Influence of sparger on energy dissipation, shear rate, and mass transfer to sea water in a concentric-tube airlift bioreactor

Influence of sparger on energy dissipation, shear rate, and mass transferto sea water in a concentric-tube airlift bioreactor

Antonio Contrerasa, Francisco Garcıáa, Emilio Molinaa,*, JoseC. Merchukb

aDepartment of Chemical Engineering, University of Almerıá, 04071 Almerıá, SpainbDepartment of Chemical Engineering, Ben–Gurion University of the Negev, Beer–Sheva, Israel

Received 16 March 1999; received in revised form 29 July 1999; accepted 10 August 1999

Abstract

Data on volumetric mass-transfer coefficient,KLaL, in a 123 1023 m3 airlift bioreactor are reported. Measurements were made in seawater. The superficial gas velocity ranged up to 0.21 m/s. Four cylindrical spargers (60–1000mm pore size) were tested. In bubbly flow,the sparger pore size strongly influenced theKLaL; the highestKLaL values were obtained with the smallest pore size. In contrast, in thetransition and heterogeneous flow regimes, the pore size had little influence onKLaL. The best correlation of the mass transfer data wasobtained when both gas holdup and liquid superficial velocity were taken as independent variables. Shear rates were estimated in thedifferent zones of the reactor. The highest values were found in the bottom zone of the reactor and in the gas-liquid separator. Thepenetration and isotropic turbulence models were used to develop a semi-theoretical equation relating the volumetric mass-transfercoefficient to shear rate; hence providing a better understanding of how the operational variables may be manipulated to attain a moderateshear rate and an appropriate level of mass transfer, two extremely important parameters for the growth of sensible microorganisms as thoseused in marine biotechnology. © 1999 Elsevier Science Inc. All rights reserved.

Keywords:Shear rate; Mass transfer; Airlift bioreactor; Sparger pore size

1. Introduction

Gas-liquid mass transfer is often the limiting step in theoverall performance of gas–liquid contactors. The masstransfer rate depends strongly on the hydrodynamics nearthe gas–liquid interface; therefore, interfacial shear rate af-fects mass transfer. In most chemical processes, the shear rateis not important in itself, except as a means of increasing heatand mass transfer. On the other hand, in biochemical pro-cesses, the shear rate itself may be important. Excessive shearis known to damage suspended cells, leading to loss of viabilityand even disruption [1,2]. However, a certain degree of shear-ing is required to attain sufficient heat and mass–transfer rates,and to achieve a homogeneous distribution of transferred com-ponents into the bulk fluid. Dead zones where possible anoxiacould alter metabolic behavior or produce other reversible orirreversible damage to cells should be prevented.

The shear tolerance of biological systems constrains

mixing, heat, and mass transfer levels. Restrictions on theacceptable level of shear rates become more severe as theless robust plant and animal cell cultures and geneticallyengineered microorganisms are put to commercial use [3,4].Consequently, bioreactors that provide a gentle culture en-vironment are in increasing demand. Airlift bioreactors of-fer a milder low-shear environment to suspended bio-cata-lysts [5,6]. The shear fields in airlift devices are relativelyhomogeneous and zones of excess turbulence do not existunder normal operational conditions [7].

In view of the above noted significance of shear rate areliable method for its estimation in the reactor is necessary.A few correlations for estimating the shear rate have beenpublished [8–11], but these equations predict shear ratesthat differ in orders of magnitude [12].

More recently, Merchuk and Ben–Zvi [12] defined shearstress in a bubble column as equaling the force acting perunit time, that may be calculated from the power input andthe sum of the area of all bubbles:

t 5~ED!bulk

H O a(1)* Corresponding author. Tel.:134-50-215032; fax:134-50-215484.

E-mail address:[email protected] (E. Molina)

Enzyme and Microbial Technology 25 (1999) 820–830

0141-0229/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved.PII: S0141-0229(99)00119-2

This approach, which is applicable to pneumatically ag-itated reactors, is based on dimensional considerations andprovides an evaluation of the shear rate acting in the bulk ofthe liquid. Similarly, for an airlift reactor, Merchuk andBerzin [13] defined the shear stress in the liquid in anysection of the reactor as equal to the energy dissipated,divided by the mean path of circulation in the section and bythe sum of the areas of all bubbles. Then, for any sectionn(riser, downcomer, separator or bottom),

tn 5~ED!bulk,n

Hn2An~aL)n

~tR!n (2)

where (tR)n is the residence time of the liquid in the section.Eq. (2) gives a global shear force related to the interfacial

area of the dispersed gas, energy dissipation rate and resi-dence time.

Shear rate can be calculated from shear stress in anyzone; thus, for a Newtonian liquid:

gn 5tn

mL (3)

This global shear rate is a function of both fluid dynamicsand rheology.

According to Eqs. (2) and (3) estimating shear rate in anysection of the airlift reactor, requires evaluation of the en-ergy dissipation, the interfacial area and the residence timein that section. This approach has been followed by Molinaet al. [6].

The model proposed by Merchuk and Berzin [13] calcu-lates the energy dissipation in airlift reactors applying thefirst law of the thermodynamics to each section of thereactor. Those sections are shown in Fig. 1. They obtainedthe following expression for the dissipated energy:In the riser:

~ED!r 5 QL~P4 2 P5! 2 QLrLgH 2 QrP4 lnSP5

P4D (4)

In the gas-liquid separator:

~ED!S 5 QL~P5 2 P2! 2 QiP4 lnSP1

P5D 2 QdP4 lnSP2

P5D

(5)

In the downcomer:

~ED!d 5 QL~P2 2 P3! 1 QLrLgH 2 QdP4 lnSP3

P2D (6)

In the bottom:

~ED!b 5 QL~P3 2 P4! 2 QdP4 lnSP4

P3D (7)

Overall balance:Because no liquid enters or leaves, the energy balance in

the overall system may be written as:

Nomenclature

A cross-sectional area of the reactor (m2)a area of a bubble (m2)aL specific interfacial area (m21)C constant, oxygen concentration (kg/m3)C* equilibrium oxygen concentration (kg/m3)DL diffusivity (m2s)dB bubble diameter (m)ED energy dissipated (W)g graviational acceleration (m/s2)H height of liquid (m)JG superficial gas velocity (m/s)JL superficial liquid velocity (m/s)KL mass transfer coefficient (m/s)KLaL volumetric mass transfer coefficient (s21)l order of magnitude of the smallest eddies trans-

porting energy (m)P pressure (Pa)Q gas flow rate (m3/s)QL liquid flow rate (m3/s)tc circulation time (s)tR residence time (s)UL linear liquid velocity (m/s)u characteristic velocity of micro-eddies (m/s)V volume (m3)VD dispersion volume (m3)

Greek symbols

a constantb constant« holdup (2)f flowing volumetric concentration (2)g shear rate (s21)m viscosity (Pa s)n kinematic viscosity (m2/s)p pi (2)u exposure time (s)r density (kg/m3)t shear stress per unit time (Pa/s)t shear stress (Pa)j energy dissipation per unit mass (W/kg)

Subscripts

b bottomd downcomeri inletL liquidmax maximummin minimunn any section of the reactorr risers seperator1–5 point in the reactor (see Fig. 1)

821A. Contreras et al. / Enzyme and Microbial Technology 25 (1999) 820–830

ED 5 QiP4 lnSP4

P1D 5 ~ED!r 1 ~ED!S 1 ~ED!d 1 ~ED!b

(8)

Substitution of Eqs. (4), (5), (6), and (7) in Eq. (8), followedby rearrangement, leads to an expression forED. Eqs. (4–8)were used for analysis of the data shown in the presentpaper.

Although it is clear that a relationship between shear rateand mass transfer in a gas-liquid contactor must exist, thereare few studies specifically addressing this point. Merchukand Ben–Zvi [12] found that a single simple relationshipexists between the volumetric mass transfer coefficient andthe global shear rate for both Newtonian and non-Newto-nian liquids in bubble columns:

KLaL 5 a~g!b (9)

The possibility of applying such simple relationship to anairlift reactor will be explored here. The model of Merchukand Berzin [13] is used to estimate the global shear rate ineach section of the reactor. The penetration model andisotropic turbulence theory are used to relate the overallmass-transfer coefficient to this global shear rate.

The present work focuses on the influence of spargerporosity on mass transfer to sea water, dissipated energy andshear rate in a concentric-tube airlift bioreactor. Sea water isthe natural medium for cultivation of marine microalgae, atype of microorganisms of great interest in marine biotech-nology because their potential for the production of such

highly valuable products as natural dyes, polyunsaturatedfatty acids, and polysaccharides. Marine biotechnology, i.e.the application of modern biotechnology to marine organ-isms and processes, is an area of significant industrial im-portance. The ramifications of marine biotechnology reachalmost every major industrial sector including health, envi-ronment, energy, food (aquaculture and agriculture), chem-ical, and advanced materials [14]. Nevertheless, no study ofthis type using sea water, a medium that suppresses coales-cence, has been carried out previously.

2. Materials and methods

A Plexiglas concentric tube airlift bioreactor was used.The reactor consisted of a 0.09 m diameter outer tube thatwas 2 m high. A 1.5 m tall concentric draft tube was locatedwithin the outer tube. The cross-sectional areas of the riser(draft tube) and the downcomer were 2.833 1023 m2 and2.80 3 103 m2, respectively. The draft tube had a bottomclearance of 0.1 m. A schematic diagram of the airliftbioreactor is shown in Fig. 1.

Four different cylindrical spargers (0.02 m diameter,0.03 m high) were tested: a perforated pipe with 30 holes of1000mm diameter (Sparger C-1); a second perforated pipewith 30 holes of 500mm diameter (Sparger C-2); and twoporous sintered glass spargers with 120mm (Sparger C-3)and 60mm (Sparger C-4) pores. The sparger was located atthe bottom of the draft tube to prevent air entry into in thedowncomer.

Air from a compressor, passed through an oil separatorand a 0.5-mm-filter, was the gas phase in all experiments.The air-flow rate varied up to 0.53 1023 m3/s, correspond-ing to superficial air velocities (based on the riser cross-sectional area) of up to 0.21 m/s (2.5 vvm). The Mediter-ranean sea water (Almerıá Bay) filtered through a 0.2-mmpore-size filter, was the liquid phase. A pumping stationpumped the sea water to the laboratory from a well on thebeach. Sea water composition was (in kg/m3): Cl2, 20.812;SO4

5, 2.866; HCO32, 0.168; Na1, 10.552; Mg21, 1.362;

Ca21, 0.519; K1, 0.413; total dissolved solids, 36.608; totalorganic carbon, negligible; ionic strength, 0.727 kg-ion/m3.The temperature of the liquid phase was 206 1°C in allexperiments.

3. Calculations

Calculation of the energy dissipation with the thermody-namic model requires that the gas-flow rate in the down-comer be known. The drift flux model of Zuber and Findlay[15] was used to estimate the gas recirculation rate. In thismodel a “flowing volumetric concentration”,f, is definedas:

f 5Q

Q 1 QL(10)

Fig. 1. Schematic representation of the bioreactor with the pressure calcu-lation points.

822 A. Contreras et al. / Enzyme and Microbial Technology 25 (1999) 820–830

When gas and liquid velocities are equal,f 5 «. When gasvelocity is higher than the liquid velocity,f . «, which isthe case for the riser of an airlift reactor. When gas velocityis lower than the liquid velocity,f , «, which is the casefor the downcomer. As a conservative estimate, an assumedmean value forf in the riser is:

f# 5fmax1 fmin

2(11)

where

fmax5Qi 1 ~Qd!max

Qi 1 ~Qd!max1 QL(12)

and

fmin 5Qi

Qi 1 QL(13)

From Eqs. (10–13), the value ofQd that corresponds to themean value off can be obtained:

Qd 5f# QL 2 ~1 2 f# !Qi

1 2 f#(14)

The pressures at points 1 through 5 of the reactor (Fig. 1)were estimated by the following expressions:

P1 5 Pa (15)

P2 5 P1 1 rLg~H1 2 H2!~1 2 «r! (16)

P3 5 P2 1 rLg~H2 2 H3!~1 2 «d! (17)

P4 5 P5 1 rLg~H5 2 H4!~1 2 «r! (18)

P5 5 P1 1 rLg~H1 2 H5!~1 2 «r! (19)

wherePa is the atmospheric pressure and the holdup in thegas–liquid separator is assumed to equal that in the riser.

Fractional gas holdup was registered by measuring thedifferential pressure between two sampling ports connectedto an inverted U-tube manometer. The sampling ports(0.83 1023 m in diameter) were positioned 0.1 m from thetop and bottom entrances of the draft tube to measureaverage holdup and eliminate entrance effects.

Mean liquid circulation time,tc was determined by sig-nal-response technique using an alkaline tracer and a pHelectrode as the detector [16]. Using this mean circulationtime, the residence time in each section of the reactor couldbe obtained with the expression:

~tR!n 5 tcVn~1 2 «n!

VD~1 2 «!(20)

whereVn is the volume of sectionn andVD is the overallvolume of the reactor. The liquid flow rate,QL, and theliquid velocity in any sectionn of the reactor were calcu-lated with the expression:

QL 5 JLnAn 5 ULnAn~1 2 «n! 5V

tc(21)

Because there are no published data on the specific interfa-cial areas in airlift reactors,aL was calculated from themeasured holdup data and the bubble diameter, using thegeneral expression:

aL 56«

dB~1 2 «! (22)

Thus, for any section of the reactor, we have:

~aL!n 56«n

~dB!n~1 2 «n!(23)

hence, the overallaL is:

aL 5O ~aL!nVnO Vn

(24)

Bubble diameters,dB, in the riser and downcomer wereestimated photographically [17]. At the highest gas flowrate used, the photographic measurements were not reliable,therefore,dB was estimated by assuming that the meanbubble size was independent of the initial bubble size at thesparger. This procedure was supported by the fact that at thehighest values of gas flow rate the gas holdup did notdepend on the type of sparger. The volumetric mean bubblesize for the reactor was calculated with the equation:

dB 5O ~dB!nVnO Vn

(25)

in which thedB in the separator is assumed to equal that inthe riser anddB in the bottom is assumed to equal that in thedowncomer. Table 1 shows thedB values obtained with Eq.(25) in bubbly flow. The standard deviation (SD) of bubblesize was small (always lower than 11%) because, as previ-ously shown [18], when sea water is used, cylindrical sparg-ers initially produced small bubbles [(1–9)3 1023 m] andthe distribution of gas obtained is quite homogeneous,hence the probability of bubble coalescence was small. Themean bubble diameter (Eq. 25) and the overall holdup wereused to calculate the overall interfacial area (Eq. 24).

The overall volumetric mass-transfer coefficient,KLaL,was determined by the dynamic gassing-in method using adissolved-oxygen electrode (Ingold, 02-sensor-12/120) con-

Table 1Mean bubble diameter in bubbly flow (3103 m) as a function of thesuperficial gas velocity in the riser for all the spargers used

JGr

(m/s)Sparger C-1(1000mmpore size)

Sparger C-2(500 mmpore size)



0.0034 3.7 2.6 1.6 1.00.0095 5.8 4.0 2.4 1.80.0169 6.8 5.2 3.2 2.60.0314 7.7 6.2 4.2 3.50.0450 8.6 7.2 5.1 4.6


nected to an Ingold 170 ppm O2 oxygen amplifier-meter. Aconstant gas phase composition and well mixed liquid phasewere assumed. Throughout this work theKLaL values werealways much lower than the inverse of the probe responsetime. Following ASCE standard [19], the initial 20% of theresponse curve was ignored in calculating theKLaL. Thus,only the data in the range 0.2C*, C , C* were taken intoaccount in the regression. According to Merchuk et al. [20],the error forKLaL in bubbly flow and transition flow re-gimes was lower than 5%; the error in the heterogeneousflow regime was less than 15%.

3.1. Shear rate calculation

On the other hand, because the shear rate can be esti-mated using expressions 2 and 3, and for a timetc thecharacteristic length of the reactor is 2H, Eq. (3) can bewritten as:

g 5EDtc

2HVDaLmL(26)

Furthermore, the volumetric mean shear rate in the systemmay be expressed as:

g 5O gnVnO Vn

(27)

Thus, rom Eqs. (26) and (27), we have:

EDtc2HaLmL

5~ED!r~tR!r

Hr~aL!rmL1

~ED!s~tR!s

Hs~aL!rmL1

~ED!d~tR!d

Hd~aL!dmL

1~ED!b~tR!b

Hb~aL!dmL(28)

where (aL)r and (aL)d are the unknowns.Assuming thatdB and that the gas holdup values in the

gas separator and the riser are similar, and the bottom andthe downcomer zones also have comparabledB, Eq. (24)may be rewritten as:

aL 5~aL!r~Vr 1 Vs! 1 ~aL!d~Vd 1 Vb!

VD(29)

where the only two unknowns are (aL)r and (aL)d.

3.2. Bubble size correlation

Multiplying both sides of Eq. (22) byKL and rearrangingleads to the following expression for the bubble diameter:

dB 5KL6«

KLaL~1 2 «!(30)

According to the Higbie penetration model, the mass trans-fer at a gas–liquid interface is assumed to occur by a seriesof encounter between the liquid and the gas. The masstransfer coefficient,KL, is a function of the surface renewal

or contact time,u, between an element of fluid and thesurface of the gas:

KL 52

ÎpÎDL

u(31)

For the case of mass transfer at a liquid–gas bubble inter-face, several authors [21–23] have proposed expression thatgive an approximate value for this contact time in terms ofKolmogoroff model of isotropic turbulence, assuming thatthe rate of mass transfer at the gas-liquid interface is largelycontrolled by the interactions between the bubbles and thesmall-scale eddies. The contact time is assumed to be of theorder of the characteristic time of an eddy given by:

u}l

u5

Sv3

jD1/4

~vj!1/4 5 Sv

jD1/2

(32)

where v is the kinematic viscosity andj is the energydissipated per unit mass. Using Eqs. (31) and (32),KL

becomes:

KL 5 CÎDL Sj

vD1/4

(33)

whereC is a proportionality constant. Kawase and Moo–Young [24] recommended aC value of 0.301.

Introducing Eq. (33) in (30) we have:

dB 5

CÎDL 6«Sj

vD1/4

KLaL~1 2 «!(34)

Once the value of the constant C is known, Eq. 34 permitsthe calculation of the mean bubble diameter in the disper-sion, so long as the correspondingKLaL and« are known.

4. Results

4.1. Gas holdup and circulation time

Three different gas holdup regimes could be observed inthe riser and the downcomer when porous spargers (C-3 andC-4) were used (Fig. 2): (a) uniform bubbly flow; (b) tran-sition flow; and (c) heterogeneous flow. When perforatedpipe spargers (C-1 and C-2) were used, the pore size in-creased, the holdup changes became more moderate, and thetransitions between regimes were not as distinct as before.

The effect of gas flow rate and the sparger design onliquid circulation time is shown in Fig. 3. In the uniformbubbly flow region (a), the circulation time declines rapidlywith increasing gas flow rate but eventually a plateau isreached. A second phase of rapid drop in circulation timeoccurs in the transition flow regime (b). This effect is lesspronounced as the pore size of the sparger increases.


4.2. Distribution of dissipated energy

The energy dissipated in each zone of the reactor isshown in Fig. 4 for sparger C-1 (similar results were ob-tained with all spargers). The contribution of any section tototal energy dissipation is unaffected by the gas flow rate.Irrespective of the kind of sparger, the largest fraction of theenergy is dissipated in the riser, followed by the separatorand the downcomer. The bottom zone makes the smallestcontribution to energy dissipation.

Although the total energy input is important, turbulence,shear stress, and shear rate in each section of the reactor aredetermined not by the absolute energy input, but by thespecific energy dissipation rate [6,17]. Plots of energy dis-sipated per unit volume are shown in Fig. 5 for sparger C-1.Clearly, the bottom zone almost always makes the greatestcontribution to specific energy dissipation.

4.3. Volumetric mass transfer coefficient

Fig. 6 showsKLaL as a function of superficial gas ve-locity in the riser (JGr). In bubbly flow, forJGr values up to0.05 m/s, theKLaL values are higher for the smaller spargerpore size. In heterogeneous regime, on the other hand, thesparger pore size does not affectKLaL, and a maximum ofabout 0.030 s21 is obtained irrespective of the sparger. Intransition regime, the behavior ofKLaL is different fromthat of holdup and circulation time in that no relative max-imum is observed.

In Fig. 6, the maximumKLaL obtained with tap water(corresponding to sparger C-4) are shown for comparisonpurpose. TheKLaL in tap water is always lower than in seawater with the same sparger.

Fig. 2. Riser holdup as a function of superficial gas velocity. (F), SpargerC-1 (pore size5 1000mm); (■), sparger C-2 (pore size5 500mm); (}),sparger C-3 (pore size5 120mm); (Œ), sparger C-4 (pore size5 60 mm).

Fig. 3. Mean circulation time as a function of superficial gas velocity. (F),Sparger C-1; (■), sparger C-2; (}), sparger C-3; (Œ), sparger C-4.

Fig. 4. Energy dissipation in the different sections of the bioreactor ex-pressed as percentage of the total dissipation for sparger C-1. (F), Riser;(■), downcomer; (}), bottom; (Œ), separator; (�), overall.

Fig. 5. Distribution of energy dissipation per unit volume in the bioreactorfor sparger C-1. (F), Riser; (■), downcomer; (}), bottom; (Œ), separator.


5. Discussion

5.1. Gas holdup and circulation time

It is well known that in bubble columns and airlift reactorwith spargers having orifice diameters of less than 13 103

mm a transition regime exists between bubbly and hetero-geneous flow over a wide range of superficial gas velocities[18,25–27].

In bubbly flow, bubbles rise in the riser and descend inthe downcomer independently, with fairly uniform spacingbetween them, and therefore, holdup rises almost linearlywhen gas velocity increases. In transition flow the uniformbubble swarm begins to meander, revealing the formation ofsmall eddies in the liquid. The change from uniform bubblyflow to transition flow is gradual, and has been attributed tovarious factor that affect the size of the bubbles by alteringthe degree of coalescence and therefore, their rise velocity[28–30]. As can be seen in Fig. 2, no relative maximum isobserved for the spargers with the larger pore sizes (C-1 andC-2). Because spargers with larger pore sizes produce bub-bles with greater diameter, this can be interpreted as anindication that coalescence begins at the lowest gas veloc-ities with these spargers [18].

The differences in circulation time in the uniform bubblyflow and transition flow regimes are directly related todowncomer holdup. In these two flow regimes, the recircu-lation of gas to the downcomer is higher for the sparger withthe smallest pore diameter, because the bubble size issmaller. This implies lower rise velocities and thus, greaterrecirculation of gas. When pore size increases, both themean size of the bubbles and their rise velocity increase, andgas recirculates less, so the difference between riser anddowncomer densities increases and, therefore the liquidcirculation time is diminished.

In heterogeneous flow, turbulence in the bulk fluid con-

trols the hydrodynamic behavior and therefore, bubble sizeis not determined by the porosity of the sparger but thedegree of coalescence, and therefore holdup and liquid cir-culation time are similar for all spargers used. This concurswith the findings of Snape et al. [25] and Zaradnı´k et al.[24].

As previously shown [18] the behavior of the systemused is basically due to the composition of the liquid phase(sea water). When sea water is used coalescence is inhib-ited, with a stronger anti-coalescence effect than a NaClsolution with the same ionic force.

Since in this work,dB measurement were available in thebubbly flow regime, Eq. (34) could be used to obtain theproportionality constant C. The C-values were 0.52, 0.35,0.25, and 0.18 for Spargers C-1, C-2, C-3 and C-4, respec-tively. The average C-value for all the spargers was 0.325,which is close to 0.301 suggested by Kawase and Moo–Young [24].

5.2. Dissipated energy and shear rate

As commented above, irrespective of the sparger, thelargest fraction of the energy is dissipated in the riser,followed by the separator, the downcomer an the bottom.The bottom zone makes the smallest contribution to energydissipation presumably because of the large bottom clear-ance in the reactor. This confirms the findings of earlierworks [13,31] showing that the liquid circulation rate and,hence the energy dissipation rate, is affected by the clear-ance of the draft tube from the bottom of airlift reactors.Nonetheless, Fig. 5, clearly shows that the bottom zonealways makes the greatest contribution to specific energydissipation which is consistent with the results presented byMerchuk and Berzin [13] and Molina et al. [6]. Therefore,the results obtained confirm that the configuration of thebottom zone in airlift reactors is especially important indetermining the shear rate to which the cells are subject.

Eq. (28), in combination with Eq. (29), allows (aL)r and(aL)d to be estimated. Now Eqs. (2) and (3) may be used toestimate the shear rate in any section of the reactor.

Fig. 7 shows the estimated shear rates for the varioussections and the four spargers tested. The shear rate seemsto behave differently in different flow regimes, as observedalso for gas holdup and circulation time. In the bubbly flowregime, the shear rate increases slightly with increasing gasflow rate. In the transition regime, the shear rate increasessharply with gas flow rate, and in the heterogeneous flowregime, the shear rate tends to flatten out.

At the lowest gas velocities, the spargers with the small-est pore size produce lower shear rates, but at the highestgas velocities, the sparger pore size does not influence theshear rate and all spargers yield similar values (Fig. 7).Irrespective of the sparger, the highest shear rate valuesoccur in the bottom zone, followed by the gas–liquid sep-arator and the riser. The lowest shear rate values are foundin the downcomer where the flow is less turbulent. These

Fig. 6. Measured volumetric mass transfer coefficient as a function ofsuperficial gas velocity. (F), Sparger C-1; (■), sparger C-2; (}), spargerC-3; (Œ), sparger C-4; (‚), sparger C-4 using tap water.


results demonstrate the importance of the bottom zone andthe separator in the overall behavior and scale-up of thistype of system and are qualitatively consistent with otherreports [6,32–35]. The calculations presented here refer tothe shear in the bulk of the liquid, and do not take intoaccount other phenomena that may be detrimental to sus-pended cells, as interfacial velocity fluctuations related withbubble disengagement.

The shear rate is strongly related to the characteristiclength or internal scale of micro-eddies. Fig. 8 shows thatthe shear rate declines as the characteristic length of micro-eddies in the fluid increases. The greatest change in shearrate occurs over a narrow range of characteristic length. Fora fixed characteristic length, the shear rate decreases whensparger pore size, i.e. bubble size, diminishes. This showsthat the smaller the eddy size, the greater the shear rate, andthus the hydrodynamic stress and the possibility of celldamage [6].

The above discussed behavior has been shown to affectsignificantly the growth in sea water ofPhaeodactylumtricornutum in this bioreactor. In a previous work [36] it isshown that in bubbly flow, the growth ofP. tricornutum

increases when gas flow rate is increased, because the en-hancement of turbulence and therefore the CO2 transport.When transition flow is reached, the growth falls dramati-cally, most probably because the shear rate increasessharply and cell damage occurs.

5.3. Mass transfer rate

Fig. 6 shows that the evolution ofKLaL with sea water issimilar to that found with other media like tap water, butalways higher. Nonetheless, as pointed above, in transitionflow, the behavior ofKLaL is different from that of holdupand circulation time in that no relative maximum is ob-served. This may be attributed to the opposite influence ofbubble size on the mass transfer coefficient,KL, and theinterfacial area,aL, because when bubble size increases, theturbulence, and therefore theKL are increased, butaL di-minishes. Hence,KLaL is less sensitive to changes in bubblediameter than are gas holdup or circulation time.

The gas–liquid volumetric mass transfer coefficient,KLaL, in pneumatically agitated reactors is usually corre-lated with the gas flow rate or with the energy input. Many

Fig. 7. Shear rate in the different sections of the bioreactor as a function of superficial gas velocity. (F), Riser; (■), downcomer; (}), bottom; (Œ), separator.


of the available correlations have been summarized byChisti [31] and Merchuk and Gluz [37].

In the present work, mass transfer rates in the airliftbioreactor were measured as detailed above, and expressedas volumetric mass transfer coefficients. The correlation ofthe experimental results revealed that for sea water gasholdup was a better correlator than the superficial gas ve-locity or the energy input, as suggested before by McMana-mey and Wase [38] for tap water. The best correlation wasfound when both gas holdup and liquid velocity were takenas independent variables and the following equation wasobtained:

KLaL 5 0.1633~«!1.0187~ JLr!20.6187 (35)

This stresses the influence of the gas sparger on the perfor-mance of the reactor in a medium such as sea water that

suppresses coalescence. Geometrical characteristic of thesparger could not be taken as independent variables becauseof the difficulty in defining a variable applicable to bothorifice spargers and porous spargers. Eq. (35) correlated93% of the data with less than 10% error (Fig. 9).

This correlation has the advantage that all the data, fordifferent spargers and different salt or biomass concentra-tions are satisfactorily represented by one single expression[17]. On the other hand, it has the shortcoming that bothholdup and liquid velocity are not real independent vari-ables, since they can not be manipulated. Additional corre-lations of experimental data are therefore needed for the useof Eq. (35). Such specific correlations were obtained byContreras [17].

5.4. Relationship of shear rate and volumetric masstransfer coefficient

KLaL is plotted as a function of global shear rate in Fig.10. The figure indicates that there is no a simple relationshiprepresenting all the data, in contrast to the findings ofMerchuk and Ben Zvi [12] for the case of bubble columns.For the lower gas velocities, corresponding to bubbly flow,the spargers with the smallest pore size produce the highestKLaL with lowest global shear rates. This can be seen as aneffect of the noncoalescing properties of sea water. Thespargers with the smallest pore sizes are more efficient formass transfer because the small size of the bubbles is con-served in the reactor, rendering a high interfacial area. Inbubbly flow, the spargers with smaller pore size producesmaller bubbles, thusaL and KLaL are higher for similarshear rates.

From Eqs. (22) and (33), and assuming that practicallyall the energy introduced to the system is finally dissipated,it can be written:

Fig. 8. Overall shear rate as a function of characteristic length of themicro-eddies. (F), Sparger C-1; (■), sparger C-2; (}), sparger C-3; (Œ),sparger C-4.

Fig. 9. Prediction of volumetric mass transfer coefficient with Eq. (35).(F), Sparger C-1; (■), sparger C-2; (}), sparger C-3; (Œ), sparger C-4.

Fig. 10. Volumetric mass transfer coefficient as a function of overall shearrate. (F), Sparger C-1; (■), sparger C-2; (}), sparger C-3; (Œ), spargerC-4.


KLaL 5 CÎDL

6«

dB~1 2 «! S ED

VDmLD1/4

(36)

Eq. (36) relatesKLaL to the energy dissipated in thereactor. The latter is given by Eq. (8).

BecauseED can be derived from Eq. (26), Eq. (36) maybe rewritten as:

KLaL 5 CÎDLS 6«

dB~1 2 «!D5/4S2Hg

tcD1/4

(37)

Eq. (37) relates the volumetric mass transfer coefficient toshear rate. Both Eqs. (36) and (37) giveKLaL as a functionof operating conditions and the physical properties of thegas and liquid phases and may be used to estimateKLaL.Eq. (37) can be used also to estimate the global shear rate inan airlift reactor if KLaL is known. Fig. 11showsKLaL

predicted by Eqs. (36) and (37) as a function of superficial gasvelocity. Only bubbly flow data are presented for which thedB-values were actually measured. These equations represent85% of the experimental results with less than 20% error.

6. Conclusions

The effect of sparger pore size on shear rate and masstransfer were studied in a concentric tube airlift bioreactorusing sea water as the liquid phase. The energy dissipationrate in each section (riser, separator, downcomer, and bot-tom) of the bioreactor, the overall volumetric mass transfercoefficient and the shear rate were estimated. In bubblyflow, the spargers with the smallest pore size produced thelowest shear rates and the highest mass transfer rates. Inheterogeneous flow, the sparger pore size did not influenceshear rates or mass transfer. The highest shear rates pre-vailed in the bottom zone, followed by the separator and the

riser. Lower shear rate values were noted in the downcomer.This indicates that the design of the bottom zone and thegas-liquid separator section is important in determining theglobal behavior and scale-up of airlift systems. The pene-tration and isotropic turbulence theories were used to obtainan equation relating the volumetric mean shear rate to thevolumetric mass transfer coefficient. The equation providesa simple method for estimating the global value of the shearrate in airlift bioreactors with a known volumetric masstransfer coefficient. In addition, Eq. (37) developed here forsea water, but applicable to any liquid of known rheologicalproperties, provides a better understanding of how the op-erational variables and the sparger pore size may be manip-ulated to attain a moderate level of shear and an appropriatelevel of mass transfer rate in airlift bioreactors.

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Influence of sparger on energy dissipation, shear rate, and mass transfer to sea water in a concentric-tube airlift bioreactor