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Ind. Eng. Chem. Res. 2011, 50, 1778–1785

Correlations of Mass Transfer Coefficients in a Rotating Packed Bed Yu-Shao Chen* Department of Chemical Engineering and R&D Center of Membrane Technology, Chung Yuan UniVersity, Chung Li, 320 Taiwan

The usefulness of a rotating packed bed (RPB) in the absorption and stripping of ammonia and volatile organic compounds (VOCs) has been examined, and numerous correlations of the overall mass transfer coefficient (KGa) have been proposed in the literature. However, these correlations do not provide acceptable predictions concerning other experimental systems. In this study, a local gas-side mass transfer coefficient (kGa) in an RPB is calculated and an empirical correlation is proposed, based on 430 experimental KGa data gathered from the literature. Results showed that, with the aid of the two-film theory and the correlation of the local liquid-side mass transfer coefficient (kLa) reported in our previous work (Chen, Lin et al. 2006), most of the experimental KGa data could be reasonably predicted. The effects of gas flow rate, liquid flow rate, liquid viscosity, and centrifugal acceleration on KGa were found to depend on the ratio of the mass transfer resistances in the gas phase and the liquid phase. Introduction The rotating packed bed (RPB or higee system), which replaces gravity with a centrifugal force of up to several hundred times the gravitational force, was recently developed as an alternative to conventional packed columns for improving the mass transfer efficiency. The device consists of a rotor, which is filled with packing material, a driving motor, and static housing, as displayed in Figure 1. Liquid enters the device from the liquid distributor at the center and is sprayed to the interior face of the rotor. Under a strong centrifugal field, thin liquid films and tiny liquid droplets are generated and flow chaotically through the packing, producing a large gas-liquid interfacial area and causing intensive mixing. Gas enters the RPB from the outer static housing, flows inward through the packing, and, consequently, contacts counter-currently the liquid in the rotor. Higher gas and liquid flow rates can be achieved in an RPB than in a conventional packed column, corresponding to higher capacity and mass transfer efficiency, because the centrifugal field reduces the tendency to flood. In recent years, RPBs have been widely applied for numerous purposes, such as stripping,1-4 absorption,5-8 distillation,9,10 adsorption,11,12 desorption,13 and production of nanoparticles.14,15 The characteristics of mass transfer in an RPB have been extensively studied. Some researchers have theoretically derived correlations for a local liquid-side mass transfer coefficient. For example, in 1985, Tung and Mah16 proposed a correlation for a liquid-side mass transfer coefficient, kL, based on the penetration theory and developed a laminar flow film model without considering the Coriolis force or the effect of the packing geometry. With the correlation of gas-liquid interfacial area for a conventional packed column, they found that the correlation could reasonably predict the experimental data of kLa reported by Ramshaw and Mallinson.5 In 1989, Munjal et al.17 proposed a correlation for kL, based on a model of the developed laminar film flow on a rotating disk and a rotating blade. Experiments on liquid-side-controlled mass transfer processes are usually carried out in an oxygen-water system because the gas-side mass transfer resistance in such a system can be neglected. In 1981, Ramshaw and Mallinson5 absorbed oxygen * To whom correspondence should be addressed. Tel.: +886-32654131. Fax: +886-3-2654199. E-mail: [email protected].

in water in an RPB and obtained a mass transfer coefficient that was 27-44 times higher than that in a conventional packed bed. In 2005, Chen et al.2 explored the effect of liquid viscosity on the rate of mass transfer in the deoxygenation of glycerol solution (Newtonian fluid) and CMC solution (non-Newtonian fluid). They found that the centrifugal force effectively enhanced the liquid-side mass transfer coefficient in viscous media. They also noticed that the dependence of the mass transfer coefficient on liquid viscosity was weaker in an RPB than in a conventional packed column. In 2005, Chen et al.3 investigated the mass transfer performance of RPBs with various rotor sizes in stripping oxygen from water to evaluate the end effect. In 2006, Chen et al.4 conducted deoxygenation in an RPB that was packed with various types of packing. A correlation which includes the end effect and the packing effect was found, which was effective in predicting kLa.

Figure 1. Main structure of a rotating packed bed.

