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 coalescence 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.
are obtained. Acknowledgment The authors are grateful for valuable advices.
Prof
T. Sakurai,
Tokyo
Inst.
Nomenclature
[cm] [cm] [cm/sec2] [g/cm- sec2] [cm/sec] [-] [-] [g/cm3] [cm] [-] [dyne/cm]
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
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 holdup 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 substances 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
Tech.,
8 = average pore diameter denned by Eq.(l) e =porosity of porous plate a - surface tension of liquid Literature
cited
1) 2)
Foulk, C.G.: Kolloid. Z., 60,115 (1932) 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
Dept. of Chem. Eng., University
x CFr)"0-05
It has
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
follows150
of
packing
was derived
= l-exp{-1.45(W<7)0-75 Received
on July
10,
(L/WO0"1 (UIPLoaty-2 Cfo)0'1
1967
** Dept. of Ind. Chem., Suzuka College of Technology, Suzuka 56
of Nagoya, Nagoya
(We)0'2
been shown that
}
Eq. (l)
(1)
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 masstransfer 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 = l-exp{-1.45U/(7)0-75 x (LW^V)-0-05
AND YOSHIO OKUMOTO
as
:
ajat
*
materials
TAKEUCHI**
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 JOURNAL
OF
CHEMICAL
ENGINEERl|NG
OF
JAPAN
Fig.
Table
I
Correlation
Experimental results organic solvents
Packings Raschig ring Berl saddle Sphere " " Rod
Size 10mm l/2-in l/2-in " 1-in 14mm
replacing at the relation vs. modified line represents kL (pL/fiLg)
I
Absorbent CC14 » " CH3OH » CC14
of liquid-phase
of gas absorption Temp. 25°C » " 20°C " 25°C
data
tration
into a 0.120 0.0862 0.0227 0.0735 0.0389 0.093
n 0.70 0.73 0.86 0.76 0.83 0.70
in Reynolds number by aw. Fig. 1 shows of kL {pL/^LgYn I
(jxj'pLDLYV2 ,.
(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 literature7>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 concenT VOL.1
Sanyo-Kasei
Co., NO.1
Ltd. 1968
for gas absorption
and desorption
by using
water
of surfactant.
The kL calculated from these data are compared with those obtained by water in Fig,1 in which the datain for a=47 dynes/cm, in this work and 42 dynes/cm, 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 absorbent. 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 obtainded 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
been correlated
by Eq. (2) within an error of ±20% for
in packed columns, have
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 literature1>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 absorption "data by using organic solvent with Eq. (2)
Fig. 3 Correlation of phase data for absorption
Reynolds number. The equation for the best line passing through the points in the follows à" koRT/atDo = 5.23(G/WG)0-7
higher
group in Fig.3
(^g/PgDg)U3
is as
feD,)"2'° (3)
(3)
into
2.00.
This
difference
gas-
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
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.
rearranging
58
JOURNAL OF CHEMICAL ENGINEERING
3.4
by
Eq. (3). For example, since atDp is 6(1-e) =
for spheres, Eq. (3) becomes > = 0.771[GDP7Ml-s)r°:30
(4) OFJAPAN
Fig. 4 investigators
Comparison of /cgO data for vaporization at L=78OOkg/m2 hr
Fig.
by various
Fig. 5 Schematic diagram of experimental apparatus for vaporization
6-a
in water-air
Fig.
system
6-b
25mm Raschig
rings
15mm Raschig
rings
I in Berl
saddles
for
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.
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.
Shulman et al.22) reported the following sublimation of dry naphthalene packings jD = 1.195[GDPV^(l-s)]"0-36
6-c
equation (5)
The agreement between Eqs. (4) and (5) is fairly good within the region 2 à"2 Vaporization
of 100
There are considerable differences VOL.
1
NO.
1
1968
<10,
000.
among the published
Fig.
6-d
I in
Spheres
5?
Fig.
7
Correlation Eq.
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 15- and 20-cm were used to make the end effect The water contents in gas phase were analyzed psychrometric method and the adsorption on chloride. The typical G in
experimental
Figs.6-a,
6-b,
; are shown as kGa vs.
results
6-c, 6-d.
of 10-, clear. by the calcium
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) into 2.00 as described in the section
might be changed of absorption.
of
vaporization
(3)
data
with
.
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 packings was calculated by the following equation. Z=Gm\ [-1 Jy.Kkaa
h-i )-* kLa-Cav1y' ~ y
C6)
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
Zact, are shown in Fig". 8 against Gm. Their agreements 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, concentration of mixture 60
because the temperature and differ greatly at each point
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 ethanol-water and benzene-toluene systems.
for
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
JOURNAL OF CHEMICAL ENGINEERING OFJAPAN
Fig. 8 Comparison of calculated and actual packed heights for distillation columns
absorption and desorption were correlated within a reasonable 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
that
the resistance
in packed columns, it was ascertained
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. JU
Fig. liquid
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
NO.1
1968.
