[MartiÌ-n, Montes, Galan, 2008] Bubbling process in stirred tank reactors II - Agitator effect on the mass transfer rates.pdf

Chemical Engineering Science 63 (2008) 3223 -- 3234

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Chemical Engineering Science

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Bubbling process in stirred tank reactors II: Agitator effect on themass transfer rates

Mariano Martn, Francisco J. Montes, Miguel A. GalnDepartamento de Ingeniera Qumica y Textil, Universidad de Salamanca, Pza. de los Cados 1-5, 37008 Salamanca, Spain

A R T I C L E I N F O A B S T R A C T

Article history:Received 19 July 2006Received in revised form 18 March 2008Accepted 21 March 2008Available online 29 March 2008

Keywords:Mass transferHydrodynamicsBubblesStirred tanksGeometry

Several impellers, perforated plates and geometrical configurations were tested in order to evaluate theeffect of the particular hydrodynamics generated by each impeller on the mass transfer rates and tooptimize the performance of the tank. Theoretical and empirical equations have been used or proposed,based on the experimental data, to study the oxygen transfer rates from air bubbles generated in anon-standard stirred tank. The empirical equations obtained depend on the impeller type, its positionand the design of the perforated plate because of their effect on the bubbles. The optimal position of theimpeller depends on the physical effect of the impeller on the bubbles. Higher mass transfer coefficientswere obtained close to the perforated plates. Not only the dispersion but also the break up of the bubblesfavors the mass transfer rates. In short, although the Rushton turbine is efficient and stable with itsrelative position, other impellers show very interesting results for lower power inputs.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

Mass transfer is a key parameter in the performance of multi-phase contactors. For example, in many microbian processes, theoxygen transfer limits the global rate process because the oxygenconcentration in the liquid phase is quickly depleted. Meanwhile,the consumption of other nutrients is relatively slow (Arjunwadkaret al., 1998a; Montes et al., 1999). That is the reason why the volu-metric mass transfer coefficient, kLa, has been the selected parame-ter in the design of gas--liquid contactors (Bouaifi et al., 2001).

Mass transfer rates depend on many factors. The effects on kLaof aeration, gas flow rate, temperature, tank geometry, physicalproperties of the liquid and its rheology, the presence of antifoamagents, the impeller type and the combination among differentstandard impellers have been studied broadly (Calderbank, 1958;Kawase and Moo-Young, 1988; Montes et al., 1999; Galindo et al.,2000; Bouaifi et al., 2001; zbek and Gayik, 2001; Alves et al., 2002;Parente et al., 2004).

Another important variable in process design is the way a gasphase is introduced into a liquid phase, whether by its surface ordirectly into the bulk. The difference between both determines theequipment: lagoons or process tanks. The latter has two possibilitiesthat are commonly used simultaneously: the use of impellers and/orperforated plates, which only generate what are known as primarybubbles.

Corresponding author. Tel.: +34923294479; fax: +34923294574.E-mail address: [email protected] (M. Martn).

0009-2509/$ - see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2008.03.035

The impeller location and its geometry determine the fractionof surface aeration in the total aeration of the bulk mass, since theimpeller can introduce gas due to vortexes, modifying the efficiencyof the mass transfer process.

The most studied impellers have been the Rushton turbines, dif-ferent pitched blade turbines as well as combinations of two orthree of them, in an attempt to optimize the power consumption(Arjunwadkar et al., 1998a, b; Montes et al., 1999; Gogate et al.,2000). However, the effect of the surface aeration due to the agita-tion has only been studied for the Rushton turbine (Wu, 1995).

On the other hand, dispersion devices allow higher kLa by mod-ifying the gas flow rate and the power input with low backmixing.However, compressors are expensive and the gas phase reduces theeffective power of the impeller (Wu, 1995).

In an attempt to rationalize the huge amount of data, several au-thors have proposed analytical expressions to predict mass trans-fer rates in stirred tank reactors (Kawase and Moo-Young, 1988;Barabash and Belevitskaya, 1995; Garca-Ochoa and Gmez, 2004).Due to the great number of variables affecting kLa, a general cor-relation for all systems is difficult to obtain (Sideman et al., 1966),making easier the use of empirical equations for particular systems(Montes et al., 1999; Bouaifi et al., 2001).

In this work, several variables are going to be studied, both ex-perimentally and theoretically, in order to obtain a wide range ofexperimental results of kLa, to be able to provide generality and de-termine the advantages and disadvantages of each configuration. Allthese factors will be explained based on the hydrodynamics of thetank previously studied (see Martn et al., 2008, part I).

3224 M. Martn et al. / Chemical Engineering Science 63 (2008) 3223 -- 3234

The experimental part consists of the study of the effect of dif-ferent impellers on kLa. Several impellers were used (two differentpitched blade turbines, Rushton turbine, a modified blade and a pro-peller), placed at different heights (h = 2, 3.5, 5 cm) above the per-forated plate. This will lead to the optimization of the location ofeach impeller and the most efficient impeller. Since mass transferdepends on the bubble size, two perforated plates were also used(D0 = 2mm with one and two orifices separated by 6mm). The ef-fect of bubble size on kLa will be established and a perforated platewill be defined as convenient.

In stirred tanks, there is always a gas region over the liquid phase,whose contribution to the mass transfer has been barely studied.The effect of the contribution of surface aeration on mass transferrates, due to the renewal of the superficial layer of fluid as a result ofmixing, has also been studied. Three more impellers, pitched bladedturbines with two, three and four blades, were also used in thissection.

We will compare the experimental results with empirical equa-tions from the literature and with some theoretical results for theprediction of kLa.

2. Theoretical considerations

2.1. Mass transfer

The rate of mass transfer is controlled by the liquid phase resis-tance and the contact area. In a stirred tank, the flow developed bythe impeller and its effect on the bubbles is what determines both(Sideman et al., 1966).

The hydrodynamics inside a stirred tank depends on its geom-etry and on the impeller. Then, to reduce the number of variables,the geometry of the stirred tanks has been standardized. Vogel andTodaro (1996) reported that the best height/diameter ratios are from2 to 3 so that it is possible not only to obtain a high residence timefor the bubbles but also to improve the dissolution of oxygen in theliquid by increasing the pressure on the dispersion device. Further-more, for the above-mentioned height/diameter ratios, the air feddecreases for the same uG . Additionally, there are also standard im-pellers such as Rushton turbine, "A'' series turbines and others.

However, the various impellers used and the geometric differ-ences among equipment (baffles, configuration of impellers, . . .) havemade easier the use of empirical correlations for each particular sys-tem instead of theories to explain and predict kLa, since the effect ofthe impeller on the bubbles is not considered in any of the availabletheories.

The first theory to be reviewed is according to Barabash andBelevitskaya (1995). The second is according to Kawase andMoo-Young (1988) and it is based on Higbie's Theory.

2.1.1. Barabash's theory (Barabash and Belevitskaya, 1995)The effect of turbulence on the mass transfer rate can be studied

from two points of view. The first approach is based on the diffusionequation at steady state in the interphase, considering the effect ofthe turbulence in the proximities of the bubble surface. The seconduses the non-constant diffusion model near the interphase.

Experimentally, it has been verified that the relaxation time ofthe surface layer is lower than that necessary for surface removalgiven by the variable diffusion model. So, the mass transfer rate canbe approximated by a stationary model at the interphase.

The effect of mixing on the mass transfer rate can be divided intothree different regions. For power inputs lower than 0.1W/kg, themass transfer rate is defined by that given by bubbles rising througha non-stirred fluid. From 0.1 to 1W/kg, mass transfer increases withthe dissipated energy. For higher dissipated energy, themass transfercoefficient remains stable with it.

There aremodels for each of the three regions. Only the predictingequations are written. Their development can be found in Barabashand Belevitskaya (1995).

Zone 3: >1W/kg

Themodel of the steady-state boundary layer and the relationshipfor turbulence damping leads to

s =0.54 ( )0.25

Sc0.5(1)

Zone 2: >0.1W/kg

This region is characterized by low agitation and gas hold-up,lower than 1%. The mechanism for the mass transfer is similar tothe one in the absence of mixing. There is a difference between themass transfer in the rear part of the bubble, rp, and the front partof it, fp. For bubbles of 5mm, the rear part of the bubble is about25%, rp = 0.25, so that the liquid film resistance can be calculatedweighing up the superficial areas.

t = rprp + fp(1 rp) (2)For the frontal region of the bubble:

fp =0.65 D

db

Re Sc (3)

For the rear region of the bubble, rp = s.This region has also been studied using the similarity between

mass and heat transfer, in the absence of viscous warming, usingHigbie's theory (Kendoush, 1994)

Nu = Sh = 2Pe0.5

(3 E2 + 4E2 + 4

)0.5(4)

Zone 1: 0.1<

M. Martn et al. / Chemical Engineering Science 63 (2008) 3223 -- 3234 3225

u = ()1/4 (7)The exposition time corresponds to the time a bubble needs to

travel a length equal to its diameter. For a Newtonian fluid, the liquidfilm coefficient can be calculated using the following equation:

kL =2

D

(

)1/4(8)

2.1.3. Specific areaBoth theories are focused on the calculus of the resistances for

the mass transfer. However, the design parameter for stirred tankreactors is kLa, which is related to the former through the specificsurface area given by Eq. (9)

a = 6Gdb

(9)

The gas hold-up can be determined empirically by Gogate's cor-relation (Gogate et al., 2000)

G = 0.21[PgV

(1 G)]0.27

u0.65G (10)

or theoretically by Garca-Ochoa (Garca-Ochoa and Gmez, 2004)

G1 G

= 0.5 u2/3G

(g long)1/3(

G

)(11)

long was defined as

long = 2(

)3/5 ( L2/5w6/5

)(

G

)0.1(12)

The resilience coefficient, , is 0.4 for a wide range of Reynoldsnumbers (1000


Fig. 1. 1, High-speed video camera; 2, optic table; 3, bubble column; 4, illumination source; 5, air compressed; 6, rotameters; 7, computer; 8, nitrogen compressed; 9,impeller; 10, oxygen electrode.

Fig. 2. Impellers.

important effect on the efficiency of the power input on kLa. Thedirect effect of the impeller on the bubbles is delayed or avoided asthe impeller is located higher and so the efficiency of the power in-put on kLa decreases with the vertical position of the impeller and,as a result, so does (Martn et al., 2008). However, the contributionof the gas flow rate to the mass transfer, given in , is similar to that

found in the literature for the air--water system (Van't Riet, 1979)because once the bubbles break, the impeller allows their scatteringacross the tank.

A higher position of the impeller results in a loss of mass transferefficiency for high rotational velocities, where the main contributionto kLa is that due to the break up of the bubbles. However, for low


Table 1Mass transfer in the absence of agitation

Qc (m3/s) kLa (s1)

1 orifice 0.6 106 0.622 1051.4 106 0.825 1052.8 106 1.067 105

2 orifices 0.3 106 0.485 1050.6 106 0.594 1051.4 106 0.982 105

Table 2Coefficients for the pitched blade turbine, one orifice, Eq. (16)

k

h = 2 cm 0.0032 0.47 0.54h = 3.5 cm 0.0020 0.39 0.50h = 5 cm 0.0021 0.29 0.53

Fig. 3. Effect of the position of the impeller in the volumetric mass transfer coefficient.Pitched blade turbine, one-orifice dispersion device.

rotational speeds the main contribution to kLa is based on bubbledeformations in the fluid flow so that the position of the impellershows small effect on kLa. Furthermore, the combined effect of su-perficial turbulence and the flow patterns developed in the liquidreveals an important contribution of the superficial aeration to kLafor locations of the impeller above 1/2 of the liquid depth. Anotherexperimental result to point out is that bubble oscillations cannotcope with the lack of superficial area available if they are not broken(Martn et al., 2007). Fig. 3 shows the experimental results.

In short, the most important contribution to the kLa for this con-figuration of impeller and dispersion device is the break up of thebubbles, so that the best location of the impeller corresponds tothe lowest position, h = 2 cm, where the effect of the impeller onthe bubbles is high (Martn et al., 2008).

4.1.2. Two-orifice dispersion deviceIn the case of smaller bubbles generated at the two-holed per-

forated plate, the efficiency of the impeller input power is lowerthan in the case of one orifice. The smaller generated bubbles are,consequently, less deformable and thus more difficult to be broken.Furthermore, the contribution of the gas flow rate decreases highly

Table 3Coefficients for the pitched blade turbine, two orifices, Eq. (16)

k

h = 2 cm 4.35 105 0.36 0.12h = 3.5 cm 17.5 105 0.31 0.26h = 5 cm 5.84 105 0.40 0.17

Fig. 4. Effect of the position of the impeller in the volumetric mass transfer coefficient.Pitched blade turbine, two-orifice dispersion device.

Table 4Coefficients for the modified blade, one orifice, Eq. (16)

k

h = 2 cm 5.7 104 0.32 0.35h = 3.5 cm 4.3 104 0.29 0.32h = 5 cm 14 104 0.23 0.46

with respect to the one-holed perforated plate, Table 3. Bubbles aredragged by the gas flow rate and are able to avoid the impeller blades,but they do not remain in the tank because they can rise without be-ing affected by the impeller. The dispersions obtained were poorer interms of area generated and distribution of bubbles across the tank.As a result, and are smaller than in the case of using a one-holedperforated plate.

Since the direct effect of the impeller on the bubbles is low, theincreasing contribution of the surface aeration as the impeller isplaced higher over the perforated plate can balance the lack of ef-fectiveness of the impeller and so, kLa is almost constant with theposition of the impeller for N = 430 rpm, but decrease for the otherrotational velocities because the bubbles can completely avoid theeffect of the impeller, Fig. 4.

4.2. Modified blade

4.2.1. One-orifice dispersion deviceThe characteristic geometry of this impeller, Fig. 2, results in val-

ues of which decrease with the distance of the impeller to thedispersion device (Table 4). Bubbles can avoid the blades if the ro-tational speed is low and this fact is easier as the impeller is locatedhigher along the vertical axis (Martn et al., 2008). Furthermore, forhigher positions of the impeller, the direct effect of the impeller on


Fig. 5. Effect of the position of the impeller in the volumetric mass transfer coefficient.Modified blade, one-orifice dispersion device.

the bubbles is delayed, and the enhancement of mass transfer dueto bubble oscillations of the big rising bubbles cannot balance thelack of superficial contact area. On the other hand, for low rotationalvelocities, as bubble break-up is difficult, the differences in the masstransfer rate with the location of the impeller are small. The masstransfer rate depends on the deformation of the bubbles during theirmotion across the tank and it is related to the fluid flow in the tank.

The values of are smaller than those of the previous impeller,see Tables 2 and 4. Bubbles are not well dispersed across the tankbecause most of them remain near the revolution cylinder generatedby the impeller for all of its locations.

However, the contribution of the surface aeration to the total kLawith the distance of the impeller to the dispersion device increases.This fact balances the loss of efficiency due to the lack of bubblebreakage and the poor dispersions obtained. As a result, the impellerbehaves almost in the same way no matter where it is placed alongthe vertical axis. The only exception is the lowest position, where,if the initial bubbles are big enough, as in the case of high gas flowrates, they can be cut by the impeller blade during the first stagesof rising, improving the mass transfer rate by increasing the contactarea between both phases (see Fig. 5).

4.2.2. Two-orifice dispersion deviceThe smaller bubbles generated at this dispersion device reduce

the empirical coefficients , compared to the one-holed dispersiondevice, as in the case of the pitched blade turbine.

The values of are smaller than those obtained for the one-holeddispersion device. The efficiency of power input on the mass trans-fer rate decreases because bubbles are barely broken due to theirsmaller size. They are more stable in the flow. The main break-upmechanism is bubble deformation near the blade, where the bub-bles are retained, while bubbles can easily avoid the direct effect ofthe blades, particularly for low rotational velocities of the impeller.The values obtained for are much smaller compared to the onesobtained for the one-orifice perforated plate. Bubble dispersion isdetermined by the dispersion device so that the superficial area islower than in the case of break-up processes taking place in thetank. Unbroken bubbles can rise mainly due to their buoyancy, littleaffected by the impeller, see Table 5.

Since bubbles can be retained at the impeller blades, the realeffect of the impeller on the bubbles does not depend on its location.

Table 5Coefficients for the modified blade, two orifices, Eq. (16)

k

h = 2 cm 8.1 105 0.25 0.16h = 3.5 cm 9.5 105 0.26 0.17h = 5 cm 13.7 105 0.29 0.21

Fig. 6. Effect of the position of the impeller in the volumetric mass transfer coefficient.Modified blade, two-orifice dispersion device.

Table 6Coefficients for the Rushton turbine, one orifice, Eq. (16)

k

h = 2 cm 0.0012 0.47 0.41h = 3.5 cm 0.00054 0.43 0.32h = 5 cm 0.00054 0.52 0.35

In addition to that, the effect of the oscillations of the bubbles and thecontribution of the atmosphere balance the lack of superficial areadue to the absence of break-up processes. The generated bubbles arestable in the flow. As a result, themass transfer rate does not decreasewith the position of the impeller. The stability of the configurationdispersion device--impeller onmass transferwith its relative positioncan be seen in Fig. 6.

4.3. Rushton turbine

Themost used impeller in fermentation processes has a particularconfiguration from which the results can be totally explained. It canbe called the "disk effect''.

4.3.1. One-orifice dispersion deviceThe disk retains the rising bubbles so that they can be broken by

the blades in their discharge. Rising bubbles cannot avoid the effectof the impeller and, as a result, the effectiveness of the break-up pro-cess is high, and so are the values of . Since bubbles are dispersedthroughout the tank and move with the flow after being discharged,the values of remain stable with the position of the impeller,Table 6.

The retention of bubbles, or the control carried out by the disk,the increment in the contribution of the surface aeration with the


Fig. 7. Effect of the position of the impeller in the volumetric mass transfer coefficient.Rushton turbine, one-orifice dispersion device.

Fig. 8. Atmospheric contribution to the mass transfer rate. Rushton turbine,one-orifice dispersion device.

vertical position of the impeller and the deformation and final break-up of the bubbles due to the developed flow under the impeller(Fig. 12, Martn et al., 2008) are able to balance the loss of masstransfer efficiency as the impeller is located higher with respect tothe dispersion device, typically shown in other impellers. As a result,this impeller is the most stable considering its vertical position forthe one-holed device, Fig. 7. However, the retention of bubbles canlead to hydrodynamic instabilities (Vogel and Todaro, 1996).

Fig. 8 shows values of the contribution of the superficial aerationto kLa, which decreases with the gas flow rate and the impellerspeed since both are, in general, the main responsible mechanismsfor mass transfer.

4.3.2. Two-orifice dispersion deviceThe above-mentioned "disk effect'' allows almost no changes in

the values of and with respect to the one-holed dispersion device.Both are only a little lower due to the difficulties in breaking the

Table 7Coefficients for the Rushton turbine, two orifices, Eq. (16)

k

h = 2 cm 7.5 104 0.43 0.35h = 3.5 cm 4.2 104 0.40 0.30h = 5 cm 2.3 104 0.49 0.24

Fig. 9. Effect of the position of the impeller in the volumetric mass transfer coefficient.Rushton turbine, two-orifice dispersion device.

Table 8Coefficients for the pitched blade turbine b, one orifice, Eq. (16)

k

h = 2 cm 4.6 104 0.46 0.29h = 3.5 cm 2.8 104 0.37 0.26h = 5 cm 3.6 104 0.42 0.30

smaller bubbles generated under these experimental conditions anddeveloping a good dispersion, Table 7.

For this configuration, the effect of the position of the impeller isalso low. The effect of the disk balances the decrease in the efficiencyof the gas flow rate, showing a stable operation with the position ofthe impeller, Fig. 9.

4.4. Pitched blade turbine b

4.4.1. One-orifice dispersion deviceBoth pitched blade turbines differ in the shape of the blades.

The blades of the first pitched blade turbine are sharper. However,bubble break-up effectiveness is higher for this turbine because theblades collect the gas phase. The bags of gas gathered at the bladesare broken at the discharge in spite of their lack of sharpness. Dueto the development of those bags of air at the end of the blades, is more stable with the vertical position of the impeller than inthe case of the other pitched blade turbine, impeller 1, where thebubbles could avoid the impeller.

The main difference is found in the values of . They are constantwith the position of the impeller above the dispersion device butlower than those obtained for the first pitched blade turbine. Thedifficulties in scattering the broken bubbles lead to poorer disper-sions, see Table 8, resulting in a reduction in the values of to halfwith respect to those given in Table 2.


Fig. 10. Effect of the position of the impeller in the volumetric mass transfercoefficient. Pitched blade turbine b, one-orifice dispersion device.

Table 9Coefficients for the pitched blade turbine b, two orifices, Eq. (16)

k

h = 2 cm 2.2 104 0.47 0.23h = 3.5 cm 3.0 104 0.36 0.27h = 5 cm 0.6 104 0.31 0.13

The effect of the impeller distance to the dispersion device issimilar to that of the first impeller. The best location of the impellerin terms of kLa is near the dispersion device, so that bubbles cannotavoid an early break and dispersion. The contribution of the surfaceaeration and the oscillations of the bigger bubbles cannot reduce theloss of mass transfer rate due to the less direct effect of the impellerbreaking the bubbles generated at the dispersion device, Fig. 10.

4.4.2. Two-orifice dispersion deviceThe smaller bubbles generated by this dispersion device reduce

and . However, the fact that bubbles are taken by the blades,limits the loss of break-up efficiency. Bubble break-up is due to thedeformation of the bags of gas at the end of the impeller blades(Martn et al., 2008). Consequently, the values of remain stable withthe location of the impeller. The reduction in the values of is moreimportant, Table 9. The bubbles are not properly dispersed whenthe location of the impeller is higher with respect to the dispersiondevice.

For this particular impeller--dispersion device configuration,there is almost an equilibrium for the two lower positions of theimpeller in terms of mass transfer rate, but the best location for theimpeller is, again, near the dispersion device, Fig. 11. If bubbles arebroken at an early stage, better dispersions are developed.

4.5. Propeller

The flow pattern developed by this impeller leads to the develop-ment of a dispersion characterized by the accumulation of bubblesbelow the impeller as well as low break-up effectiveness, since thereis almost no physical contact of the impeller with the bubbles. Bub-ble break-up is due to its deformation under the impeller (Martnet al., 2008).

Fig. 11. Effect of the position of the impeller in the volumetric mass transfercoefficient. Pitched blade turbine b, two-orifice dispersion device.

Table 10Coefficients for the propeller, one orifice, Eq. (16)

k

h = 2 cm 8.97 104 0.28 0.40h = 3.5 cm 3.66 104 0.30 0.30h = 5 cm 3.06 104 0.21 0.31

4.5.1. One-orifice dispersion deviceTable 10 presents the fitting parameters of the experimental val-

ues of kLa to Eq. (16). For big initial bubbles, k, and are similar tothe ones presented in the other impeller--dispersion device configu-rations. Bubbles can easily be broken and scattered across the tank.

The characteristic dispersion generated, the retention of the bub-bles below the impeller maintaining them in the liquid (Fig. 12 ofMartn et al., 2008), together with the contribution of the superficialaeration, stable with the power input, results in an optimal positionof the impeller at 3.5 cm from the dispersion device. Figs. 12 and 13report that. The contribution of the surface aeration to kLa is par-ticular for this impeller since, in contrast to other impellers, it doesnot depend on the power input, due to the flow pattern developedby this impeller.

4.5.2. Two-orifice dispersion deviceSimilar to other impellers, bubble break-up efficiency is lower for

smaller bubbles because they are stable in the flow so, the values of are also smaller, Table 11. The decrease in the values of is alsoremarkable. Bubble size, as a result of a lack in break-up processes,allows the formation of a gas cluster made of a large group of bubblesunder the impeller (Martn et al., 2008). The effective area is lowerthan that given by the bubbles due to their surface. Bubbles are closeand part of their surface may be too close to another bubble to beeffective for the mass transfer since no concentration gradients canbe developed.

Furthermore, the generated bubbles, due to their size, can avoidthe effect of the impeller. In addition to that, impeller effectivenessin mass transfer decreases with the distance of the impeller to thedispersion device. However, for low rotational speeds this decreaseis almost non-existent. The increase in the atmospheric contributionbalances the loss of area due to the decrease in break-up efficiencyas the impeller is located higher, Fig. 14.


Fig. 12. Effect of the position of the impeller in the volumetric mass transfercoefficient. Propeller, one-orifice dispersion device.

Fig. 13. Atmospheric contribution to the mass transfer rate. Propeller, one-orificedispersion device.

Table 11Coefficients for the propeller, two orifices, Eq. (16)

k

h = 2 cm 1.3 104 0.33 0.17h = 3.5 cm 0.9 104 0.28 0.15h = 5 cm 0.7 104 0.22 0.16

4.6. Theoretical--empirical--experimental comparison

Mass transfer theories focus on calculating the liquid film resis-tance. It is necessary to determine the specific area in order to com-pare the experimental values of kLa with the theoretical ones.

It has been proved that Eq. (9), with the gas hold-up calculatedusing the empirical correlation given by Eq. (10) and Eq. (15) givesimilar results for all the experimental conditions. The gas hold-upcalculated using Eq. (11) shows bigger values than those obtained by

Fig. 14. Effect of the position of the impeller in the volumetric mass transfercoefficient. Propeller, two-orifice dispersion device.

Eq. (10), and the specific area resulting is bigger than that calculatedusing Eq. (15) or (9). From now on, the value of the area givenby Eq. (15) is going to be used since it has some theoretical basis(Kolmogorov's theory).

In order to use the Barabash's model, zone 2 is considered, ac-cording to the experimental results of the power input.

Fig. 15 shows an example of the comparison among theoretical,experimental and empirical values of kLa for the Rushton turbines.Similar figures were obtained for the other impellers and dispersiondevices.

In general, the theoretical results of Kawase and Barabash(Kawase and Moo-Young, 1988; Barabash and Belevitskaya, 1995),give high values of kLa. In case of using Garca-Ochoa's model, apartfrom the fact that the gas hold-up equation is particularly developedfor a Rushton turbine, the results of kLa are ever bigger than thoseof Barabash. This is because the predicted gas hold-up is higherthan the one predicted by typical empirical equations (Gogate et al.,2000; Shukla et al., 2001) and so, the calculated area is bigger thanthe actual.

The comparison among experimental values and the empiricalvalues from Arjunwadkar et al. (1998a, b) gives better results inspite of the fact that the geometry of the system used to obtain theempirical equation, almost standard, is different from the one usedfor this work.

The general trend is that the theoretical results are always higherthan the empirical and experimental ones, which are both close.These models do not cope with the loss of energy due to the ge-ometry of the systems nor the actual area. The experimental resultsare between the empirical and very close to them and the theoret-ical ones. Results like these have popularized the use of empiricalcorrelations in the design and scale-up of stirred tanks.

4.7. Effect of the dispersion device on kLa

In a stirred tank, the dispersion of the gas phase into the liq-uid phase relies on two mechanisms: the dispersion device and theimpeller itself. If the bubbles generated at the dispersion devicesare small enough to be stable in the fluid flow developed in thetank for both dispersion devices used, the one-holed and the two-holed dispersion devices, the smaller the bubbles generated themoreefficient the system is. However, if the bubbles generated at the


Fig. 15. Theoretical--empirical--experimental comparison of the volumetric transfer mass coefficient: Rushton turbine, h = 2 cm.

Table 12Air--water system: dispersion device effect

k

1 orifice 4 104 0.28 0.312 orifices 2 104 0.21 0.25

one-holed dispersion device can be broken and those generated atthe two-holed dispersion device cannot, the break-up process pro-vides more area than that generated by the dispersion device aloneand bubbles, due to the discharge, are better dispersed across thetank. Furthermore, for the same final mean diameter, the break-upprocess deforms the bubbles before breaking them and the break-upitself, due to the modification of the concentration pattern surround-ing the bubbles, improving the mass transfer rate of the system.

The effect of the dispersion device can also be seen in the coeffi-cients of typical empirical equations like Eq. (16). Table 12 presentsthe results.

Bubble break-up improves the efficiency of the power input. Foreasily breakable bubbles, the values of are bigger than in the case

of no break-up. This is because power input translates into the gen-eration of contact area and the modification of the concentrationprofiles surrounding the bubbles as they deform previous to theirbreakage. The values of become higher due to the scattering of thebroken bubble, providing a higher available area and a better dis-persion. In terms of k, the smaller the bubbles of the dispersion thebigger the coefficient is.

To sum up, not only a better dispersion in terms of gas--liquidcontact area but also the break-up process itself improves the masstransfer.

4.8. Effect of the impeller on the contribution of the superficialaeration to kLa

Each impeller develops a particular flow pattern inside the tank.The turbulence generated in the surface liquid--atmosphere definesthe contribution of that interphase to kLa in the liquid bulk. Twoeffects have been studied, the effect of the position of the impeller,summarizing the results impeller by impeller exposed during thediscussion of each of the first five impellers, and the effect of thenumber of the blades of an impeller.


Table 13Coefficients of Eq. (17) for the effect of the impeller location on the volumetricmass transfer coefficient

k

Impeller 1 6.17 106 0.22 0.31Impeller 2 1.56 105 0.12 0.57Impeller 3 1.80 105 0.27 0.60Impeller 4 9.89 106 0.29 0.34Impeller 5 1.31 105 0.30 0.40

Fig. 16. Effect of the number of blades on the atmospheric contribution on kLa.

The location of the impeller defines the liquid vortexes inside thetank. In the absence of air input, it is possible to determine the valueof kLa due to superficial aeration following an equation of the form:

kLaatm = k (

P

V

) (h) (17)

Table 13 collects the data of the fitting values k, and for thefive impellers. The height of the blade is what defines in Eq. (17). Abigger size of the blade results in bigger values of . The value of isrelated to the power input, and it has a constant value for impellers3, 4 and 5 but a lower value for the other two. The liquid circulationrenovating the surface is less effective for these two impellers.

In the empirical equations for kLa given by Eq. (16), the effectof the position of the impeller (k h ) is included in k. Therefore,k gathers the effect of the geometry on the mass transfer rate. Inaddition to that, it can be seen how the effectiveness of the powerinput is not only determined by the generation of area but also bythe effect of the impeller in the surface liquid--atmosphere. Anyway,it is small compared with the contribution of the aeration providedby the bubbles.

For the second part of this study, three impellers were designedwith two to four blades, Fig. 2. The number of blades increases theinput power for a particular agitation speed, determines the effect onthe bubbles, which cannot avoid the blades in their rising movementas the number of blades increase, as well as define the turbulencein the air--liquid surface. As a result, there is an increment in thecontribution of the superficial aeration on kLa with the number ofblades of the impeller. Fig. 16 shows the contribution of the surfaceaeration on the total kLa versus the power input.

In general, the increment in the total input power reduces thefraction of kLa due to surface aeration because bubble break-up

generates more contact area. However, as the number of bladesincreases, the superficial turbulence increases. Therefore, the con-tribution of the surface aeration increases with the number ofblades.

To analyze the effect of the number of the blades on the con-tribution of the surface aeration to the total kLa, the volumetricmass transfer coefficient was measured in the absence of air in-put. The experimental results were fitted to an equation similar toEq. (17):

kLaatm = 1.48 106 (

P

V

)0.18 (no. blades)0.59 (18)

Although the number of the blades also determines the powerinput, the circulation in the gas--liquid interphase depends on thefrequency with which the blades go through a fixed point. This hasa linear dependency with the number of blades, whereas the powerinput does not depend lineally on it.

5. Conclusions

Mass transfer rate depends heavily on the hydrodynamics of thesystem generated by the impellers and the dispersion devices.

The most important effect of the impeller is that affecting the gasphase. The effect of the impeller on the bubbles, direct or that dueto the flow generated, determines the contact area between phasesand the concentration profile surrounding the bubbles and so, themass transfer rate. If bubbles are only dragged by the developed flowpattern or move freely, kLa values are lower than in the case of acombination between break-up process and flow movement. In gen-eral, a higher position of the impeller with respect to the dispersiondevice reduces that physical effect of the impeller or delays it, andso, there is a decrease in the values of kLa.

A direct result of the effectiveness of the power input in kLa isbubble break-up, which increases the mass transfer rate due to thegeneration of superficial area and by modifying the concentrationprofile surrounding the bubbles. We found that is a measure ofthe power input efficiency in relation to the contacting performanceof a stirred tank. Furthermore, bubble breakage improves bubbledispersions. This fact is one of the reasons for the high efficiency inthe mass transfer rate when the impellers are located next to thedispersion devices. If the bubbles break, an early break-up makeseasy the development of a dispersion. Furthermore, the oscillationsof these big bubbles cannot cope with the superficial area generatedin case of their breakage.

The available specific area and the scattering of the bubbles de-termine the experimental value of .

In an industrial fermentor, there is a gas phase over the liq-uid phase, whose contribution must be taken into consideration.The effect of the atmospheric gas--liquid contact makes it possi-ble that the highest mass transfer coefficients were obtained ata distance of the impeller above the dispersion device instead offeeding the gas phase too close to the impeller. The surface aera-tion contribution affects the k coefficient in the empirical equationsfor kLa.

Although the most stable impeller with respect to its relativelocation above the dispersion device in terms of kLa is the Rush-ton turbine, some others are very stable, with interesting values ofkLa which generate less stress in the liquid phase; for example, thepitched turbine with hydrodynamic blades. Its advantage can be thatfor high gas flow rates the Rushton turbine usually decays in thepower input more than other impellers (Vogel and Todaro, 1996).

Since the bubble break-up process improves the mass transferrate, dispersion devices should generate bubbles whose size allowstheir breakage. The gas flow rate across an orifice must be optimized.


It has been proved that smaller bubbles in the dispersion lead tobigger k coefficients.

The differences among the theoretical, empirical and exper-imental results support the effect of the geometry of the sys-tem in the mass transfer and the difficulties in predicting kLatheoretically.

Notation

a specific surface area, m1c concentration, mol/m3

D diffusivity, m2/sdb bubble diameter, mE eccentricityh position of the impeller above the dispersion

device, mH height of the impeller blade, mkL transport resistance in the liquid phase, m/sN rotational velocity, s1P unaerated input power, W/m3

Pg aerated input power, W/m3

Pe Peclet number Pe = U db/DQc gas flow rate, m3/sr bubble radius, mSh Sherwood number, Sh = kL db/DT impeller diameter, mu fluctuation velocity, m/suG superficial gas velocity, m/sU rising velocity of the bubble, m/sV liquid volume, m3

w velocity of the blade, m/sWe Weber number We = N2T3/

Greek letters

, , , , empirical coefficientsi fraction of the bubble surfacei mass transfer coefficient, m/s dissipatedenergy, W/kgg gas hold-up turbulent characteristic length, m liquid viscosity, Pa s kinematic viscosity, m2/s liquid density, kg/m3

G gas density, kg/m3

superficial tension, N/m

Acknowledgments

The support of the Ministerio de Educacin y Ciencia of Spainproviding a F.P.U. fellowship to M. Martn is greatly welcomed. Thefunds from the project reference CTQ 2005-01395/PPQ are also ap-preciated. We thank Prof. J. Cuellar of Chemical Engineering Depart-ment at University of Salamanca for lending us some of the impellersused in this paper.

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