Co- and counter-current mass transfer in bubble column

International Journal of Heat and Mass Transfer 54 (2011) 2283–2293

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Co- and counter-current mass transfer in bubble column

Manoj Kumar Singh, Subrata Kumar Majumder ⇑Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam, India

a r t i c l e i n f o

Article history:Received 13 September 2010Received in revised form 7 February 2011Accepted 8 February 2011

Keywords:Bubbly flowGas–liquid interfacial areaOverall gas holdupVolumetric mass transfer coefficientNon-adjustable parameter

0017-9310/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2011.02.036

⇑ Corresponding author.E-mail address: [email protected] (S.K. Majumde

a b s t r a c t

Design and scale-up has gained considerable attention in recent years because of complex hydrodynam-ics and its influence on bubble column reactor performance. The concentration difference is importantvariable while characterizing bubble column reactor efficiency and this is a function of hydrodynamicsprevailing inside the column. The efficiency of bubble column reactor is a function of physical propertiesof phases, geometry of column and operating conditions. Literature lacks on the simulation work on var-iation of concentration of solute for mass transfer rate and mass transfer efficiency in the complex systemof bubble column device. In the present work a mechanistic model is formulated to predict the masstransfer efficiency of column and its dependency on various physical parameters, operating conditionand column geometry. In this work the mass transfer efficiency has been analyzed based on a mechanisticmodel in the case of both co-current and counter current operations in bubble column reactor. The con-centration variation of the phases obtained by simulation of model may be useful for further understand-ing the mass transfer phenomena in bubble column reactor.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Bubble column reactors/contactors are cylindrical vessel with agas distributor at the bottom of column and above it is liquid as acontinuous phase, when gas is passed through the gas distributorin to the continuous liquid phase small bubble are produced whichintern gives high gas–liquid interfacial area for mass and heat trans-port. Bubble columns are extensively being used in chemical,biochemical, petrochemical and metallurgical industries as multi-phase contactor and reactor. Operation and performance of bubblecolumn reactor are appreciably affected by the flow characteristicand flow regimes (homogeneous flow regime (bubble flow regime),heterogeneous flow regime (Churn turbulent flow regime), slugflow, etc.) inside the bubble column. In these different flow regimes,the interaction of the dispersed gas phase with the continuous liquidphase varies considerably [1]. However, bubbly and churn-turbulentflow regimes are most frequently encountered [2]. Shaikh and Al-Dahhan [2] reported that the homogeneous flow regime generallyoccurs at low to moderate superficial gas velocities. There is practi-cally no coalescence and break-up, hence there is a narrow bubblesize distribution. The gas holdup distribution is radially uniform;therefore bulk liquid circulation is insignificant [2]. Depending onthe system and operating conditions several correlations have beenproposed so far to evaluate the hold up. It depends on the gas super-ficial velocity, liquid property, column dimension, operating condi-tion, sparger design, solid property and the mode of operation

ll rights reserved.

r).

[1,3,4]. They summarized research on the design parameters of bub-ble columns with and without solid suspensions and introduce newtrends in research activities such as applications of computationalfluid dynamics and of newly developed experimental techniquesto bubble columns and research on high pressure bubble columns.Majumder [5,6] reported the different operating conditions for masstransfer in isothermal conditions in two-phase flow. Majumder [6]analyzed the mass transfer efficiency of the bubble column basedon mixing characteristics. Kulkarni and Joshi [7] developed a meth-odology for the prediction of true mass transfer coefficient in thestirred cell as well as in bubble column reactor. In the gas–liquidmass transfer operation volumetric liquid mass transfer coefficientis the most important parameter that characterizes the performanceof bubble column reactor. Chaumat et al. [8] studied mass transferefficiency and volumetric mass transfer coefficient under widerange of industrially useful experimental condition. Han andAl-Dahhan [9] studied the gas to liquid mass transfer in high pres-sure bubble column with different sparger design. Billet and Schul-tes [10] studied the gas to liquid mass transfer and its prediction inpacked bed. Gourich et al. [11] studied the gas–liquid mass transferin air-lift reactor and performed laboratory experiment to validatetheir model. Martin et al. [12] studied the effect the influence of sur-face active agent, contaminants and salts on mass transfer charac-teristic in bubble column reactors. As per literature survey,considering its high industrial application due to high heat and masstransfer characteristic, compactness, low operating and mainte-nance cost, vast amount of study has been done so far on designand operation of bubble column reactors [1]. Although lot of studieshave been done, it is still difficult to understand the bubble column.

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Nomenclature

C1 concentration in the dispersed phase [moles/m3]C2 concentration in the continuous phase [moles/m3]C10 known concentration of gas at inlet of sparger [moles/m3]C20 known concentration of liquid at inlet [moles/m3]dc column diameter [m]db bubble diameter [m]do gas distributor hole diameter [m]ds sauter mean bubble diameter [m]D diffusivity of gas [m2/s]hm height of gas–liquid mixture in the column [m]k dimensionless mass transfer coefficient (k = (Khm)/(elu)) [–]Ki coefficient of mass transfer of the ith substance [m/s]Kbi coefficient of mass transfer of the ith substance from

single bubble [m/s]mei equilibrium coefficient of distribution of the substance

between phases [–]m0e equilibrium distribution coefficient defined as meel=eg

[m]n number density of bubbles [–]P parameter defined in Eq. (10) [moles/m3]rb radius of bubble [m]R unknown concentration of gas at outlet [moles/m3]R0 unknown concentration of liquid at outlet [moles/m3]t time [s]ug velocity of gas phase [m/s]

ul velocity of liquid phase [m/s]u slip velocity [m/s]ul actual liquid velocity (usl/el) [m/s]ug actual gas velocity (usg/eg) [m/s]usl superficial liquid velocity, [m/s]usg superficial gas velocity, [m/s]U ratio of liquid to slip velocity (=ul/u) [–]Z dimensionless distance along the vertical z-axis

(=z/hm) [–]eg volume fraction of gas phase [–]el volume fraction of liquid phase [–]ql density of liquid [kg/m3]qg density of gas [kg/m3]r surface tension of liquid [N/m]ll dynamic viscosity of liquid [Poise]gco mass transfer efficiency for concurrent operationgcount mass transfer operation for countercurrent operation

Subscript1 gas phase2 liquid phaseb bubbleg gasl liquid

2284 M.K. Singh, S.K. Majumder / International Journal of Heat and Mass Transfer 54 (2011) 2283–2293

The research on design and scale-up has gained considerable atten-tion in recent years because of complex hydrodynamics and its influ-ence on bubble column reactor performance [13]. Kantarci et al. [13]reviewed the different studies on bubble column and described thedifferent prospect of bubble column. They enunciated that the col-umn length has immense effect on the degree of conversion of thereactant in the bubble column reactor. They also reported that largediameter and large column height causes severe problem in opera-tional ease. This causes need of optimization process in design andscale-up of bubble column reactors. The concentration differenceis important variable while characterizing bubble column reactorefficiency and this is found to be a function of hydrodynamics pre-vailing inside the column. The variation of the concentration of thereactive solute inside the column depends on the mode of operationlike whether the column is operated in co- or countercurrent opera-tions. The efficiency of bubble column reactor is found to be thefunction of physical properties of phases, geometry of column andoperating conditions [6,14]. From the literature survey it is seen thatseveral authors has described the different hydrodynamics andtransfer processes in bubble column reactor. But there is lack of com-parative studies on mode of operation of the bubble column thoughthe mode of operation influences the efficiency of the mass transferof the bubble column. In the present work a mechanistic model for-mulated to predict the mass transfer efficiency of column and itsdependency on various physical parameters, operating conditionand column geometry in the case of both co-current and counter cur-rent operations in bubble column reactor. The concentration varia-tion of the phases obtained by simulation of model has beenutilized to obtain the mass transfer efficiency of bubble columnreactor.

2. Theoretical background

2.1. Model description

Consider the two phase (dispersed and continuous) systemconsist of i components participating in mass transfer process

without chemical reaction in a bubble column reactor. In the bubblecolumn gas is dispersed as a dispersed phase of bubble in a continu-ous liquid phase. Let the concentration in the dispersed and contin-uous phases are respectively C1i and C2i where i = 1, 2, 3, . . . , i. Thematerial balance of these components can be written in both phasesas:

For dispersed phase:

@ðegqgÞ@t

þ@ðugqgegÞ

@r¼ �

XKiðmeiC1i � C2iÞ ð1Þ

For continuous phase:

@ðelqlÞ@t

þ @ðulqlelÞ@r

¼X

KiðmeC1i � C2iÞ ð2Þ

where,

eg þ el ¼ 1 ð3Þ

Ki ¼ nKbi ð4Þ

n ¼ eg43 pr3

b

ð5Þ

In the continuous medium, in general it is necessary to considerconvective diffusion of component within the bubble and sur-rounding this bubble, otherwise it is impossible to formulate theboundary condition on the surface of the bubble. This complicatesthe problem. Therefore one usually takes the concentration of thecomponent i in the dispersed phase equal to the concentration ofthe component in the surface of the gas bubble. In the followingsection, a simplified equation for both co-current and counter cur-rent flow of the gas–liquid two phases is analyzed to interpret themass transfer process in the bubble column.

2.2. Model for counter current operation

Consider a one dimensional flow in a counter current bubblecolumn as shown in Fig. 1. The z-axis is considered in the direction

Fig. 1. Schematic diagram of co- and counter current bubbly flow.

M.K. Singh, S.K. Majumder / International Journal of Heat and Mass Transfer 54 (2011) 2283–2293 2285

of movement of the gas phase and the origin is selected at the placeof its entrance into the column. To investigate the mass transferfrom gas to liquid at steady state, Eqs (1) and (2) can be simplified.Introducing dimensionless quantities, the following equations canbe represented:

ð1� UÞdC1

dZþ kðm0eC1 � C2Þ ¼ 0 ð6Þ

UdC2

dZþ kðm0eC1 � C2Þ ¼ 0 ð7Þ

where U ¼ ul=u; m0e ¼ meel=eg ; k ¼ ðKhmÞ=elu, 0 6 U 6 1, k > 0.Z = Dimensionless distance along the vertical z-axis (Z = z/hm),ul = vsl/el is the actual velocity of liquid, usl = superficial liquid veloc-ity. u = ug ± ul = usg/eg ± usl/el, is the slip velocity or relative velocityof gas with respect to liquid (+ve for countercurrent and �ve forco-current), hm is the height of gas–liquid mixture in the column,K = nKb is volumetric mass transfer coefficient [s�1], el is the frac-tional liquid holdup, me is the equilibrium distribution coefficient.Here for small and moderate Reynolds numbers based on bubblediameter up to approximately equal to 700, the following expres-sion can be expressed [15] as

ug � ul ¼ a1qlr

2b

llf1ðegÞ ð8Þ

Kb ¼ a2Dqleggf1ðegÞ

ll

� �0:5

f2ðegÞr2:5b ð9Þ

where the functions f1(eg) and f2(eg) take into account the hinderednature of the bubble flow and the effects of diffusion from their sur-faces. As per Levich [15] at small Reynolds number, a1 = 2/9, a2 = 8/3(p/3)0.5 and at large Reynolds number, a1 = 1/9, a2 = 8/3(p/2)0.5.From Eqs. (6) and (7) one can get,

ð1� UÞC1 � UC2 ¼ P ð10Þ

where P is a constant. At Z = 1, C1(1) = R and C2(1) = C20. Therefore,

ð1� UÞR� UC20 ¼ P ð11Þ

Similarly between Z = 1 and Z = Z,

C2 ¼1� U

UðC1 � RÞ þ C20 ð12Þ

Substituting the C2 in terms of C1 by Eq. (12) into the differentialequation (6) and after rearranging one gets

dC1

ðm0eU � ð1� UÞÞC1 þ ð1� UÞR� UC20¼ �kdZ

Uð1� UÞ ð13Þ

Integrating Eq. (13) with boundary condition, at Z = 0, C1 = C10, onecan obtain

1m0eU � ð1� UÞ lnð ðm

0eU � ð1� UÞÞC1 � ð1� UÞR� UC20

ðm0eU � ð1� UÞÞC10 � ð1� UÞR� UC20Þ

¼ �kZð1� UÞU ð14Þ

Defining A ¼ 1�Um0eU�ð1�UÞ and rearranging Eq. (14), one gets

C1 ¼C20UA1� U

þ RAþ C10 � RA� C20UA1� U

� �exp

�kZUA

� �ð15Þ

Putting Z = 1 and C1(1) = R in above Eq. (15), one can get,

R ¼ C10

Aþ ð1� AÞ exp kUA

� �þ C20UA expð kUAÞ � 1

� �ð1� UÞ Aþ ð1� AÞ exp k

UA

� �� ð16Þ

If the liquid is having no gaseous component which is to be ab-sorbed at the entry, C20 = 0, then,

R ¼ C1ð1Þ ¼C10

Aþ ð1� AÞ exp kUA

� � ð17Þ

Similarly substituting C1 ¼ UC21�U þ R� UC20

1�U from Eq. (12) in Eq. (7),integrating with boundary condition at Z ¼ 0; C2 ¼ C2ð0Þ ¼ R0 andrearranging, one can represent it as:

1� Um0eU � ð1� UÞ ln

ðm0eU � ð1� UÞÞC2 þm0eRð1� UÞ �m0eUC20

ðm0eU � ð1� UÞÞR0 þm0eRð1� UÞ �m0eUC20

� �

¼ �kZU

ð18Þ

Now substituting 1�Um0eU�ð1�UÞ ¼ A and rearranging the terms one can

get,

R0 ¼ C20Um0eA

1� U

� �þ exp

kUA

� �� m0eRA 1� exp

kUA

� �� ð19Þ


Mass transfer efficiency for countercurrent operation is defined as,

gcount ¼ 1� C1ð1ÞC1ð0Þ

ð20Þ

Putting the values of C1(1) from Eq. (16) and C1(0) = C10, in Eq. (20),one gets mass transfer efficiency as:

gcount ¼ 1� 1Aþ ð1� AÞ exp K

UA

� ��

C20UAðexp kUA

� �� 1Þ

C10ð1� UÞðAþ ð1� AÞ exp kUA

� �Þ

ð21Þ

General observation under limiting conditions of U as:

U !1; gcount ! 0; A! 0U ! 0; gcount ! 1; A! 1

ð22Þ

2.3. Model for co-current operation

Again substituting the boundary conditions, Z ¼ 0; C1ð0Þ ¼C10; C2ð0Þ ¼ C20 in Eq. (10) it can be written

ð1� UÞC1 þ UC2 ¼ ð1� UÞC10 þ UC20 ð23Þ

Substituting the profile of C2 in terms of C1 from Eq. (23) into gov-erning equation (6) for co-current operation one can represent theequation as:

dC1

ðm0eU þ ð1� UÞÞC1 � ð1� UÞC10 � UC20¼ �kdZð1� UÞU ð24Þ

Integrating Eq. (24) with boundary condition at Z ¼ 0; C1ð0Þ ¼ C10

one can get

1m0eU þ ð1� UÞ ln

ðm0eU þ ð1� UÞÞC1 � ð1� UÞC10 � UC20

ðm0eU þ ð1� UÞÞC10 � ð1� UÞC10 � UC20Þ

� �

¼ �kZð1� UÞU ð25Þ

Substituting Z ¼ 1; C1 ¼ C1ð1Þ, into Eq. (25) it can be expressed as:

C1ð1Þ ¼ C10 Aþ exp�kUA

� �ð1� AÞ

� �þ C20

� UA1� U

1� exp�kUA

� �� ð26Þ

Similarly putting C1 in terms of C2 in Eq. (7), Eq. (7) can be repre-sented as

ð1� UÞdC2

�ðm0eU þ ð1� UÞÞC2 þm0eðð1�ÞC10 þm0eUC20Þ¼ k dZ

Uð27Þ

With the boundary conditions, at Z ¼ 0; C2ð0Þ ¼ C20 integrating Eq.(27), we get

�ð1� UÞm0eU þ ð1� UÞ ln

�ðm0eU þ ð1� UÞÞC2 þm0eðð1� UÞC10 þm0eUC20Þ�ðm0eU þ ð1� UÞÞC20 þm0eðð1� UÞC10 þm0eUC20Þ

� �

¼ kZU

ð28Þ

Defining A0 ¼ 1�Um0eUþð1�UÞ and substituting into Eq. (28), we get

C2 ¼ C20 �m0e A0C10 þA0C20m0eU

1� U

� �� exp � kZ

UA0

� �

þm0e A0C10 þA0C20m0eU

1� U

� �ð29Þ

At Z ¼ 1; C2 ¼ C2ð1Þ ¼ R0, Eq. (29) becomes,

R0 ¼ C20 �m0e A0C10 þA0C20m0eU

1� U

� �� exp

�kUA

� �

þm0e A0C10 þA0C20m0eU

1� U

� �ð30Þ

In this operational mode with the help of Eq. (26) the mass transferefficiency can then be expressed as

gco ¼ 1�ðC10ð1� AÞð1� UÞ � UAC20Þ exp �k

UA

� �1� U

� A� UAC20

C10ð1� UÞð31Þ

Observation under limiting condition of U infers that

U !1; A! 0; gco ! 1U ! 0; A! 1; gco ! 0

ð32Þ

3. Ranges of operating variables considered in this study

The mass transfer variation was analyzed only in the homoge-neous flow regime of bubble column. In this study, the operatingconditions are considered as minimum to maximum of the existingdata in the literature as: 0.01 < Vsg (m/s) < 0.08, 0.0 < usl (m/s) < 0.44, 0.152 < Dc (m) < 0.6, 0.126 < hm (m) < 0.35, 800 < ql (kg/m3) < 1600, 0.00058 < ql (Pa s) < 0.02, 0.0241 < r (N/m) < 0.0728.In Fig. 1, C10 = known concentration of gas at inlet of sparger,C20 = known concentration of liquid at inlet, R = unknown concen-tration of gas at outlet, R0 = unknown concentration of liquid atoutlet.

Since the bubble column design and scale up are highly correla-tion based, most useful and as per applicability range of the pres-ent study, the following correlations were used to calculate thebubble diameter and gas holdup. To calculate the bubble diameterthe following correlation [16] is used:

ds ¼8:8rgql

� �0:5 usgll

r

� ��0:02 r3ql

gl4l

� ��0:06 ql

qg

!0:11

ð33Þ

The Gestrich and Rahse correlation [17] was used to calculate thegas holdup in this study which is given by:

eg ¼ 0:89hm

dc

� �0:036ð�15:7þlog KÞ db

dc

� �0:30 V2g

dbg

!0:025ð2:6þlog KÞqlr3

l4l g

� �0:047

ð34Þ

0.01 6 usg (m/s) 6 0.08; 0.02 6 hm (m) 6 3.5; 800 6 ql (kg/m3) 61600; 0.00043 6 ll (Pa s) 6 0.02; 0.0241 6 r (N/m) 6 0.0728;0.03 6 d0 (cm) 6 0.05.The correlations have been chosen for thepresent study as per suitability range of application of thecorrelations.

4. Results and discussion

In this section axial concentration change and degree of masstransfer efficiency in bubble column reactor both in countercurrentand co-current operations obtained from the simulation have beenexplained. Then absorption efficiency of the column has been stud-ied in detail. The mass transfer phenomena in bubbly flow regimedepend on the different dynamic variables like gas and liquidvelocities, geometric variables like column diameter, gas distribu-tor, column height and the different physiochemical properties ofgas and liquid phases. The range of important variables that hasbeen considered for the analysis of mass transfer behavior in BCRhas been mentioned in the section. The mass transfer efficiencyin bubble column reactor has been deduced from the change inthe gas phase concentration from inlet of column to outlet. Results


are obtained from numerical simulation of mass transfer model ina gas–liquid bubble column reactor/contactor using MATLABsoftware.

4.1. Mass transfer in counter current operation

Variation of the liquid and gas phase axial concentration duringmass transfer operation in counter current bubble column reactoris shown in Fig. 2. Solute concentration in gas phase is decreasingas it move from top to bottom. At the same time the liquid phaseconcentration is rising as it moves from top to bottom of the

Fig. 2. Axial concentration profile in counter current operation at d

Fig. 3. Axial concentration variation with superficial gas velocity at

column. Result is valid because it fallows the law of mass conser-vation. Variation of radial concentrations have not been consideredin this work. Further work is going on the radial variation of con-centration profile as well as mixing characteristics and its effecton overall mass transfer efficiency of the bubble column of largediameter. Generally for small diameter bubble column reactorthe radial variation of mass transfer is negligible compared to largediameter bubble column. This is because of backmixing phenom-ena of the fluid in large diameter column.

Axial concentration profile for different gas superficial velocitiesis shown in Fig. 3. It is seen that the concentration profile is very

c = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s, system of air–water.

dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s, system of air–water.


steep for the case having higher superficial velocity. At highersuperficial gas velocity the gas holdup is higher, which results inhigher gas–liquid mass transfer area and volumetric mass transfercoefficient.