.
9
Ratio of gas phase resistance concentration, x, for distillation
to total
one against
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
Greek letters s = void fraction P- - viscosity p =.density
[m3 [m3/ni33 [kg/m-hr3 [kg/m3] 61
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 1) 2) 4)
S. and T. Hayakawa:
Furnas, C. C. and Engrs., 36, 135 (1940)
ibid.,
M. L. Taylor:
Trans.
H., M.ibid.,Sugata24, and K. Kamo: ibid., H.: 9 (1960)
Am. Inst.
Chem.
Kagaku Kogaku,
ibid.,
30, 226
9) 22,Katayama, S., T. Koyanagi and F. Yoshida: Kagaku Kogaku, 764 (1958) E.J.
and C.R. Wilke:
ibid.,
1, 9(1955
ll) Engrs., Norman,41, W.109 S. (1963)and F. Y. Y. Sammak: Trans. Inst.
Chem.
12)235 Onda, K., E. Sada and Y. Murase: A. I. Ch. E. Journal, (1959)
Sherwood,
T. K. and
5,
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)
F.A.L.
Holloway:
36, 21 (1940) T.K. andC.F.F.A.L. Holloway: H.L., Ullrich, A.Z.
merman: A. I. A.E. Ch. E. Journal, Surosky, and B.F.
23)
(1950) 24) Ueyama,
K.,
Uchida,
S.,
al.:
S. Nishigami
ibid.,
ll,
D. W. and P. J. Hoftijzer
27)
and
Vivian, (1964) 28) Yoshida, (1958)
J.E.
29) Yoshida, 30) (1962) Yoshida,
F. and T. Koyanagi: F. and T. Koyanagi:
31)
F. and
Weisman, (1950)
J. and
King:
Bonilla:
Chem.,
and
42,1112
S. Funahashi:
: Chem. Eng. Progrs.,
A. I. Ch. E.Journal,
T. Koyanagi:
C.F.
36, 39 (1940) J.O. Zim-
and
53 (1947)
26)44, Van529Krevelen, (1948)
C.J.
ibid.,
Proulx
1, 253Ind.(1955) Eng.
H. Hikita,
et
Trans. Am. Inst.
Dodge:
Kagaku Kogaku, 18, 68 (1954)
25)
18, 454 (1954)
R.W. and C.A. Walker: Ind. Eng. Chem., 42, 1105
10) Lynch,
17)(1966) Onda, K., E. Sada, C. Kido and S. Kawatake:
Chem. Engrs., 21) Sherwood, 22) Shulman,
(1941) 18, 64 (1954)
20, 113 (1956)
5) 24,Hikita, H., T. Kataoka and K. Nakanishi: 2 (1960) 8) (1950) Houston,
27, 140
20)
Fellinger, L.: Sc. D. thesis, M.L.T., Cambridge Fujita, S. and S. Sakuma: Chem. Eng.(Japan),
6) Hikita, 7) Hikita,
ibid.,
18) Onda, K., H. Takeuchi and Y. Koyama: ibid., 31, 126(1967) 19)(1959) Sawistowski, H. and W. Smith: Ind. Eng. Chem., 51, 915
cited
3) Fujita,
16)(1963)Onda, K., E. Sada, C. Kido and A. Tanaka:
Ind.
Eng.
10,
221
Chem., 50,
365
ibid., 46, 1756 (1954) A. I. Ch. E. Journal, 8, 309 Ind.
Eng.
Chem., 42,
1099
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
Dept. of Chem. Eng., University
Introduction
CO2into aqueous solutions
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) koR T/atDo = 5.23
(GWff)
~Q^ (L2/pLaaty-2} °"7 (fiG/PODG)m
kL {pL/[JtLgy n
(atDp)
"2-°
(fiL/PLDL)
-1/2
(atDpy-i
(3)
10,
1967
*å * Dept. of Ind. Chem., Suzuka College of Technology, Suzuka 62
these
of NaOHin a packed column correlations.
Furthermore,
the assumption of a-aw is ascertained by comparing with the data for the gas absorption with pseudo fist-order reaction. I.
Experimental
1 à"1 Apparatus
Work 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 ceramic spheres. The liquid
acryl-resin
ring and distributor
1/2- and 1-in. was made of
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 atheating in the thermostat tank which was controlled 30±l°C.
In this paper, the applicability of the film theory18) of gas absorption with second order reaction to the absorption of on July
by using
of Nagoya, Nagoya
Air from a blower and carbon dioxide
= 0. 005l (L/aw^Ly/'
* Received
is confirmed
TAKEUCHI**
from a cylinder
were fed to the bottom of the packed column after the gas mixture waswell mixed and saturated with water vapor. The CO2content in the air was controlled by a reducing valve at the CO2cylinder. The partial pressure of the solute gas, p, was maintained constant in each run JOURNAL OF CHEMICAL ENGINEERING
OF JAPAN
