Modeling of mass transfer characteristics of bubble column reactor with surfactant present

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1 74 Zhao et al. / J Zhejang Unv SCI 004 5(6):74-70 Journal of Zhejang Unversty SCIENCE ISSN E-mal: jzus@zju.edu.cn Modelng of mass transfer characterstcs of bubble column reactor wth surfactant present ZHAO We-rong ( 赵伟荣 ), SHI Hu-xang ( 史惠祥 ), WANG Da-hu ( 汪大翚 ) (Department of Envronmental Engneerng, Zhejang Unversty, Hangzhou 007, Chna) E-mal: werong@mal.hz.zj.cn Receved Mar. 7, 004; revson accepted Apr., 004 Abstract: Danckwert s method was used to determne the specfc nterfacal area, a, and the ndvdual mass transfer coeffcent, k L, durng absorpton of CO n a bubble column wth an anonc surfactant n the carbonate-bcarbonate buffer soluton and NaAsO as catalyst, the presence of whch decreases the specfc nterfacal area and the ndvdual mass transfer coeffcent. he specfc nterfacal area and the ndvdual mass transfer coeffcent ncrease wth ncreasng superfcal gas velocty. he specfc nterfacal area decreases whereas the ndvdual mass transfer coeffcent ncreases wth ncreasng temperature. he results of experments were used to determne the dependence of a, k L, and k L a on the surface tenson, the temperature of the absorpton phase, and the superfcal velocty of the gas. he calculated results from the correlaton were found to be wthn 0% devaton from the actual expermental results. Key words: Mass transfer coeffcent, Surfactant, Bubble column reactor, Gas absorpton Document code: A CLC number: Q08; X5 INRODUCION Bubble columns are wdely used n the chemcal ndustry where heterogeneous gas-lqud or gas-sold reactons take place, partcularly, n whch the lqud phase controls mass transfer processes due to the relatve nsolublty of gases (Vázquez et al., 000; Lye and Stuckey, 00). Important applcatons of bubble columns nclude oxdaton, hydrogenaton, ozonolyss, alkylaton, column flotaton, wastewater treatment, etc. (Yang et al., 00; Wu et al., 00). he desgn parameters for bubble columns are: gas-lqud specfc nterfacal area, a, ndvdual mass transfer coeffcent, k L, flow regme, bubble sze dstrbuton, and coalescence of bubbles. Most studes on bubble columns were devoted to the expermental determnaton of some of these parameters, and more specfcally, of the volumetrc mass transfer coeffcent, k L a, whch depends fundamentally on the superfcal gas velocty and on the physcal propertes of the absorpton phase. Numerous correlatons have been proposed for the superfcal velocty of the gas as well as for the vscosty of the lqud phase (Josh, 00; Mtsuharu et al., 00), but correlatons for the surface tenson of the lqud phase are seldom nvestgated. he most frequently used chemcal method for determnng k L and a s the Danckwerts method (Vázquez et al., 000; Cents et al., 00) based on the absorpton of CO n carbonate-bcarbonate buffer solutons. he major advantage of ths chemcal absorpton method over a physcal absorpton technque s that, when the reacton s fast enough, the bulk concentraton of the dssolved gas s neglgble whch smplfes the determnaton of drvng force for mass transfer calculaton (Cents et al., 00). As a result, t allows for determnaton of the

