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14-110 EQUIPMENT FOR DISTILLATION, GAS ABSORPTION, PHASE DISPERSION, AND PHASE SEPARATION
Overall Mass-Transfer Coefficient In systems with relatively
sparing soluble gases, where the gas-phase resistance is negligible, the
mass-transfer rate can be determined by using the concept of an overall
volumetric mass-transfer coefficient k La as follows:
M s = kLa(Cs* − Cs,b) (14-218)
where Ms = solute molar mass-transfer rate, kg⋅mol/s; kLa = overall
mass-transfer coefficient, 1/s; Cs* = solute concentration in equilibrium
with the liquid phase, kg⋅mol/s; and C s,b = solute concentration in
bulk of liquid.
Bakker et al. (op. cit.) have given a correlation for kLa for aqueous
systems in the absence of significant surface active agents.
kLa = CkLa(Pg/V) avsg b (14-219)
where CkLa = 0.015, 1/s; Eq. (14-219) applies for both 6BD and CD-6.
Interfacial Phenomena These can significantly affect overall
mass transfer. Deckwer, Bubble Column Reactors, Wiley, Hoboken,
N.J., 1992, has covered the effect of surfactants on mass transfer in
bubble columns. In fermentation reactors, small quantities of surface-active
agents (especially antifoaming agents) can drastically
reduce overall oxygen transfer (Aiba et al., op. cit., pp. 153, 154), and
in aerobic mechanically aerated waste-treatment lagoons, overall oxygen
transfer has been found to be from 0.5 to 3 times that for pure
water from tests with typical sewage streams (Eckenfelder et al., op.
cit., p. 105).
One cannot quantitatively predict the effect of the various interfacial
phenomena; thus, these phenomena will not be covered in detail
here. The following literature gives a good general review of the
effects of interfacial phenomena on mass transfer: Goodridge and
Robb, Ind. Eng. Chem. Fund., 4, 49 (1965); Calderbank, Chem. Eng.
(London), CE 205 (1967); Gal-Or et al., Ind. Eng. Chem., 61(2), 22
(1969); Kintner, Adv. Chem. Eng., 4 (1963); Resnick and Gal-Or, op.
cit., p. 295; Valentin, loc. cit.; and Elenkov, loc. cit., and Ind. Eng.
Chem. Ann. Rev. Mass Transfer, 60(1), 67 (1968); 60(12), 53 (1968);
62(2), 41 (1970). In the following outline, the effects of the various
interfacial phenomena on the factors that influence overall mass
transfer are given. Possible effects of interfacial phenomena are tabulated
below:
1. Effect on continuous-phase mass-transfer coefficient
a. Impurities concentrate at interface. Bubble motion produces
circumferential surface-tension gradients that act to retard
circulation and vibration, thereby decreasing the mass-transfer
coefficient.
b. Large concentration gradients and large heat effects (very
soluble gases) can cause interfacial turbulence (the Marangoni
effect), which increases the mass-transfer coefficient.
2. Effect on interfacial area
a. Impurities will lower static surface tension and give smaller
bubbles.
b. Surfactants can electrically charge the bubble surface (produce
ionic bubbles) and retard coalescence (soap stabilization of an
oil-water emulsion is an excellent example of this phenomenon),
thereby increasing the interfacial area.
c. Large concentration gradients and large heat effects can
cause bubble breakup.
3. Effect on mean mass-transfer driving force
a. Relatively insoluble impurities concentrate at the interface,
giving an interfacial resistance. This phenomenon has been used in
retarding evaporation from water reservoirs.
b. The axial concentration variation can be changed by changes
in coalescence. The mean driving force for mass transfer is therefore
changed.
Gas Holdup (ε) in Bubble Columns With coalescing systems,
holdup may be estimated from a correlation by Hughmark [Ind. Eng
Chem. Process Des. Dev., 6, 218–220 (1967)] reproduced here as Fig.
14-104. For noncoalescing systems, with considerably smaller bubbles,
ε can be as great as 0.6 at U sg = 0.05 m/s, according to Mersmann
[Ger. Chem. Eng., 1, 1 (1978)].
LIVE GRAPH
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FIG. 14-104 Gas holdup correlation. [Ind. Eng. Chem. Process Des. Dev., 6,
218 (1967).]
It is often helpful to use the relationship between ε and superficial
gas velocity (Usg) and the rise velocity of a gas bubble relative to the
liquid velocity (Ur + UL, with UL defined as positive upward):
ε= � (14-220)
Ur + UL Rise velocities of bubbles through liquids have been discussed previously.
For a better understanding of the interactions between parameters,
it is often helpful to calculate the effective bubble rise velocity
Ur from measured valves of ε; for example, the data of Mersmann
(loc. cit.) indicated ε =0.6 for Usg = 0.05 m/s, giving Ur = 0.083 m/s,
which agrees with the data reported in Fig. 14-43 for the rise velocity
of bubble clouds. The rise velocity of single bubbles, for db ∼ 2 mm,
is about 0.3 m/s, for liquids with viscosities not too different from
water. Using this value in Eq. (14-220) and comparing with Fig. 14-
104, one finds that at low values of Usg, the rise velocity of the bubbles
is less than the rise velocity of a single bubble, especially for smalldiameter
tubes, but that the opposite occurs for large values of Usg.
More recent literature regarding generalized correlational efforts
for gas holdup is adequately reviewed by Tsuchiya and Nakanishi
[Chem. Eng Sci., 47(13/14), 3347 (1992)] and Sotelo et al. [Int. Chem.
Eng., 34(1), 82–90 (1994)]. Sotelo et al. (op. cit.) have developed a
dimensionless correlation for gas holdup that includes the effect of gas
and liquid viscosity and density, interfacial tension, and diffuser pore
diameter. For systems that deviate significantly from the waterlike liquids
for which Fig. 14-104 is applicable, their correlation (the fourth
numbered equation in the paper) should be used to obtain a more
accurate estimate of gas holdup. Mersmann (op. cit.) and Deckwer et
al. (op. cit.) should also be consulted.
Liquid-phase mass-transfer coefficients in bubble columns have
been reviewed by Calderbank (“Mixing,” loc. cit.), Fair (Chem. Eng.,
loc. cit.), Mersmann [Ger. Chem. Eng. 1, 1 (1978), Int. Chem. Eng.,
32(3) 397–405 (1991)], Deckwer et al. [Can. J. Chem. Eng, 58, 190
(1980)], Hikita et al. [Chem. Eng. J., 22, 61 (1981)] and Deckwer and
Schumpe [Chem. Eng. Sci., 48(5), 889–911 (1993)]. The correlation
of Ozturk, Schumpe, and Deckwer [AIChE J., 33, 1473–1480 (1987)]
is recommended. Deckwer et al. (op. cit.) have documented the case
for using the correlation:
Ozturk et al. (1987) developed a new correlation on the basis of a modification
of the Akita-Yoshida correlation suggested by Nakanoh and Yoshida
(1980). In addition, the bubble diameter db rather than the column diameter
was used as the characteristic length as the column diameter has little
influence on kLa. The value of db was assumed to be approximately constant
(db = 0.003 m). The correlation was obtained by nonlinear regression
is as follows:
U sg