10.1021/ie101251z  2011 American Chemical Society Published on Web 01/10/2011

Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011

(

)

kLadp Vo Vi 0.17 0.3 0.3 1 - 0.93 - 1.13 ) 0.35Sc0.5 L ReL GrL WeL DLat Vt Vt at -0.5 σc 0.14 (1) ap′ σw

() ( )

The ranges of the dimensionless groups in eq 1 are 10.26 e (kLadp)/(DLat) e 2.89 × 103, 0.12 e (1 - 0.93Vo/Vt - 1.13Vi/ Vt) e 0.65, 4.95 × 102 e ScL e 1.19 × 105, 2.30 × 10-3 e ReL e 8.76, 61.59 e GrL e 2.36 × 108, 3.73 × 10-6 e WeL e 9.43 × 10-4, 0.23 e at/ap′ e 0.69, and 0.30 e σc/σw e 1.03. Their results revealed that this correlation was useful in predicting the kLa values in an RPB with various forms of packing, bed sizes, and viscous Newtonian and non-Newtonian fluids. Most of the kLa values reported in the higee literature can also be reasonably estimated using this correlation. While there are several studies of a liquid-side-controlled mass transfer system, only a few results concerning the gasside-controlled process in an RPB have been published, mainly because the flow pattern of gas in an RPB is quite complicated and so establishing a model for predicting the gas-side mass transfer coefficient is very difficult. In 2000, Zheng et al.18 developed a model of the flow pattern of gas based on conservation of the angular momentum of the gas phase. They obtained the velocity profile of the gas across an RPB. Their results showed that the angular velocity of the gas outside the rotor increased as the gas moved inward owing to the conservation of angular momentum. However, the relative angular velocity between the gas and the packing was very low in the rotor, because the packing retarded the rotation of gas. In 2001, Sandilya et al.19 suggested that the gas rotated like a solid body in the rotor because of the drag that was caused by the packing and that, consequently, the gas-side mass transfer coefficient should be similar to that in a conventional packed column. In 2002, Chen and Liu6 performed VOCs absorption in an RPB and obtained kG data in a similar range to those for a conventional packed column. They also concluded that an increase in the effective gas-liquid interfacial area was responsible for most of the enhancement of the mass transfer coefficient (KGa) by the centrifugal force. Although the theoretical development of a gas flow model for evaluating the gas-side mass transfer coefficient in an RPB is quite difficult, many experimental measurements of KGa are available in the literature. The physical systems that have been investigated involve the absorption and stripping of ammonia and volatile organic compounds (VOCs), such as ethanol, isopropyl alcohol, acetone, and ethyl acetate. However, the liquid-side mass transfer resistance is not negligible in most of these processes and the overall mass transfer coefficient was obtained in each of the relevant studies. In 1981, Ramshaw and Mallinson5 examined the performance of an RPB by absorbing ammonia in water. Glass beads with a diameter of 1.5 mm and stainless steel gauze were used as the packing materials in the experiment. Their results demonstrated that KGa is enhanced by increasing the centrifugal force. Additionally, the KGa value in an RPB was found to be 4-9 times that in a conventional packed column that was packed with Intalox Saddles. In 1996, Liu et al.1 stripped ethanol from water in an RPB using various plastic pellets as packing material. Their results showed that KGa increased with gas flow rate, liquid flow rate, and rotational speed. The correlations for a conventional packed column underestimated their results. They provided an empirical equation for KGa in an RPB.

KGa DGa2t

) 0.003ReG1.163Re0.631 GrG0.25 L

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(2)

The ranges of the dimensionless groups in eq 2 are 0.21 e (KGa)/(DGat2) e 3.00, 1.82 e ReG e 8.21, 1.34 e ReL e 6.08, and 3.41 × 104 e GrG e 1.70 × 106. In 2002, Chen and Liu6 presented results concerning the absorption of isopropyl alcohol, acetone, and ethyl acetate in water in an RPB that was packed with plastic beads. They attributed the increase in KGa with the centrifugal force to the enhancement of the gas-liquid interfacial area (a). The local gas-side mass transfer coefficient (kG) was found to be independent of the rotational speed, and its value was similar to that in a conventional packed column. They also found that the solute considerably affected the mass transfer efficiency and that Henry’s law constant was included in the correlation of KGa. KGaH0.27 y DGa2t

) 0.077ReG0.323Re0.328 GrG0.18 L

(3)

