Ind. Eng. Chem. Res. 2002, 41, 1905-1913
1905
Absorption and Desorption of Carbon Dioxide into and from Organic Solvents: Effects of Rayleigh and Marangoni Instability Z. F. Sun* Physics Department, University of Otago, P.O. Box 56, Dunedin, New Zealand
K. T. Yu, S. Y. Wang, and Y. Z. Miao Chemical Engineering Research Center, Tianjin University, Tianjin, China
Interfacial turbulence caused by both Rayleigh and Marangoni instablity in the physical absorption and desorption of carbon dioxide into and from nonaqueous solvents was studied experimently. Orderly roll and polygonal convection patterns in liquid films were observed using schlieren photography. Liquid mass-transfer coefficients were measured in a quiescent gasliquid contactor and in a gas-liquid channel for stratified, laminar, and cocurrent flows, and the results were compared with values calculated by penetration theory. The measured data indicate that the mass-transfer rate is largely enhanced by interfacial turbulence. Correlations for liquid-phase mass-transfer enhancement factors were developed. Introduction Interfacial turbulence can greatly enhance the massor heat-transfer rate across the interface between fluids. The determination of transfer enhancement factors has become important in relation to chemical engineering applications, such as gas-liquid absorption and desorption,1 liquid-liquid extraction,2 distillation,3 and condensation.4 A large amount of experimental work has been conducted to obtain observations of the structure of interfacial convection and quantitative expressions for mass-transfer enhancement factors. Using schlieren techniques, Orell and Westwater2 observed polygonal cells with three to seven or more sides in the ethylene glycol-acetic acid-ethyl acetate liquid-liquid extraction system. Bakker et al.5 continued this study for the ethylene glycol-acetic acid-ethyl acetate, water-acetic acid-isobutyl alcohol, and wateracetic acid-ethyl acetate liquid-liquid extraction systems. They obtained optical results similar to those of Orell and Westwater. Imaishi and Fujinawa6 studied interfacial turbulence accompanying chemical absorption with a vertical-plane wetted-wall gas-liquid contactor. They observed stripe flow patterns in falling liquid films. Cellular convection caused by buoyancy due to gravity fields, or the Rayleigh effect, has an important influence on mass-transfer rates in gas-liquid mass-transfer processes. Burger et al.7 performed unsteady masstransfer experiments with sulfur dioxide being absorbed into deep water layers. They found that the masstransfer rates were enhanced by Rayleigh instability. Hozawa et al.8 conducted carbon dioxide absorption experiments on stationary organic solvents with a liquid depth of 5.95 cm. They found that the rate of absorption was greater than that predicted by penetration theory when the liquid density increased with increasing absorbed-gas concentration. * To whom all correspondence should be addressed. Tel.: 64 3 479 7812. Fax: 64 3 479 0964. E-mail: zhifa@ physics.otago.ac.nz.
Cellular convection driven by interfacial tension inhomogeneities, or the Marangoni effect, also has a significant influence on mass-transfer rates in two-fluid systems. Among other authors, Brian et al.1 experimentally investigated the effect of cellular convection on the gas-liquid mass-transfer rate of the desorption process of four surface-tension-lowering solutes from aqueous solution in a short wetted-wall column. The masstransfer coefficients were enhanced as much as 3.6-fold by cellular convection when the Marangoni number was increased above its critical value. Imaishi et al.9 extended this study and conducted experiments on the desorption of six surface-active solutes from their aqueous solutions in a liquid-jet column and a wetted-wall column. They correlated the enhancement factor R and the Marangoni number Ma using the relation R ) (Ma/Mac)n, where n is a constant equal to 0.4 ( 0.1. A common feature of the work by previous authors is that their experiments were conducted in a way to eliminate the Rayleigh effect or the Marangoni effect. In fact, in a two-fluid mass-transfer process, both the Marangoni and Rayleigh effects can enhance or inhibit each other, as described by the linear theory of Nield,10 which was demonstrated experimentally by Pantaloni et al.11 in their heat-transfer experiments. It is noted that Hozawa et al.12 conducted experiments by absorbing carbon dioxide into nonaqueous solvents using a two-dimensional source flow and a quiescent liquid cell. Because the values of the Marangoni number were negative under their experimental conditions, the Rayleigh effect was inhibited by the Marangoni effect. The quiescent liquid cell and source flow cell used by these authors had liquid depths of 20 and 10 cm, respectively, which are much larger than the thickness of a liquid layer on the surface of modern packings in separation devices. The present authors have extended this study by conducting gas-liquid absorption and desorption experiments in a stationary gas-liquid contactor and in a gas-liquid flow channel, where thin liquid films on a horizontal plane were 1-5 mm thick. Using the gasliquid contactor and the gas-liquid channel, the influ-
10.1021/ie010707+ CCC: $22.00 © 2002 American Chemical Society Published on Web 03/09/2002
1906
Ind. Eng. Chem. Res., Vol. 41, No. 7, 2002
Figure 1. Schematic diagram of experimental apparatus.