2 Zhao et al. / J Zhejang Unv SCI 004 5(6): mass transfer parameters of k L and a to be accurate durng statonary condtons. In ths paper, k L and a were determned (by Danckwerts method) from a system of CO absorbed by Na CO -NaHCO ( mol/l) buffer soluton wth NaAsO as catalyst, and an anonc surfactant, dodecyl benezene sulfonc acd sodum (DBS), as surface tenson modfer. he k L, a, and k L a were then correlated to a functon of temperature, superfcal gas velocty, and surface tenson of the lqud phase. HEORY he chemcal method proposed by Danckwerts (Vázquez et al., 000; Cents et al., 00) used to calculate k L and a requres that the gas absorbed undergoes a moderately fast pseudo-frst-order reacton wth some of the solutes n the lqud phase. Under these condtons, the absorpton rate s gven by: N = C a k k D () e d L d wth N beng the absorpton rate per unt volume (mol/l s); a the specfc nterfacal area (m ); C d e the gas solublty n soluton (mol/l); D d the gas dffusvty n soluton (m /s); k L the ndvdual mass transfer coeffcent (m/s); and k the rate-constant of the pseudo-frst-order reacton (s ). Eq.() shows that by changng the value of k a straght lne can be obtaned by plottng (N/C d e ) versus k D d. In ths plot the slope equals to a and (k L a) equals the ntercept wth the vertcal axs. In ths way k L and a can be determned smultaneously. he catalytc absorpton of carbon doxde by alkal carbonates soluton occurs as follows: k HCO CO () kh O CO H O HCO H () CO H O HCO H (4) kc k HCO CO HO (5) w H k HO (6) Eq.() s a second-order reacton wheren rateconstant k (L/mol s) varaton wth temperature, (K), and onc strength, I (mol/l), beng calculated as (Hkta et al., 976; Vázquez et al., 000): lg k = lg k 0.0 I 0.08 I 985 lg k =.65 (7) (8) he frst-order rate-constant of Eq.(), k HO (s ), can be calculated as: 765 lg kho= lg (9) he rate-constant of catalytc Eq.(4) at varous temperatures, k C (L/mol s), can be calculated by the Nernst equaton takng actvaton energy as 47.4 kj/ mol (Danckwerts, 970) and rate-constant as 50 L/mol s at 98.5 K (Cents et al., 00). he results are lsted n able. he equlbrum constant of Eq.(5), k (L/mol), can be calculated as (Hkta et al., 976; Vázquez et al., 000; Cents et al., 00):.0 [Na ] lg k = lg k 0.5[Na ].7 [Na ] (0) able Calculaton of k 0 and k C (K) k HO 0 (s ) k 0 - (L/mol s) C 0 5 (mol/l) k C (s ) k 0 (s ) k C (L/mol s)

3 76 Zhao et al. / J Zhejang Unv SCI 004 5(6): lg k = () and, the equlbrum concentraton of hydroxyl on, [ ] (mol/l), can be calculated as: [CO ] [ ] = () k [HCO ] Under certan condtons, the absorpton of CO by carbonate-bcarbonate buffer soluton catalyzed by sodum arsente can be consdered as pseudo-frst-order reacton wth rate-constant k (s ). he global reacton s: CO CO H O HCO () k For Eq.() to be pseudo-frst-order, t s necessary that the concentratons of CO, HCO, and on must keep constant, wthout decreasng from the lqud bulk to the nterface. herefore, the followng condton must be fulflled (Vázquez et al., 000; Cents et al., 00): C Dk (4) e d d [CO ] [HCO ] kl Under the expermental condtons, the maxmum value of left-hand term of Eq.(4) s 0.0 takng the relevant data from ables 4, shown the crteron of Eq.(4) s well satsfed n the experments. Accordng to Eqs.()(4), the rate-constant of Eq.(), k, s gven by: k = k k [ ] k [Cat] = k k [Cat] (5) HO C 0 C where k 0 (s ) and k C (L/mol s) are the contrbutons able Dffusvtes of carbon doxde n absorpton Phase (K) D W 0 9 (m /s) D d 0 9 (m /s) able Solubltes of CO n absorpton phase (K) ( KI s ) NaCO ( KI s ) e NaHCO C (mol/l) e ( KsI) C d (mol/l) = (K) able 4 Summary of expermental results usng Danckwerts plots and the calculatons of Eqs.(0)() 0 (m/s) [DBS] (mg/l) σ 0 () Expermental data k L 0 5 (m/s) a (m ) k L a 0 (s ) Calculaton from Eq.(0) Expermental data Calculaton from Eq.() Expermental data Calculaton from Eq.()