From Fig. 4 it could be seen that the mass transfer efficiency isincreasing as superficial gas velocity increases. At high superficialvelocity gas holdup will be high, this leads to increase in higherinterfacial mass transfer area and high volumetric liquid masstransfer coefficient. Therefore mass transfer rate will increase asthe gas superficial velocity increases. In homogeneous bubbly flowregime the gas holdup is found to be increasing linearly with gas

Fig. 4. Effect of superficial gas velocity on mass transfer efficiency at

Fig. 5. Effect of liquid viscosity on concentration pro

superficial velocity, whereas in churn turbulent flow regime the ef-fect of gas superficial velocity on gas holdup is less pronounced. Inchurn turbulent flow, the bubbles are coalesced and form biggerbubbles like slug bubbles which reduces the homogeneity of theflow. The better homogeneity will result in more gas holdup dueto more bubble population. The mass transfer increased withincreasing gas velocity in the same trend as the gas holdup in-creased with superficial gas velocity [18,19]). Verma and Rai [20]reported that the mass transfer increases monotonically with thegas velocity. Behkish et al. [21] investigated the volumetric masstransfer coefficient and bubble size distribution for four different

dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s, system of air–water.

file at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s.


gas phases and in two different organic liquid mixtures and re-ported that mass transfer increases with gas velocity in slurrysystem.

Concentration profiles for liquids of different viscosities havebeen shown in Fig. 5. From simulation it was found that as the li-quid viscosity increases the mass transfer rate from gas to liquidphase is decreasing. As the liquid viscosity increases larger sizebubble forms. Larger bubble has its higher bubble rise velocitydue to their buoyancy effect. The residence time of the gas bubbledecreases as the increase in bubble rise velocity which may de-crease gas to liquid mass transfer rate. Also larger bubble forma-

Fig. 6. Effect of liquid viscosity on mass transfer efficie

Fig. 7. Effect of surface tension on mass transfer in bubble

tion results in decrease in gas holdup and the interfacial areabetween gas and liquid. This also shows the decrease in masstransfer rate with increase in surface tension. For the same reasonthe efficiency of the mass transfer drastically decreases from morethan 80% to 30% as liquid viscosity increases from 0.8CP to 1.1CP asshown in Fig. 6. Majumder [6] reported that the efficiency of masstransfer of bubble column is quietly controlled by transport mech-anism of species in the liquid viscous boundary layer around thebubbles. Haut and Cartage [22] explained that the gas–liquid masstransfer between a single bubble and the surrounding liquid. Theyreported that the contact time between liquid particles and the

ncy at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s.

column at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s.


bubble as well as the interfacial area are the important factor toinfluence the variation of mass transfer efficiency with viscosity.The details of the mechanism have been enunciated by Majumder[6] and Haut and Cartage [22]. They described that the contact timebetween a bubble and a liquid element active for the transfer is in-versely proportional to gas–liquid relative velocity of bubble. Themass transfer rate between the bubble and the surrounding liquidis increased with the interfacial area and is decreased with increasein contact time [22].

More viscous liquid resumes the more contact time between abubble and a liquid element active for the transfer of solute which

Fig. 8. Mass transfer efficiency variation with liquid surfac

Fig. 9. Variations of concentration profile at different superficial gas veloci

may cause the decrease in mass transfer efficiency with increase inviscosity as shown in Fig. 6. Behkish et al. [21] and Verma and Rai[20] studied the mass transfer phenomena with viscous media.They showed that the mass transfer decrease with increasing li-quid viscosity. They barbed out that higher viscosity led to increaseof the volume fraction of the large bubbles which leads to muchlower gas–liquid interfacial areas. Liquid with low viscosity willprovide lower resistance to mass transfer from gas to liquid phase.Mass transfer coefficient decreases with liquid surface tension. Itmay be due to the effect of resisting the stretching of interfaceand reducing disturbances in the bulk phase.

e tension at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s.

ties at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s, system of air–water.

Fig. 10. Effect of superficial gas velocity on mass transfer efficiency at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s, system of air–water.


The bubble size strongly depends on coalescence and breakupbehavior of bubble in the medium. A decrease in surface tension(due to surfactant addition) diminishes the bubble coalescence fre-quency and hence the size of the bubble. In bubble columns, thesurface tension effect is similar to trend for single bubbles. Achange in surface tension changes bubble size and bubble velocityand affects mass transfer coefficient which may change the effi-ciency of mass transfer as shown in Fig. 6. The surface tension ef-fect is effective in homogeneous and transition regime and lessin the heterogeneous regime where the reduction of coalescenceis over-shadowed by the predominant effect of macro-scale turbu-lence [6]. Effect of surfactant addition causes decrease in surfacetension of the liquid, liquid having smaller surface tension arecapable of forming smaller size bubbles. Smaller size bubble willgive high overall gas holdup and interfacial mass transfer area. Li-quid side volumetric mass transfer coefficient increases with in-crease in gas holdup and interfacial area, and this causes thehigh gas to liquid mass transfer rate. Concentration profile for liq-uids with different surface tension is shown in the Fig. 7. It is seenthat as the surface tension of liquid rises from 42 mN/m to 72 mN/m the efficiency of mass transfer increases from 20% to 34% asshown in Fig. 8.

Fig. 11. Parity of mass transfer efficiency between co- and countercurrentoperations at different gas velocities at dc = 0.152 m, hm = 0.35 m, usl = 0.0589 m/s,system of air–water.

4.2. Mass transfer in co-current operation

Mass transfer in co-current operation follows the same trend asit was in the counter current operation; the basic differencebetween two types of operations may be due to the difference inmass transfer rate and enhance the difference in the mass transferefficiency. The mass transfer rate and mass transfer efficiency fol-lows the same trend in co-current and counter current mass trans-fer operation. For explanation of dependence of mass transferphenomenon on crucial operating, physiochemical and geometri-cal parameters description given in counter current operationcan be referred. The typical results of variation of concentrationprofile and mass transfer efficiency with the gas velocity are shownin Fig. 9 and 10 respectively. After simulation it is observed that gasconcentration in liquid phase is increasing as liquid–gas mixture

move up the column co-currently. This nature seems to be correctbecause as the gas and liquid move up the column solute particlesfrom gas phase are transferred to the liquid phase by molecularand convective diffusion. The superficial gas velocity has signifi-cance effect on the mass transfer phenomena. As the superficialgas velocity increases, the mass transfer from gas to liquid in-creases. The effect of superficial gas velocity on the liquid phaseconcentration is shown in Fig. 9. As the same reason discussed inthe countercurrent operation, with increase in superficial gasvelocity the mass transfer rate are found to be increased. As thesuperficial gas velocity increases the gas holdup increases whichresults in increase of gas transfer from gaseous phase to liquidphase. Also the interfacial area between gas and liquid increaseswith increase in gas holdup. As per explanation of Chaumat et al.[8], mass transfer efficiency increases with superficial gas velocitybecause of more turbulence and the more interfacial area. But

Table 1Typical data of mass transfer efficiency obtained with variation in various parameters has been tabulated below.

Counter current operation Co-current operation

Variables Gasholdup

Specificinterfacial area

Volumetric masstransfer coefficient

% Mass transferefficiency

Variables Gasholdup

Specificinterfacialarea

Volumetric masstransfer coefficient

% Mass transferefficiency

Sup. gas velocity0.02 0.1292 173.4302 0.0657 3.07 0.02 0.1292 173.4302 0.0657 3.070.04 0.233 317.0342 0.1285 15.51 0.04 0.233 317.0342 0.1285 13.820.06 0.3197 438.5062 0.1876 41.91 0.06 0.3197 438.5062 0.1876 35.150.08 0.3968 547.4857 0.2499 94.41 0.08 0.3968 547.4857 0.2499 80.69

Density1000 0.3197 639.3741 0.1876 36.05 1000 0.3197 639.3741 0.1876 35.151200 0.3222 644.4099 0.2191 45.73 1200 0.3222 644.4099 0.2191 43.561300 0.3233 646.6315 0.2345 50.65 1300 0.3233 646.6315 0.2345 47.771400 0.3243 648.6943 0.2498 55.56 1400 0.3243 648.6943 0.2498 51.95

Viscosity0.0008 0.3322 664.3564 0.2128 81.21 0.0008 0.3322 664.3564 0.2128 76.970.0009 0.3255 651.0665 0.1991 53.17 0.0009 0.3255 651.0665 0.1991 48.810.001 0.3197 639.3741 0.1876 38.49 0.001 0.3197 639.3741 0.1876 35.150.0011 0.3145 628.9539 0.1778 30.06 0.0011 0.3145 628.9539 0.1778 27.46

Surface tension0.042 0.2981 596.1771 0.2193 20.33 0.042 0.2981 596.1771 0.2193 19.950.052 0.3065 612.9832 0.2061 23.52 0.052 0.3065 612.9832 0.2061 22.670.062 0.3136 627.1283 0.1959 27.78 0.062 0.3136 627.1283 0.1959 26.50.072 0.3197 639.3741 0.1876 33.72 0.072 0.3197 639.3741 0.1876 31.15


there is a negative effect of increasing liquid velocity due to de-crease in liquid residence time and a less extent of gas hold-up.Chaumat et al. [8] carried out an experimental work on mass trans-fer phenomena at steady-state conditions high gas and liquid flowrates. They studied the effects of gas and liquid flow rates, columndesign (sparger hole diameter and perforated plates) on masstransfer efficiency. They enunciated the partition plates introduc-tion for gas distribution have no significant effect on the volumet-ric mass transfer coefficient but only superficial gas velocity has aclear influence. The global liquid side mass transfer coefficient kL

increases with superficial gas velocity which suggest some effectsof bubble-induced turbulence.

4.3. Comparison between counter current and co-current operations

A typical comparison between co-current and countercurrentoperation based on mass transfer efficiency has been shown inFig. 11. From the result it is seen that the counter-current opera-tion shows better efficiency compared to the co-current operationat different operating variables. In counter-current operations theintensity of backmixing of the phases is more prominent thanthe co-current operation. The back mixing phenomena may changethe mass transfer efficiency. Majumder [6] and Prakash andMajumder explained the mass transfer efficiency based on mixingphenomena. As the quality of mixedness, increases, the mass trans-fer efficiency of the column increases. Also the efficiency increaseswith the increase in inverse of modified effective Sherwood num-ber ((Ezeg)/(kLds)) [23]. For counter current operation opposite flowdirections of the phases increase the momentum transfer betweenthe phases which may increase the number of more circulation cellinside the column. The more circulation of the phases results inmore backmixing of the phases. But in case of co-current operation,the momentum exchange between phases is relatively less thanthe countercurrent operation due to decrease in relative velocityof the phases. Some calculated values are shown in Table 1. Thismay cause the decrease in mass transfer efficiency in case of co-current operation. So from the result it is concluded that the coun-ter-current operation of bubbly flow may be suitable for designand installation of the bubble column in industry for their specificapplication. The enhance factor (E) of mass transfer efficiency by

the countercurrent operation has been correlated with the superfi-cial gas velocity within the range of superficial gas velocity 0.02 to0.08 m/s as:

E ¼ ðgcount � gcoÞ=gco ¼ 0:1353 lnðusgÞ þ 0:543; R2 ¼ 0:8969

5. Conclusions and recommendation for future work

The modeling and simulation of mass transfer operation in thebubble column reactor has been done in this project work. Varia-tions of gas and liquid phase concentration with column heightare done by numerical simulation of the proposed model usingMATLAB software. Dependence of liquid phase concentration onvarious operating, geometrical and physiochemical properties ofgas–liquid phase has been shown graphically. Mass transfer coeffi-cient is dependent on gas superficial velocity and other physio-chemical properties of the phases. It was found that masstransfer efficiencies are higher for counter current mass transferoperation as compared to the co-current operation. The presentanalysis of gas–liquid mass transfer operation and mass transferefficiency analysis in bubble column reactor may give insight intofurther understanding, modeling and simulation of real multiphasebubble column reactors. Design and scale up of BCR is highlyempirical. Lots of correlations have been proposed to investigatethe non adjustable parameter in the column, but these correlationsare highly particular and system specific, therefore it would be bet-ter to propose more general correlations which are applicable tomore general systems. In present study we have assumed thatthe gas side mass transfer resistance is negligible, hence the overallmass transfer rate depends on liquid side mass transfer coefficient.For better and accurate understanding of mass transfer phenome-non in BCR it recommended for future to include the influence ofgas side mass transfer resistance to evaluate the overall masstransfer coefficient for gas to liquid mass transfer.

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Co- and counter-current mass transfer in bubble column

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