Mass Transfer Coefficients Between Gas and Liquid Phases in Packed Columns

(1)

enhances the probability of the bubble coalescence and

makes bubble larger.

On the other hand, in the present

study the dimention of the apparatus is far larger than that 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 Houghton

et al.'s case, because the circulation of the liquid in the

apparatus makes bubbles easy to apart each other. This

fact is recognized when the porous plate distributor

is used

for liquid

of group A and C in the bubble column with

continuous liquid flow.

Summary

Bubbles which have been just generated from the porous

plate are small and have an equal size, but sometime coalescence 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 in pure water and pure solvents. The surface active sub-stances in water and solvents obstruct this coalescence of bubbles. In concentrated inorganic salt solutions, this obstruction is also recognized. For the extreme cases

when no coalescence is observed and the coalescence occurs

at the maximumrate, the correlations of the average

bubble 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 diameter d = average bubble diameter

g = gravitational acceleration

z/Po = excess pressure required to generate bubble ug = gas flow rate per unit area of porous plate Fr = ug2/e2gd, Froude numer

We = ug2dp/e2o, Weber number p -density of liquid

8 = average pore diameter denned by Eq.(l)

e =porosity of porous plate a - 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 by

many mvestigators3'5>11>22>26l30>31). Assuming that the wetted surface on packing pieces is identical with the gas-liquid interface, Onda et al. presented the empirical equations of the gas and liquid-side mass transfer coefficients, kG and 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 the

surface energy of packing materials was derived as

follows150 :

ajat = l-exp{-1.45U/(7)0-75 (L/WO0"1 x (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 Raschig

rings, Berl saddles,

Spheres and rods made of ceramic,

glass, and polyvinylchloride,

and also coated with paraffine

film.

This paper presents the correlations on the

masstrans-fer coefficients

for gas absorption and desorption based on

Eq. (l) of aw and confirms the applicability of those to the vaporization of water and the gas absorption into organic solvents. Furthermore, its applicability to the distillation in packed columns is also discussed.

I. Liquid-side

Mass Transfer

Coefficient

: kL

1 à" 1 Gas absorption and desorption with water

The &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

(2)

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

Table I Experimental results of gas absorption into organic solvents

Packings Size Absorbent Temp. a n

Raschig ring 10mm CC14 25°C 0.120 0.70

Berl saddle l/2-in » » 0.0862 0.73

Sphere 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 shows the relation of kL {pL/^LgYn I <jiLl'pLDLyin {atDvYA vs. modified Reynolds number, (L/<z«,/O, and a straight

line represents

kL (pL/fiLg) m = O.OO5l(L/aw^Lyn (jxj'pLDLYV2

x (atDp)0A ,. (2)

The exponent of Rbl in Eq. (2) coincides with that derived

on the wetted area basis by Krevelen-Hoftijzer26)

and

Fujita-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 added

a surfactant in packed columnwas carried out to confirm

the 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 were

47 dynes/cm. The kLa data obtained

give smaller values

than are obtained with water as well as in the

litera-ture7>36). This effect of addition of surfactant

may result

from the two phenomena à"the reduction

of liquid mixing

at the junction of packing pieces as pointed out by Hikita7)

and the inter facial resistance with increase in

concen-T Sanyo-Kasei Co., Ltd.

tration of surfactant.

The kL calculated

from these data are compared with

those obtained by water in Fig,1 in which the data for

a=47 dynes/cm, in this work and 42 dynes/cm, in the

literature7)

deviate pretty from Eq. (2).

1.2 Gas absorption by organic solvent

Many 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 CO2

into methanol and carbon tetrachloride

were carried out.

The columns used were 6-and 12cm I. D. and packed

with 10~25mmRaschig rings,

Berl saddles,

spheres and

rods for 20~30cm height.

The mass transfer

results

are given in Table 1 as a

relation

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 in

Fig. 2 in which the agreement of the observed values

and Eq. (2) is also satisfactory.

Thus, the liquid-side mass transfer coefficients, kz, for

gas absorption and desorption in packed columns, have

been correlated

by Eq. (2) within an error of ±20% for

organic solvents as well as water.

2. Gas-side Mass Transfer Coefficient

: kG

2.1 Absorption

The 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

(3)

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

Fig. 3 Correlation of phase data for absorption

gas-Reynolds number. The equation for the best line passing

through the points in the higher group in Fig.3 is as follows 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 smaller

than 15mmare situated on the lower group and are best

correlated

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 decrease

monotonously with the increase of at as reported in the

literatures1 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)

(4)

Fig. 4 Comparison of /cgO data for vaporization by various

investigators 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 was

about 25°C and the differ ence of the

temperature between top and bottom of 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 for sublimation of dry naphthalene packings

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

The agreement between Eqs. (4) and (5) is fairly

good

within the region of 100<GD3,7j"fl(l-e) <10, 000. 2 à"2 Vaporization

There are considerable differences

among the published

data10'21>23'30) for vaporization because of the difficulties in

the experimental techniques, as shown in Fig.4, in which

kGa for air-water system are plotted against the gas

massvelocity, G, for 1-in. Raschig rings.

To ascertain their results, the rates of vaporization were measured for air-water system under the condition of adiabatic process-i. e, constant temperature of water.

(5)

Fig. 7

Correlation of vaporization data with

Eq. (3) .

The schematic diagram of the apparatus is shown in

Fig. 5. The column consisted of 15cm I.D. acryle-resin

pipe 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 the

psychrometric method and the adsorption on calcium

chloride. ;

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 been

divided 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 the

data for vaporization

as well as gas absorption,

but for

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

3. Applicability for Distillation

Distillations in the packed column have been studied by 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 constant

through out the packed column. Yoshida-Koyanagi30) have

discussed 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 is unidirectional, 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 distillation

column it is meaningless, because the temperature and concentration 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 and

hh calculated

:from Eqs. (3) and (2) for gas absorption

and

gas-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 be

constant. Thus, the heights of packings calculated from

Eq. (6) has been compared with the actual height used to

obtain the published data because the estimation of Kg<z

or Hog used in the previous literature is insignificant, especially for non-ideal mixtures.

The published data used for this calculation include the system of benzene-toluene29), methanol-water9'255 and ethanol-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 agreements

are within ±30% except columns higher than 1.0m in

which the maldistribution of liquid might have occured.

The relative magnitude of individual phase resistances

depends on the group m G/L, but the variable range in

L/G is more restricted in distillation than in gas

ab-sorption. Furthermore mand physical properties of liquid

mixtures mayvary widely from top to bottom throughout

the 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 phase

resistance to total one upon the liquid composition for ethanol-water and benzene-toluene systems.

Conclusion

Assuming that the wetted surface area evaluated by

Eq. (l) is identical

with the gas-liquid

inter facial area, the

mass transfer^coefficients in packed columns on the gas

(6)

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

absorption and desorption were correlated within a

reason-able error

with Eq. (2) for kL and Eq. (3) for ka except

Raschig rings smaller than l|mm and Berl saddles smaller;

than 1/2".

It was found that the difference between the mass transfer data for absorption and that for vaporization is quite 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

mass

transfer coefficient, Eq. (2) is applicable within ±20% error to the columns packed with Raschig rings, Berl saddles, spheres and rods, and irrigated with organic solvents as well as water systems of higher surface tension

than about 50 dynes/cm.

For the distillation

in packed columns, it was ascertained

that the resistance in both phases should be taken into

account, and the height of packing could be evaluated by

Eq.(6)

with Eq.(3)

for kG, Eq.(2)

for kL and Eq. (l) for

a 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]

JU

Fig. 9 Ratio of gas phase resistance to total one against liquid 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) [-3

Sh = Sherwood number defined by (kaRT/atDo) [-1

T = 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 [-3

Z - height

of packings

[m3

Greek letters

s = void fraction [m3/ni33

P- - viscosity [kg/m-hr3

(7)

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

Subscrip ts

1, 2 = bottom and top of column, respectively

G, 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(1955

ll)_Engrs.,Norman, W. S. and F. Y. Y. Sammak: Trans. Inst._41, ₁₀₉ ₍₁₉₆₃₎ Chem.

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 PACKED

COLUMNS"

KAKUSABURO ONDA, EIZO SADA AND HIROSHI TAKEUCHI**

Dept. of Chem. Eng., University

of Nagoya, Nagoya

Introduction

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

mass transfer coefficients and the inter facial area can not

be estimated strictly at present.

The assumption that the wetted surface in packings is

identical with the gas-liquid interface is not only

con-venient for estimation of the area but also reasonable for

mass transfer between gas and liquid phases. In our previous papers11>12\ the correlations for aw, ko and kL were 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 gas

absorption 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 column

is confirmed by using these correlations. Furthermore,

the assumption of a-aw is ascertained by comparing with

the 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. jacketed

acryl-resin

tube packed to the heights of 0.2m or 0.3m

with 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 nipples

arranged 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 in

the thermostat tank which was controlled at 30±l°C. Air from a blower and carbon dioxide from a cylinder