enhances the probability of the bubble coalescence and

makes bubble larger. On the other hand, in the presentstudy the dimention of the apparatus is far larger thanthat of the distributor and the depth of the liquids is

shallow. Therefore, the probability of the bubble coales-cence over the distributor is less than that of the Houghtonet al.'s case, because the circulation of the liquid in the

apparatus makes bubbles easy to apart each other. Thisfact is recognized when the porous plate distributor is usedfor liquid of group A and C in the bubble column withcontinuous liquid flow.

Summary

Bubbles which have been just generated from the porousplate are small and have an equal size, but sometimecoalescence of these small bubbles occurs at a location

slightly removed from the distributor, where the gas hold-up is very large. Therefore, large and wide size distri-bution of bubbles are observed. This occurs easily inpure water and pure solvents. The surface active sub-stances in water and solvents obstruct this coalescence ofbubbles. In concentrated inorganic salt solutions, thisobstruction is also recognized. For the extreme cases

when no coalescence is observed and the coalescence occursat the maximumrate, the correlations of the averagebubble diameter and the conditions of bubble generation

are obtained.

Acknowledgment

The authors are grateful Prof T. Sakurai, Tokyo Inst. Tech.,for valuable advices.

Nomenclature

d = volume equivalent bubble diameterd = average bubble diameterg = gravitational accelerationz/Po = excess pressure required to generate bubbleug = gas flow rate per unit area of porous plateFr = ug2/e2gd, Froude numerWe = ug2dp/e2o, Weber numberp -density of liquid8 = average pore diameter denned by Eq.(l)e =porosity of porous platea - surface tension of liquid

[cm][cm]

[cm/sec2][g/cm- sec2]

[cm/sec][-][-]

[g/cm3][cm][-]

[dyne/cm]

Literature cited

1) Foulk, C.G.: Kolloid. Z., 60,115 (1932)2) Gleim, V. G. and Shelomov, I. K.: J. Appl. Chem. USSR,

32, 799 (1959)3) Gleim, V.G., Shelomov, I.K. and Shidlovski, B.R.: J. Appl.

Chem. USSR, 32, 1069 (1959)4) Houghton, G., Mcleam, A.M. and Ritchie, P. D.: Chem.

Eng. Sd.f 7, 40 (1957)5) Koide, K. Hirahara, T. and Kubota, H.: Kagaku Kogaku,

30, 712 (1966)

6) Vershoor, H. : Trans. Inst. Chem. Eng.(London), 28,52(1950)

MASS TRANSFER COEFFICIENTS BETWEEN GAS AND LIQUID

PHASES IN PACKED COLUMNS*

KAKUSABURO ONDA, HIROSHI TAKEUCHI** AND YOSHIO OKUMOTO

Dept. of Chem. Eng., University of Nagoya, Nagoya

Introduction

Mass transfer coefficients for gas absorption, desorption

and vaporization in packed columns have been studied bymany mvestigators3'5>11>22>26l30>31). Assuming that the wettedsurface on packing pieces is identical with the gas-liquidinterface, Onda et al. presented the empirical equationsof the gas and liquid-side mass transfer coefficients, kGand kL, for the gas absorption and desorption12~18).

Recently, a newequation for the wetted surface area,aw, taking into account the liquid surface tension and thesurface energy of packing materials was derived asfollows150 :

ajat = l-exp{-1.45U/(7)0-75 (L/WO0"1x (LW^V)-0-05 (UIPLoaty-2

= l-exp{-1.45(W<7)0-75 Cfo)0'1

* Received on July 10, 1967

** Dept. of Ind. Chem., Suzuka College of Technology, Suzuka

56

x CFr)"0-05 (We)0'2 } (1)

It has been shown that Eq. (l) can be applicable

within ±20%error to the column packed with Raschigrings, Berl saddles, Spheres and rods made of ceramic,glass, and polyvinylchloride, and also coated with paraffinefilm.

This paper presents the correlations on the masstrans-fer coefficients for gas absorption and desorption based onEq. (l) of aw and confirms the applicability of those tothe vaporization of water and the gas absorption intoorganic solvents. Furthermore, its applicability to thedistillation in packed columns is also discussed.

I. Liquid-side Mass Transfer Coefficient : kL1 à" 1 Gas absorption and desorption with waterThe &l a data for gas absorption into water and desorp-ton from water reported in the Iiterature3'6ll2'16>18'2()>24l27'28)are divided by aw of Eq. (1). The kL thus obtained are

correlated as well as that in our previous paper12>18) by

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Fig. I Correlation of liquid-phase data for gas absorption and desorption by using water

Table I Experimental results of gas absorption intoorganic solvents

Packings Size Absorbent Temp. a nRaschig ring 10mm CC14 25°C 0.120 0.70Berl saddle l/2-in » » 0.0862 0.73Sphere l/2-in " " 0.0227 0.86

" " CH3OH 20°C 0.0735 0.76" 1-in » " 0.0389 0.83

Rod 14mm CC14 25°C 0.093 0.70

replacing at in Reynolds number by aw. Fig. 1 showsthe relation of kL {pL/^LgYn I <jiLl'pLDLyin {atDvYA

vs. modified Reynolds number, (L/<z«,/O, and a straightline representskL (pL/fiLg) m = O.OO5l(L/aw^Lyn (jxj'pLDLYV2

x (atDp)0A ,. (2)

The exponent of Rbl in Eq. (2) coincides with that derivedon the wetted area basis by Krevelen-Hoftijzer26) andFujita-Hayakawa3), and also is nearly equal to 0.61 of

that derived by Norman11}in a model apparatus.Furthermore, the gas absorption of CO2into water addeda surfactant in packed columnwas carried out to confirmthe applicability of Eq. (2) for various inter facial. area.Such absorption data have been reported by Hikita7).In this work, a non-foaming surfactant, NewpolPE-61f,were used and the surface tensions of solutions were47 dynes/cm. The kLa data obtained give smaller valuesthan are obtained with water as well as in the litera-ture7>36). This effect of addition of surfactant may resultfrom the two phenomena à"the reduction of liquid mixingat the junction of packing pieces as pointed out by Hikita7)

and the inter facial resistance with increase in concen-T Sanyo-Kasei Co., Ltd.

VOL.1 NO.1 1968

tration of surfactant.The kL calculated from these data are compared withthose obtained by water in Fig,1 in which the data fora=47 dynes/cm, in this work and 42 dynes/cm, in the

literature7) deviate pretty from Eq. (2).1.2 Gas absorption by organic solventMany investigation on the gas absorption in packed

column have been carried out by using water as an ab-sorbent. However, there are so far only a few data5>13>28)on the gas absorption by organic solvent.

In the present work, the gas absorption of pure CO2into methanol and carbon tetrachloride were carried out.The columns used were 6-and 12cm I. D. and packedwith 10~25mmRaschig rings, Berl saddles, spheres androds for 20~30cm height.

The mass transfer results are given in Table 1 as arelation of kLa-aLn. Applying Eq. (l) to kLa data ob-tainded in this work and reported in the literature5>13>28)

for organic solvents, the same plottings are shown inFig. 2 in which the agreement of the observed values

and Eq. (2) is also satisfactory.Thus, the liquid-side mass transfer coefficients, kz, forgas absorption and desorption in packed columns, have

been correlated by Eq. (2) within an error of ±20% fororganic solvents as well as water.

2. Gas-side Mass Transfer Coefficient : kG2.1 AbsorptionThe Izgci data for gas absorption reported in the lite-

rature1>8ll5>16'17'30'32) are divided by aw calculated from Eq.(l). The ko thus obtained are shown in Fig. 3 as a

plot of {kGRT/atDG)/{^G/pGDGyn UA,) "2 0 vs. modified

57

Fig. 2 Correlation of ab-sorption "data by using organicsolvent with Eq. (2)

Fig. 3 Correlation ofphase data for absorption

gas-

Reynolds number. The equation for the best line passingthrough the points in the higher group in Fig.3 is asfollows à"koRT/atDo = 5.23(G/WG)0-7 (^g/PgDg)U3 feD,)"2'°

(3)

In Fig. 3, data for Raschig rings and Berl saddles smallerthan 15mmare situated on the lower group and are bestcorrelated by merely changing the constant, 5.23, in Eq.

58

(3) into 2.00. This difference comes from the fact that

kaa data for packing smaller than 15mmtend to decreasemonotonously with the increase of at as reported in theliteratures1 16). However,this cause is not clear at present.

The jD-factor for mass transfer can be obtained by

rearranging Eq. (3). For example, since atDp is 6(1-e) =3.4 for spheres, Eq. (3) becomes

> = 0.771[GDP7Ml-s)r°:30 (4)

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Fig. 4 Comparison of /cgO data for vaporization by variousinvestigators at L=78OOkg/m2 hr

Fig. 5 Schematic diagram of experimental apparatusfor vaporization in water-air system

Fig. 6-a 15mm Raschig rings Fig. 6-b 25mm Raschig rings

Fig. 6 Vaporization data in this work(Operational temperature of water wasabout 25°C and the differ ence of the

temperature between top and bottomof the column was within 0.1°C.)

Fig. 6-c I in Berl saddles Fig. 6-d I in Spheres

Shulman et al.22) reported the following equation forsublimation of dry naphthalene packings

jD = 1.195[GDPV^(l-s)]"0-36 (5)

The agreement between Eqs. (4) and (5) is fairly goodwithin the region of 100<GD3,7j"fl(l-e) <10, 000.

2 à"2 Vaporization

There are considerable differences among the published

VOL. 1 NO. 1 1968

data10'21>23'30) for vaporization because of the difficulties inthe experimental techniques, as shown in Fig.4, in whichkGa for air-water system are plotted against the gasmassvelocity, G, for 1-in. Raschig rings.To ascertain their results, the rates of vaporization weremeasured for air-water system under the condition ofadiabatic process-i. e, constant temperature of water.

5?

Fig. 7

Correlation of vaporization data withEq. (3) .

The schematic diagram of the apparatus is shown inFig. 5. The column consisted of 15cm I.D. acryle-resinpipe with water jacket and was packed with ceramic Raschig

rings, Berl saddles and spheres. Packed heights of 10-,15- and 20-cm were used to make the end effect clear.The water contents in gas phase were analyzed by thepsychrometric method and the adsorption on calciumchloride. ;

The typical experimental results are shown as kGa vs.G in Figs.6-a, 6-b, 6-c, 6-d. To compare the kGa for

vaporization with that for absorption, kGa data have beendivided by aw of Eq. (l) and (kGRT/atDG)/(ptG/PGDG)uz(atDp)~2'Q axe plotted against the modified Reynolds

number, (G/at[tG), in Fig. 7.As shown in Fig.7, Eq.(3) correlates almost all of thedata for vaporization as well as gas absorption, but for

1/2-in. sphere the constant of Eq.(3) might be changedinto 2.00 as described in the section of absorption.

3. Applicability for Distillation

Distillations in the packed column have been studiedby many investigators. Most of them, however, have

reported the H. E. T. P. which is theoretically unfavorable,or H. T. U., assuming that the slope of the equilibrium

line and the physical properties of mixture is constantthrough out the packed column. Yoshida-Koyanagi30) havediscussed the applicability of HG and HL derived for gas

absorption to the distillation in a packed column.Actually, the distillation process is equimolar counter

diffusion, while the gas absorption or vaporization isunidirectional, but this difference in this case may have

little effect on the individual mass transfer coefficients.In gas absorption, it is reasonable to obtain the average

film coefficient in a packed column, but in the distillationcolumn it is meaningless, because the temperature andconcentration of mixture differ greatly at each point

60

through the column. From this point of view, Sawistowski19)reported the relation of Hog vs. x.

In the present work, using the point values of ka andhh calculated :from Eqs. (3) and (2) for gas absorption andgas-liquid inter facial area from Eq. (l), the height of pack-ings was calculated by the following equation.

Z=Gm\ [-1 h-i )-* C6)Jy.Kkaa kLa-Cav1y' ~ y

in which the gas molar flow rate, Gm, is assumed to beconstant. Thus, the heights of packings calculated fromEq. (6) has been compared with the actual height used toobtain the published data because the estimation of Kg<zor Hog used in the previous literature is insignificant,especially for non-ideal mixtures.

The published data used for this calculation includethe system of benzene-toluene29), methanol-water9'255 andethanol-water4) at total and finite reflux ratios. Com-parisons of the calculated value, Zcai, with the actual,

Zact, are shown in Fig". 8 against Gm. Their agreementsare within ±30% except columns higher than 1.0m in

which the maldistribution of liquid might have occured.The relative magnitude of individual phase resistancesdepends on the group m G/L, but the variable range inL/G is more restricted in distillation than in gas ab-sorption. Furthermore mand physical properties of liquidmixtures mayvary widely from top to bottom throughoutthe column, and hence the relative magnitude of individu-al phase contributions depends on the liquid composition.Fig". 9 shows the dependencies of the ratio of gas phaseresistance to total one upon the liquid composition forethanol-water and benzene-toluene systems.

ConclusionAssuming that the wetted surface area evaluated by

Eq. (l) is identical with the gas-liquid inter facial area, themass transfer^coefficients in packed columns on the gas

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Fig. 8 Comparison of calcu-lated and actual packed heightsfor distillation columns

absorption and desorption were correlated within a reason-able error with Eq. (2) for kL and Eq. (3) for ka exceptRaschig rings smaller than l|mm and Berl saddles smaller;

than 1/2".

It was found that the difference between the masstransfer data for absorption and that for vaporization isquite small and practically could be neglected. Thus,Eq. (3) for gas absorption is also applicable to the vapori-

zation process within ±30%error. For the liquid-side masstransfer coefficient, Eq. (2) is applicable within ±20%error to the columns packed with Raschig rings, Berlsaddles, spheres and rods, and irrigated with organic

solvents as well as water systems of higher surface tensionthan about 50 dynes/cm.

For the distillation in packed columns, it was ascertainedthat the resistance in both phases should be taken into

account, and the height of packing could be evaluated byEq.(6) with Eq.(3) for kG, Eq.(2) for kL and Eq. (l) fora within reasonable error.

Nomenclature

a = inter facial area in packing [m2/m3]at = total surface area of packing [m2/m3]aw = wetted surface area of packing [m2/m3]Cav = average molar density [kg-moles/m3]D = diffusivity [m2/hr]Dp = nominal size of packing , [m]Dp = diameter of sphere possessing the same surface area

as a piece of packing [m]Fr å = Froude number denned by (atL2/gpL2) [-]G = superficial mass velocity of gas [kg/m2-hr]Gm= superficial molar velocity of gas [kg-moles/m2-hr]g = gravitational constant [m/hr2]H =å height of a transfer unit [m]jD å = mass transfer factor defined by Eq.(4) [-]Kg - overall coefficient [kg-moles/m2 -hr-atm]kG = gas-phase mass transfer coefficient [kg-moles/m2-hr-atm]kL = liquid-phase mass transfer coefficient ' [m/hr]L = superficial mass velocity of liquid [kg/m2<hr]

VOL.1 NO.1 1968. .

JU

Fig. 9 Ratio of gas phase resistance to total one againstliquid concentration, x, for distillation

m= slope of equilibrium line [-]R = gas constant [m3-atm/kg-mole- °K]Re = Reynolds number defined by {GlatPo) or (L/atPz) or

(L/ovPl) [-]Sc = Schmidt number defined by (p/pD) [-3Sh = Sherwood number defined by (kaRT/atDo) [-1T = absolute temperature [°K]We - Weber number defined by (L2/'pLoat) [-3^c = mole fraction of more volatile component in liquid [-]y = mole fraction of solute or vapor in gas phase [-]3^* = mole fraction of vapor in equilibrium with liquid

composition, x [-3Z - height of packings [m3Greek letters

s = void fraction [m3/ni33P- - viscosity [kg/m-hr3

p =.density [kg/m3]

61

Oc - critical surface tension of packing material [dynes/cm]a = surface tension [dynes/cm] or [kg/hr2]

Subscrip ts1, 2 = bottom and top of column, respectivelyG, L = gas and liquid phase, respectively

Literature cited

1) Fellinger, L.: Sc. D. thesis, M.L.T., Cambridge (1941)2) Fujita, S. and S. Sakuma: Chem. Eng.(Japan), 18, 64 (1954)

3) Fujita, S. and T. Hayakawa: ibid., 20, 113 (1956)4) Furnas, C. C. and M. L. Taylor: Trans. Am. Inst. Chem.

Engrs., 36, 135 (1940)

5) Hikita, H., T. Kataoka and K. Nakanishi: Kagaku Kogaku,24, 2 (1960)

6) Hikita, H., M. Sugata and K. Kamo: ibid., 18, 454 (1954)7) Hikita, H.: ibid., 24, 9 (1960)

8) Houston, R.W. and C.A. Walker: Ind. Eng. Chem., 42, 1105(1950)

9) Katayama, S., T. Koyanagi and F. Yoshida: Kagaku Kogaku,22, 764 (1958)

10) Lynch, E.J. and C.R. Wilke: ibid., 1, 9(1955ll) Norman, W. S. and F. Y. Y. Sammak: Trans. Inst. Chem.

Engrs., 41, 109 (1963)

12) Onda, K., E. Sada and Y. Murase: A. I. Ch. E. Journal, 5,235 (1959)

13) Onda, K. and E. Sada: Kagaku Kogaku, 23,220 (1959)14) Onda, K., T. Okamoto and H. Honda: ibid., 24, 490(1960)15) Onda, K., E. Sada and M. Saito: ibid., 25, 820 (1961)

16) Onda, K., E. Sada, C. Kido and A. Tanaka: ibid., 27, 140(1963)

17) Onda, K., E. Sada, C. Kido and S. Kawatake: ibid., 30, 226(1966)

18) Onda, K., H. Takeuchi and Y. Koyama: ibid., 31, 126(1967)19) Sawistowski, H. and W. Smith: Ind. Eng. Chem., 51, 915

(1959)20) Sherwood, T. K. and F.A.L. Holloway: Trans. Am. Inst.

Chem. Engrs., 36, 21 (1940)21) Sherwood, T.K. and F.A.L. Holloway: ibid., 36, 39 (1940)22) Shulman, H.L., C.F. Ullrich, A.Z. Proulx and J.O. Zim-

merman: A. I. Ch. E. Journal, 1, 253 (1955)23) Surosky, A.E. and B.F. Dodge: Ind. Eng. Chem., 42,1112

(1950)24) Ueyama, K., H. Hikita, S. Nishigami and S. Funahashi:

Kagaku Kogaku, 18, 68 (1954)25) Uchida, S., et al.: ibid., ll, 53 (1947)

26) Van Krevelen, D. W. and P. J. Hoftijzer : Chem. Eng. Progrs.,44, 529 (1948)

27) Vivian, J.E. and C.J. King: A. I. Ch. E.Journal, 10, 221(1964)

28) Yoshida, F. and T. Koyanagi: Ind. Eng. Chem., 50, 365(1958)

29) Yoshida, F. and T. Koyanagi: ibid., 46, 1756 (1954)30) Yoshida, F. and T. Koyanagi: A. I. Ch. E. Journal, 8, 309

(1962)31) Weisman, J. and C.F. Bonilla: Ind. Eng. Chem., 42, 1099

(1950)

32) Wen, C.Y., H.D. Simons and M. Leva: West Virg. Univ.Bull. Eng. Expt. Sta., 26 (1953)

GAS ABSORPTION WITH CHEMICAL REACTION IN PACKEDCOLUMNS"

KAKUSABURO ONDA, EIZO SADA AND HIROSHI TAKEUCHI**

Dept. of Chem. Eng., University of Nagoya, Nagoya

Introduction

Theoretical analyses for gas absorption with chemicalreaction have been made by many investigators3>4>6'18):However, it is difficult to apply these theories to theprocesses in a packed column, because the individual

mass transfer coefficients and the inter facial area can notbe estimated strictly at present.

The assumption that the wetted surface in packings isidentical with the gas-liquid interface is not only con-

venient for estimation of the area but also reasonable formass transfer between gas and liquid phases. In ourprevious papers11>12\ the correlations for aw, ko and kLwere derived as follows :

ajat = 1 - exp{- 1.45UWU5aW(Vat/pL2g) ~Q^ (L2/pLaaty-2}

koR T/atDo= 5.23 (GWff) °"7 (fiG/PODG)m (atDp) "2-°

kL {pL/[JtLgy n= 0. 005l (L/aw^Ly/' (fiL/PLDL) -1/2 (atDpy-i (3)

In this paper, the applicability of the film theory18) of gasabsorption with second order reaction to the absorption of

* Received on July 10, 1967

*å * Dept. of Ind. Chem., Suzuka College of Technology, Suzuka

62

CO2into aqueous solutions of NaOHin a packed columnis confirmed by using these correlations. Furthermore,

the assumption of a-aw is ascertained by comparing withthe data for the gas absorption with pseudo fist-order re-action.

I. Experimental Work

1 à"1 Apparatus and procedure

The packed column consisted of a 12.0-cm I.D. jacketedacryl-resin tube packed to the heights of 0.2m or 0.3mwith 15mm ceramic Raschig ring and 1/2- and 1-in.ceramic spheres. The liquid distributor was made of

acryl-resin and had sixty one 3.5mm I. D. glass nipplesarranged in a ll.6mm triangular pitch.

The aqueous solutions of 0.05, 0.1, 0.25, 0.5 and 1.0iV-

NaOHwere irrigated over the packings after heating inthe thermostat tank which was controlled at 30±l°C.Air from a blower and carbon dioxide from a cylinder

were fed to the bottom of the packed column after thegas mixture waswell mixed and saturated with watervapor. The CO2content in the air was controlled by areducing valve at the CO2 cylinder. The partial pressureof the solute gas, p, was maintained constant in each run

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