The ranges of the dimensionless groups in eq 3 are 0.14 e (KGa)/(DGat2) e 1.00, 2.29 e ReG e 4.69, 0.95 e ReL e 2.25, and 8.52 × 102 e GrG e 1.67 × 105. In 2004, Lin et al.7 studied the mass transfer efficiency in an RPB by the absorption of isopropyl alcohol and ethyl acetate in water using high-voidage packing. Their results showed that an RPB that was packed with stainless steel wire meshes could achieve a mass transfer similar to that achievable using lowvoidage RPB. They provided a correlation to estimate the overall mass transfer coefficient in the high-voidage RPB. KGaH0.315 y DGa2t

) 0.061ReG0.712Re0.507 GrG′0.326 L

(4)

The ranges of the dimensionless groups in eq 4 are 0.14 e (KGa)/(DGat2) e 1.00, 2.29 e ReG e 4.69, 0.95 e ReL e 2.25, and 64 e GrG′ e 3.32 × 102. In 2009, Chiang et al.8 examined the performance of the absorption of ethanol by glycerol solution in an RPB that was packed with wire mesh. They investigated the effect of the liquid viscosity on the mass transfer coefficient at various concentrations of the glycerol solutions. Their results indicated that KGa was proportional to the gas flow rate, the liquid flow rate, and the centrifugal acceleration, raised to powers of 0.65-0.87, 0.33-0.51, and 0.28-0.35, respectively. They also found that KGa decreased in proportion to the increase in liquid viscosity raised to the power of 0.21-0.32. Moreover, the enhancement factor of KGa in an RPB and in a conventional packed column increased from 9 to 193 as the absorbent viscosity increased from 1 to 103 mPa · s. Although the gas-flow models in an RPB have been developed and several empirical correlations for KGa can be found in the literature, the related equations have yet to be validated. The purpose of this work is to examine the validity of these equations and to develop an approach to evaluate the mass transfer efficiency in an RPB by local mass transfer coefficients. This study investigated a total of 430 experimental KGa values and values calculated using empirical equations in the literature. The equations examined include the empirical correlations for KGa that have been proposed for an RPB and the ones for a conventional packed column because of similar gas-flow patterns. Additionally, this work obtained the local gas-side mass

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Table 1. Experimental Systems and Specifications of the RPBs Used in the Literature specifications of RPB (cm) authors

experimental systems

ri

ro

z

rs

Ramshaw and Mallinson5 ammonia-water (absorption)

4

9

(2)a

(10)a

Liu et al.1 Chen and Liu6 Lin et al.7 Chiang et al.8

4.5 2 3.5 2

7 4 8 4

2 2 3.5 2

11 6 15 9

a

ethanol-water (stripping) isopropyl alcohol, acetone, ethyl acetate-water (absorption) isopropyl alcohol, ethyl acetate-water (absorption) ethanol-glycerol solutions (absorption)

packing used type

at (1/m)

ε

glass beads wire gauze rectangular grain palstic bead wire mesh wire mesh

2400 1650 524 1200 791 1024

0.40 (0.90)a 0.53 0.4 0.96 0.94

Values estimated.

Table 2. Properties of the Solutes and Absorbents experimental systems ammonia/water isopropyl alcohol/water acetone/water ethyl acetate/water ethanol/water ethanol/glycerol solutions

µL (mPa · s)

σ2 (10-3 kg/s2)

H6,8 [10-4 (mol/L3)/ (mol/L3)]

DL6,22,23 (10-9 m2/s)

DG6,22 (10-6 m2/s)

1 1 1 1 1 1.95 9.32 40.5 102.8

73.0 73.0 73.0 73.0 73.0 71.5 68.6 66.1 64.5

6.70 4.50 17.5 54.7 5.50 4.47 4.17 3.28 2.75

1.64 0.87 1.16 1.00 0.84 0.50 0.15 0.05 0.02

21.9 9.9 9.5 8.7 10.2 10.2

transfer coefficient, kGa, from the experimental systems in the literature using two-film theory, and the local liquid-side mass transfer coefficient, kLa, was estimated by an empirical correlation provided in our previous study, shown as eq 1.4 An empirical equation for kGa was therefore proposed, and the validity of this correlation was examined by comparing experimental KGa data reported in the literature and the calculated results using two-film theory, the correlations for kLa (eq 1), and the equation proposed in this study. Analysis of Mass Transfer Coefficients Two-film theory, expressed as eq 5, describes the mass transfer at the interface in a two-phase system.20 1 H 1 + ) KGa kGa kLa

(5)

In eq 5, H is the Henry’s law constant, KGa is the overall mass transfer coefficient, kGa is the local gas-side mass transfer coefficient, and kLa is the local liquid-side mass transfer coefficient. Equation 5 also states that the total resistance of gas-to-liquid mass transfer equals the sum of the resistances associated with the stagnant liquid and gas interfacial films, given by the following equation. RT ) R G + R L

(6)

In eq 6, RT denotes the overall resistance of mass transfer and RG and RL are gas-side and liquid-side mass transfer resistances, respectively. In this investigation, the local gas-phase mass transfer coefficient, kGa, was calculated based on two-film theory as follows. kGa )

1 H 1 KGa kL a

were used in these investigations. In eq 7, kLa is local liquidside mass transfer coefficient and several relating correlations have been given in the literature based on theoretical and empirical derivations. Tung and Mah16 and Munjal et al.17 theoretically proposed correlations for kL in an RPB based on the developed laminar film flow on a rotating disk. However, Chen et al.4 found that these equations were not applicable for estimating kLa of different types of packing. Singh et al.21 presented an empirical correlation for KLa, and results showed that KLa was proportional to liquid viscosity to a power of 0.3, which is intuitively controversial. On the other hand, Chen et al. correlated the experimental data of kLa in an RPB with various forms of packing, bed sizes, and liquid viscosity. They reported an empirical equation for kLa, shown as eq 1, and proved that this equation was valid for most of the experimental data in the higee literature. In this work, the kLa values in eq 7 were calculated by eq 1. Table 2 presents the properties of the solutes and absorbents in the experiments. The Henry’s law constants of the solutes in water and glycerol solution are taken from the works of Chen and Liu6 and Chiang et al.8 The diffusion coefficients of the solutes in air and water are taken from Cussler22 and Chen and Liu.6 The diffusion coefficients of ethanol in glycerol solution are estimated using the method of Jordan et al.23 The surface tension of the liquid is taken from Chen et al.2

(7)

In eq 7, KGa was obtained from the available literature on the absorption and stripping of ammonia and VOCs, which includes 430 measurements.1,5-8 Table 1 describes in detail the specifications of the equipment and the experimental systems that

Results and Discussion Comparison with Correlations of a Conventional Packed Column. The liquid-side mass transfer in an RPB has been extensively analyzed theoretically. Most of the models used were derived from a film flow of liquid over the packing surface. Although such models lack a theoretical basis since various forms of liquid flow, including droplet and pore flow, can also occur in an RPB, the results of the models have been found to be consistent with experimental results.16,17 However, developing a model of gas-side mass transfer is difficult because the gas flow pattern is much more complicated than the liquid flow pattern. Some studies have mentioned that in view of the negligible tangential slip velocity of the gas in the rotor, the gas flows radially through the packing, whose behavior is similar to that in a conventional packed column.19 Accordingly, the kG

Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011

Figure 2. Comparison of experimental and predicted KGa using correlations in a conventional packed column.

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Figure 3. Comparison of experimental and calculated KGa by eq 2.

values in an RPB should be similar to those in a conventional packed column. Onda et al.24 and Puranik and Vogelpohl25 provided the following commonly used equations for the local liquid and gas mass transfer coefficients, kL and kG, and interfacial area, a, in a conventional packed column. kL ) 0.0051

( ) ( ) FL µLac

-1/3

L µL a

2/3

0.4 Sc-0.5 L (atdp)

kG ) 2atDGReG0.7ScG1/3(atdp)-2

( )

a ) 1.05atRe0.047 We0.135 L L

σ σC

(8)

(9)

-0.206

(10)

