Biochemical Engineering Journal 49 (2010) 289307

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Biochemical Engineering Journal

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Review

Oxygen

Felix Gara Department ob Department o

a r t i c

Article history:Received 28 SReceived in reAccepted 27 Ja

Keywords:Oxygen uptakOxygen transfBioprocesses dBioreactor desScale-up

Contents

1. Introd2. Pheno3. Oxyge

3.1.

4. Kinet5. Inue

5.1.5.2.5.3.

6. Scale-7. Concl

AcknRefer

CorresponE-mail add

1369-703X/$doi:10.1016/j.uptake rate in microbial processes: An overview

cia-Ochoaa,, Emilio Gomeza, Victoria E. Santosa, Jose C. Merchukb

f Chemical Engineering, Faculty of Chemistry, Complutense University, 28040 Madrid, Spainf Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 84105, Beer-Sheva, Israel

l e i n f o

eptember 2009vised form 19 January 2010nuary 2010

e rateer rateescriptionign

a b s t r a c t

In aerobic process oxygen must be continuously supplied in order to achieve acceptable productivities,Since the role of oxygen in microorganism growth and its metabolism is of vital importance, both theoxygen consumptionby the cell and the oxygen transfer rate (OTR) into the systemhave to beunderstood.

The main function of a properly designed bioreactor is to provide a controlled environment and aconcentrationofnutrients (dissolvedoxygen,mainly) sufcient to achieveoptimal growthand/oroptimalproduct formation in a particular bioprocess. Dissolved oxygen in the broths is the result of a balance of itsconsumption rate in the cells, and the rate of oxygen transfer from the gas to the liquid phase.Monitoringdissolved oxygen in the broth is mandatory because often oxygen becomes the factor governing themetabolic pathways in microbial cells.

In this work the oxygen uptake rate (OUR) in different fermentation broths is examined. Experimen-tal techniques have been compiled from the literature and their applicability to microbial processesreviewed. The reciprocal inuence of OUR and OTR is presented and an analysis of rate-limiting variablesis carried out.

Mathematical models are a fundamental tool in bioprocess design, optimisation, scale-up, operationand control at large-scale fermentation. Kinetic models describing aerobic bioprocesses have to includean oxygen balance taking into account OTR and OUR. Many different specic rate expressions forcell growth, substrate consumption, product formation and oxygen uptake have been developed andincorporated in the models, and simulations of different bioprocess have been carried out. Some of themare presented here.

2010 Elsevier B.V. All rights reserved.

uction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290menology of aerobic bioprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292n uptake rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Experimental determination of OUR values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2943.1.1. Gas balancing method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2943.1.2. Dynamic method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2943.1.3. Yield coefcient method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2953.1.4. OUR determination from oxygen concentration prole data knowing OTR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2953.1.5. Comparison of OUR values determined by the dynamic method and from the oxygen prole data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

ic modelling of our in bioprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296nce of OTR on OUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298Oxygen transfer characteristics on microbial processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298Inuence of oxygen transport conditions on OUR and qO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Rate-limiting step analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

up and modelling of dissolved oxygen concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302usions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305owledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305ences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

ding author.resses: fgochoa@quim.ucm.es, felixg.ochoa@micinn.es (F. Garcia-Ochoa).

see front matter 2010 Elsevier B.V. All rights reserved.bej.2010.01.011

290 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

Nomenclature

a specic interfacial area (m1)Cj concentration of compound j (kgm3 or molm3)CX cell concentration (kgm3)Da Damkhler numberDi oxygen diffusion coefcient in layer i (m2 s1)DO dissolved oxygendb bubble diameter (m)E biological enhancement factorH Henry constant (molm3 atm1)Ha Hatta numberJ ux density molar (mol O2 m2 s1)K consistency index in a power-law model (Pa sn)kL mass transfer coefcient (ms1)KLa volumetric oxygenmass transfer coefcient in pres-

ence bio-transformation (s1)kLa volumetric oxygen mass transfer coefcient in cell

free medium (s1)mO2 dissolved oxygen consumption coefcient formain-

tenance (mol O2 kg1 X s1)N stirrer speed (s1 or rpm)n Flow index in a power-law modelOTR oxygen transfer rate (mol O2 m3 s1)OUR oxygen uptake rate (mol O2 m3 s1)Q gas ow rate (m3 s1)qO2 specic oxygen uptake rate (mol O2 kg

1 s1)t time (s or h)te exposure time (s)V volume of the liquid in the vessel (m3)VS supercial gas velocity (ms1)XBDS percentage of desulphurization

(% 2-hydroxybifenyl)YG macroscopic yield on the substrate (kgXkg1 S)Yij macroscopic yield of compound i into compound j

(kgi kg1j)YXO biomass yield on oxygen (kgXmol1 O2)Y XO overall biomass yield on oxygen (kgXmol

1 O2)z lm thickness or distance from the gasliquid inter-

face (m)

Greek letters parameter for growth associated product formation parameter for non-growth associated product for-

mation energy dissipation rate (Wkg1) effectiveness factor gas hold-up specic culture growth rate (h1); viscosity (Pa s) generalised degree of reduction density (kgm3) interfacial tension (Nm1)

SubindexesBDS referred to biodesulphurizationd relative to dynamic measurementG relative to gas phaseL relative to liquid phasem relative to cell monolayermax relative to maximum valueO2 relative to oxygenp relative to process measurementS relative to substrates relative to surfactant

X relative to biomass

Superindcinout*o

1. Introdu

In aerobfor growth,product synally aqueoua gas phaseis needed fodissolved oganisms, deon the rateuptake rate

Both oxyits consumpin many prmicrobial gfact has beebiochemicacontinued t

Oxygenactors, butpneumaticabe found inbeen improof uid propby Akita anreactors, thbetween poistics [14,1bioreactorsbeen publis

The OTRfer coefcimass transfSince the tindividuallyeter, calledinformationrelations hseveral revibased on furenewalmobased on u

The oxycharacterising the fermuptake rateexperimentattention inof xanthan[36], xylitolalso in bioding is also i[4143].exesrelative to the intermediaterelative to inletrelative to outletrelative to equilibrium value in each phasecell free medium

ction

ic bioprocesses, oxygen is a key substrate employedmaintenance and in other metabolic routes, includingthesis. Due to its lowsolubility in broths,which areusu-s solutions, oxygen must be continuously provided by, and thus the knowledge of oxygen transfer rate (OTR)r bioreactor design and scale-up. The concentration ofxygen in the broth, a suspension of respiring microor-pends on the OTR from the gas to the liquid phase, andof its consumption by the microorganism, the oxygen(OUR).gen mass transfer from the gas to the liquid phase andtionbymicroorganismhas a decisive importance, sinceocesses oxygen transfer is the controlling step for therowth, and can affect the evolution of bioprocesses. Thisn identied and reviewed early in the development ofl engineering [13] and work in this matter has beenill these days [411].transfer rate is not a privative characteristic of biore-rather belongs to classical chemical engineering. Forlly agitated reactors one of the rst correlations canthe book of Sherwood and Pigford [12] and those haveved over the years to include more detailed inuenceerties and equipment geometry on kLa; the correlationd Yoshida [13] remains as a reference. For stirred tanke early work was directed towards expressions the tieswer input, liquid properties and geometric character-

5]. Extensive literature on the oxygen transfer rate inis nowadays available and a considerable part of it hashed in the last years [6,8,1626].in a bioreactor depends on the liquid side mass trans-

ent, kL, the total specic surface area available forer, a, and the driving force in terms of concentrations.wo parameters, kL and a, can not be measured easily, they are usually lumped together as one single param-volumetric mass transfer coefcient, kLa. The availableon kLa in bioreactors is extensive. Many empirical cor-

ave been proposed for kLa estimation; and there areews on this subject [17,21,27,28]. There are alsomodelsndamental approaches, using concepts based on surfacedels,where theparametersneeded for thosemodels areid-dynamic considerations in the bioreactor [2831].

gen uptake rate is one of the fundamental physiologicaltics of culture growth and has been used for optimis-entation process [32,33]. Usually the specic oxygen

, qO2 , is calculated from OUR which is determinedally. OUR measurement has recently received the duedifferent bioprocess studies, such as in production

gum [34], toluene hydroxylation [35], bio-insecticidesproduction [37], benzaldehyde lyaseproduction [7] andesulphurization processes [3840]. The OUR monitor-mportant for assessment of the viability of the culture

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 291

Pirt [44] found that the actual substrate consumption rate canbe expressed as the sum of two terms: one representing the the-oretical rate of substrate consumption for biomass synthesis andone showing the rate of substrate consumption for maintenance ofthe culture [45,46]. This implies the denition of two parameters:the theoretical yield, and the maintenance rate. Some of the workspreviously quoted model the OUR using these pioneer concepts[5,7,36,39,40,4751], but only a few works present a model of theevolution of DO concentration along the bioprocess [3840,50,52].

OUR is consecutive toOTR, and the slower step is that controllingthe overall rate. However, the consumption of oxygen can affectOTR. In biological systems, where gas (oxygen) absorption is fol-lowed by a biochemical reaction, two steps can control the overallrate: the mass transfer of gas to liquid phase and the biochemicalreaction in the cells. Sometimes, the transport of substrates into

the microorganism occurs at a rate which is considerably fasterthan the rate of the biochemical reactions inside. However, if thebiochemical reaction phenomenon is faster than the mass transfer,the concentration prole of the absorbed gas may be affected bythe biochemical reaction, and the absorption rate into the pseudo-homogeneous liquid be enhanced because oxygen is consumedwhile it diffuses into the liquid. The extent of this enhancementcan be derived from different theories for mass transfer; the lmmodel is the most used because its simplicity [31,5355].

This interaction of OTR and OUR should be included in themodelling of aerobic microbial processes, which implies a math-ematical description based on physicalchemical principles. Themodel allows making predictions and gaining insights into theunderlying phenomenon. The oxygen available in the broth is fun-damental in the microbial process if the biocatalyst used is a strict

Fig. 1 rk [57. (a) Steps of oxygen transfer from gas bubble to cell (adapted from Blanch and Cla ]). (b) Oxygen concentration prole from gas bubble to cell.

292 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

aerobicmicroorganism. Therefore, the kineticmodel that describesthe growth of the microorganism, the nutrients consumption andthe product formation has to consider the inuence of the DO con-centration on the bioprocess [5,39,40,56].

The aimof thiswork is to examine the oxygen uptake rate (OUR)in several systems taking into account different experimental tech-niques and to model those systems involving oxygen consumptionfor maintenance, cell growth and product formation, presentingan adequate description of the actual oxygen concentration pro-les. The information collected in the present work will be usefulfor a better understanding of the importance of DO concentrationin aerobic microbial processes and of the inuence of biochemicalreactions on oxygen transfer phenomena (and vice versa), as wellas for nding better operation conditions for oxygen transfer andfor scale-up in bioreactors.

2. Phenomenology of aerobic bioprocesses

Bioreactors are heterogeneous, gasliquidsolid systems andoxygen is one of the most important substrates in aerobic bio-processes. It is essential to study the inuence of the gasliquidtransport in bioreactors, and this is truenot only in aerobic systems,where oxygen transport is obviously focussed, but also in the caseof anaerobic systems, where usually the transport of other gasessuch as methane or carbon dioxide takes place. Transfer of oxygenfromagas bubble to a cell can be represented by the following steps(as schematised in Fig. 1a and b) [57]:

(i) transfer from the interior of the bubble to the gasliquid inter-face;

(ii) movement across the gasliquid interface;(iii) diffusion through the relatively stagnant liquid lm surround-

ing the bubble;

(iv) transport through the bulk liquid;(v) diffusion through the relatively stagnant liquid lm surround-

ing the cells;(vi) movement across the liquidcell interface; if the cells are in a

ock, clump or solid particle, diffusion through the solid to theindividual cell;

(vii) transport through the cytoplasm till the site where the reac-tions take place;

(viii) biochemical reactions involving oxygen consumption and pro-duction of CO2 or other gases;

(ix) transfer of the produced gases in the reverse direction.

Steps (i)(vii) and (ix) correspond to physical phenomena, inprinciple better known and easier to describe than the biochemicalphenomena.

Vigorous agitation is required to insure homogeneous distri-bution of the nutrients. In shake asks scale, oxygen transport byaeration and agitation are accomplished by the rotary or recipro-cating action of the shaker apparatus. In laboratory and pilot scale,oxygen is generally supplied as compressed air and distributed by agas distributor, andmechanical devices are used to improvemixingof the broth, for better distribution of gas bubbles and to rupturelarge bubbles into small ones obtaining a larger interfacial area.The oxygen is transferred from a suspended gas bubble into a liq-uid phase, where it is taken up by the microorganism and nallytransported to the site of reaction inside the cell. The power input,which generates the mixing, is however restricted by physical, bio-logical and mechanical constrains, which become more severe asthe scale increases. The cells may be damaged by hydrodynamicstress when agitation and/or aeration are too vigorous. Typical aer-obic large-scale cultures, 10,000 L or greater, are oxygen limited. Inthis case gasliquid interfacial area and bubble residence time arethe limiting steps in the process of oxygen delivery to the microor-

iologiFig. 2. (a) Pathway of chain respiratory aerobic bacteria. (b) A schematic of the b cal reactions expected to occur in an aerobic culture.

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 293

Fig. 3. Simula ion forsaturation) (ad

ganisms. Ththe productvessel sizesthat is, thean initial ba56 days. Smust be keis accompliserves to agnoxious volrange of 0.5the gas bubagitation aninput couldtal for theforces geneon lament

In aerobtion. A simpthe generatbiomass, prdirectly relaactivities. Tprovision omembrane,(Fig. 2b).

Simulatia metabolicshown in Fsources) coare shown.phase) folloa stationaryitations. Alarge-scale

A kinetichas to consin the set oof the proc

d ofsed ac oxy

gen

en thbrotescrigh ds theedemt mimonlis IGevetion of microbial growth curve for Xanthomonas campestris culture in batch operatapted from Garcia-Ochoa et al. [5]).

e classic example of large-scale aerobic bioprocess ision of penicillin by a specic mould, where commercialfrom40 to 200m3 are used. The operation is semibatch,nutrient, lactose or glucose, is fed at controlled rates totch of liquid nutrients and cell mass. Reaction time isince oxygen is essential for growth, DO concentrationpt at a high level for the organism to survive, and thisshed by continuous aeration of culture. Aeration alsoitate the mixture and to sweep out the CO2 and anyatile by-products that are formed. Air supply is in the1.5 vvm. Mechanical agitation is needed to break upbles but must avoid rupturing the cells. Power input byd air sparging is 14WL1. An increase of the powersubstantially improve theOTR, butwould be detrimen-process as a whole because the higher uid-dynamicrated could damage the microorganisms. These effects

rate anexpresspeci

3. Oxy

Givin the[47] dthe hireachebecausof mosXanthothropo

How

ous microorganisms have been indicated early on [58].ic processes the energy is generated by substrate oxida-le scheme is presented in Fig. 2a; the energy is used forion of ATP, which is employed in production of newoduct formation and in other functions that are notted to growth, commonly referred to as maintenancehis includes re-synthesis of damaged cellular material,f the necessary concentration gradients across the cellcell motility and other non-growth related processes

ons of typical batch microbial culture carried out withkinetic model [5] and varying DO concentrations are

ig. 3. Biomass growth, substrate (carbon and nitrogennsumption and product (xanthan) formation patternsThe growth patterns show a slow initial phase (lagwed by a fast exponential phase (log phase), and thenphase where no growth occurs due to nutrient lim-

shortened lag phase is desirable for more economicalcultures.model that describes the growth of themicroorganism

ider the inuence of the dissolved oxygen in the brothf differential equations representing the kinetic modeless. This requires knowledge of the oxygen transport

DO concentincrease evspite of imow rate, sPseudomonconcentrativalue beforreaches a 5the rst casequal to zerenzymes [3duction of xrate, and toduring the

The specmicroorganmicrobial gment withand qO2 asfermentatiogrowth pharate takes ping in metatwo constant values of dissolved oxygen concentration (10 and 20%

the oxygen consumption rate by the microorganisms,s the volumetric mass transfer coefcient (kLa) and thegen consumption (qO2).

uptake rate

e low solubility of oxygen in aqueous solutions, DOh can be the limiting nutrient. Pinches and Pallentbed the fall of DO concentration in broths due toemand during fast growth, until the microorganismstationary phase and the DO concentration increases,andbecomes smaller. This evolutionts thebehaviour

croorganisms cultures available in literature, such asas campestris [34], Escherichia coli [59], Rhodococcus ery-TS8 [60].r, in some cultures, oxygen demand is so high that the

ration decreases until it approaches zero, and does noten when the culture reaches the stationary phase, inprovement in oxygen transfer rate (by increasing gastirrer speed or the oxygen concentration in gas phase).as putida for example has a very high OUR and the DOon in the broth drops to 5% of the oxygen saturatione 2h of growth [39]. X. campestris has a slower OUR and% of oxygen saturation only after 10h of growth [5]. Ine, on P. putida growth, DO concentration is practicallyo till the end of the production of biodesulphurization9]. In the second case, X. campestris cultures for the pro-anthan gum, it is necessary to increase oxygen transferachieve this stirrer speed and/or gas ow are increasedbioprocess [5].ic oxygen uptake rate (qO2) is characteristic for eachism and is usually considered constant during therowth, although experimental results are not in agree-this assumption [5]. A typical evolution of both OURwell as a typical oxygen concentration prole duringn is shown in Fig. 4. OUR increases in the exponentialse, because in this step a high substrate consumptionlace; after that OUR decreases because of the decreas-bolic activity of cells. On the other hand, a decrease of

294 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

Fig. 4. Typical(qO2 ) and DO c

the DO concbioprocessthe beginnioxygen conthe growth

OUR canabout the memployed fgrowth phacharacteriz[41,43] ortor to adjusRecently OUhydrodynam

3.1. Experim

The tranbeen descrferent methexperimentdeterminatment.

A numbecultures. Thoxygen upt

(i) Mass btion me

(ii) The dyn(iii) Techniq(iv) From th

The masmixed liqui

dC

dt= KLa (

where dC/drst term oand the secocan be expr

3.1.1. Gas bThis me

oxygen con

bioreactor. This technique is themost reliable andaccurate, but alsorequires very accurate instruments. The OTR can be determinedfrom gas oxygen mass balance on the bioreactor as follows:

Q

V( )

Q isCout

tlet,then

OTR

Q

V

it islturedrawcom

ous od ou

tionof sm

ut ma

Dynadyn

smsinle

ew, ise ofxygeus opr ratcon

an bethes

d=

ing Otimewn iss conof o

, ande gased oy-str anevolution of oxygen uptake rate (OUR), specic oxygen uptake rateoncentration (CO2 ) in time course of fermentation.

entration is often observed in the rst moments of thedue to the high specic oxygen demand by the cells atng, in the lag phase [3840]; after reaching a minimum,centration prole gradually increases until the end ofand/or the production process.

be easily measured, giving important informationetabolic activity of the cells in the culture. It has beenor on-line estimation of viable cell concentration andse of insect and mammalian cell cultures [32,61], foration of the organic composition in waste treatmentsits activity [6264]; and it can be used as an indica-t the amino acids feeding in animal cell culture [65].R has been proposed as a factor indicating the possibleic stress, cell damage and cell death [66,67].

ental determination of OUR values

sport of oxygen and its consumption have usually notibed together, and have been often measured by dif-ods in the past. Nowadays it is usual to obtain bothal values using the same technique, i.e. simultaneousion of both OUR and OTR (or KLa) in the same experi-

r of methods have been developed to calculate OUR ine main experimental techniques employed to measureake rate are:

alance by inlet and outlet gas phase oxygen concentra-asurement.

OTR =

whereCin andand ouOUR is

OUR =

OUR =

wherethe cuis with(this isa gaseinlet ancentrain caseand Co

3.1.2.The

organiairowutes (fdecreaby an opreviotransfethe DOdure cUnder(

dC

dt

)obtainversusbe knobiomachangeperiodping this turna steadtransfeamic technique.ues based on the yield coefcient method.e oxygen concentration prole data, knowing OTR.

s balance for the dissolved oxygen in the assumed well-d phase can be written as

C C) qO2 CX (1)

t is the accumulation of oxygen in the liquid phase, then the right hand side is the oxygen transfer rate (OTR)nd term is the oxygen uptake rate (OUR). This last termesed by the product qO2 CX.

alancing methodthod uses a gaseous oxygen analyzer to measure thecentration of the gas streams entering and leaving the

response cucan be solvFor the appelectrode mfor the masis not negliin the elabooxygen conoff and on i

A rapidmethod isOUR, due tHowever, thinwhich OUis turned ofchanges aremethod canC inO2 CoutO2

(2)

the oxygen gas ow, V the volume of bioreactor, andthe oxygen concentration measured at bioreactor inlet

andwell-mixing of the gas phase has been assumed. Thecalculated from:

Accumulation (3)

(C inO2 CoutO2

) CLt

(4)

assumed that OUR, and therefore the metabolic state of, remains constant along the t considered. A samplen from the vessel to determine biomass concentrationmon to all methods). Therefore, this method requiresxygen analyzer to measure the oxygen content of thetlet gas streams and a probe for measuring the DO con-in the liquid. This method may not be the best choice

all bioreactors, where the difference between and Cin

y be very small because of the short contact time.

mic methodamic method is based on the respiratory activity ofwhich are actively growing inside the bioreactor: thet to the fermentation broth is interrupted for a fewmin-n order to avoid inuences on process evolution), and aDO concentration is observed, which can be recordedn probe. Afterwards, air is reintroduced under the sameerational conditions, thus ensuring the same oxygene [68]. The OUR is determined from the depletion incentration after stopping the air ow, and the proce-repeated several times during the production process.

e conditions, the Eq. (1) can be simplied to:

qO2 CX = OURd (5)

URd from the slope of the plot of DO concentrationafter stopping air ow. Biomass concentration must

n this point in order to relate the OURd calculated tocentration. The underlying assumption is that no inter-xygen between gas and liquid occurs during the testthat the change in uid dynamics associated to stop-circulation does not affect the OUR. When the aeration

n again, the DO concentration increase until it reachesate concentration. In this conditions both the oxygend oxygen uptake rate terms apply. The slope of therve at a given point is measured to get dC/dt, and Eq. (1)ed for KLa because all the other values are known [5].lication of this method the response time of the oxygenust be considerably lower than the characteristic times transfer process. If the response time of the electrodegible, it can be taken into account in the modelling andration of the experimental data. A prole of dissolvedcentration fromEq. (1) during a cycle of turning aerations shown in Fig. 5.review of the recent literature shows that, the dynamicstill the most commonly used in the determination ofo its simplicity and reproducibility [5,7,9,10,36,43,65].is method can be difcult to apply to certain situationsR can not be determined correctlywhen the gas supplyf, because when the DO concentration is very low, thedifcult to evaluate. In this case a modied dynamicbe used [39,69]. The modication consists in using a

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 295

Fig. 5. Simuladuring fermen

step changeversa. The etwo pseudo

The intethe boundayields the fo

CL =(C0

while, if thenow with tt= t2 C=C

CL =(C1

Eqs. (6)centration iCL1 , after chair. Accordideterminedof the abovregression t

Severalposed, someet al. [70] pment, wherstep in thean agitationconcentratisimilar to th

3.1.3. YieldThis tech

method forduring bioporganism raliquid phasbiomass togfollowing re

OUR = Y X

where ispresents th

This method for oxygen uptake rate determination is very sim-ple; however, Eq. (8) is based on the assumption that substrate iscompletely converted into carbon dioxide, water and biomass, andthis can be in doubt in many cases.

iallyltivamax

his isnancnancs enl intnsumrela

1

m

mO2O theO, arfromineddictsrallthe ogrowcongrating re

t2t1

K

e spient,me ijnenon elation

ScS

1YcXO

S anbiomtion of response of DO for dynamic measurement of OUR and KLatation.

of air to pure oxygen in the inlet gas stream or vicevolution of DO concentration in the transition between-steady states allows the OUR and KLa calculations.gration of Eq. (1) in oxygen absorption process withry conditions: t=0 C = C0 and C = CL0 ; t= t1 C=CL,llowing equation:

OURKLa

)(C0 CL0

OURKLa

) eKLat (6)

desorption mode is applied, the integration of Eq. (1),he boundary conditions: t= t1 C = C1 and C = CL1 ;L, results in:

OURKLa

)+(CL1 C1 +

OURKLa

) eKLat (7)

and (7) describe the evolution in time of the DO con-n the liquid phase from a starting concentration, CL0 oranging from air to pure oxygen or from oxygen pure tong to the above procedure, OUR and KLa values can beduring thebioprocess, at several cellular ages, byttinge equations to the experimental data using non-linearechniques.modications of the dynamic method have been pro-ofwhich standout because their ingenuity. Thus, Linek

roposed a dynamic pressure method for kLa measure-e the step in oxygen concentration is replaced by a

Initever, cuthan rate. Tmaintemainteof GibboptimaATP co

The

1Y XO

=

whereand YXand YXlinear;determ(9) prethe ove

OndataofYXO isby intefollow

Y XO =

If thcoefceach ti

Heibasedthe rel

1YXO

=

1YXO

=

whereand oftotal pressure. Mignone [71] proposed to make rather-step for kLa measurement. In both cases the oxygenon is the variable followed and analysed, in a mannerat given above.

coefcient methodnique was found to be a reliable and quite satisfactoryestimating the oxygen uptake rate by microorganismsrocesses. It is based on the oxygen uptake rate of thether than the rate of depletion of oxygen in the gas ore. By using a stoichiometric balance of oxygen in theether with the kinetic model for the growth rate, thelationship during growth can be obtained:

CX

O(8)

the specic growth rate of the organism, and YXOe overall yield of cell on oxygen.

intermediaare theyieldin oxidation

The modprobable paThe yield csponding stis not tempposition dowith the mmated a vathe availablof microorg

3.1.4. OURknowing OT

When oequation orthe overall yield was introduced as a constant. How-tionsofmicroorganismundergrowthratesmuch lowershowed that it was dependent on the specic growthexplained in terms of the endogenous respiration, ore, concept [72,73]. In this concept it is assumed thate of cellular function requires the availability of a owergy for restoring leaky gradients, preservation of theracellular pH, the replacement of denatured proteins,ption in futile cycles, cellular mobility, etc.

tionship between YXO and can be established as

O2 +1

YXO(9)

is the oxygen consumption coefcient for maintenanceyield of oxygen consumed for cell growth. If both, mO2e practically constant, a plot of 1/YXO versus 1/ isthe slope, mO2 and from the intercept, YXO could be

. Note that for an assumed constant value of mO2 , Eq.that any variation in will affect observed values of

growth yield.ther hand, YXO can be estimated from experimentalth andvolumetric oxygenmass transfer. Assuming that

stant for a short time interval between time t1 to t2,ing and rearranging Eq. (1) and inserting in Eq. (8), thelationship is obtained [49]:

(CX2 CX1

)La (C C)dt + (C1 C2)

(10)

ecic growth rate, , and the volumetric mass transferKLa, are known, Eq. (10) can be numerically solved fornterval, calculating YXO values.and Roels [74] showed that a macroscopic analysisemental and enthalpy balances successfully describesship between biomass yield on oxygen, according to:

1YcXO

+ S cS

4 XcS

mO2 =ScS

mcO2 S > cS (11)

mO2 = mcO2 S cS (12)

d X are generalised degrees of reduction of substrateass, respectively, cS is the degree of reduction of an

te which is coupled to ATP generation, and YcXO and mcO2

of biomass andmaintenanceonoxygenwhichareuseds reactions coupled to energy generation.el agrees with data available in literature and the mostrameters values cS and Y

cXO are 4.0 and 2, respectively.

oefcients of biomass on oxygen (YXO) (and its corre-orageproducts,YPO),which is a stoichiometric constant,erature dependent, assuming that the molecular com-es not change with temperature. This is in contrastaintenance coefcient; Heijnen and Roels [74] esti-lue for the activation energy of 9000kcalmol1 frome data on maintenance requirements of a great varietyanisms.

determination from oxygen concentration prole dataRxygen transfer rate is known, either from an empiricalusing a predictivemodel and the oxygen concentration

296 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

prole in the liquid phase measured during the course of fermen-tation, oxygen uptake rate during the process can be obtained fromEq. (1), as

OURp = KLa( )

ThereforOTR (deterues and thederivative o

3.1.5. Compmethod and

Oxygenmethod; homay interftion of themethod anresults havthe classicaby tting aoxygen constrated in athe dynamgen consumobserved. Fthe oxygenthe dynamiand Rhodocexperimentle are highdiscrepancyple: duringcells consum

4. Kinetic

The conconsumptioture of Aeroconsideredany substraported by e

Accordinconcentratitenance agrowth [5

OUR = qO2

where CX isumption cconsumed f

Assuminaccording t

dCXdt

= C

in an aerobitenance and

OUR =[mO

ifferences between oxygen uptake rate experimental values obtained fromtechnique (OURd) and from oxygen prole data (OURp) for different stirrer) in Xanthomonas campestris culture (b) in Rhodococcus erythropolis IGTS8adapted from Santos et al. [40]).

OX =1/YXO; and therefore:

mO2 + YOX )

YOXCXmax

CX (17)

m the slope and the intercept of the plot of qO2 versus CXxygen consumption for maintenance and yield of oxygened for cell growth can be obtained. Both relations havesed for determination of the characteristic parameters ofption [3840].

eriments show that OUR values present an increase duringstage and especially during the exponential growth stage;

ards the values of OUR decrease slowly till reaching a practi-nstant value during the stationary stage. On the other hand,

ecic oxygen uptake, qO2 , increases dramatically in the lagst exponential stages of growth, until a maximum value isd. At the beginning of the process qO2 increases mainly duencreasing of biomass production and substrate consumptiont longer fermentation times, when the substrate consump-d biomass production rates decrease qO2 decreases as well.as been shown that themaximumOURvalue inXanthomonasstris culture was obtained in the middle of the exponentialwith values ranging from1.15 to 1.84103 molO2 m3 s1,ding on the biomass concentration during the experi- (CO2 CO2) dCO2dt

p

(13)

e, experimental OURp values can be calculated frommined from volumetric mass transfer coefcient val-

oxygen concentration prole) and the values of thef oxygen concentration versus time curve [40,43,75].

arison of OUR values determined by the dynamicfrom the oxygen prole datauptake rate is commonly measured by the dynamicwever, in some cases the use of a non-aerated periodere on microbial growth and lead to underestima-OUR value. When OUR is measured by the dynamicd modelled as above indicated, some differences ine been observed, because YOX values determined byl dynamic method are different from those obtainedmetabolic kinetic model to experimental values of

centration versus time. Santos et al. [40] have demon-biodesulphurizationmicrobiological system, thatwhenic technique is employed to measure OUR the oxy-ption decreases, which can explain the differences

ig. 6 compares experimental OUR values obtained fromconcentration prole data and those obtained using

c technique for twobioprocess,Xanthomonas campestrisoccus erythropolis IGTS8 cultures. As it can be seen,al OUR values obtained from the DO concentration pro-er than those obtained by the dynamic method. Thiscould be explained using the cellular economyprinci-the time that oxygen is not transferred,microorganisme oxygen at a lower rate [76,77].

modelling of our in bioprocesses

cept of a maintenance energy coefcient for substraten was rst proposed by Pirt [72] in the study of the cul-bacter cloacae grown in chemostat. Pirt model [44] isvalid for maintenance description; it applies to almostte involved in cellular energy metabolism and is sup-xperimental data and energetic considerations.g to that, OUR has been usually related both to biomasson in the broth oxygen necessary for biomass main-nd to biomass production rate oxygen necessary for,7,36,39,40,4751], as follows:

CX = mO2 CX +1

YXO dCX

dt(14)

s the biomass concentration, mO2 is the oxygen con-oefcient for maintenance and YXO the yield of oxygenor cell growth.g that thegrowthrateofmicrobial cells canbemodelledo a logistic equation:

X (

1 CXCXmax

)(15)

c processwhere oxygen is only consumed for cellmain-cell growth, the above equations lead to:

2 + YOX (

1 CXCXmax

)] CX (16)

Fig. 6. Ddynamicspeed (aculture (

being Y

qO2 =(

Froboth oconsumbeen uconsum

Expthe lagafterwcally cothe spand rreacheto the irates. Ation an

It hcampephasedepen

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 297

Fig. 7. Variatiof qO2 () anand the timeed bacteria aVS = 2.5103

ment; the m4.2103 mlag phase [5seems to deing lag stagstage, takinfor a biomaOUR decreaputida cultuthe middleto 3.510tion; the m5103 mostage.

Fig. 7 shcentration aspeed of 20(gas ow of(16) and (1describe sat

There arsumption pbacteria arestant valuethat prevaienced by obe obtained

altered, as it occurs in the case of using the dynamic method [5,40].In this table results obtained by macroscopic model proposed byHeijnen and Roels [74] for mO2 and YOX estimation are also shown.Although uctuations are considerable in both parameters, it is

hat ited vmo

onsidrocenancerg

ed thas thdogesumpydethe

docales: ceed,in Eq

mO2

t terion c

dC

dt

isclear tpredic

Thebeen cof biopmaintein submassumOUR wand enthis aszaldeh[9] forlus acipurpos

Indduced

OUR =

The lasformat[78]:

dCPdt

=

whereon of experimental values (symbols) and prediction model (lines),d OUR (), using Eqs. (16) and (17), with biomass concentrationcourse of fermentation of Pseudomonas putida (a genetically modi-ble to carry out the DBT biodesulphurization process) (N=200 rpm;ms1) (adapted from Gomez et al. [39]).

aximum value of specic OUR, qO2 max, was aroundolO2 kg1 s1, which would be taken as the end of the]. In the case of Rhodococcus erythropolis cultures, OURpend on culture growth phase: rstly increasing dur-e and especially during the rst exponential growthg amaximumvalue (from 5 to 7104 molO2 m3 s1)ss concentration of 1 kgm3; afterwards the values ofse slowly at the stationary stage [40]. In Pseudomonasre [39] the maximum OUR value was also obtained inof the exponential phase, with values ranging from 3.03 molO2 m3 s1, depending on the biomass concentra-aximum value of the specic OUR, qO2 max, was aroundlO2 kg1 s1, and was observed at the end of the lag

ow the evolution of OUR and qO2 with the biomass con-nd time course of P. putida fermentation, for a stirrer0 rpm and supercial gas velocity of 2.5103 ms12 Lmin1) [39]. In this gure values predicted by Eqs.

7) are also presented. It can be seen that the equationsisfactorily experimental data of OUR and qO2 .e not many experimental values of these oxygen con-arameters in the literature; some values for yeasts andshown in Table 1. The parameter mO2 presents a con-independently of the conditions of oxygen transportl in the broth, whereas parameter YXO can be inu-xygen transport. For this reason different values canfor this last parameter if the transport conditions are

is the termodel wastation, but iformed as aYamani andbe applied tapproach topenicillin fe

As indicbetween OUand from oimental val(14) providrelated to mthe experimingbatchgrhigher oxygthe authorsYOBDS), acco

OURp = mOwhereYOBDdevelopmethat can be

dXBDSdt

=

Considebe modellerst term ienzymes m(20) can be

OURp = mOn general available data in literature agree well withalues.delling of OUR using several metabolic functions hasered in different ways depending on the characteristicss. Koutinas et al. [52] considered the OUR for growth,e and glucoamylase production (YOG) by fungal cellsed cultures of Aspergillus awamori. Giordano et al. [42]at in aerobic biodegradationof contaminated sedimentse sum of two terms, related, respectively, to exogenousnous respiring, modelling the OUR prole according totion. Calik et al. [59] studying the effects of pH on ben-

lyase production by Escherichia coli and Kocabas et al.l-tryptophan production by thermoacidophilic Bacil-darius, established that oxygen is consumed for threeell growth, by-product formation and maintenance.in cases of product synthesis a new term must be intro-. (14), yielding the following expression:

CX +1

YXO

dCXdt

+ 1YPO

dCPdt

(18)

m corresponding to oxygen consumption for productan be expressed according to the following equation

X + CX (19)

the term for growth associated product formation andm for non-growth associated product formation. Thisderived on the basis of an analysis of lactic acid fermen-t is inprinciple validonly formetabolic products that aredirect consequence of the growth process, as shown byShiotani [79]. However, the model may in some caseso other products. Heijnen et al. [80] described a formalmodelling of secondary metabolite formation in the

rmentation, which is not growth related.ated above, Santos et al. [40] observed differencesR values determined by the classic dynamic techniquexygen concentration prole. The tting of the exper-ues obtained from the rst technique using Equationes the values of the oxygen consumption parametersaintenance (mO2) and growth (YOX). However, whenental the oxygen concentration prole obtained dur-

owth is employed todetermineOUR(processmethod),en consumption rateswere observed and consequentlydescribed OUR using three parameters (YOX, mO2 andrding to:

2 CX + YOXdCXdt

+ YOBDSdXBDS

dt(20)

S is theyieldof oxygen tobiodesulphurizationcapabilitynt and XBDS desulphurization capability of whole cellexpressed by a simplied LuedekingPiret equation:

dCXdt

(21)

ring that the growth rate of the microbial culture cand according to a logistic equation and that only thenvolving growth due to synthesis of desulphurizationust be considered to inuence oxygen uptake rate, Eq.rearranged into:

2 CX + (YOX + YOBDS) CX (

1 CXCXm

)(22)

298 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

Table 1Parameter consumption values for some microorganism.

Microorganism qO2 (mol O2 kgX1 h1) mO2 (mol O2 kgX

1 h1) YOX (mol O2 kgX1) Substrate (carbon source) Reference

Xanthomomas campestrisNRRL 1775

215 1.0 0.6 Sucrose Garcia-Ochoa et al. [5]

Escherichia cBacillus acid

NRRC-207Phafa rhodo

1100Bacillus thur

subspeciesHD-1

RhodococcusIGTS8a

PseudomonaCECT 5279

Trigonopsis v4095

Escherichia cCandida bom

Y-17069Hansenula a

CBS6759Biomass mo

formulaCH1.79O0.5

a Changingb Overall bioc Changing

This equoxygen convalues mO2method [40

In summthe dynamiOUR. OTR c[21]. On theuid-dynampossible in

5. Inuenc

Indepenbatch, or cacceptableagitation oftransfer towhich are rformation i

The studhas been seing the voluoxygen conever, adequaccount the

5.1. Oxygen

Taking intration is lifocussedonof hydrodyuid, operation KLa havOchoa anddetermine

pingcolu

ctorsefcion centlyuidFor tationuid tn-Ness troli K 12a 0.923 2.46.4 12.5520b

ocaldariusF

3.131.2 2.216.6 0.343.8

zyma ENMS 1.9

ingiensiskurstaki

215.5 0.9 17.2

erythropolis 0.24.3 0.8 16.420

s putida 218 1.9 52.6

ariabilis CBS 23 0.03 1316

oli K 12c 0.917.2 0.47.2 0.0113.6*

bicola NRRL 0.31 0.01 4.4

nmala 0.8

lecular

N0.20

1.0 20.3

oxygen transport conditions.mass yield on oxygen (mol O2 kgX1).

pH of the fermentation medium.

ation has been employed to obtain the parameters ofsumption in this bioprocess, and it was found that theand YOX were similar to those obtained by the dynamic].ary, a complete description of a bioprocess includesc behavior of the oxygen, and therefore both OTR andan nowadays be predicted, as shown in recent worksother hand, OUR values can also be affected by OTR, oric conditions: the following section is devoted to thisuence.

e of OTR on OUR

develobubblebioreaport cooperat

Recgasliqposed.penetrgasliqand nothe madently the mode of the aerobic process (batch, semi-ontinuous), oxygen must be continuously supplied ifproductivities are the objective. Sufcient aeration andthe culture are important in promoting effective massthe liquid medium and good mixing in the bioreactorequired for achieving optimal growth and/or productn the particular bioprocess focused.y of oxygen mass transfer characteristics, traditionally,parated into the parameters related to transport (study-metric mass transfer coefcient, kLa, mainly) and thesumption by microorganism (determining OUR). How-ate description of bioprocess must be made taking intorelationship between both of them.

transfer characteristics on microbial processes

to account that the maximum value of oxygen concen-mited due to the low solubility, most efforts has beenthevolumetricmass transfer coefcient. The inuencesnamic parameters (physical properties of gas and liq-on conditions, geometric parameters of the bioreactor)e been widely investigated (see for references Garcia-Gomez [21]). There are many empirical equations tokLa, and recently great efforts have been made toward

kL = 2

The evalmogoroffsparametersvelocity. Botion per matime is usuaa length eqbetween throff.

If the rhdescriptioning equatio

te =(

K

)

kL =2

For New

kL =2

Glucose Calik et al. [7]Fructose Kocabas et al. [9]

Glucose Liu et al. [10]

Glucose Rowe et al. [36]

Glucose, glutamic acid and citrate Gomez et al. [38]

Glucose, glutamic acid and citrate Gomez et al. [39]

Glucose Montes et al. [49]

Glucose Calik et al. [59]Glucose Casas [104]

Glucose Djelal et al. [105]

Glucose Heijnen and Roels [74].Estimated from Eqs.(11) and (12)

mathematical models able to predict this parameter inmnsof different types [28,29,8183], and in stirred tank[28,30,31,84]. These methods aim at predicting trans-ient for bioreactors of different sizes andunder differentonditions., prediction techniques based on theoretical models ofcontact and on turbulence description, have been pro-he prediction of kL, theoreticalmodels based onHigbiestheory, which is widely accepted for description of

ransfer, were applied by several authors for Newtonianwtonian uids [29,30,82,85]. According to this model,ansfer coefcient can be calculated asDL te (23)

uation of contact time, te, can be done according to Kol-theory of isotropic turbulence, from two characteristicof eddies, namely the eddy length and the uctuationth parameters depend on the rate of energy dissipa-ss unit, , and on the cinematic viscosity. The exposurelly calculated as the time spent by the bubble to travelual to its diameter, and it is estimated using the ratioe eddy length and the uctuation velocity of Kolmogo-

eological model of Ostwaldde Waele is adopted forof non-Newtonian ow behaviour of uids, the follow-n for te and kL are obtained [31,81]:

1/(1+n)(24)

DL

( k

)1/2(1+n)(25)

tonian media (n=1; k=L), Eq. (25) is reduced to:

DL

( L

)1/4(26)

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 299

Thespecic interfacial area,a, is a functionof thehydrodynamicsandof the vessel geometry. Assuming spherical bubbles the specicinterfacial area can be calculated from the average bubble size, db,and the gas hold-up, , by the following equation:

a = 6db

Both hydrostirred tank

1 = 0.8

db = 0.7 (Oxygen

absorptionmicroorganfore an enhIndeed, Tsaa surface-aphysical abgasliquid isuch as pheworking indence that ttransfer rateematical minuence oactor operatransport effound an enganism. Siman investigasis of the eby KocabasB. acidocaldsuch as bloreportedby

To takeenhancemetor, E, is deto the oxygits absenceforce, accor

E = JJ0

Some wcal enhancebroths, andbution have[31] have plogical enhasubstancestrolytes, suwater, it caobservedwport resistalayers in sersidered to dinterfacial sganism adslm and (iii

The different layer resistances are taken into account by thediffusion coefcient (Di) in each layer and its thickness (zi). If a lin-ear relationship for the cell concentration in stagnant liquid layeris assumed [53] as a rst approximation, the following equation

ined-Och

CXL

CXLss cone ga

ordinat thayer,ygen

Dm

O2Cx

DL

i/Di

]

absosamer is t

Dm

ombined

+ q2D

zL/D

izi

st brtioncal ergan[

H

Hamcelld as

qO2Di seco

nce tusly.

=[

endiemect haof Ergan(27)

dynamic parameters, db and , can be estimated forbioreactors using the followings equations [30]:

19 V2/3s N

2/5T4/15

g1/3

(L

)1/5(

LL G

)(

LG

)1/15(28)

0.6

P/V)0.4 0.2L

(LG

)0.1(29)

absorption into a culture broth can be considered as theof a gas into a liquid where it reacts, the suspendedisms being the consumer of the oxygen, and there-ancement of oxygen mass transfer rate can take place.o [86] founded that the absorption rate of oxygen inerated stirred vessel was higher than expected fromsorption. The accumulation of microorganism near thenterface was proposed by Tsao [86] as explanation ofnomenon. On the other hand, Yagi and Yoshida [87]a sparged stirred fermenter reported experimental evi-he activity ofmicroorganismdoes not affect the oxygen. Both of these observationswere reconciled by amath-

odel proposed by Merchuk [53] taking into account thef the different hydrodynamics conditions in the biore-tion.More recently, Calik et al. [88] studying the oxygenfects in growth of P. dacunhae for l-alanine productionhancement on transport due to presence of microor-ilar results have been reported by Calik et al. [7,59], intion of the effects of oxygen transport on the synthe-

nzyme benzaldehyde lyase in recombinant E. coli, andet al. [9] in culture of the thermoacidophilic bacteriaarius in l-tryptophan. On the other hand, other effects,cking effects of cells on gasliquid interface have beenGalactionet al. [17] forbacteria, yeasts and fungibroths.into account the possibility of mass transfer rate

nt in a biological system, a biological enhancement fac-ned as the ratio of the absorption ux of oxygen dueen consumption by the cells to the absorption ux inunder the same hydrodynamic conditions and drivingding to:

(30)

orks in the literature have discussed the biologi-ment factor for oxygen absorption into fermentationseveral models with different cell concentration distri-been proposed [53,54,86]. Garcia-Ochoa and Gomez

roposed a model for estimation of the potential bio-ncement factor in bioreactors taking into account theusually added to the broths, such as surfactants, elec-gars, etc. Because oxygen has a very low solubility inn often be assumed that no mass transfer limitation isithin thegasphaseandonly the liquidphasemass trans-nce needs be considered. This model considers threeies. Therefore, three mass transfer resistances are con-escribe the oxygen transport: (i) the resistance at anurfactant lm, (ii) the resistance of layers of microor-orbed at the interface, next to the surfactant monolayer) the liquid lm resistance.

is obtaGarcia

CX(z) =

wherebiomafrom th

Accuatedmonolthe ox

JO2 = [Dmq

[1

iz

Theat thetransfe

J0O2 =

By cis obta

E =[1

[The ra funcbiologimicroo

f (Ha) =

wherein thedene

Hai =

Theresistaprevio

g(

z

D

)Dep

enhancThis favaluemicroofor the biomass concentration prole (for details seeoa and Gomez [31]):

CXm CXLzL

(z zT) zs + zm z zs + zm + zL (31)

is the biomass concentration in the bulk, CXm is thecentration adsorbed in themonolayer, z is the distancesliquid interface and zT is the total thickness lm.g to this approach, the oxygen transfer ux can be eval-e boundary between the surfactant lm and the cellconsidering the uptake rate as zero order respect toconcentration [54,55], obtaining:

dC

dz

z=zs

=

mzmzL +z2lqO2

(2CXm + CXL

)6

+ z2mqO2CXm+2(C CL)

2

]

(32)

rption ux in absence of biochemical reaction (qO2 = 0)hydrodynamic conditions and driving force for mass

hen given by

dC

dz

z=zs

= (C CL)zL/DL

(33)

ining Eqs. (30), (32) and (33), the following expression:

O2Cxmz2m

m (C CL)(

1+2 zlDmzmDL

+ 2z2L

3z2m

)+1

3 qO2CXLz

2L

2DL (CCL)

]

L

/Di

](34)

acket in Eq. (34) is always 1 and can be written asof the Hatta number, which takes into account thenhancement factor due to the oxygen uptake by theisms in the different layers, according to:

am (

1 + 2 zL Dmzm Dl

+ 2z2L

3z2m

)+ 1

3HaL

](35)

and HaL represent the dimensionless Hatta numbermonolayer and in the liquid layer, respectively, being

2CX,iz2i

(C CL)(i = L,m) (36)

nd bracket of Eq. (34) is always 1, representing theo diffusion exerted by each of the three lms denedSince the resistances are in series:

zL/DLzs/Ds + zm/Dm + zL/DL

](37)

ng on the relative values of both terms in Eq. (34) thent factor E, can take values below, equal or above unity.s been previously described in the literature; the naldepends on the presence of surfactants, the kind ofisms and the biomass concentration [17,54,87].

300 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

The oxygen mass transfer rate can be expressed as

OTR = a J = a E J0 = kGa (pG pi) = E kLa (Ci CL) (38)where J is the absorption ux of oxygen in presence of microorgan-ism, a is thepG is the oxgen dissolvthe magnitu

Considecoefcientcoefcients

OTR = KGabeing

1KLa

= 1H k

where H isIt canbe

cient in thparametergen due to soxygen conenhancemetance can ucan be writ

KLa = E kLThus, the

volumetricreactions (cquently assnot take plakLa and the

5.2. Inuen

In biopronly with tport conditbioreactors[7,9,38].

Typicalenhancemeare showncan be calcthe inuencthe rheologcell monolathe microorness of surfdiffusion coWilkeChanism adsorbemonolayer,

Fig. 8a srate, qO2 , anE, during thbacteriaXanSpecic oxyganism groand the bedecreases dfactor, E, instage of grospite of the

ypical time course proles of specic oxygen uptake rate () and enhance-tor predicted () by Eq. (34) in different cultures. (a) Production of xanthanXanthomonas campestris. (b) Growth culture of Candida bombicola. (c) Pro-of surfactant by Candida bombicola (adapted from Garcia-Ochoa and Gomez

due to the inuence of the viscosity of broth, which dramati-creasing and produces an increase of the resistance to massort (a decrease on the volumetric mass transfer coefcient).is the ratio of the actual OTR to the hypothetical OTR that

be observed in a system of the same physical characteristics,thout biochemical activity, E continues to increase in spitedecrease in qO2 . This decrease is partially compensated ine by increasing of the agitation speed from 250 to 500 rpm.8b shows experimental values of the specic oxygen uptakeO2 , and the variation of the biological enhancement factor,

biomass evolution in the course of a typical fermenta-f the yeast Candida bombicola, in a medium where onlyis relevant. It can be observed that the specic OUR, qO2 ,

lag phase and rst exponential phase, achieves values ofinterfacial area, kG and kL are mass transfer coefcient,ygen partial pressure in the gas phase, and CL the oxy-ed concentration in the liquid phase; index i refers tode values at the gasliquid interface.

ring Henrys law, an overall volumetric mass transfercan be used, being it related to the individual phasesaccording to:

(pG p) = KLa (C CL) (39)

Ga+ 1

E kLa(40)

the Henry constant.observed that theoverall volumetricmass transfer coef-e presence of a biochemical reaction, KLa, is a lumpedcomprising the resistances to mass transport of oxy-everal lms around the gasliquid interface, and to thesumption, whose effect can be expressed by a biologicalnt factor, E. Taking into account that the gas phase resis-sually be neglected, the overall resistance to transportten as

a (41)

biological enhancement factor is the ratio between themass transfer coefcient in the presence of biochemicalonsumption) and that under inert conditions, being fre-umed to be equal to 1. When biochemical reactions doce, E=1 and the overall mass transfer will be denotedux Jo.

ce of oxygen transport conditions on OUR and qO2

ocesses, OTR as well as the OUR values change nothe presence of biomass but also with oxygen trans-ions (determined by hydrodynamics conditions in the). Thus, OUR also can depend on oxygen mass transfer

time proles of specic oxygen uptake rate and thent factor predicted values obtained in different culturesin Fig. 8. For E calculation, the liquid lm thickness, zl,ulated from the contact time Eq. (24) consideringe of viscosity on the mass transfer coefcient throughical parameters k and n The lm thickness of adsorbedyer, zm, has been considered to be the average size ofganism used (bacteria or yeast); and for the lm thick-actant, a value of 1107 m has been assumed; oxygenefcient in bulk liquid, DL, has been estimated fromge correlation [89], while in the layer of microorgan-d is calculated as Dm =0.3DL [90], and in the surfactantDs is assumed to be 4.2109 m2 s1 [31].hows experimental values of specic oxygen uptaked the variation of the biological enhancement factor,e biomass evolution in time for a typical growth of thethomonas campestris in theproduction of xanthan gum.gen uptake rate seems to be inuenced by the microor-wth phase: there is an increase during the lag phaseginning of the exponential phase, and afterwards qO2uring the stationary growth phase. The enhancementcreases because of the increased OUR during the rstwth, as expected. The increase of E after this stage, inlower biochemical demand as shown by the descent of

Fig. 8. Tment facgum byduction[31]).

qO2 , iscally intranspSince Ewouldbut wiof thepractic

Fig.rate, qE, withtion ogrowthin the

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 301

Fig. 9. Variatio 6) as lines) with biomass concentration (a) and growth time (b) for differentstirrer speed o urization process) (adapted from Santos et al. [40]).

3.5103 mhowever inconcentratition of sophshow the sThe biologidecreases dwhich is a ninterface); i0 to 107 mincrease inof higher th

In Fig. 9tures, undeof 150, 250inuencedgrowth phathe rst expfor a biomaOUR decreametabolic aare observeoxygen trangrowth inh

In Fig. 10and biomasshown. Expa linear reincreases. Smaintenancvalue (that

RegardinoxygenconYXO, dependthe broth. Tism is growdamage pro

5.3. Rate-lim

A methotransfer ratbeen appliechemical remethodologimmobilise

wo dimensionless parameters, the observed effectivenessand the modied Damkhler number, which contain mea-parameters only, have been used to determinewhether thereactionwas limited by oxygendiffusion or by the biochem-ction [7,38,59,91,92].effetiondas alimitce an.s, inupt

micass tr

URRma

s parrgany is nfusion of oxygen uptake rate (experimental values as symbols, and predictions by Eq. (1n Rhodococcus erythropolis cultures (a bacteria able to carry out the DBT biodesulph

ol kg1 s1 and then decreases with time. The E valuecreases continuously due to the increasing of biomasson andOUR, reaching values of 1.14. During the produc-orolipids by the same yeast shown in Fig. 8c, qO2 valuesame tendency, but at one order of magnitude above.cal enhancement factor E predicted by the model rstue to the accumulation of the sophorolipid produced,ew resistance to mass transfer (a new layer around thet is considered that the surfactant layer increases from, but the increase of biomass concentration produces anthe OUR, and the enhancement factor fall into the rangean unity.variations of OUR on Rhodococcus erythropolis cul-

r different transport conditions (changing stirrer speedand 400 rpm) are shown. In all runs, OUR seems to beby the stirrer speed employed and the microorganismse (increasing during lag stage and especially duringonential growth stage, then taking a maximum valuess concentration of 1 kgm3. After that, the values ofse slowly at the stationary stage because of decrease inctivity of the cells. In general, the lowest OUR valuesd under oxygen transport limitations; however, highersport conditions can produce a decrease in OUR due toibition by oxygen [7].the relationship between specic oxygen uptake rate

s concentration under different transport conditions iserimental results of qO2 , according to Eq. (17), showlationship with CX and increase when stirrer speedpecic OUR has a minimum value that corresponds to

cells. Tfactorsurableoverallical rea

Theinteracdenefusionreferenreactio

Thuoxygenbiocheout ma

= OOU

Thimicrooactivitthe dife; this value will be reached when CX has a maximumis, in stationary phase).g consumptionparameters in general, the coefcient of

sumption formaintenance,mO2 , and theyieldofoxygen,on the conditions of oxygen transport that prevail in

hey may decrease dramatically when the microorgan-n at high stirrer speed, due to metabolic changes or cellduced by hydrodynamic conditions [66].

iting step analysis

d similar to that employed for inter- and intra-phasee limitations in heterogeneous catalytic systems hasd to compare relative rates of mass transfer and bio-action and to determine the rate-limiting step. Thisy has been applied to complex bioprocess involving

d enzymes or cells, microbial agglomerates and singleFig. 10. Variadifferent stirrectiveness factor is alternative way of looking into theof diffusion and reaction. The effectiveness factor, , isratio of reaction rates of substratewith andwithout dif-ations, while in the case of the enhancement factor thedopted is the rate of absorption in absence of chemical

aerobic microbial processes, effectiveness factor forake rate can be expressed by the ratio of the observedl reaction rate and the biochemical reaction rate with-ansfer resistance, according to:

x(42)

ameter indicates the relative utilisation of oxygen byisms in a bioprocess. If is close to 1, the respiratoryot limited by oxygen diffusion. If

302 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

Fig. 11. Evoluconcentrationpolis growth (a

In Eq. (1

OURmax =(

Conside

OURmax =

where de macteristic pconcentrati

During tOUR becauscient oxygbased on thably less th

Likewisecan be dete

OTRmax = Ebeing C* theenhanceme

Inorderand to ndDamkhlerbe also exp

Da = OURmOTRm

This ratibiochemicaregime. W

Evoluration9 grotionofDamkhlernumber (a) andeffectiveness factor (b)withbiomassfor different mass transport conditions during Rhodococcus erythro-dapted from Gomez et al. [38]).

6), the maximum oxygen uptake rate is given by

Fig. 12.concentCECT527mO2 +maxYXO

) CX (43)

ring the overall oxygen yield, YXO:

max

Y XOCX (44)

aximum demand of oxygen depends on the char-arameters of the microbial process and on biomasson.he growthphase theOURmax is often greater than actuale of the inability of the aeration system to provide suf-en transfer. However, in the stationary phase, OUR ise maintenance requirements and is therefore consider-an maximum value., the maximum mass transfer rate from gas to liquidrmined as

kLa C (45)saturation concentration in the liquid phase and E the

nt factor due to biochemical reaction.to compare thepotentialOURandOTRmaximumvaluesthe rate-limiting step of the bioprocess, the modiednumber can be used. The Damkhler number (Da) canressed as [7,38,59,91]:

ax

ax(46)

o indicateswhether the bioprocess is transport-limited,l reaction-limited, or in an intermediate operationhen Da>1, the biochemical reaction rate is large

compareddominant);is large comreaction lim

InFigs. 1tration, forof RhodococFigs. 11a anof biomasswith increaand 250 rpmincrease, mthe low mabiomass coUnder othethere is noIn Figs. 11btor, , estimreaction ratresistance,process, ina high rateare approacteria are codemand.

6. Scale-upconcentrat

Aerationeffective mtionofDamkhlernumber (a) andeffectiveness factor (b)withbiomassfor different mass transport conditions during Pseudomonas Putidawth.to transport rate (mass transfer resistances becomeon the other hand, if Da1 the rate of mass transportpared to the biochemical reaction rate (biochemicalitations are dominant).1 and12 theevolutionofDaandwithbiomass concen-different mass transport conditions during the growthcus erythropolis and Pseudomonas putida are shown. Ind 12a it can be seen that Da increases with the increaseconcentration. It can also be observed that Da decreasessing stirrer speed (Fig. 11a). In the runsperformedat150, when biomass concentration and oxygen uptake rate

ass transfer resistance is clearly the limiting step due toss transfer rate, and Da takes values higher than 1 forncentration of 0.2 kgm3 (for growth time above 3h).r operation conditions (with stirrer speed of 400 rpm),transport limitation and Da takes values lower than 1.and 12b it can be observed that the effectiveness fac-ated by the ratio between the observed biochemicale and the intrinsic reaction rate without mass transfertakes values close to 1 at the beginning of the bio-dicating that the cells are consuming oxygen at suchthat the maximum possible oxygen utilisation valueshed. The decrease in after that indicates that the bac-nsuming oxygen at a rate that is below the maximum

and modelling of dissolved oxygenion

and agitation of culture are important in promotingass transfer from gas phase to liquid medium and good

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 303

Fig. 13. Expering time courcampestris: (a)dissolved oxyg

mixing intotor must prDO concentand/or prodThe probletimes in theprinciple offorward theinput (P/V)tip speed otime (tm). Hprocess keemass transfessary to ch[21].

In laborplished by

pilot-scale and in production-scale, oxygen is generally suppliedby compressed air, and mechanical devices are used to mix thebroth and to facilitate the gasliquid contact. OTR often can be

mportant in scale-up due to effect of DO concentrationl groy toTR iequ

p pactorsn wam3).ngesandthemedy, alurseinede ofcentmost ion celthe kestant OOUR isscale-ubioreaductio(0.050

Chaof C*,cessesis assunativelthe codetermA valuDO conimental values (points) and prediction by the model (lines) dur-se bioprocess of the production of xanthan gum by Xanthomonasbiomass concentration; (b) sucrose and xanthan concentrations; (c)en concentration (adapted from Garcia-Ochoa et al. [5]).

the bioreactor. Therefore the scale-up of a bioreac-ovide a controlled environment and an appropriatedration to achieve the optimal microorganism growthuct formation in the particular bioprocess employed.m of bioreactor scale-up has been addressed manyliterature The empirical approach integrated with thesimilarity and dimensional analysis for scale-up putsgeneral principles of the equalities of specic power

, volumetric mass transfer coefcient (KLa); impellerf the agitator or shear rate of stress (ND), or mixingowever, in general, it is impossible to scale-up a bio-ping simultaneously all conditions (hydrodynamics orer) similar at different scales [93] and it is therefore nec-oose a variable to be considered as the most important

atory shake asks, aeration and agitation are accom-the rotary or reciprocating action of the shaker. In

for a less vas 1030%observed dactor, wherproduction

The conthe oxygenand on thand also ostudy of thtion with g[88] have, with DOhae for l-alKoutinas ecentrationincreasingciency in goxygen limby Calik eincreased wet al. [37] fnii UFV-170limited conprocess ofgrowth ofability of o[96] and Lof Blakesleagrowth andsupply.

For desihave a matincluding thfore, the kito includethe dissolvemost impoMathematioxygen con[48,97100substrate cobeen utilise

Monod ttion of thewth and product formation. Furthermore, it can bescale-up the bioreactor; when the criterion of con-s used in scale-up, the underlying assumption is thatal to the OTR. Zou et al. [33] have used OUR as arameter that was successfully applied in industrial(132m3 and 372m3); the nal erythromycin pro-s similar to that obtained at the pilot plant scale

in pressure with scale-up can inuence the valuesconsequently on CL. Since for most aerobic biopro-critical dissolved oxygen concentration is very low, CLto be zero. This fact severely affects growth rate. Alter-though OUR (and KLa) can change dramatically overof the fermentation, an optimal value for CL may befrom laboratory studies and used for scale-up [94].

CL above 3070% saturation usually assures adequateration in less mixed regions of a viscous mycelia broth;iscous yeast fermentation broth, a value of CL as lowsaturation can be adequate [95]. A similar result wasuring xanthan gum fermentation in stirred tank biore-e a CL over 20% saturation improves the biopolymer[5].centration of dissolved oxygen changes depending ontransfer rate from the air bubbles to liquid phase

e oxygen uptake rate for growth, on maintenance,n the metabolic production by the cells. So, thee different variables affecting oxygen and its rela-rowth and yield is of great importance. Calik et al.

shown that variation of specic growth rate values,concentration in the growth of Pseudomonas dacun-

anine production obeys a substrate inhibition model.t al. [52] have shown that increasing of DO con-(changing aeration rate and stirrer speed) causes anin the yield of biomass on substrate and that the ef-lucose and oxygen consumption is hampered underiting conditions; similar results have been obtainedt al. [7], determining that cell yield on substrateith increase in oxygen transfer rate. Also, Sampaio

ound that metabolism of yeast Debaryomices hansen-results to be practically inactive under strict oxygen

ditions. Olmo et al. [60] have shown in aerobic bio-biodesulphurization by Rhodococcus erythropolis thatthe bacteria is strongly dependent on the avail-xygen. Experimental results of Mantzouridou et al.iu et al. [10] have shown in shake ask culturestrispora and Phafna rhodozyma, respectively, that

carotenoid production depend strongly on the oxygen

gn and optimisation of bioprocesses, it is essential tohematical model that represents the system kinetics,e evolution and inuence of DO concentration. There-netic models proposed to describe bioprocesses haveas a key-compound in its set of differential equationsd oxygen concentration, because very often this is thertant nutrient for success of the production process.cal models incorporating oxygen uptake and dissolvedcentration have been developed for different cultures] and different specic rate expressions for cell growth,nsumption, product formation andoxygenuptakehaved.ype kinetic [101] has been frequently used for descrip-specic culture growth rate when dissolved oxygen is

304 F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307

Fig. 14. Expertime course bmass transferization capabi[38]).

the limiting

= max KO2 +

and the samrate [49,97,

qO2 =qO2 mKO2

The abostructuredxanthan guaccount vsource, xanconsider thlution and,closer to exis also abletionof all th

model values for biomass concentration, consumption of sucrose,xanthan gunproduction andDO concentration during time are rep-resented inFig. 13. In a laterwork [5] this kineticmodelwasused forpredicting the behaviour of the system in scale-up when a trans-

arameter (KLa, air ow and DO concentration) is changed.s showed that increases of DO concentration produce fastsource consumption and favours the production of xanthanee Fig. 3). It can be observed that, as found by other authorsthe increase of DO concentration favours the production ofymer.inetic model for DBT desulphurization has been proposed toe the growth of R. erythropolis in batch operation and undernt operation conditions [38,60]. Experimental and predictedof biomass concentration, desulphurization capability, XBDS,O concentration during the course of the bioprocess ofulphurization by R. erythropolis are shown in Fig. 14, for dif-OTR values, changing the stirrer speed. In Fig. 14a, it can beed that the maximum cell concentration obtained increasestirrer speed increases, that iswhenOTR increases. In Fig. 14b,port pResultcarbongum (s[103],biopol

A kdescribdifferevaluesand Dbiodesferentobservwhensimental values (points) and prediction by the model (lines) duringioprocess of the growth of Rhodococcus erythropolis under differentoperational conditions: (a) biomass concentration; (b) desulphur-lity; (c) dissolved oxygen concentration (adapted from Gomez et al.

nutrient for growth:

CO2CO2

(47)

e formalism has been used for specic oxygen uptake102]:

ax CO2+ CO2

(48)

ve approach has been considered in the metabolickinetic model proposed by Garcia-Ochoa et al. [99] form production by X. camprestris. This model takes intoe key compounds: biomass, carbon source, nitrogenthan gum and dissolved oxygen. The model is able toe inuence of DO concentration on the bioprocess evo-therefore, the results obtained are more realistic andperimental evidence. It should be noted that this modelto predict the inuence of temperature on the evolu-edescribed compounds. Experimental andpredictedby

Fig. 15. Expertime course btransfer operacapability; (c)imental values (points) and prediction by the model (lines) duringioprocess of the growth of Pseudomonas putida under different masstional conditions: (a) biomass concentration; (b) desulphurizationdissolved oxygen concentration (adapted from Gomez et al. [39]).

F. Garcia-Ochoa et al. / Biochemical Engineering Journal 49 (2010) 289307 305

desulphurization capability is represented in time for differenttransport conditions; it can be seen that the maximum percentageof desulphurization capability is similar for stirrer speeds between250 and 400 rpm (approximately of 80% for 30h of growth); afterthat, this cadecrease ismost probaduringgrowtration valuin Fig. 14c.

In a preto describeseveral medditions (gasCECT5279 (bility of thebiomass grothe culturedbiocatalystrer speeds,oxygen conare showedbetween thfound in alconditions a

7. Conclus

The biormechanicalenvironmenpH, nutriengrowth andmental andoxygen is ato be providditions OURon the desigcentration idescriptionessary to kmany physiaccount the

Acknowled

This worde Proceso60919/PPQ,de GruposUniversidad

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