ence of both the Rayleigh and Marangoni effects, which can enhance or inhibit each other, was investigated. In this paper, optical observations of interfacial turbulence structures and measured mass-transfer rates are reported. Experimental Apparatus and Procedure The experimental apparatus is shown schematically in Figure 1, which is essentially similar to that used by Byers and King.13 Some features of the experimental systems designed by Imaishi and Fujinawa6 and Hozawa et al.12 were also adopted for optical observations and for unsteady gas-liquid mass-transfer experiments. In the experimental system shown in Figure 1, the most important component is the horizontal channel for the study of interphase mass transfer in stratified, laminar, and cocurrent flow. This gas-liquid channel is slightly different from that used by Byers and King.13 Whereas the length (11 cm) of the gas-liquid contact section is smaller than that of the contact section used by Byers and King, the height (3 cm) and width (11 cm) are larger than the corresponding dimensions of their test section. The aspect ratio, the ratio of the channel width to the thickness of the liquid phase, is equal to 20-50, which is much bigger than the aspect ratio (6) of the channel used by Byers and King.13 To mitigate the end effects, as with the channel used by Byers and King,13 thin horizontal plates were used at the entry and exit of the gas-liquid channel to separate the gas and liquid phases and to guide the liquid flow. The vertical positions of the thin plates could be adjusted to control the depth of the liquid flow layers. Using a reasonably long horizontal exposure, the problems of rippling in mass-transfer devices involving liquid flow over vertical surfaces can be minimized.13
In particular, a horizontal exposure allows us to investigate the Rayleigh effect together with the Marangoni effect on the mass-transfer rates. Because of the longer exposure in the horizontal channel, the penetration depth is deeper, and hence, the effect of the shape of the concentration distribution in the liquid layer is smaller. A similar device has been used by Davis and Choi14 to study the Raileigh effect on the heat-transfer rate. Steady absorption and desorption experiments were conducted using the gas-liquid channel. The gas used was CO2, and the absorbents were the nonaqueous organic solvents methanol, toluene, chlorobenzene, and isobutanol, which were analytical reagents. Water was also used as an absorbent. When the absorption experiments were conducted, purified CO2 (>98 vol % + air) was mixed with N2 (>99.9 vol %) to obtain the required concentration. Before entering the gas-liquid channel, the gas mixture was saturated with the solvent to prevent liquid evaporation. Meanwhile, the solvent was saturated with N2 to avoid any absorption of N2. In the desorption experiments, the liquid phase consisted of the nonaqueous solvent dissolving a certain amount of CO2, and the gas phase was N2. The gas and liquid flow rates were controlled by rotameters. All experiments were carried out at a temperature of 25 ( 0.5°C and a pressure of 1 atm. Sampling in both the gas and liquid phases was carried out at the inlet and exit of the gas-liquid channel. The cup-mixing concentrations of the gas and liquid phases were analyzed by gas chromatography. The gas-liquid channel can also be used as a stationary gas-liquid contactor for unsteady mass-transfer experiments, if the inlet and exit for both the gas and liquid are closed. A soap-film flowmeter can be used to measure the absorption rate of carbon dioxide.
