Biochemical Engineering Journal 8 (2001) 111–119

Volumetric oxygen transfer coefficients (kLa) in batchcultivations involving non-Newtonian broths

A.C. Badino Jr. a, M.C.R. Facciotti b, W. Schmidell b,∗a Department of Chemical Engineering, Universidade Federal de São Carlos, P.O. Box 676, SP 13565-905 São Carlos, Brazil

b Department of Chemical Engineering, Escola Politécnica da Universidade de São Paulo,P.O. Box 61548, SP 05424-970 São Paulo, Brazil

Received 21 June 1999; accepted 9 January 2001

Abstract

The oxygen transfer in non-Newtonian fermentation broths of Aspergillus awamori, during batch cultivations in conventional 10 lbioreactor has been investigated. Values of the volumetric oxygen transfer coefficient (kLa), obtained at various impeller speeds, air flowrates and at distinct initial substrate concentrations were correlated with operational variables, geometric parameters of the system andphysical properties of the broths utilising rigorous techniques in order to obtain a set of reliable and accurate data. An experimental devicewas constructed for on-line rheological measurements, and the apparent dynamic viscosity was determined from the broth rheograms. Inorder to measure power requirements, a torque meter was developed and non-Newtonian fluids with rheological characteristics similar tothe Aspergillus fermented broths were utilised to obtain reference curves and correlations in the fermentor where the cultivations took place.Gas balancing method and a modified dynamic method were utilised simultaneously to determine kLa values. The rigorous methods thusdeveloped allowed adequate evaluation of the oxygen transfer in the cultivations and also permitted good fits of four different traditionalcorrelations for kLa to the experimental data. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Volumetric oxygen transfer coefficient; Power consumption; Broth rheology

1. Introduction

Fermentation broths containing mycelial cells frequentlyexhibit a pseudoplastic non-Newtonian rheological be-haviour, which can be described by the power-law model.This behaviour exerts a profound effect on the bioreactorperformance, affecting mixing pattern, power requirement,heat and mass transfer processes [1]. The increase in thebroth apparent viscosity (µap) during aerobic fermentationscan be partially compensated by increments in the operatingconditions (N and Q), in order to maintain adequate kLavalues. Nevertheless, high impeller speeds (N) lead to theformation of high shear zones close to the impellers, withconsequent physical damage to the cells and a reduction inthe process productivity [2]. Due to the importance of thevolumetric oxygen transfer coefficient (kLa) in the perfor-mance and scale-up of conventional bioreactors, the litera-ture describing various correlations for kLa in Newtonianfluids is rather extensive. However, particular care should be

∗ Corresponding author. Tel.: +55-11-818-2284; fax: +55-11-211-3020.E-mail addresses: badinojr@deq.ufscar.br (A.C. Badino Jr.),wschmide@usp.br (W. Schmidell).

taken when applying these correlations to non-Newtoniansystems containing electrolytes such as fermentation broths[3].

Two types of correlations have been proposed for the vol-umetric oxygen transfer coefficient (kLa). The first does notmake use of any dimensional criterion. In these correlations,kLa is related to the gassed power consumption per unit vol-ume of broth (Pg/V) and the superficial gas velocity (vs), asoriginally proposed by Cooper et al. [4]:

kLa α

(Pg

V

)a1

(vs)b1 (1)

where the values of the constants a1 and b1 may vary con-siderably, depending on the system geometry, the rangeof variables covered and the experimental methodologyused. Although initially developed for fluids very distinctfrom fermentation broths, this type of correlation has beenwidely used in fermentation systems [3,5–7]. In a morerecent work, Montes et al. [8] determined values of kLa inyeast broths (Trigonopsis variabilis) over wide ranges ofboth impeller speeds and superficial gas velocities in threedifferent mechanically-stirred, sparger-aerated and baffledbioreactors (2, 5 and 15 l) in order to consider the effect

1369-703X/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S1369 -703X(01 )00092 -4