Since the kG values in an RPB and a conventional packed column are similar, the consistency of eq 9 with experimental data for an RPB was examined. On the basis of the two-film theory, given by eq 5, kG in an RPB was estimated using eq 9. Equation 10 is used to calculate a because no equation exists for the gas-liquid interfacial area in an RPB. The local liquidside mass transfer coefficient, kLa, in an RPB can be estimated using the empirical correlation that was provided by Chen et al.,4 shown as eq 1. This equation has been proven to estimate reasonably most of the experimental kLa data in the literature for liquid-side-controlled processes in an RPB. Hence, the overall mass transfer coefficient, KGa, can be calculated by substituting eqs 1, 9, and 10 into eq 5. Figure 2 compares the experimental and estimated KGa values. The KGa values that were calculated from the correlations for conventional packed column were much lower than the experimental values, probably because eq 10 underestimates the effective interfacial area in an RPB. Under a centrifugal field, thin liquid films and tiny liquid droplets are generated and flow chaotically in the packing, dramatically increasing the gas-liquid interfacial area. On the other hand, outside the rotor, the gas flow pattern differs considerably from that in the rotor. As a result, the discrepancy between the experimental and the calculated KGa values using eq 9 may also be caused by ignorance of the mass transfer in this region.

Figure 4. Comparison of experimental and calculated KGa by eq 3.

Comparison with Prior Empirical Correlations. In spite of the lack of theoretical models of gas-side mass transfer, several empirical equations for KGa in an RPB have been proposed. They are presented here as eqs 2-4. However, the applicability of these equations to other experimental systems must be investigated. Figures 3-5 compare the experimental KGa data in the literature with the values calculated using eqs 2-4, respectively. Figure 3 reveals that the correlation that was proposed by Liu et al.,1 given by eq 2, effectively predicted their own ethanol-stripping data but clearly underestimated the KGa values in other experimental systems, probably because they used only ethanol as the solute and, therefore, their equation did not capture the effect of different solutes on mass transfer. Figure 4 plots eq 3, which was proposed by Chen and Liu,6 who explored the absorption of IPA, acetone, and ethyl acetate in water in an RPB. The figure shows that although the equation included the Henry’s law constant to correct for the effects of various solutes, some calculations, such as those of Lin et al.,7 clearly deviated from that equation. According to Figure 5, the equation for the absorption of IPA and ethyl acetate in water in a high-voidage RPB, proposed by Lin et al.7 (eq 4), reasonably

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Figure 5. Comparison of experimental and calculated KGa by eq 4.

Figure 6. Comparison of experimental and calculated KGa by this work.

kGa

Table 3. Standard Deviation of the Correlations standard deviation

DGa2t

databases

eq 2

eq 3

eq 4

present work

Ramshaw and Mallinson5 Liu et al.1 Chen and Liu6 Lin et al.7 Chiang et al.8

1.45 0.49 5.57 8.18 7.83

0.72 2.53 2.61 8.82 3.65

0.21 11.41 1.20 1.05 3.28

0.29 0.77 2.22 2.24 1.53

estimated most of the experimental data. However, it overestimated the data of Liu et al.1 and underestimated some of the data of Chiang et al.,8 which were obtained using viscous glycerol solutions. Table 3 presents the standard deviations of the results calculated using eqs 2-4. According to Figures 3-5, another possible cause of the deviation between the calculated and the experimental results may be the various packings and sizes of the rotors used in these investigations. The packing effect and end effect in an RPB have been studied in a deoxygenation system, and an equation for kLa, eq 1, has been proposed.3,4 These two effects should also be considered in deriving an equation for a gasside controlling process. Additionally, although the Henry’s law constant was included in eqs 3 and 4, these equations still did not give satisfactory results. In fact, the powers of the dimensionless groups in the correlations for KGa should not be constant as the mass transfer resistances in the gas and liquid phases vary. Consequently, the correlations for local mass transfer coefficients are more useful in evaluating the mass transfer efficiency. Correlation of Present Work. In this work, the local volumetric mass transfer coefficients (kGa and kLa) were of particular interest because the effective interfacial area in an RPB is difficult to obtain. The equation for kLa, eq 1, was presented in our earlier study.4 Therefore, the local gas-side mass transfer coefficient, kGa, in an RPB can be calculated using eq 7, where KGa is obtained from the experimental data in the literature1,5-8 and kLa was calculated using eq 1. Then, an empirical equation for kGa in a rotating packed bed can be obtained.

(

1 - 0.9

)

()

Vo at 0.31 0.07 ) 0.023ReG1.13Re0.14 L GrG WeL Vt ap′

1.4

(11) In eq 11, ap′ is the surface area per unit volume of the 2 mm diameter bead and has a value of 3000 m2/m3. The ranges of the dimensionless groups in eq 11 are 6.46 × 10-2 e (kGa)/ (DGat2) e 5.35, 0.28 e (1 - 0.9Vo/Vt) e 0.83, 1.15 e ReG e 8.98, 1.60 × 10-3 e ReL e 6.08, 8.52 × 102 e GrG e 1.20 × 107, 5.37 × 10-8 e WeL e 2.66 × 10-4, and 0.17 e at/ap′ e 0.80. The local gas-side mass transfer coefficient, kGa, is proportional to the gas flow rate, the liquid flow rate, the centrifugal acceleration, and the liquid viscosity raised to powers of 1.13, 0.28, 0.31, and -0.14, respectively. Figure 6 compares experimental KGa values in the higee literature and values calculated using two-film theory (eq 5), where the values of kLa and kGa were calculated by eqs 1 and 11, respectively. It can be seen that most of the overall mass transfer coefficients in various experimental systems are reasonably predicted, probably because the mass transfer resistances in the two phases can be properly estimated by the empirical equations. The standard deviation in this study was less than that for other empirical equations, as indicated in Table 3. The effects of gas and liquid flow rates, centrifugal acceleration, and liquid viscosity on the overall mass transfer coefficient, expressed as KGa ∝ QGmQLnacpµLq, were also investigated. The values of m, n, p, and q can be estimated from the equations for kLa and kGa (eqs 1 and 11) and the two-film theory. For comparison, the powers obtained from prior empirical equations for KGa (eqs 2-4) are also examined. The exponents for a conventional packed column were evaluated using eqs 8-10. Figure 7 plots m, n, p, and q as a function of RG/RT. Figure 7a and 7b shows that the value of m calculated using eqs 1 and 11 increases from 0 to 1.13 as the liquid-sidecontrolled mass transfer process becomes a gas-side-controlled process. Similarly, n declines from 0.77 to 0.28, indicating that the liquid flow rate most strongly affects KGa in the liquidside-controlled process. The m and n values calculated using eqs 2-4 were constants, limiting the applicability of these equations to various mass transfer processes. However, the values of m and n obtained from eqs 2-4 were close to those calculated by eqs 1 and 11. Furthermore, the mass transfer

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Figure 7. Effect of RG/RT on m, n, p, and q for different correlations.

coefficient in an RPB was more obviously influenced by the gas flow rate than that in a conventional packed column, and the effect of liquid flow rate on the mass transfer coefficient was similar in the two equipments. In Figure 7c and 7d, KGa obtained in this investigation was not apparently changed with centrifugal acceleration (p ) 0.30-0.31) under various mass transfer resistances. The p value was larger than those obtained from eqs 2 and 3 and similar to that of Lin et al.7 (eq 4) and Chiang et al.8 (p ) 0.28-0.35). With respect to the effect of liquid viscosity, the q value obtained in this work increased from -0.27 to -0.14 as the gas-side mass transfer resistance increased. This finding implies that the mass transfer efficiency is less influenced by the liquid viscosity in a gas-side-controlled transfer process than in a liquid-sidecontrolled transfer process. The q values obtained in this work were clearly higher than those obtained from eqs 2-4, probably because the effect of liquid viscosity was not actually investigated in studies from which eqs 2-4 were taken. Chiang et al.8 conducted ethanol absorption in glycerol solution to study

the effect of liquid viscosity on mass transfer. Their results demonstrated that KGa decreased with liquid viscosity by an exponent of 0.21-0.32, which was similar to the finding in this study. Conclusion Although liquid-side mass transfer in an RPB has been extensively examined, gas-side mass transfer is still poorly understood. Models of gas-side mass transfer are difficult to develop because the gas flow is complicated. However, the experimental data from which KGa for the absorption and stripping of ammonia and VOCs in an RPB can be found in the literature. Several empirical equations for KGa have been proposed. This study investigated a total of 430 experimental KGa values and values calculated using empirical equations in the literature. The results revealed that the experimental KGa values were underestimated using the equations for kG and a that have been proposed for a conventional packed column.

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Although the kG values in an RPB are expected to be similar to the values in a conventional packed column, because the gas flow patterns inside the rotor are similar, the gas-liquid interfacial area in the RPB may be much larger. The empirical equations for KGa in the higee literature may not accurately predict the experimental results of different physical systems. Possible reasons for the deviation include the effect of packing, size of the equipment, and liquid viscosity. Moreover, the empirical equations for KGa cannot reasonably predict the experimental values because the mass transfer resistances in gas and liquid phases vary among experimental systems. In this investigation, a local mass transfer coefficient, kGa, was obtained using two-film theory, the correlation for kLa that was provided by Chen et al.,4 and the experimental KGa data were taken from the higee literature.1,5-8 An empirical equation for kGa was therefore proposed and found to estimate reasonably most obtained experimental data that related to KGa in an RPB. The value of kGa was found to be proportional to the gas flow rate, the liquid flow rate, the centrifugal acceleration, and the liquid viscosity raised to powers of 1.13, 0.28, 0.31, and -0.14, respectively. The overall mass transfer coefficient in an RPB increased with the gas flow rate and the liquid flow rate to powers of 0-1.13 and 0.28-0.77, respectively, and decreased with liquid viscosity to the power of 0.14-0.27. The exact exponents depended on the ratio of the mass transfer resistance in the gas phase to that in the liquid phase. Additionally, KGa was proportional to the centrifugal acceleration to the power of 0.3 and was not significantly affected by the ratio of mass transfer resistances. Acknowledgment The author wishes to express the sincere gratitude to the Center-of-Excellence (COE) Program on Membrane Technology from the Ministry of Education (MOE), R.O.C., to the project Toward Sustainable Green Technology in the Chung Yuan Christian University, Taiwan, and the National Science Council (NSC) for their financial support. Nomenclature a ) gas-liquid interfacial area (1/m) ac ) centrifugal acceleration (m/s2) ap′ ) surface area of the 2 mm diameter bead per unit volume of the bead (1/m) at ) surface area of the packing per unit volume of the bed (1/m) DG ) diffusion coefficient in the gas phase (m2/s) DL ) diffusion coefficient in the liquid phase (m2/s) dp ) spherical equivalent diameter of the packing ) (6(1 - ε))/ (atψ) (m) dp′ ) spherical equivalent diameter of the packing ) (6(1 - ε))/at (m) G ) gas mass flux [kg/(m2s)] H ) Henry’s law constant [(mol/L)/(mol/L)] Hy ) Henry’s law constant [(mol/mol)/(mol/mol)] KGa ) overall volumetric gas-side mass transfer coefficient (1/s) KLa ) overall volumetric liquid-side mass transfer coefficient (1/s) kG ) local gas-side mass transfer coefficient (m/s) kGa ) local volumetric gas-side mass transfer coefficient (1/s) kLa ) local volumetric liquid-side mass transfer coefficient (1/s) L ) liquid mass flux [kg/(m2s)] QG ) gas flow rate (m3/s) QL ) liquid flow rate (m3/s) RG ) 1/(kGa) ) mass transfer resistance in the gas phase (s)

RL ) H/(kLa) ) mass transfer resistance in the liquid phase (s) RT ) 1/(KGa)) total mass transfer resistance (s) ri ) inner radius of the packed bed (m) ro ) outer radius of the packed bed (m) rs ) radius of the stationary housing (m) Vi ) volume inside the inner radius of the bed ) πri2z (m3) Vo ) volume between the outer radius of the bed and the stationary housing ) π(rs2 - ro2)z (m3) Vt ) total volume of the RPB ) πrs2z (m3) z ) axial height of the packing (m) Greek Letters ε ) porosity of the packing µG ) viscosity of gas (Pa · s) µL ) viscosity of liquid (Pa · s) FG ) density of gas (kg/m3) FL ) density of liquid (kg/m3) ψ ) sphericity of packing σ ) surface tension (kg/s2) σc ) critical surface tension of packing (kg/s2) σw ) surface tension of water (kg/s2) Dimensionless Groups GrG ) gas Grashof number ) dp3acFG2/µG2 GrG′ ) gas Grashof number ) dp′3acFG2/µG2 GrL ) liquid Grashof number ) dp3acFL2/µL2 ReG ) gas Reynolds number ) G/atµG ReL ) liquid Reynolds number ) L/atµL ScG ) gas Schmidt number ) µG/FGDG ScL ) liquid Schmidt number ) µL/FLDL WeL ) liquid Weber number ) L2/FLatσ

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ReceiVed for reView June 8, 2010 ReVised manuscript receiVed November 2, 2010 Accepted December 3, 2010 IE101251Z