Ind. Eng. Chem. Res., Vol. 41, No. 7, 2002 1907
The upper and lower boundaries of the test section of the gas-liquid channel are made of optical flat plates. Hence, the structures of cellular convection could be observed through the upper and lower boundaries using optical schlieren photography. As shown in Figure 1, the optical schlieren system consists of two lenses, CM and SM, with diameters of 150 mm and focus lengths of 1500 mm, which serve as the collimating and schlieren lenses, respectively. The other components include a light source (S), which is a 24-V, 250-W halogen lamp; a light source slit (N); a condenser lens (LS); two flat mirrors (M1 and M2); a knife edge (K); and an objective lens (L). The gas-liquid interface was photographed with a still camera. Calculation Method for Mass-Transfer Coefficients and Definition of Enhancement Factors for Mass Transfer For mass transfer during brief exposures of a gas and a liquid in confined flow, it is permissible to consider only the region very near the interface and to neglect the effect of the confining walls on the mass-transfer process. Although a more accurate numerical solution has been obtained by Byers and King,15 for simplicity, we used the analytical solutions15,16 and the addition principle of resistances15 to obtain mass-transfer coefficients from our experimental data. Using the asymptotic solutions for gas-phase controlled mass transfer obtained by Beek and Bakker16 for the case of a > 0 and by Byers and King15 for the case of a < 0, the expressions for the average masstransfer coefficients over the gas-liquid contact distance L of the gas-liquid channel can be obtained for short exposures (a2DgL/U03 , 1) as
( )
U0Dg kcg,avg ) 2 πL
1/2
1 aDg + (a > 0) 4 U0
Equations 3 and 4 for the liquid-phase mass-transfer coefficients are valid only for gas-liquid mass-transfer processes without the occurrence of interfacial turbulence. When the concentration difference between the interface and the bulk liquid is sufficiently high and the penetration depth of the solute is sufficiently large, the buoyancy or the interfacial tension of the liquid layer begins to overcome the viscous force, and cellular or chaotic convection occurs at the interface between the gas and liquid phases. Consequently, the true liquidphase mass-transfer experiments should be larger than those predicted by eqs 3 and 4. The experimental results obtained by Brian et al.1 show that the effect of cellular convection on the gasphase mass-transfer coefficient is negligible, whereas the effect on the liquid mass-transfer coefficient is very strong. Accordingly, the true liquid-phase mass-transfer coefficient can be evaluated by using the addition principle15 as follows
1 1 RT ) kcl,avg Kcl,avg Hkcg,avg
where the average gas-phase mass-transfer coefficient, kcg,avg, is evaluated by eqs 1 and 2. As the mass-transfer rates in the experiments conducted by the present authors were controlled by liquid-phase resistance, the use of eq 5 allows for the effect of gas-phase resistance to be taken into account. In eq 5, the average overall mass-transfer coefficient of the liquid phase, Kcl,avg, can be calculated from the experimental absorption or desorption rate of carbon dioxide, N, using
Kcl,avg )
( )
1/2
1 aDg (a < 0) 4 U0
( )
N)
()
Dl ) πt
Ql(Cl,out - Cl,in) A
(2) C* )
PCO2
1/2
(4)
(8)
H
N)
P∆V RTA∆t
(9)
and the instantaneous true liquid-phase mass-transfer coefficient can be evaluated by
kcl,ins ) (3)
(7)
For unsteady experiments involving carbon dioxide absorption into a quiescent organic solvent film, the absorption rate N can be evaluated from the measured volume change of CO2 in a soap-film flowmeter by
1/2
When both the gas and liquid layers are stationary, unsteady mass transfer occurs, and the instantaneous liquid mass-transfer coefficient is given by 0 kcl,ins
(6)
and
Similar relations have also been derived for long exposures (a2DgL/U03 . 1) from solutions obtained by Beek and Bakker16 for gas-phase controlled mass transfer. In the ranges of the operating conditions of the steady mass-transfer experiments conducted in the gas-liquid channel, it was found that U03/a2Dg is much larger than the contact length of the gas-liquid channel. This indicates that the channel has a short exposure. For liquid-phase controlled mass transfer, the penetration model has been shown to be appropriate,15 according to which the average mass-transfer coefficient of the liquid phase over the gas-liquid contact distance L of the gas-liquid channel is expressed as
U0Dl 0 )2 kcl,avg πL
N C* - Cl,in
(1)
or
U0Dg kcg,avg ) 2 πL
(5)
N C*
(10)
According to Brian et al.,17 the enhancement factor for liquid-phase mass transfer, which is the ratio of the true mass-transfer coefficient to that predicted by penetration theory, is defined as
Φ)
kcl,ins 0 kcl,ins
and Φ )
kcl,avg 0 kcl,avg
(11)
1908
Ind. Eng. Chem. Res., Vol. 41, No. 7, 2002
Table 1. Physical Properties of the Solvents12 solvent
F × 10-3 (kg/m3)
µ × 103 (Pa s)
Dl × 109 (m2/s)
σ0 × 106 (N m2/mol)
R × 106 (m3/mol)
methanol toluene chlorobenzene isobutanol
0.7853 0.8620 1.1008 0.7979
0.553 0.552 0.751 3.319
3.75 4.62 3.76 2.20a
0.955 2.121 2.157 1.323
-11.34 -6.15 1.96 -9.95
a
Hozawa et al.8
Table 2. Variation Ranges of Rayleigh and Marangoni Numbers for Carbon Dioxide and the Organic Solvents Ra solvent methanol toluene chlorobenzene isobutanol
Ma
absorption desorption absorption desorption >0 >0 0