4 Zhao et al. / J Zhejang Unv SCI 004 5(6): of the non-catalyzed and catalyzed reacton, respectvely; and [Cat] represents the concentraton of the catalyst,.e. the concentraton of the arsente on. Under the expermental condtons, k 0 can be calculated through Eqs.(7)(). he results are lsted n able. As shown n able, the advantage of ths method s that the apprecable dfferences of k can be obtaned usng very small catalyst concentratons, thereby, not affectng the physcal propertes of the absorpton phase. MAERIALS AND MEHODS Mass transfer measurements Mass transfer measurements were carred out usng the apparatus shown n Fg Fg. Schematc dagram for expermental set-up : carbon doxde; : humdfer; : thermostat; 4: flowmeter; 5, 9: soap-flm meter; 6: barometer; 7: bubble column reactor; 8: thermometer; 0: gas out A bubble column wth heght of 60 cm (7) was used as the contact devce, made of glass cylndrcal tube, sealed wth rubber cap and o-rng. he nternal and external dameters of the column are 0. cm and 0.8 cm, respectvely. he absorpton phases used ( mol/l sodum carbonate-bcarbonate buffer solutons wth sodum arsente as catalyst, and DBS as surface tenson modfer) were thermostated before CO gas was ntroduced nto the contact devce. For each batch run, the lqud load was.5 L. he concentraton ranged from 0 to mol/l for sodum arsente, and from 0 to 5 mg/l for DBS. he pure CO gas () to be absorbed was pass ed through a humdfer () and then entered the contact devce (7) at a constant flow rate measured wth a soap-flm meter (5). Gas outflow through the outflow port n the top-plate was measured wth another soap-flm meter (9) before the gas released nto the atmosphere. he gas absorpton rate was calculated as the dfference between nflow and outflow rate. In the experments, nflow was between mol/s and 0 4 mol/s. Physcal propertes Interpretaton and correlatons of the mass transfer data obtaned requre knowledge of the denstes, ρ (kg/m ), vscostes, µ (kg/m s), and surface tensons, σ (), of the lqud phases, as well as the solubltes and dffusvtes of the gas n absorpton phases. he denstes and vscostes of the sodum carbonate-bcarbonate buffer solutons, wth surfacetant and sodum arsente, were measured at 98.5 K usng a Gay-Lussac type pycnometer and an Ubbelohde vscometer, respectvely. However, nether of these propertes dffered sgnfcantly from the values for the buffer solutons: ρ=04 kg/m and µ=.9 0 kg/m s. he surface tenson was determned by a stalagmometer. he surface tensons of the solutons at 98.5 K are lsted n able 4. he dffusvty of CO n buffer soluton of Na CO -NaHCO, D d, can be estmated from the dffusvty of CO n pure water, D w (m /s), by the followng equaton (Hkta et al., 976; Vázquez et al., 000; Cents et al., 00): d W D / D = ( ξ C ) (6) = where C s concentraton of electrolyte (Na CO or NaHCO ) n buffer soluton (mol/l); and ξ s functon of temperature for electrolyte whch can be estmated by: ξ = ω (7) the coeffcent, ω, can be estmated from the vscosty of pure water and soluton of electrolyte as:

5 78 Zhao et al. / J Zhejang Unv SCI 004 5(6):74-70 µ w = µ ( ωc ) (8) where µ w and µ are the vscosty of pure water and soluton of electrolyte, respectvely. he dffusvtes of CO can then be calculated at varous temperatures usng D W (Perry and Green, 997) as lsted n able. he solubltes of CO n buffer solutons wth DBS and/or sodum arsente, due to the electrolytc nature, were calculated from Eq.(9) proposed by Danckwerts and Gllham (Hkta et al., 976; Cents et al., 00) for solutons contanng more than one electrolyte: C lg = ( ) e e Ks I (9) C d = where I and K s (L/mol) are the onc strength and the saltng out parameter for electrolyte (Na CO or NaHCO ), respectvely; and C e s the solublty of CO n pure water (mol/l). In able, the values of I were calculated from the experments, K s was taken from Danckwerts (970), and C e was taken from Perry and Green (997). It was proved that the addton of sodum arsente affected nether the dffusvty nor the solublty of CO due to ts low concentraton. RESULS AND DISCUSSION he absorpton rate of CO, n (mol/l), depends on the superfcal gas velocty, (m/s), and the concentraton of catalyst and surfactant, as Fg. showng that n, the plateau value of the absorpton curve, ncreases wth ncreasng concentraton of catalyst, and decreases wth ncreasng concentraton of DBS. When the absorpton rate of CO was evaluated, the specfc nterfacal area, a, and the ndvdual mass transfer coeffcent, k L, were determned by Danckwerts method. In accordance wth ths method, Fg. shows N plotted versus k for one of the superfcal gas veloctes and for dfferent temperatures, whereas Fg.4 shows N plotted versus k for one of the temperatures and for dfferent superfcal gas veloctes; Fg.5 shows N plotted versus k for one of the temperatures and for dfferent surface tensons. he Danckwerts plots of Fgs., 4, and 5 show excellent lnearty, mplyng that ths method can be used for determnng a and k L smultaneously, whose values are lsted n able 4. able 4 shows that the specfc nterfacal area, ndvdual mass transfer coeffcent and volumetrc mass transfer coeffcent apparently depend on the temperature, superfcal gas velocty, and aqueous surface tenson. a decreases, but k L and k L a ncrease wth ncreasng temperature. When temperature ncreased, the decreased surface tenson of the soluton caused a to decrease, whereas the ncreased molecular random movement caused the k L to ncrease. When the gas flow rate or superfcal gas velocty decreased, the gas hold-up decreased, whch caused a, k L, and k L a to declne. a, k L, and k L a decreased wth ncreasng concentraton of DBS, or decreased wth decreasng of surface tenson. hs reducton may be attrbuted to the effect of the surface-actve agent, whch can reduce the nterfacal movement when t occupes part of the surface of the bubble. Furthermore, the surface concentraton of the surfactant ncreases wth the surfactant concentraton n the lqud bulk (Vázquez et al., 997; Josh, 00). Usng non-lnear least square regresson to analyze the expermental results n able 4, the specfc nterfacal area, ndvdual mass transfer coeffcent, and volumetrc mass transfer coeffcent can be correlated wth temperature, superfcal gas velocty, and surface tenson as follows:.59 0 ln( kl) = ln( σ ) 0.4ln( ug) r=0.99 (0) = σ 9 ) r=0.97 () ln( a) ln( ) 0.64 ln( ug.0 0 ln( ka L ) = ln( σ).045ln( ug) r=0.98 ()

6 Zhao et al. / J Zhejang Unv SCI 004 5(6): n 0 4 (mol/s) [NaAsO ]=0 mol/l,[dbs]=0 mg/l [NaAsO ]=0.004 mol/l,[dbs]=0 mg/l [NaAsO ]=0.004 mol/l,[dbs]=.0 mg/l t (s) N 0 7 (mol/l s) =88.5 K 0. =98.5 K =08.5 K =8.5 K k (s ) Fg. me-dependence of n for dfferent concentratons of NaAsO and DBS. = 98.5 K Fg. Danckwerts plots when temperatures vared. [DBS]=0 mg/l, =0.00 m/s.0.0 N 0 7 (mol/l s) 0.8 =0.00 m/s 0.6 =0.00 m/s =0.00 m/s k (s ) N 0 7 (mol/l s) σ= σ= σ= σ= σ= k (s ) Fg.4 Danckwerts plots when superfcal gas veloctes vared. [DBS]=0 mg/l, = 98.5 K Fg.5 Danckwerts plots when surface tensons vared. =0.00 m/s, = 98.5 K he calculated values from Eqs.(0)() are lsted n able 4. Consderng the values of the specfc nterfacal area, ndvdual mass transfer coeffcent, and volumetrc mass transfer coeffcent, the devatons between the expermental results and the calculatons from Eqs.(0)() were actually always lower than 0%, whch demonstrated that the correlaton equatons ftted the expermental results well. CONCLUSIONS In ths study, the presence of the surfactant nduced reducton of the specfc nterfacal area and the ndvdual mass transfer coeffcent. Both specfc nterfacal area and ndvdual mass transfer coeffcent ncreased wth ncreasng superfcal gas velocty. he specfc nterfacal area decreased, whereas the ndvdual mass transfer coeffcent ncreased wth ncreasng temperature. he specfc nterfacal area, ndvdual mass transfer coeffcent, and volumetrc mass transfer coeffcent were well correlated wth temperature, superfcal gas velocty, and surface tenson wth a devaton wthn 0% usng non-lnear least square regresson analyss. References Cents, A.H.G., Brlman, D.W.F., Versteeg, G.F., 00. Gas absorpton n an agtated gas-lqud-lqud system. Chem. Eng. Sc., 56:

7 70 Zhao et al. / J Zhejang Unv SCI 004 5(6):74-70 Danckwerts, P.V., 970. Gas-Lqud Reactons. McGraw- Hll, New York, p Hkta, H., Asa, S., akatsu,., 976. Absorpton of carbon doxde nto aqueous sodum hydroxde and sodum carbonate solutons. Chem. Eng. J., :-4. Josh, J.B., 00. Computatonal flow modelng and desgn of bubble column reactors. Chem. Eng. Sc., 56: Lorenzen, L., Klengeld, A.W., 000. New generaton leachng reactors for effectve mass transfer n mneral processng operatons. Mnerals Engneerng, (0-):07-5. Lye, G.J., Stuckey, D.C., 00. Extracton of erythromycn-a usng collodal lqud aphrons: Part II. Mass transfer knetcs. Chem. Eng. Sc., 56: Mtsuharu, I., Hrok, U., oshfum, I., 00. Mass transfer characterstcs n gas bubble dspersed phase generated by plungng jet contanng small solute bubbles. Chem. Eng. Sc., 56:65-6. Perry, R.H., Green, D.W., 997. Perry s Chemcal Eng- neers Handbook, 7th Edton. McGraw-Hll, New York, p.-0. Vázquez, G., Cancela, M.A., Varela, R., Alvarez, E., Navaza, J.M., 997. Influence of surfactants on absorpton of CO n a strred tank wth and wthout bubblng. Chem. Eng. J., 67:-7. Vázquez, G., Cancela, M.A., Rverol, C., Alvarez, E., Navaza, J.M., 000. Applcaton of the Danckwerts method n a bubble column: Effects of surfactants on mass transfer coeffcent and nterfacal area. Chem. Eng. J., 78:-9. Wu, Z.C., Zhou, M.H., Huang, Z.W., Wang, D.H., 00. Electrocatalyss method for wastewater treatment usng a novel beta-lead doxde anode. Journal of Zhejang Unversty SCIENCE, (): Yang, Y.P., Wu, X.Y., Xu, X.H., Wang, D.H., 00. reatment of dyeng wastewater by photo-asssted Fenton system. Journal of Chemcal Engneerng of Chnese Unverstes, 5():4-47 (n Chnese). Welcome vstng our journal webste: Welcome contrbutons & subscrpton from all over the world he edtor would welcome your vew or comments on any tem n the journal, or related matters Please wrte to: Helen Zhang, Managng Edtor of JZUS E-mal: jzus@zju.edu.cn el/fax: