LIQUID PHASE MASS TRANSFER IN PACKEDBED REACTOR WITH COCURRENTGAS-LIQUID DOWNFLOVT

Tsutomu HIROSE, Mikio TODA** and Yuji SATODepartment of Chemical Engineering, Kyushu University, Fukuoka

Volumetric absorption coefficient (ka)ig, specific inter facial area aig and mass transfer coef-ficient kig were measured for two-phase cocurrent flow of O2-water and CO2-NaOHsystems

in a column packed with glass spheres of 3 different sizes (2.59-12.2mm). Values of (ka)igobserved were so high as to be that can be hardly attainable in conventional gas-liquid contactors.This is due to large aig of small bubbles dispersed in liquid where aig very often exceeds thegeometrical surface area of packing. Values of kig range from 2 to 8 xlQ~4m/sec, which arecomparable to that of circulating bubbles in the usual systems. The effect of superficial gas veloc-ity on (ka)ig and aig is much greater than that in a countercurrent packed column, while theeffect of liquid velocity is approximately same. A liquid-phase energy loss Ei per unit volume ofliquid contained in a bed was newly defined as a measure of microscopic flow intensity and wasused for discussion and correlation of mass transfer properties. It was found that the bubblediameter is proportional to £T 2/5.

1. Introduction

Advantages of packed column reactors with cocur-rent gas-liquid flow have been pointed out by manyinvestigators4'5 7 10 14 163. This type of reactor may be

employed in a) gas-liquid reaction with inert packing,b) gas-liquid reaction catalyzed by packing solid7},

and c) solid-catalized gas reaction in inert liquid phaseintroduced for temperature control143. In any case,the reactant gas must first be dissolved in liquid

for the reaction to proceed. Thus, gas-liquid masstransfer is one of the most fundamental steps indetermining the overall reaction rate as well as the

intrinsic chemical kinetics and liquid-particle (catalyst)mass transfer, if any.

Volumetric absorption coefficient (ka)ig, specific

gas-liquid inter facial area aig and mass transfer coef-ficient kig have been used for characterizing the masstransfer performance of various gas-liquid contactors.

However, surprisingly little is known about thesefactors for coccurrently contacting packed columns.No prediction correlations are available except thoseof Reiss10) for (ka)ig and of Gianetto, Baldi and

Specchia5) for aig. As for ktg, not even the order ofmagnitude has been reported yet. Thus, much more

investigation is desired to understand the masstransfer behaviour.

* Received on July 23, 1973Presented at the First Pacific Chem. Eng. Congress, Kyoto,

Japan, Oct. 10-14, 1972** Daicel Ltd., Himeji

Fromthis point of view, the purpose of the presentarticle is to present new data and correlations of

gas-liquid mass transfer properties and to discuss theresults in the light of the fluid flow behaviour reportedpreviously12 '133.

2. Experiments

A schematic diagram of the experimental apparatusis shown in Fig. 1. Since no appreciable effect ofcolumn diameter was found in the fluid flow charac-teristics12il3), one column of 65.8mm5* I.D. and0.25 m long was used. The column height was maderather short to prevent the attainment of equilibriumbetween phases in the exit stream. The range ofvariables investigated is summarized in Table 1. Thedetails of the distributor head and void fraction ofbed were reported previously12\

D.O.METER.LIQUIDSAMPLING I""* IG-Ch"*

K MIXINGPORTION]

XAXAXt-+±-tt__CO2

I _-N2

_1 CO L UM N ^WTT

BY- PASS - ^ ^^DRAIn JT:FEED *"*** SETTLERfep ^AS-LIQUID MIXTURE ^Sfifu^

TANK | ^ LINE ^Jd^L^°2 r, m IRETURNLINE ,, ~á"

I SPARGER-mJ-^) © MLIQUIDLINE 1L1 à"- ^ ^-^ ^D.0.METER, -'

LIQUID SAMPLING

Fig. 1 Schematic diagram of apparatus for masstransfer measurements

VOL.7 NO. 3 1974 187

Table 1 Range of variables investigatedColumn Packing Superficial velocity

Measurement Solute Liquid Dia. Height Dia. Void Gas Liquid Temp.Dx103[m] h[m] dx103[m] e[-] Ua[m/sec] Ui [m/sec] t[°C]

Volumetric absorption O2 H2O 65.8 0.25 2.59 0.370 0.05-1.0 0.01-0.2 - 15coefficient 5. 61 0. 391

8.01 0.40812.2 0.438

Specific inter facial CO2 0.1-1 N 65.8 0.25 2.59 0.370 0.01-1.0 0.01-0.1 30area NaOH 5. 61 0. 391

12.2 0.438

10°- d=12.2mm | jf j£'_I Ug(m/sec] å Oy£> jxT -- O0.980 I/ / D:

å¡0.208 FLOWcr ^/ J*S ~

<>0.0A9 <5 ^/! P/

$L I GASCONTINUOUS V/ >^! Icn _ FLOW PV/>* DISPERSED^ _ Jj\ |BUBBLEFLOW

10~2= <&' #1/2"SPHERE20) =

5 oo^^« å 1/2*RASCHIGRING15) =

3X1O3I<MMII 1 '''"I" 1 III"'II 1

3x10 10 KT 101 2x10

U^ fm/sec)Fig. 2 Typical examples of results for volumetricabsorption coefficient

Volumetric absorption coefficient (ka)ig was de-termined through desorption mass transfer of dis-

solved oxygen from the presaturated water into thenitrogen stream. An oxygen analyzer (Toshiba-

Beckman Co., Model 777) was immersed in the en-trance stream to detect the inlet concentration Cz°.

Gas-liquid dispersion issuing from the column wasseparated in the bottom and part of the liquid

was led to a liquid line, where another oxygen analyzerwas set to detect the outlet concentration Cn. Since

unfortunately no information is available on the

longitudinal dispersion, the present data were analyzedtentatively in terms of plug flow and volumetric

absorption coefficient (ka)ig was calculated from theequation

(Mi,=(tf*/'0 1n (Cf/Cll) (1)Oxygen partial pressure in the bulk gas phase waspractically zero due to the low solubility. The gas-phase resistance to mass transfer was neglected.Desorption was preferred to absorption since the

latter case was complicated by the longitudinal varia-tion in gas-phase concentration of oxygen due to

pressure drop through the bed.Specific inter facial area aig was measured using a

diffusion-limited chemical absorption of carbon diox-ide into aqueous sodium hydroxide. Carbon dioxidewas diluted with nitrogen so that the total flow rate

5X1CP. , , , , , , ,

d (mm)o 2.59

A 5.61 //o

n 12.2 °/yY&

2Xi62L , _^ , , L_ , 1

2x103 102 nQ fto 10"1 5x10]

Uf Ug^Km/sec)1-6)Fig. 3 Correlation of volumetric absorption coefficientin terms of operating parameters

of CO2 and N2 did not change more than 30 % betweenentrance and exit. Feed gas and liquid were sampledfrom the entrance streams. Outlet liquid was sampledfrom the outlet liquid line while outlet gas samplewas taken after the removal of entrainment drops.Gas (CO2) and liquid (NaOH), respectively, wereanalyzed by gas chromatography and by Warder'stitration. The rate of gas absorption N was determin-ed from the difference of the concentrations of bothNaOHin solution and CO2in bulk gas between theentrance and exit streams, the material balance beingsatisfactorily checked.

Under the condition of a fast pseudo first-orderreaction the absorption rate per unit volume of bedN is given by

N=alglCg V^KCb (2)

To evaluate ai{n arithmetic and logarithmic meanconcentrations, respectively, between entrance and exitwere used for Cb and Cg. The intrinsic reaction rateconstant kr, the diffusion coefficient & and solubilityI, respectively, were estimated for the above deter-mined mean concentration according to Yoshidaand Miura22), Wilke19), and van Krevelen and Hoffti-jzer17).

The mass transfer coefficient kLg for oxygen was

determined by dividing (ka)ig by atg obtained above.188 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

101 d iPULSElBUBBLEl1 ' ' ' ' ' *~ ' ~

[mm]FLOW FLOW2.59 à" O

t k ~5^T a a -

^ T2TT~i"I u I ° o^WT

fa- -1Q1! I I | I | | I I I I |

101 1 02 103 1 0A 5X104Ej£ (Kg-m/sec-m3)

Fig. 4 Correlation of volumetric absorptioncoefficient in terms of liquid-phase energy loss

The requirements for a diffusion-limited first-order

reaction were examined using the resultant kig.

3. Volumetric Absorption CoefficientSome experimental results of the volumetric ab-

sorption coefficient (ka)ig are shown in Fig. 2 togetherwith available data obtained for the correspondingsystems in countercurrent flow15'20). The values of

(ka)ig at low gas flow rate fall on a line extrapolatedfrom countercurrent data. Increase in gas flow rate

increases these values up to ten times their valuesat low gas flow rate.

This strong dependence on gas flow rate is quitea different behaviour from that in countercurrent

flow, where (ka)ig is known to be independent of gasflow rate lower than the loading point. At high flowrate of gas and liquid, some values of (ka)ig exceed1 sec"1, which can hardly be attained in other types

of gas-liquid contactors such as an agitated vesselor a bubble column.