112 A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119

Nomenclature

a1, a2, a3 constants of Eqs. (1), (2) and (8) (–)b1, b2, b3 constants of Eqs. (1), (2) and (8) (–)c2, c3 constants of Eqs. (2) and (8) (–)C dissolved oxygen concentration in the

broth in steady-state (mmol O2 l−1)C∗ dissolved oxygen saturation

concentration in the broth (mmol O2 l−1)d3 constant of Eq. (8) (–)Di impeller diameter (m)Dt tank diameter (m)Fr (=DiN2/g) Froude number (–)GLA glucoamylase activity (U l−1)k constant of Eq. (10) (–)ke electrode sensitivity (h−1 or s−1)kLa volumetric oxygen transfer coefficient

(h−1 or s−1)K consistency index (Pa sn )n flow behaviour index (–)nin inlet dry molar gas flow rate

(mol O2 h−1)nout outlet dry molar gas flow rate

(mol O2 h−1)N impeller speed (rpm)NP power number (–)P0 ungassed power consumption (W)Pg gassed power consumption (W)Pgi gassed power consumption per

impeller (W)(Pgi/Q)∗ (= (Pgi/Q)/(ρ(gvap)

2/3))dimensionless group of Eq. (8) (–)

Q air flow rate (m3 s−1)QO2 specific oxygen uptake rate

(mmol O2 g−1 h−1)Qmax

O2maximum specific oxygen uptakerate (mmol O2 g−1 h−1)

QO2X global oxygen uptake rate(mmol O2 g−1 h−1)

R2 correlation coefficient (–)Rem modified Reynolds number (–)S substrate concentration (g l−1)S0 initial substrate concentration (g l−1)Sc (= µap/(ρDO2)) Schmidt number (–)Sh∗ kLaD2

i /DO2 , modified Sherwoodnumber (–)

Si∗ dimensionless group in Eq. (7) (–)vs (= 4Q/(πD2

t )) superficial gasvelocity (m s−1)

V broth volume (l or m3)Vi broth volume per impeller (m3)X cell concentration (g l−1)Y in

O2oxygen molar fraction in inlet gas (–)

Y outO2

oxygen molar fraction in outlet gas (–)

Y outCO2

carbon dioxide molar fractionin outlet gas (–)

Greek lettersα constant of proportionalityφair specific air flow rate (vvm: air volume

per broth volume per minute) (min−1)γ av average shear rate (s−1)µap apparent dynamic viscosity (Pa s)µg air viscosity (Pa s)µw water viscosity (Pa s)νap apparent kinematic viscosity (m2 s−1)ρ density (kg m−3)σ surface tension of filtrate (N m−1)σ ∗ (= σ/(ρ(ν4

apg)1/3)) Eq. (8) (–)

τ av average shear stress (Pa)

of the fermentor scale-up on kLa. Experimental data werefitted using the correlation proposed by Cooper et al. [4]and the values for the parameters a1, b1 and proportionalityconstant were 0.35, 0.41 and 3.2 × 10−3, respectively. Dueto the fact that most of the yeast broths behave as slightlynon-coalescent fluid, according to the authors, the corre-lation improved the prediction of kLa values with respectto other generic correlations usually developed for strongcoalescent and non-coalescent fluids. Extended forms ofthis first type of relationship have been proposed in theliterature, incorporating terms like impeller speed (N) andthe fluid apparent viscosity (µap). For example, Ryu andHumphrey [9] observed the influence of the broth appar-ent viscosity (µap) on kLa in penicillin fermentation andproposed the following correlation:

kLa α

(Pg

V

)a2

(vs)b2(µap)

c2 (2)

where again, the constants a2, b2, c2 as well as theproportionality constant, depend on the geometry of the sys-tem. More recently, Garcıa-Ochoa and Gómez [10] utilisedthis correlation to fit experimental data obtained in a stirredtank reactor of 20 l of working volume. The rheology of thexanthan gum solutions was described both in terms of thepower-law and the Casson models. Experiments were per-formed considering the effect of the number and type of stir-rers (paddle or turbine), the number of blades of the stirrersand the sparger type (ring and disk) in the volumetric oxygentransfer coefficient (kLa). In the same way, Gavrilescu et al.[1] have assessed the problem of oxygen transfer in antibioticbroths produced by nine different microorganisms belongingto the actinomycetes and the fungi. The following equationfor kLa was established from a wide variety of experimentaldata obtained in 20 and 100 m3 stirred tank bioreactors:

kLa = 0.025

(Pg

V

)0.4

(vs)0.5(N)0.5

(µap

µg

)0.65

(3)

A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119 113

Additionally, Shin et al. [11] verified that in high celldensity cultures of fast-growing aerobes such as recombi-nant E. coli where the cell mass increases up to more than70 g/l, the oxygen availability can be the rate-limiting ofthe fermentation process. In that way, the following corre-lation for kLa incorporating the effect of cell density (X) inoxygen transfer has been proposed:

kLa = 0.0192

(Pg

V

)0.55

(vs)0.64

× (1 + 2.12X + 0.20X2)−0.25 (4)

The second type of correlation for kLa is based on dimen-sional analysis. This approach presents certain advantagesbecause the correlations obtained for a known system canbe used to estimate kLa in other systems with differentdimensions. Yagi and Yoshida [12] proposed the followingcorrelation, valid for both Newtonian and non-Newtonianfluids, for the standard six-bladed turbine in standard con-figuration in a vessel of 0.25 m diameter:

Sh∗ = 0.060(Rem)1.50(Sc)0.50(Fr)0.19

×(µapvs

σ

)0.60(

NDi

vs

)0.32

(5)

This correlation fitted to the experimental data in areasonable extent, with maximum deviations of 30 and80%, between experimental and calculated Sh∗ values,for Newtonian and non-Newtonian fluids, respectively. Inorder to determine the combined effects of the variables,including operational conditions, liquid and gas propertiesand geometry of the tank, Garcıa-Ochoa and Gómez [10]employed a similar dimensionless equation to fit the setof experimental data of kLa obtained in the same systemunder operational conditions above specified. Li et al. [13]proposed a relationship among kLa, the impeller speed (N)and the apparent viscosity (µap), for fermentation brothsof Aureobasidium pullulans and Xanthomonas campestrisin 100 l fermentor, which correlated quite well the greatvariety of experimental data, as follows, respectively:

Sh∗ = 5.40 × 104(Fr)0.45(µap

µw

)−0.33

(6)

Sh∗ = 3.32 × 103(Fr)0.23(µap

µw

)−0.58

(7)

Zlokarnik [14] suggested, also through dimensional analysis,a general dependence of kLa on physico-chemical propertiesand operating conditions, as follows:

kLa

(Q

Vi

)−1

α

[(Pgi

Q

)∗]a3

(Sc)b3(σ ∗)c3(Si∗)d3 (8)

where the dimensionless variable Si∗, not exactly defined,is related to the coalescence behaviour of solutions. How-ever, this correlation presents a feature not found in the

others since the variable Pgi represents the gassed powerconsumption per impeller, this equation can be applied tosystems with different numbers of impellers and, therefore,with different geometries. This possibility was verified byJurecic et al. [3], investigating submerged cultures of Bacil-lus licheniforms for bacitracin production in bioreactorsof 100 l and 67.5 m3 with two and four turbine impellers,respectively.

Although several correlations have been developed fordifferent systems, most of them are not specific to fermenta-tion broths or, when developed with such a purpose, they donot determine all the variables throughout the cultivation.Surface tension of the liquid (σ ), for instance, is consideredto be constant throughout the whole cultivation and, there-fore, it is not considered in the correlations. Furthermore, inthe development of kLa correlations in cultivations involv-ing filamentous microorganisms, particular care should betaken when measuring some variables, like the rheologicalproperties of the broth and the kLa itself, when traditionalequipment and methodologies are utilised. In recent works,Badino Jr. et al. [15], as well as Svihla et al. [16], verifiedthat the use of conventional bench rheometers, such as theconcentric cylinder, to determine rheological properties ofviscous mycelial suspensions, is often unsatisfactory. Themain problems are caused by pellet’s size, generally of thesame order of magnitude as the annulus, as well as the ten-dency of the suspension to become heterogeneous due tosettling and particle interaction. Thus, they propose the useof rotational rheometer provided with a helical impeller toobtain reliable and accurate rheological data for filamentousfermentation broths. In addition, Olsvik and Kristiansen[17] concluded that on-line continuous measurement ofbroth rheology enables the uniform treatment of the samplesand statistically more “correct” measurements.

The aim of this work is to investigate the influence ofoperating conditions on the rheological properties of thefermented broth and on the oxygen transfer during batchcultivations of A. awamori in a bench scale fermentor.Methodologies for on-line rheological measurements andfor determination of both power consumption and kLa havebeen developed in order to obtain a set of reliable and accu-rate data. Four classical correlations mentioned previously(Eqs. (1), (2), (5) and (8)) for the volumetric oxygen transfercoefficient (kLa), including the operating conditions, geo-metrical parameters of the system and physical propertiesof the broth (apparent viscosity and also surface tension ofthe filtrated broth), were fitted to the experimental values.

2. Materials and methods

2.1. Microorganism and culture media

A spore suspension (2×107 spores per millilitre) of A.awamori NRRL 3112, stored in cryotubes (glycerol 20%v/v) at −20◦C, was used throughout this work.

114 A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119

Growth medium was composed of (in g/l): total reducingsugars (TRS) from cassava flour and assayed as glucose,20.0; yeast extract, 0.2; MgSO4·7H2O, 1.0; (NH4)2SO4,10.0; Na2HPO4·12H2O, 7.56; KH2PO4, 7.0, pH 5.0. Twofermentation media with different compositions wereutilised. The first had the same composition as the growthmedium and the second had initial TRS concentration (S0)of 40.0 g/l, with addition of silicone antifoam (0.08 ml/l) toboth.

2.2. Fermentation equipment and cultivation procedure

Nine batch cultivations were conducted at 35◦C and pH5.0 in a 10 l Microferm MF-14 fermentor (New BrunswickSci. Co. Inc., USA) provided with four baffles in order tofavour turbulence and to prevent vortex formation. For eachfermentation, spores were initially germinated in five 1 lErlenmeyer flasks, each holding 200 ml of growth medium.Flasks were inoculated with 1 ml of the spore suspensionfrom the cryotubes and inoculated in a rotary shaker (NewBrunswick Sci.) for 24 h at 35◦C and 300 rpm. The con-tents of the flasks were transferred to the fermentor with9 l of fermentation medium, performing a total of 10 l offermentation broth. The cultivations were carried out at dif-ferent operational conditions. The ranges of impeller speed(300 < N < 700 rpm) and specific air flow rate (0.2 <

φair < 1.0 vvm) are frequently utilised during filamentousfungal cultivations in bench-scale bioreactors, in order toprovide adequate mixing and oxygen supply to the cells.The assays were designated as follows: E20-7-3, E20-5-6,E20-7-9, E40-5-2, E40-5-6, E40-5-10, E40-7-2, E40-7-6and E40-7-10. The label E20-7-3, for instance, specifiesthe following experimental conditions: S0 = 20 g/l, N =700 rpm and φair = 0.3 vvm, respectively. Samples werewithdrawn each 3 h for analytical determinations.

Fig. 1. Experimental apparatus.

Dissolved oxygen concentration was measured by asterilisable galvanic electrode (Mettler-Toledo InPro6000Series), bearing a 0.0254 mm thick FEP (fluorinated ethy-lene propylene) membrane. Readings of the oxygen (YO2 )and carbon dioxide (YCO2 ) molar fractions in the outletgas were furnished by gas analysers produced by BeckmanIndustrial (model 755) and Fuji Electric (model IR-730),respectively. The experimental apparatus is shown in Fig. 1.

2.3. Analytical determinations andsurface tension measurement

Cell concentration (X) was evaluated as dry matterobtained after vacuum filtration and drying at 85◦C for 6 h.Substrate concentration (S) was determined as equivalentglucose utilising Glucose Autoanalyser II (Bran-Luebbe),after the polysaccharide in the sample had previously beenconverted to glucose through an enzymatic hydrolysis [18].Liquid surface tension of the filtrated broth (σ ) was mea-sured with a Fisher Scientific Co. ring tensionmeter.

2.4. Rheological properties

Continuous on-line rheological measurements wererecorded every 2 h of cultivation, utilising the experimen-tal device constructed and calibrated by Badino Jr. et al.[15] based upon the original reports of Kemblowski andKristiansen [19]. In order to determine flow curves of fer-mentation broths, a rotational helical ribbon impeller wasconnected to Brookfield rheometers, models LV-DVIII andRV-DVIII (Brookfield Eng. Lab. Inc., USA), which mea-sured the impeller torque (T) at different rotational impellerspeeds (N). The average shear rate, γ av, and the averageshear stress, τ av, around the impeller were calculated fromthe calibration equations, γ av = 28.91N and τ av = 10530T .

A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119 115

For these continuous on-line rheological measurements,the fermentation broth was pumped out of the bioreactorthrough silicone rubber tubing and into the impeller rheome-ter by a peristaltic pump. The outlet of the impeller shaftin the rheometer was provided with a rotating labyrinthseal. Aseptic conditions were ensured by introducing sterileair through the glass tubing next to the head of the ves-sel. The average residence time in the loop was fixed at90 s, in order to allow good measurements, without causingparticle settling or even disturbing the performance of thecultivation.

The power law model (τav = Kγ nav) was fitted to on-line

experimental data and the rheological properties, con-sistency index (K) and flow behaviour index (n), wereestimated.

2.5. Power consumption

Ungassed and gassed power consumptions were esti-mated under the previously mentioned different operatingconditions (N and Q), every hour during cultivation, by us-ing traditional reference curves and correlations to interpretdata from a purpose-built torque meter based on flat straingauges of 120# resistance. The new device was connectedto the stirrer shaft inside the fermentor, to avoid frictionallosses in the mechanical seal. In order to obtain the referencecurves and correlations, non-Newtonian fluids of similarrheological characteristics to the fermentation broths wereused [20]. Ungassed power consumption (P0) was obtainedthrough a graph of power number (NP) as a function ofmodified Reynolds number (Rem), as proposed by Metzneret al. [21] for non-Newtonian pseudoplastic fluids.

NP = P0

ρN3D5i

(9)

Rem = ρN2−nD2i

K(kn−1)(10)

where k = 11.4, under the conditions considered.Gassed power consumption (Pg) was estimated through a

traditional correlation, proposed by Michel and Miller [22],obtained for the experimental system used in cultivations:

Pg = 0.832

(P 2

0 ND3i

Q0.56

)0.44

(11)

2.6. Oxygen transfer

Global oxygen uptake rate (QO2X) as well as the volu-metric oxygen transfer coefficient (kLa) were obtained byboth steady-state and dynamic methods. By the gas balanc-ing method, QO2X was determined from an oxygen massbalance in the gas phase by the following expression:

QO2X = ninYintO2

− noutYoutO2

V(12)

The inlet molar gas flow rate (nin) was measured utilis-ing a mass flowmeter model 5811-N (Brooks InstrumentDivision), and the outlet molar gas flow rate (nout) wascalculated from the nitrogen mass balance in the gas phaseby the following equation:

nout = 0.79nin

1 − Y outO2

− Y outCO2

(13)

The volumetric oxygen transfer coefficient (kLa) could becalculated for the steady-state condition, from the massbalance for dissolved oxygen as follows:

kLa = QO2X

C∗ − C(14)

where C is the dissolved oxygen concentration in thebroth at the steady-state given by the galvanic electrodeand C∗ is the dissolved oxygen saturation concentration inthe broth estimated by the method proposed by Schumpeet al. [23].

The volumetric oxygen transfer coefficient (kLa) wasalso evaluated through an alternative method, based on thetraditional dynamic method taking into consideration theelectrode sensitivity (ke) [24]. The electrode sensitivity (ke)is defined as the inverse of the time taken for the electrodeto reach 63.2% of its final value when exposed to a stepchange in oxygen concentration. After each cultivation theelectrode sensitivity (ke) was determined in triplicate as-says utilising xanthan gum solution 0.4% w/v at 35◦C tosimulate the fermentation broth.

3. Results and discussion

3.1. Rheological behaviour of fermentation broths

With the average shear rate (γ av) ranging from 0.96 to72.27 s−1, all fermentation broths at different cultivationtimes, behaved as non-Newtonian pseudoplastic fluids.Good fits between the power law model and the experimen-tal data were achieved, showing that on-line rheologicalmeasurement is a consistent and reliable technique formycelial cultivations. Fig. 2 illustrates typical flow curves(rheograms) obtained at different times for the run E40-7-6.Significant changes in the rheological parameters, fluidconsistency index (K) and flow behaviour index (n) asdepicted the Fig. 3 for the run E40-7-6, were observed asthe fermentations proceeded: K increased rapidly while ndecreased to values between 0.3 and 0.5. Interestingly, anadded feature of the on-line technique was its ability to ac-curately anticipate the instant at which the culture mediumis depleted of carbon source, especially when measure-ments are taken frequently. As can be observed in Fig. 3,immediately after the carbon source is exhausted (∼27 h),the K value decreases suddenly, probably as a consequenceof both hyphae fragmentation and lysis.

116 A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119

Fig. 2. Typical flow curves obtained at different times of the run E40-7-6(10 h: τav = 0.019γ 0.60

av , 16 h: τav = 0.261γ 0.43av , 22 h: τav = 0.837γ 0.47

avand 30 h: τav = 1.554γ 0.39

av ).

Fig. 3. Variation in substrate concentration (S) and rheological parametersK and n during run E40-7-6.

3.2. Characteristics of oxygen uptake and oxygen transfer

Typical time course profiles of specific oxygen uptake rate(QO2 ) and of dissolved oxygen concentration (C) obtainedduring an experiment with oxygen limitation (E40-5-2) isshown in Fig. 4. Considering all runs, the maximum valuesof specific oxygen uptake rate (Qmax

O2) ranged from 2.8 to

4.5 mmol O2 g−1 h−1. Metwally et al. [25], as well as Shuler

Fig. 4. Time profiles of specific oxygen uptake rate (QO2 ) and of dissolvedoxygen concentration (C) for the experiment E40-5-2.

and Kargi [26], both cultivating Aspergillus niger strains,utilising glucose as the main carbon source, found Qmax

O2

values in the range 3–4 mmol O2 g−1 h−1, which agrees verywell with the present results.

With respect to kLa determinations, the simultaneous useof the two measuring methods allowed reliable determina-tions of kLa over a wide range (60.1–768 h−1) showing thatthe gas balancing and the alternative dynamic method takinginto account the electrode response time, should be used ina complementary manner: while the gas balancing methodprovides accurate measurements mainly after the cell con-centration reaches higher values, the alternative dynamicmethod is particularly useful to evaluate kLa at the begin-ning of the fermentation, when the differences in oxygencomposition between inlet and outlet gas are quite small andthe levels of dissolved oxygen concentration are very high,a situation at which the gas balancing and other methodolo-gies are often inadequate. Nevertheless, dynamic methodsfor determinations of kLa are useful only when the dissolvedoxygen concentration is fairly above the critical value (Ccrit);for lower values, the gas balancing method would be moreappropriate [24].

