correlations of mass transfer coefficients in a rotating packed bed

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 volatileorganic compounds (VOCs) has been examined, and numerous correlations of the overall mass transfercoefficient (KGa) have been proposed in the literature. However, these correlations do not provide acceptablepredictions 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 datagathered from the literature. Results showed that, with the aid of the two-film theory and the correlation ofthe 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 flowrate, liquid viscosity, and centrifugal acceleration on KGa were found to depend on the ratio of the masstransfer resistances in the gas phase and the liquid phase.

Introduction

The rotating packed bed (RPB or higee system), whichreplaces gravity with a centrifugal force of up to several hundredtimes the gravitational force, was recently developed as analternative to conventional packed columns for improving themass transfer efficiency. The device consists of a rotor, whichis filled with packing material, a driving motor, and statichousing, as displayed in Figure 1. Liquid enters the device fromthe liquid distributor at the center and is sprayed to the interiorface of the rotor. Under a strong centrifugal field, thin liquidfilms and tiny liquid droplets are generated and flow chaoticallythrough the packing, producing a large gas-liquid interfacialarea and causing intensive mixing. Gas enters the RPB fromthe 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 RPBthan in a conventional packed column, corresponding to highercapacity and mass transfer efficiency, because the centrifugalfield reduces the tendency to flood. In recent years, RPBs havebeen widely applied for numerous purposes, such as stripping,1-4

absorption,5-8 distillation,9,10 adsorption,11,12 desorption,13 andproduction of nanoparticles.14,15

The characteristics of mass transfer in an RPB have beenextensively studied. Some researchers have theoretically derivedcorrelations for a local liquid-side mass transfer coefficient. Forexample, in 1985, Tung and Mah16 proposed a correlation fora liquid-side mass transfer coefficient, kL, based on the penetra-tion theory and developed a laminar flow film model withoutconsidering the Coriolis force or the effect of the packinggeometry. With the correlation of gas-liquid interfacial areafor a conventional packed column, they found that the correla-tion could reasonably predict the experimental data of kLareported by Ramshaw and Mallinson.5 In 1989, Munjal et al.17

proposed a correlation for kL, based on a model of the developedlaminar film flow on a rotating disk and a rotating blade.

Experiments on liquid-side-controlled mass transfer processesare usually carried out in an oxygen-water system because thegas-side mass transfer resistance in such a system can beneglected. In 1981, Ramshaw and Mallinson5 absorbed oxygen

in water in an RPB and obtained a mass transfer coefficientthat was 27-44 times higher than that in a conventional packedbed. In 2005, Chen et al.2 explored the effect of liquid viscosityon the rate of mass transfer in the deoxygenation of glycerolsolution (Newtonian fluid) and CMC solution (non-Newtonianfluid). They found that the centrifugal force effectively enhancedthe liquid-side mass transfer coefficient in viscous media. Theyalso noticed that the dependence of the mass transfer coefficienton liquid viscosity was weaker in an RPB than in a conventionalpacked column. In 2005, Chen et al.3 investigated the masstransfer performance of RPBs with various rotor sizes instripping oxygen from water to evaluate the end effect. In 2006,Chen et al.4 conducted deoxygenation in an RPB that waspacked with various types of packing. A correlation whichincludes the end effect and the packing effect was found, whichwas effective in predicting kLa.

* To whom correspondence should be addressed. Tel.: +886-3-2654131. Fax: +886-3-2654199. E-mail: [email protected]. Figure 1. Main structure of a rotating packed bed.

Ind. Eng. Chem. Res. 2011, 50, 1778–17851778

10.1021/ie101251z 2011 American Chemical SocietyPublished on Web 01/10/2011

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 eReL e 8.76, 61.59 e GrL e 2.36 × 108, 3.73 × 10-6 e WeL e9.43 × 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 inpredicting the kLa values in an RPB with various forms ofpacking, bed sizes, and viscous Newtonian and non-Newtonianfluids. Most of the kLa values reported in the higee literaturecan also be reasonably estimated using this correlation.

While there are several studies of a liquid-side-controlledmass transfer system, only a few results concerning the gas-side-controlled process in an RPB have been published, mainlybecause the flow pattern of gas in an RPB is quite complicatedand so establishing a model for predicting the gas-side masstransfer coefficient is very difficult. In 2000, Zheng et al.18

developed a model of the flow pattern of gas based onconservation of the angular momentum of the gas phase. Theyobtained the velocity profile of the gas across an RPB. Theirresults showed that the angular velocity of the gas outside therotor increased as the gas moved inward owing to the conserva-tion of angular momentum. However, the relative angularvelocity between the gas and the packing was very low in therotor, because the packing retarded the rotation of gas. In 2001,Sandilya et al.19 suggested that the gas rotated like a solid bodyin the rotor because of the drag that was caused by the packingand that, consequently, the gas-side mass transfer coefficientshould be similar to that in a conventional packed column. In2002, Chen and Liu6 performed VOCs absorption in an RPBand obtained kG data in a similar range to those for aconventional packed column. They also concluded that anincrease in the effective gas-liquid interfacial area wasresponsible for most of the enhancement of the mass transfercoefficient (KGa) by the centrifugal force.

Although the theoretical development of a gas flow modelfor evaluating the gas-side mass transfer coefficient in an RPBis quite difficult, many experimental measurements of KGa areavailable in the literature. The physical systems that have beeninvestigated involve the absorption and stripping of ammoniaand volatile organic compounds (VOCs), such as ethanol,isopropyl alcohol, acetone, and ethyl acetate. However, theliquid-side mass transfer resistance is not negligible in most ofthese processes and the overall mass transfer coefficient wasobtained in each of the relevant studies. In 1981, Ramshaw andMallinson5 examined the performance of an RPB by absorbingammonia in water. Glass beads with a diameter of 1.5 mm andstainless steel gauze were used as the packing materials in theexperiment. Their results demonstrated that KGa is enhancedby increasing the centrifugal force. Additionally, the KGa valuein an RPB was found to be 4-9 times that in a conventionalpacked column that was packed with Intalox Saddles.

In 1996, Liu et al.1 stripped ethanol from water in an RPBusing various plastic pellets as packing material. Their resultsshowed that KGa increased with gas flow rate, liquid flow rate,and rotational speed. The correlations for a conventional packedcolumn underestimated their results. They provided an empiricalequation for KGa in an RPB.

The ranges of the dimensionless groups in eq 2 are 0.21 e(KGa)/(DGat

2) 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 theabsorption of isopropyl alcohol, acetone, and ethyl acetate inwater in an RPB that was packed with plastic beads. Theyattributed the increase in KGa with the centrifugal force to theenhancement of the gas-liquid interfacial area (a). The localgas-side mass transfer coefficient (kG) was found to be inde-pendent of the rotational speed, and its value was similar tothat in a conventional packed column. They also found that thesolute considerably affected the mass transfer efficiency andthat Henry’s law constant was included in the correlation ofKGa.


2) 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 anRPB by the absorption of isopropyl alcohol and ethyl acetatein water using high-voidage packing. Their results showed thatan RPB that was packed with stainless steel wire meshes couldachieve a mass transfer similar to that achievable using low-voidage RPB. They provided a correlation to estimate the overallmass transfer coefficient in the high-voidage RPB.


2) 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 theabsorption of ethanol by glycerol solution in an RPB that waspacked with wire mesh. They investigated the effect of the liquidviscosity on the mass transfer coefficient at various concentra-tions of the glycerol solutions. Their results indicated that KGawas proportional to the gas flow rate, the liquid flow rate, andthe centrifugal acceleration, raised to powers of 0.65-0.87,0.33-0.51, and 0.28-0.35, respectively. They also found thatKGa decreased in proportion to the increase in liquid viscosityraised to the power of 0.21-0.32. Moreover, the enhancementfactor of KGa in an RPB and in a conventional packed columnincreased from 9 to 193 as the absorbent viscosity increasedfrom 1 to 103 mPa · s.

Although the gas-flow models in an RPB have been devel-oped and several empirical correlations for KGa can be foundin the literature, the related equations have yet to be validated.The purpose of this work is to examine the validity of theseequations and to develop an approach to evaluate the masstransfer efficiency in an RPB by local mass transfer coefficients.This study investigated a total of 430 experimental KGa valuesand values calculated using empirical equations in the literature.The equations examined include the empirical correlations forKGa that have been proposed for an RPB and the ones for aconventional packed column because of similar gas-flow pat-terns. Additionally, this work obtained the local gas-side mass

kLadp

DLat(1 - 0.93

Vo

Vt- 1.13

Vi

Vt) ) 0.35ScL

0.5ReL0.17GrL

0.3WeL0.3

( at

ap′ )-0.5( σc

σw)0.14

(1)

KGa

DGat2) 0.003ReG

1.163ReL0.631GrG

0.25 (2)

KGaHy0.27

DGat2

) 0.077ReG0.323ReL

0.328GrG0.18 (3)

KGaHy0.315

DGat2

) 0.061ReG0.712ReL

0.507GrG′0.326 (4)

Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011 1779

transfer coefficient, kGa, from the experimental systems in theliterature using two-film theory, and the local liquid-side masstransfer coefficient, kLa, was estimated by an empirical correla-tion provided in our previous study, shown as eq 1.4 Anempirical equation for kGa was therefore proposed, and thevalidity of this correlation was examined by comparing experi-mental KGa data reported in the literature and the calculatedresults 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 masstransfer at the interface in a two-phase system.20

In eq 5, H is the Henry’s law constant, KGa is the overall masstransfer coefficient, kGa is the local gas-side mass transfercoefficient, and kLa is the local liquid-side mass transfercoefficient. Equation 5 also states that the total resistance ofgas-to-liquid mass transfer equals the sum of the resistancesassociated with the stagnant liquid and gas interfacial films,given by the following equation.

In eq 6, RT denotes the overall resistance of mass transfer andRG and RL are gas-side and liquid-side mass transfer resistances,respectively.

In this investigation, the local gas-phase mass transfercoefficient, kGa, was calculated based on two-film theory asfollows.

In eq 7, KGa was obtained from the available literature on theabsorption and stripping of ammonia and VOCs, which includes430 measurements.1,5-8 Table 1 describes in detail the speci-fications of the equipment and the experimental systems that

were used in these investigations. In eq 7, kLa is local liquid-side mass transfer coefficient and several relating correlationshave been given in the literature based on theoretical andempirical derivations. Tung and Mah16 and Munjal et al.17

theoretically proposed correlations for kL in an RPB based onthe developed laminar film flow on a rotating disk. However,Chen et al.4 found that these equations were not applicable forestimating kLa of different types of packing. Singh et al.21

presented an empirical correlation for KLa, and results showedthat KLa was proportional to liquid viscosity to a power of 0.3,which is intuitively controversial. On the other hand, Chen etal. correlated the experimental data of kLa in an RPB withvarious forms of packing, bed sizes, and liquid viscosity. Theyreported an empirical equation for kLa, shown as eq 1, andproved that this equation was valid for most of the experimentaldata in the higee literature. In this work, the kLa values in eq 7were calculated by eq 1.

Table 2 presents the properties of the solutes and absorbentsin the experiments. The Henry’s law constants of the solutes inwater and glycerol solution are taken from the works of Chenand Liu6 and Chiang et al.8 The diffusion coefficients of thesolutes in air and water are taken from Cussler22 and Chen andLiu.6 The diffusion coefficients of ethanol in glycerol solutionare estimated using the method of Jordan et al.23 The surfacetension of the liquid is taken from Chen et al.2

Results and Discussion

Comparison with Correlations of a ConventionalPacked Column. The liquid-side mass transfer in an RPB hasbeen extensively analyzed theoretically. Most of the models usedwere derived from a film flow of liquid over the packing surface.Although such models lack a theoretical basis since variousforms of liquid flow, including droplet and pore flow, can alsooccur in an RPB, the results of the models have been found tobe consistent with experimental results.16,17 However, develop-ing a model of gas-side mass transfer is difficult because thegas flow pattern is much more complicated than the liquid flowpattern. Some studies have mentioned that in view of thenegligible tangential slip velocity of the gas in the rotor, thegas flows radially through the packing, whose behavior is similarto that in a conventional packed column.19 Accordingly, the kG

Table 1. Experimental Systems and Specifications of the RPBs Used in the Literature

specifications of RPB (cm) packing used

authors experimental systems ri ro z rs type at (1/m) ε

Ramshaw and Mallinson5 ammonia-water (absorption) 4 9 (2)a (10)a glass beads 2400 0.40wire gauze 1650 (0.90)a

Liu et al.1 ethanol-water (stripping) 4.5 7 2 11 rectangular grain 524 0.53Chen and Liu6 isopropyl alcohol, acetone, ethyl acetate-water (absorption) 2 4 2 6 palstic bead 1200 0.4Lin et al.7 isopropyl alcohol, ethyl acetate-water (absorption) 3.5 8 3.5 15 wire mesh 791 0.96Chiang et al.8 ethanol-glycerol solutions (absorption) 2 4 2 9 wire mesh 1024 0.94

a Values estimated.

Table 2. Properties of the Solutes and Absorbents

experimental systemsµL

(mPa · s)σ2

(10-3 kg/s2)H6,8 [10-4 (mol/L3)/

(mol/L3)]DL

6,22,23

(10-9 m2/s)DG

6,22

(10-6 m2/s)

ammonia/water 1 73.0 6.70 1.64 21.9isopropyl alcohol/water 1 73.0 4.50 0.87 9.9acetone/water 1 73.0 17.5 1.16 9.5ethyl acetate/water 1 73.0 54.7 1.00 8.7ethanol/water 1 73.0 5.50 0.84 10.2ethanol/glycerol solutions 1.95 71.5 4.47 0.50 10.2

9.32 68.6 4.17 0.1540.5 66.1 3.28 0.05102.8 64.5 2.75 0.02

1KGa

) 1kGa

+ HkLa

(5)

RT ) RG + RL (6)

kGa ) 11

KGa- H

kLa

(7)

1780 Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011

values in an RPB should be similar to those in a conventionalpacked column.

Onda et al.24 and Puranik and Vogelpohl25 provided thefollowing commonly used equations for the local liquid andgas mass transfer coefficients, kL and kG, and interfacial area,a, in a conventional packed column.

Since the kG values in an RPB and a conventional packedcolumn are similar, the consistency of eq 9 with experimentaldata for an RPB was examined. On the basis of the two-filmtheory, given by eq 5, kG in an RPB was estimated using eq 9.Equation 10 is used to calculate a because no equation existsfor the gas-liquid interfacial area in an RPB. The local liquid-side mass transfer coefficient, kLa, in an RPB can be estimatedusing the empirical correlation that was provided by Chen etal.,4 shown as eq 1. This equation has been proven to estimatereasonably most of the experimental kLa data in the literaturefor liquid-side-controlled processes in an RPB. Hence, theoverall mass transfer coefficient, KGa, can be calculated bysubstituting eqs 1, 9, and 10 into eq 5. Figure 2 compares theexperimental and estimated KGa values. The KGa values thatwere calculated from the correlations for conventional packedcolumn were much lower than the experimental values, probablybecause eq 10 underestimates the effective interfacial area inan RPB. Under a centrifugal field, thin liquid films and tinyliquid droplets are generated and flow chaotically in the packing,dramatically increasing the gas-liquid interfacial area. On theother hand, outside the rotor, the gas flow pattern differsconsiderably from that in the rotor. As a result, the discrepancybetween the experimental and the calculated KGa values usingeq 9 may also be caused by ignorance of the mass transfer inthis region.

Comparison with Prior Empirical Correlations. In spiteof the lack of theoretical models of gas-side mass transfer,several empirical equations for KGa in an RPB have beenproposed. They are presented here as eqs 2-4. However, theapplicability of these equations to other experimental systemsmust be investigated. Figures 3-5 compare the experimentalKGa data in the literature with the values calculated using eqs2-4, respectively. Figure 3 reveals that the correlation that wasproposed by Liu et al.,1 given by eq 2, effectively predictedtheir own ethanol-stripping data but clearly underestimated theKGa values in other experimental systems, probably becausethey used only ethanol as the solute and, therefore, their equationdid 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 acetatein water in an RPB. The figure shows that although the equationincluded the Henry’s law constant to correct for the effects ofvarious solutes, some calculations, such as those of Lin et al.,7

clearly deviated from that equation. According to Figure 5, theequation for the absorption of IPA and ethyl acetate in water ina high-voidage RPB, proposed by Lin et al.7 (eq 4), reasonably

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

kL ) 0.0051( FL

µLac)-1/3( L

µLa)2/3ScL

-0.5(atdp)0.4 (8)

kG ) 2atDGReG0.7ScG

1/3(atdp)-2 (9)

a ) 1.05atReL0.047WeL

0.135( σσC

)-0.206(10)

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

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


estimated most of the experimental data. However, it overes-timated the data of Liu et al.1 and underestimated some of thedata of Chiang et al.,8 which were obtained using viscousglycerol solutions. Table 3 presents the standard deviations ofthe results calculated using eqs 2-4.

According to Figures 3-5, another possible cause of thedeviation between the calculated and the experimental resultsmay be the various packings and sizes of the rotors used inthese investigations. The packing effect and end effect in anRPB have been studied in a deoxygenation system, and anequation for kLa, eq 1, has been proposed.3,4 These two effectsshould also be considered in deriving an equation for a gas-side controlling process. Additionally, although the Henry’s lawconstant was included in eqs 3 and 4, these equations still didnot give satisfactory results. In fact, the powers of thedimensionless groups in the correlations for KGa should not beconstant as the mass transfer resistances in the gas and liquidphases vary. Consequently, the correlations for local masstransfer coefficients are more useful in evaluating the masstransfer efficiency.

Correlation of Present Work. In this work, the localvolumetric mass transfer coefficients (kGa and kLa) were ofparticular interest because the effective interfacial area in anRPB is difficult to obtain. The equation for kLa, eq 1, waspresented in our earlier study.4 Therefore, the local gas-side masstransfer coefficient, kGa, in an RPB can be calculated using eq7, where KGa is obtained from the experimental data in theliterature1,5-8 and kLa was calculated using eq 1. Then, anempirical equation for kGa in a rotating packed bed can beobtained.

In eq 11, ap′ is the surface area per unit volume of the 2 mmdiameter bead and has a value of 3000 m2/m3. The ranges ofthe dimensionless groups in eq 11 are 6.46 × 10-2 e (kGa)/(DGat

2) e 5.35, 0.28 e (1 - 0.9Vo/Vt) e 0.83, 1.15 e ReG e8.98, 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′ e0.80. The local gas-side mass transfer coefficient, kGa, isproportional to the gas flow rate, the liquid flow rate, thecentrifugal acceleration, and the liquid viscosity raised to powersof 1.13, 0.28, 0.31, and -0.14, respectively.

Figure 6 compares experimental KGa values in the higeeliterature and values calculated using two-film theory (eq 5),where the values of kLa and kGa were calculated by eqs 1 and11, respectively. It can be seen that most of the overall masstransfer coefficients in various experimental systems are reason-ably predicted, probably because the mass transfer resistancesin the two phases can be properly estimated by the empiricalequations. The standard deviation in this study was less thanthat for other empirical equations, as indicated in Table 3.

The effects of gas and liquid flow rates, centrifugal accelera-tion, and liquid viscosity on the overall mass transfer coefficient,expressed as KGa ∝ QG

mQLnac

pµLq, were also investigated. The

values of m, n, p, and q can be estimated from the equationsfor kLa and kGa (eqs 1 and 11) and the two-film theory. Forcomparison, the powers obtained from prior empirical equationsfor KGa (eqs 2-4) are also examined. The exponents for aconventional 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 usingeqs 1 and 11 increases from 0 to 1.13 as the liquid-side-controlled mass transfer process becomes a gas-side-controlledprocess. Similarly, n declines from 0.77 to 0.28, indicating thatthe liquid flow rate most strongly affects KGa in the liquid-side-controlled process. The m and n values calculated usingeqs 2-4 were constants, limiting the applicability of theseequations to various mass transfer processes. However, thevalues of m and n obtained from eqs 2-4 were close to thosecalculated by eqs 1 and 11. Furthermore, the mass transfer

Figure 6. Comparison of experimental and calculated KGa by this work.Figure 5. Comparison of experimental and calculated KGa by eq 4.

Table 3. Standard Deviation of the Correlations

standard deviation

databases eq 2 eq 3 eq 4 present work

Ramshaw and Mallinson5 1.45 0.72 0.21 0.29Liu et al.1 0.49 2.53 11.41 0.77Chen and Liu6 5.57 2.61 1.20 2.22Lin et al.7 8.18 8.82 1.05 2.24Chiang et al.8 7.83 3.65 3.28 1.53

kGa

DGat2(1 - 0.9

Vo

Vt) ) 0.023ReG

1.13ReL0.14GrG

0.31WeL0.07( at

ap′ )1.4

(11)


coefficient in an RPB was more obviously influenced by thegas flow rate than that in a conventional packed column, andthe effect of liquid flow rate on the mass transfer coefficientwas similar in the two equipments.

In Figure 7c and 7d, KGa obtained in this investigation wasnot apparently changed with centrifugal acceleration (p )0.30-0.31) under various mass transfer resistances. The p valuewas larger than those obtained from eqs 2 and 3 and similar tothat 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 obtainedin this work increased from -0.27 to -0.14 as the gas-sidemass transfer resistance increased. This finding implies that themass transfer efficiency is less influenced by the liquid viscosityin a gas-side-controlled transfer process than in a liquid-side-controlled transfer process. The q values obtained in this workwere clearly higher than those obtained from eqs 2-4, probablybecause the effect of liquid viscosity was not actually investi-gated in studies from which eqs 2-4 were taken. Chiang etal.8 conducted ethanol absorption in glycerol solution to study

the effect of liquid viscosity on mass transfer. Their resultsdemonstrated that KGa decreased with liquid viscosity by anexponent of 0.21-0.32, which was similar to the finding in thisstudy.

Conclusion

Although liquid-side mass transfer in an RPB has beenextensively examined, gas-side mass transfer is still poorlyunderstood. Models of gas-side mass transfer are difficult todevelop because the gas flow is complicated. However, theexperimental data from which KGa for the absorption andstripping of ammonia and VOCs in an RPB can be found inthe literature. Several empirical equations for KGa have beenproposed. This study investigated a total of 430 experimentalKGa values and values calculated using empirical equations inthe literature. The results revealed that the experimental KGavalues were underestimated using the equations for kG and athat have been proposed for a conventional packed column.

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


Although the kG values in an RPB are expected to be similar tothe values in a conventional packed column, because the gasflow patterns inside the rotor are similar, the gas-liquidinterfacial area in the RPB may be much larger. The empiricalequations for KGa in the higee literature may not accuratelypredict 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, theempirical equations for KGa cannot reasonably predict theexperimental values because the mass transfer resistances in gasand liquid phases vary among experimental systems. In thisinvestigation, a local mass transfer coefficient, kGa, was obtainedusing two-film theory, the correlation for kLa that was providedby Chen et al.,4 and the experimental KGa data were taken fromthe higee literature.1,5-8 An empirical equation for kGa wastherefore proposed and found to estimate reasonably mostobtained experimental data that related to KGa in an RPB. Thevalue of kGa was found to be proportional to the gas flow rate,the liquid flow rate, the centrifugal acceleration, and the liquidviscosity raised to powers of 1.13, 0.28, 0.31, and -0.14,respectively. The overall mass transfer coefficient in an RPBincreased with the gas flow rate and the liquid flow rate topowers of 0-1.13 and 0.28-0.77, respectively, and decreasedwith liquid viscosity to the power of 0.14-0.27. The exactexponents depended on the ratio of the mass transfer resistancein the gas phase to that in the liquid phase. Additionally, KGawas proportional to the centrifugal acceleration to the power of0.3 and was not significantly affected by the ratio of masstransfer resistances.

Acknowledgment

The author wishes to express the sincere gratitude to theCenter-of-Excellence (COE) Program on Membrane Technologyfrom the Ministry of Education (MOE), R.O.C., to the projectToward Sustainable Green Technology in the Chung YuanChristian 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 ) πri

2z (m3)Vo ) volume between the outer radius of the bed and the stationary

housing ) π(rs2 - ro

2)z (m3)Vt ) total volume of the RPB ) πrs

2z (m3)z ) axial height of the packing (m)

Greek Letters

ε ) porosity of the packingµG ) 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 packingσ ) 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 ) dp3acFG

2/µG2

GrG′ ) gas Grashof number ) dp′3acFG

2/µG2

GrL ) liquid Grashof number ) dp3acFL

2/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, 2010ReVised manuscript receiVed November 2, 2010

Accepted December 3, 2010

IE101251Z


correlations of mass transfer coefficients in a rotating packed bed

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