Most of the data were taken under the pulse ordispersed bubble flow regime. At liquid velocitylower than 1 cm/sec the flow approached gas con-tinuous flow, in which it has been reported that(ka)ig decreases rapidly, probably due to the poordistribution of liquid5\ Thus pulse and dispersedbubble flow, containing gas-liquid dispersion, seem

preferable from a mass-transfer point of view.The volumetric absorption coefficient (ka)ig is pro-

portional to £/? 8, as shown in Fig. 2, and is observedto decrease with increasing packing diameter d as

shown in Fig. 3. Thus the present data are correlat-edby

(ka)lg=l.O d-Q-bUl*Ug-* (3)in terms of flow rates and packing size.

Mass transfer properties in two-phase dispersionhave sometimes been related to energy dissipation,in which various geometrical factors may be ex-

cluded from the resulting correlations. For example,such treatment was applied to agitated gas-liquid

contactors by Cooper, Fernstrom and Miller3) andYoshida, Ikeda, Imagawa and Miura21), to two-phasetubular contactors by Gregory and Scott6} and to two-phase flow in packed beds by Reiss10).

When gas flows with a high velocity, as in two-phase flow in a packed bed, a considerable amount

of energy dissipation occurs in the gas phase as wellas in the liquid phase. However, the energy dissi-

pation in the liquid phase is of primary importancefor the present system, the liquid-phase resistance

to mass transfer being controlling. Thus, the liquid-phase energy loss per unit volume of liquid containedin the bed is defined in this work as

El ^(APl gIAh) UlleRl (4)

Strictly speaking, the above-defined Ex is the powergiven to liquid by an external machine (i.e. pump)and is not always equal to the energy dissipatedin liquid phase when energy is exchanged between

gas and liquid phases. However, it may be a goodmeasure to characterize the latter quantity.

When the energy loss Et and the interstitial gasvelocity UJe are chosen as two correlating param-

eters, the correlation shown in Fig. 4 is obtained.

It is explicitly independent of packing size althoughthe packing diameter affects (ka)ig by changing theenergy loss Et. The best-fit line to the present data

is given by(ka)lgls=0 A 63(Ugle)^E^ (5)

for the dispersed bubble flow regime and(ka)lg/e=0 A 35(Ug/e)^E^ (6)

for the pulse flow regime. APlg and Rt necessary forcalculation of Et are evaluated by previously reportedcorrelations12 \

(f>l= V^iV^iW - 30+1. 85r0-85 CORl=0.04 al/3z°'22 (8)

The value of (kd)ig in pulse flow is a little lowerthan that in dispersed bubble flow since the bubble

dispersion does not occupy the whole bed, unlike thecase in the latter regime.

189VOL 7 NO. 3 1974

5Xl0Ar- r i i i i I-i , 1 naaa/vw VOYER et Ql1^~1/2CORRUGATED SCREEn I , , GIANETTO et al. 6mm SPHERE,RING| .* J 5)&BERLSADDLE j g |(ZZD|dODDS etalA) f]L" BERLSADDLE | ^^^

103- XfU^tf n°a Ithic;I |d[ml^T " ^^ ^^ WORK, ° 2-59 - q, /aa SPHERE A 5-61 ^^a I Ia|12.2 I 2x102L5-1^--1 1 l_^ 1 1 l^ 1 1 5x10z 102 101 10° 5x10° Ug (m/sec)

Fig. 5 Correlation of specific inter facial area interms of operating parameters

i r~ i i ~i 1 1 1 1 1 1° D ^EQ.I^HINZE9* d (mm]

10 ^\P n ^\ o 2.59^^-Cdo a * 5.61

2x10~A' 1 1 1 1--i- 1 å -i 1- 1--^ 1

2x10° 101 1 02 103 1 0AEi [Kg-m/sec-m3]

Fig. 6 Bubble diameter calculated from gas holdup andspecific inter facial area

Reiss10) has proposed a correlation (ka)lg=0. 0542(UlJPlJ/lh) (9)

for spheres and rings, which is independent of gasflow rate as well as of packing size. The presentdata included in his reported range of gas velocity(£/z>0.5 m/sec) are consistent with the Reiss10) equa-tion. However, to cover the data at lower gasvelocity, the gas velocity must be included in thecorrelation.

4. Specific Inter facial Area

The specific inter facial area atg was found to beproportional to the square root of liquid flow rate

Ui. Its dependence on packing size and gas flow rateare shown in Fig. 5. The values ofatg decrease withpacking diameter to 0.8 power and increase with gasflow rate to 0.6 power till they tend to flatten at

high gas flow rate as shown in Fig. 5. An empiricalequation is sought as

alg=175d-'-'U^U0^, Ug<0.6m/sec (10)

The gas-liquid inter facial area very often exceedsthe geometrical surface area of packings, indicatinga large contribution of small bubbles in pulse flowand dispersed bubble flow regimes. Some available results are also reproduced in the

figure for comparison. Data of Voyer and Miller18}

and Gianetto, Baldi and Specchia5) were read directlyfrom their figures. Those of Dodds, Stutzman,

Sollami and McCarter4) were evaluated from the tabu-lated absorption rates of CO2 into 2N-NaOHsolu-

tion according to Eq. (2) by the present authors.

The density of gas, if necesssary, was taken as thatof air under atmospheric pressure. The agreementbetween the present data and these results seemsreasonable in spite of the different geometries andsizes of packing. Results of Dodds et al.4) andGianetto et al.5) show the same dependence on gas

flow rate as do the present data, but lower dependenceon liquid flow rate, i.e. 0.3-0.4 power instead of 0.5.The mechanism of the dispersion of bubbles anddrops has been interpreted in the light of turbulence

theory9\ It is assumed that the diameter of a bubbleor drop is controlled by a balance of the kineticenergy of turbulence and the surface energy, i.e.

there exists a critical WebernumberWe^t=p^db/a (1 1)

In Eq. (ll), v2 is the average value of the squaresof velocity differences over a distance equal to the

bubble diameter db and is given byv^ (EigcdbIpcy/3 (1 2)

for an isotropic homogeneous turbulence where theKolmogoroff energy distribution law applies. Sub-stituting Eq. (12) into Eq. (ll) gives

db =ap;^a^5ET2/5gc1/5 (1 3)

Hinze9) determined a=0.725 for the maximumdrop diameter in two coaxial cylinders, and Rodri-guez, Groze and Englen) gave a=0.286 for the averagedrop size in agitated vessels.For the present system (pc^Wkg/m3, <7=7x lO~3Kg/m) Eq. (13) reduces to

db==\ A6x l0~2Er2/5 (a-0.725, Hinze9)) (14)db=0. 5S x l0~2Er2/5

(a-0.286, Rodriguez ^ al.11>) (15)Assuming that all the gas holdup is in the form ofspherical bubbles, the bubble diameter was calculatedfrom the equation

db=6(l -Ri)e/alg (16)where liquid holdup Ri was evaluated by Eq. (8).The results are shown in Fig. 6 and compared withEqs.(14) and (15) for the drop dispersion in thedifferent apparatuses. Data for %>10 are not in-

cluded in Fig. 6 because the values of Rt are close tounity for large % and a large error is produced in

evaluating the term (1-Ri) in Eq. (16). As shown inFig. 6, the bubble diameter in the dispersion in

packed beds under two-phase flow again follows the-2/5 power law of the energy loss in liquid phase.In particular, the numerical agreement with Hinze'sequation, Eq. (14), is interesting.

JOURNAL OF CHEMICAL ENGINEERING OF JAPAN190

It is somewhat unreasonable that the calculatedbubble diameter is sometimes large than the inter-stitial void or the packing diameter. This is inter-

preted by the fact that two-phase flow is in or closeto gas continuous flow at the lowest liquid flow rate(jjl=0.122 cm/sec), for which the equivalent bubblediameter becomes very large. When data in this

region are excluded, it reduces to the more reasonableresult that db/d is smaller than 1/2.

When db is proportional to E^2/5, Eq. (16) is re-written as follows, and finally the interfacial area

dig is related to a two-phase parameter %.az^r2/5ocs(l -i?0=^(z) (17)

The present results are plotted in this manner inFig. 7. Data of Gianetto, Baldi and Specchia5) andDodds, Stutzman, Sollami and McCarter4) fall withina dotted circle. In spite of the wide scatter the

data for different geometries and sizes of packingsfollow a relation of the type of Eq.(17). A sharpdecrease ofaig/Ei/5 for %>5 is due to the correspondingdecrease of gas holdup, l-Ri.5. Mass Transfer CoefficientThe mass transfer coefficient kig for oxygen-watersystem was separated from the volumetric absorp-tion coefficient (ka)ig by dividing by inter facial areaaig9 based on an assumption that atg for water isequal to that for NaOH solution at the same flowrates of gas and liquid despite some difference in

liquid properties. The kig thus determined for about1 5°C (experimental temperature) ranges from 2 x 10~4to 8xl0~4m/sec. This range of ktg is consistent inorder of magnitude with that for circulating bubbles

in free rise2), in bubble columns1} and agitated gas-liquid contactors1). Thus, it is concluded that the

high values of (ka)ig encountered in cocurrent packedcolumns is attributable to large interfacial area atgof small dispersed bubbles, but not to the mass

transfer coefficient kig.Eqs. (3) and (10) for (ka)ig and aig, respectively,

imply kig to be proportional to t/?-3. kig\JJ\-z is

plotted against the gas velocity Ug in Fig. 8, whereit is seen that the effect of Ug is small. kXg de-creases slightly with increasing packing diameter.

The calculated bubble diameter is smaller for smallerpacking at the same flow rates. Thus, according

to the mass transfer theories, kig is expected to behigher for smaller packing, to which the present ex-perimental trend is opposite. This disagreement maybe explained tentatively by the fact that the relative

motion between a bubble and liquid may be restricteddue to narrow channels surrounded by small pack-ings.

Substituting the root meansquare fluctuation veloc-ity a/W given by Eq. (12) and the bubble diameter

E i<r^ ** ¥m o｣ oj

｣CTbd

3 LU10 12 x

ｰ a A * ^ w - A O

10

A D - A U L A s

n

10 ' icr lO ' 5 x%

Fig. 7 Alternate correlation of inter facial area in termsof liquid-phase energy loss

eno R - n

9 k u a ; 4 1

1 ? 0 . 5

0 . 3

> h u 3CD O

｣

ｰb

d = 2 . 5 9 ( m m ) 0 ) <->

ｰt >

0. 3o .2 * n = >* %<

3

C O9 k

ｰｰo0 . 5

0 . 3 ^ S I S *

0 -

蝪

- * - i

o d = 5 .6 1 (m m )

o

d = 8 .0 1 [ m m ]

*v v

V

_ _ m A - -& '

ｫ e ^ 0 5

3

d = 1 2 . 2 [ m m )

I l l I I10 ' 10 ' 10 - 2 x

U g (m / s e c )

U^x iO2(m/sec) X o 蝪 V o A

1. 9 6 3 .6 8 4 . 9 0 9 . 8 0 1 4 . 7 2 4 . 5

Fig. 8 Results of mass transfer coefficient

1 0 J

oa )n

d C m m ) ' : ' ' ' ' r

c

�" 2 . 5 9A 5 .6 1蠑 8 .0 1蝪12.2

E

m

ｫ ? *

1 0 A

1

aｮ

1 0 3

E Q ( K g - m / s e c -m 3 )

Fig. 9 Correlation of mass transfer coefficient with liquid-phase energy loss

given by Eq. (13) into an equation of the penetra-

tion theory of gas absorption, one gets^oc ( V^A4)1/2oc£l1/3° (18)

In Fig. 9, kig is plotted against Et. Although a singlecorrelation is obtained for each packing diameter,it gives lower values of ktg for smaller packing, pro-bably due to the restriction of relative motion betweenphases mentioned in the preceding paragraph.

VOL. 7 NO. 3 1974 191

Acknowledgment

Greatful acknowledgment is made to the Asahi Glass Founda-tion for Contribution to Industrial Technology for financialsupport of this project.

Nomenclature

aig = specific inter facial area per unit volume of bed[m2/m3]

as = geometrical surface area of packing perunit volume of bed [m2/m3]

Cl9 Cn = liquid-phase concentration of O2 atentrance and exit [kg-mol/m3]=average concentration of CO2 [kg-mol/m3]

= average concentration of NaOH [kg-mol/m3]= diffusion coefficient of CO2 [m2/sec]= diameter of packing and bubble [m]

=liquid-phase energy loss, Eq. (4) [Kg-m/sec-m3]

= height of packed bed [m]= mass transfer coefficient [m/sec]= reaction rate constant [m3/sec- kg-mol]

=volumetric absorption coefficient [1/sec]=absorption rate per unit volume

of bed [kg-mol/sec - m3]APi = single-phase pressure loss for gas and

liqu id [K g/m 2]A P io = two-phase pressure loss [K g /m *]

R i = liquid holdup per unit void volume [- ]U a, U l = su perfi cial ga s an d liqu id velo city [m /sec]

a = constant for Eq. (13)

｣ = void fraction of bed [- ]1 = Ostwald absorption coefficient [- ]

9c = density of continuous phase [kg/itf ]

a = inter facial tension [K g/m ]

4>i = two-phase p arameter, = VdPi glJpi [- ]

1 = tw o-phase par ameter, = V dPilJpg [- ]

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192 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN