase of theH,O loading, C,,., - tin, during th eir fall thr ough thepa cked column . [,., - ci. was calcula ted accordin g t o

c.., Ti. = _HZG(G - CO,).To eliminat e th e gas-solids mass tr an sfer contr ibu-tion in th e ent ry section, th e inlet water vapourconcentra tion C, was corr ected for adsorption in tha tsection. Between th e gas distributor and t he packing(colum n length 0.12 m), th e following condit ions wer eassumed to be valid:

-Gas--solids mass tra nsfer is th e rat e-determ iningstep.

-Axial dispers ion is negligible in both phas es.-The effective interfacial area for mass tran sfer isequal to the external surface area of the particles.-The Ranz-Marsha ll correlat ion applies for th e

mass transfer coefficient, kg.-The gas velocity is equa l to th e sup erficial gas

velocity in the column.-The solids velocity is equa l to th e time -avera ged

velocity, II,, as calculat ed from t he hydrodyn -amic model with < = 1 and us0 as presented inTable 2.

k l 0.30

ii%

0.25

0.200.150. LO0.05

/0.00 1 - . - ; . . I . 1 . - . I

0.0 0 . 5 1.0 1.5 2.0c-r,kg 30 1 100 kg ads

Fig. 4. Values of the apparent gas-solids mass transfercoefficient, kf , as calculated from the experimental valuesof C,_/C,, by eq. (8), vs the increase of the H,O loadingC,,., - Cs for the 640 q ;iz&ra;ion at different gas mass3

8/3/2019 Kiel93mass

7/9

Mass transferbetween gas and part icles n a gas-solid tr ickle flow r eact or 123Accordin g to th ese ass um ptions, a bout 15% of th etotal decrea se in water vapour concentr ation tookplace in th is entr y section in case of the 0.53 mcolumn . This per centa ge will be even lower if, to acerta in exten t, pore d iffusion is also involved in thetransfer process.

In Fig. 4, th e increas e of k: with a decreasingg__,,t C,. clear ly r eflects t he influence of pore diffusion.But th e increase of k: with increasing gas mass flux,G, at th e same [.,,, - C,, indicates a distinct in fluen ceof gas-solids mass tra nsfer on the adsorption ra te aswell. The experimenta l results of Fig. 4 ar e n otaffected by the value of the solids mass flux, S. How-ever, S could be varied only over a limited ra nge, viz.from 0.09 to 0.20 kgm-s-l.

To achieve H,O loadin gs which are low enough forth e gas-solids mass tr an sfer to become ra te-determin-ing, some experiments were condu cted with a packingheight of 0.27 m inst ead of 0.53 m, with th e solidsma ss flux, S, var ied be tween 0.19 and 0.38 kg rn-s-l.As expected, these experiment s yielded a furt her in-creas e of k,+ at lower values of &,., - &, but it seemsthat the maximum values of k: (= k,) were not yetrea ched. Appar ent ly, th e influence of pore diffusionwas st ill considerable. J ust a s for t he 0.53 m column,variation of S within the given limited range yieldedthe same k: vs con, - Tin curve. Unfortunately, theactual avera ge gassolids mass tra nsfer coefficient, k,,cannot be deduced from th e experimental da ta pre-sented in Fig. 4.

This pr oblem is illust ra ted in F ig. 5, wher e somespeculative extra polations of the observed kz vsle., - &,, curves a re sketch ed for th e loadin g regime&.I - tin < 0.5 wt%, which can be expected if th eintr insic adsorpt ion is inst an ta neous an d if cj. = 0. Atvery low Hz0 loadings, th e interface concentra tion Ciis equal to zero and t he adsorption ra te is completelydeterm ined by gassolids mass tra nsfer (kt = k,). Ifthe H,O loading increases, pore diffusion star ts tobecome importa nt . As a cons equen ce, Ci > 0 an dk: +c k,. The shape of the curve for higher H,O

1.5 2.0a-r

k~H20/100k~adsFig. 5. Illustration of the problem of how to derive the valueof kd from experimentally obtained values of k:. Speculati veextrapolations of the apparent gassolids mass transfer coef-ficient, k;, to Loti - Cm= 0 are shown. The experimentaldata are Identical to the ones presented in Fig. 4 for the64Opmsize fraction at G = OAOkgm-*s-l.

loadin gs, [, will depen d on t he way in which th e porediffusion coefficients, for gas phase diffusion of watervapour an d for surface diffusion of absorbed wat er,are related to c. Finally, kt = 0 will be reached at aH,O loading equal to th e satu rat ion capacity of th emolecular sieve part icles for the applied t empera tu reand inlet water vapour concentr ation. Since the dif-fusion coefficients ar e un kn own for th e molecula rsieve par ticles app lied, and th e initial H,O loadin g,tin, ma y deviat e from zer o, extr apolat ion of kt todeterm ine t he actua l a verage mass tra nsfer coefficient,k,, at [ = 0 is impossible.

Nevertheless, the experiments do provide conserva -tive estimates for k ,. The straight lines in Fig. 4 werecalculated from t he experimenta l data by linearregression. For the three mass fluxes investigated,these straight lines appear to have the same slope.Conservative estimates for k , are taken to be equal tothe values of kt at co., - ci, = 0.5 wt% accordin g toth ese lines.Experiment s with th e 2200 pm molecular sieve sizefraction we re carr ied out only for a pa cked columnlength of 0.53 m. The solids mass flux, S, was variedbet ween 0.20 an d 0.74 kgm -s- for gas ma ss fluxesG = 0.40-0.93 kgm -s- , a nd bet ween 1.15 an d1.84 kgm -*s-l forG = 1.11-2.78 kgm -2s-.InF ig.6, th e experiment al k f values ar e given as a function ofi;,,,l - &. for differ en t ga s m ass fluxes, G. Both kz and[,., - &,, were correct ed for th e adsorpt ion in theentr y section bet ween the gas distributor and t hepacking accordidg to th e assum ptions describedearlier for t he 640 Fr n size fraction. It appear s tha t k:is nea rly cons ta nt (0.05-0.07 m s-l) for all values ofI,., - iin. The H ,O loadin g itself, however, in creaseswith increasing gas mass flux, G, and, at a fixed valueof G, with a n increase of th e inlet wat er vapourconcent ra tion (C,, = 0.6, 1.0 an d 1.5 ~01%). Withinthe rath er nar row experimental ranges, no dist inctinfluence of the solids mass flux on kz or [,, - &,, wasobserved. Most likely, th e influence of pore diffusionwas also cons idera ble for th is 2200 pm size fraction.The presented kt values are then merely conservative

0.00 I I . . I . I . I . I0.0 0.2 0.4 0.6 0.X 1.0

&u-r+,kg H20/ 100 kg ads

Fig. 6. Values of kf , as calculated from the experimentalvalues of C,,/C,, by eq. (8). vs the increase of the H,Oload% S.., - (,,,. for the 2200 p size fraction at differentgas mass fluxes, G.

8/3/2019 Kiel93mass

8/9

124 J. H. A. KEL et al.estimates of the actual average mass transfer coefi-cients, k,.

Figure 7 shows a compa rison between th eSher wood num bers based on th e experimenta lly de-termined, conservative estimates of k, and Sherwoodnum bers calculated from the Ranz-Marsh all correla-tion according to th e rough a pproach presen ted inSection 2 [eqs (l)-(4)]. It app ear s t ha t th e cons erva -tive estimat es amount to 40-80% of th e theoretical Shvalues.

As discussed in Section 4.1, th e hydr odynam icmeasurements indicate that k , values should havebeen measured, which are somewhat higher than theones calculat ed from eqs (l)-(4) if th e ad sorption ra tewas completely det ermined by gas-solids mass tran s-fer, without any mutu al interference of th e concentr a-tion bounda ry layers of different par ticles. Unfortu -nately, it remains unclear which part of the differencebetween the expected and the actually measuredvalues of k , is due to the pore diffusion resistance andwhich part to particle shielding, causing mutual inter-ference of concent ra tion bounda ry layers. However,from th e results of th e hydrodynamic measu rement s itcan be concluded tha t the influence of particleshielding with interfering concentr ation boun dar ylayers of differen t par ticles on gass olid ma ss tr an sferis very limited for the millimetre-sized par ticles an dth e experimental conditions investigated.

100

Sh

10

1

0.1

Fig. I. Particle Sherwood number, Sh, vs particle Reynoldsnumber, Re. The open symbols represent values obtainedfrom the experimental values of k: at C, - cr. = 0.5 for the640 jan molecular sieve size fraction. For the 22OD~m sizefraction, Sh ranges are indicated b ased on the experimentalranges of k :. Also shown are (i) the theoretical curve derivedby using the Ranz-Marshall correlation according to therough approach presented i n Section 2 and (ii ) the experi-mental data on gas-solids heat transfer reported by Ververand van Swaaij (1986b) and Kato et al. (1983) taking theNusselt number, Nu, equal to the Sherwood number, Sh, andthe interfacial area equal to the solids external surface area.From their experimental results, Kato et al. defiv@ thefollowing correlation: Nu = 2.38 x IO -R e[(l - fi )//?],9,n = 2.48[(1 - B)lp]-=.

5. CONCLUSIONSThe expected high ra tes of gas-solids mass tra nsfer

for count er-curr ent flow of gas and millimetre-sizedsolid pa rt icles ha ve been confirmed by th e experi-ment al results. Values of th e avera ge gas-solids masstransfer coefficient, kg , were calculated from thedecrease of th e water vapour concentr at ion over th eheight of th e gas-solid tr ickle flow react or by using asimple plug flow model. They amoun t to 40-80% ofth e theoretical values obtained by applying th e well-known Ranz-Marsh all correlat ion for a single spher ein an un distu rbed gas flow. In th e plug flow model, itis assu med th at(i) gas-solids mass tr an sfer is th e onlyresistan ce for the ad sorption and (ii) th e effective areafor mass transfer is equal to the external surface areaof th e spheres. Unfortu na tely, it appea red to beimpossible to choose th e experimen ta l conditions in away tha t justified th e first assu mption. The porediffusion resistance could not be eliminated com-pletely. Consequen tly, th e ma ss tra ns fer coefficient spresen ted are conser vative est imates.

Despite the remaining influence of the pore dif-fusion res ista nce, however, it can be concluded fromth e experimental data on gas-solids mass tra nsfer incombination with th e experimenta l da ta on hydrody-nam ics (gas-solids momentu m tra nsfer) tha t the influ-ence of particle shielding with interfering concentra-tion bounda ry layers of different pa rticles was smallfor th e millimetre-sized part icles and th e experimentalconditions investigated. Gas-solids mass tran sfer aswell as gas-solids momentu m tra nsfer were mainlydetermined by single-particle Aow behaviour.

NOTATIONspecific int erfacial ar ea, mz m,;&,Orgas-pha se concentr at ion, mol m- 3average particle diameter, mmolecular diffusion coefficient, m s-rcoefficient of axia l disper sion, mz s-rgas mass flux, kgm-s-(avera ge) gas-solids ma ss tr an sfer coef-ficient , m s - appa rent gas-solids mass tr an sfer coeffi-cient, m s- Ipacking length, mmolar mass, kg mol - rpower of Re as applied by Kat o et al. (1983)solids ma ss flux, kg me2 s- local gas velocity, m s- reffective ga s velocity, m s -local solids ve locity, m s- time-aver aged solids velocity, m s-tterm inal velocity, m s- sup erficial gas velocity, m s- 1axial coordina te, m

Greek symbolso( aver age gassolids hea t tr an sfer coefficient ,WmmZK-

s aver age solids hold-up, m3 m .&.,

8/3/2019 Kiel93mass

9/9

Mass transfer betweengas and particles in a gassolid trickle flow reactor 125F

average packing porosityHz0 loading, k g H,O/lOO kg ads

I thermal conductivity, W m- 1 K-lp dynamic viscosity, kg m- s-c hydrodynamic effectiveness factor [seeeq. (31P density, kg rns3Subscripts0 initial conditionsB gas phase conditionsi conditions at the gas-solids interfacein inlet conditionsout outlet conditionss solids phase conditionsDimensionless groupsNu particle Nussel t number (= CU.&/&)P% gas-phase P&let number (= GL/sp,D,,)Re particle Reynolds number

(= P ,&l u* - ug I/P ,)SCSh

Schmidt number (= pJ p,D,)particle Sherwood number (= k,dJD,)

REFERENCESChilton, T. H. an d Colbum, A. P., 1934, Mass transfer(absorption) coefficients. nd. Engng Chenc. 6,1183-1187.Guigon, P., Large, J. F. and Molodtsof, Y., 1986, Hydro-dynamics of raining packed bed heat exchangers, inEncyclopaedia of Fluid Mechanics (Edited by N. P.CheremisinoR ), Vol. 4, Chap. 39. Gulf, Houston.Horsley, D. M. C. and Rothwell, E., 1972, A laboratory scale

feeder for non-cohesive powders. Powder Technol. 6,117-120.

Kato, K, Onozawa, I. and Noguchi, Y., 1983, Gas-particletransfer in a dispersed bed. J. them. Engng Japan 16,l-B-182.Kiel, J. H. A.. 1990. Removal of sulphur oxides and nitrogenoxides from flue gas in a gas-s&id trickle flow reactor.Ph.D. thesis, University of Twente, Enschede.Kiel, .I. H. A. and van Swaaii, W. P. M., 1989, A theoreticalmodel for the hydrodyn&nic.s of gas-solid trickle flowover regularly stacked packings. A.1.Ch.E. Symp. Ser.85(270), 11-XKiel, J. H. A., Prim, W. and van Swaaij, W. P. M., 1990, Fluegas desulphurization in a gas-solid trickle flow reactorwith a regenerable sorbent, in Process Technology Pro-ceedings Vol. 8: Gas Separation Technology (Edited byE. F. Vansant and R. Dewolfs), pp. 539-548. Elsevier,Amsterdam.Kuczynski, M., 1986, The synthesis of methanol in agas-solid-solid trickle flow reactor. Ph.D. thesis, Univer-sity of Twente, Enschede.Noordergraaf, I. W., Roes, A. W. M. and van Swaaij,W. P. M., 1980, Proceedings 3rd International Conferenceon Fluidization, New Hampshire.Ram, W. E. and Marshall, W. R., 1952, Evaporation fromdrops. Chem. Engng Prog. 48(3), 141-146 (Part I); 48(4),173-l 80 {Part II).Roes. A. W. M. and van Swaaij, W. P. M., 1979a, Axialdispersion of gas and solid phases in a gas-solid packedcolumn at trickle flow. C/tern. Engng J. 18, 13-28.

Roes, A. W. M. and van Swaaij, W. P. M., 1979b, Masstransfer in a gassolid packed column at trickle flow.Ghem. Engng J. 18, 29-37.Verver, A. B. and van Swaaij, W. P. M., 1986a, The hydro-dvnamic behaviour of eas-solid trickle flow over a repu-I&ly stacked packing. Fowder Technol. 45, 119-132. yVerver, A. B. and van Swaaii. W. P. M., 1986b. The heat-transfer performance of gas-solid trickle flow~over regu-Iarly stacked packings. Powder Technol. 45, 133-144.Verver, A. B. and van Swaaij, W. P. M., 1987, The gas-solidtrickle-flow reactor for the catalytic oxidation of hydrogensulphide: a trickle-phase model. Chem. fingng Sci. 42,435-445.