It is known that besides the agitation (N) and aeration (Q)conditions, a variable that negatively affects kLa is the brothapparent viscosity (µap), because it offers resistance to theoxygen transfer from the gaseous to the liquid phase. Val-ues of apparent viscosity (µap) varied between 0.013 and0.257 Pa s and the estimated maximum value of ungassedpower consumption (P0) was 187 W. The strong influenceof the broth apparent viscosity (µap) on the volumetric oxy-gen transfer coefficient (kLa) during experiment E40-5-10 isshown in Fig. 5. It can be observed that kLa decreased from381 to 124 h−1 when µap increased from 0.013 to 0.257 Pa sin the time interval from 0 to 37 h of cultivation. In addi-tion, in Fig. 5 the time course of the relative surface ten-sion of the filtrated broth (σ /σw) is depicted, where σw =7.04.10−2 N m−1 is the surface tension of water at 35◦C[27]. The relative surface tension of the filtrated broth pre-sented an ascendant behaviour, varying from 0.897 to 0.943for the same time period considered before. Such variation isrelatively modest and it is probably due to the consumption

Fig. 5. Influence of apparent viscosity (µap) and relative surface tensionof filtrated broth (σ /σw) on the kLa during run E40-5-10 (γ av = 95 s−1).

A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119 117

Table 1Correlations for the volumetric oxygen transfer coefficient (kLa)

Correlation Reference Regressioncoefficient (R2)

Experimentalvalues

kLa = 41.44(Pg/V )0.47(vs)

0.39 Cooper et al. [4] 0.90 286kLa = 19.89(Pg/V )

0.53(vs)0.43(µap)

−0.12 Ryu and Humphrey [9] 0.92 305

Sh∗ = 1.45(Rem)0.83(Sc)0.43(Fr)0.74

(µapvs

σ

)−0.02(

NDi

vs

)−0.25

Yagi and Yoshida [12] 0.94 316

kLa

(Q

Vi

)−1

= 1.45

[(Pgi

Q

)∗]0.53

(Sc)−0.20(σ ∗)−0.40 Zlokarnik [14] 0.96 318

of the dissolved nutrients from the original culture mediumas the fermentation proceeds.

3.3. Correlations for kLa

As mentioned before, four classical correlations have beenutilised to correlate the volumetric oxygen transfer coef-ficient (kLa) with the operation variables (N, Q, and Pg),geometric parameters of the system (V and Di) and phys-ical properties of the broths (µap and σ ), as described byCooper et al. [4], Ryu and Humphrey [9], Yagi and Yoshida[12] and Zlokarnik [14]. The correlations were fitted tothe experimental values and the parameters were estimatedthrough Marquardt’s procedure that utilises the least squaresnon-linear regression [28]. The criterion for the best fit andparameter optimisation was the sum of squares of residuals(SSR). No convergence problems were found in non-linearregression and all confidence intervals, computed for the95% of probability, were below 25% of the estimated values.The fitted correlations, together with the respective correla-tion coefficients (R2) and numbers of experimental valuesused in the regressions, are presented in Table 1. Figs. 6–9illustrate the quality of the fits.

The simultaneous use of the two methods, gas balancing(GB) and dynamic method (DM), allowed a great number ofkLa values to be obtained as previously discussed, with theobtention of similar values in the same operating conditions.

Fig. 6. Comparison of the experimental data with those calculated usingthe correlation proposed by Cooper et al. [4] (DM: dynamic method, GB:gas balancing for kLa determination).

Fig. 7. Comparison of the experimental data with those calculated usingthe correlation proposed by Ryu and Humphrey [9] (DM: dynamic method,GB: gas balancing for kLa determination).

The data in Table 1, as well as the figures, show that goodfits were obtained for all the correlations, indicating that anyof the adjusted models can be used to estimate, with goodprecision, the volumetric oxygen transfer coefficient (kLa)in these cultivations.

However, it can also be observed that the more complexis the correlation, also the better is the quality of the fit(higher R2 values). The correlation proposed by Cooperet al. [4], for instance, being less complex because it onlyconsiders the effects of the gassed power consumption per

Fig. 8. Comparison of the experimental data with those calculated usingthe correlation proposed by Yagi and Yoshida [12] (DM: dynamic method,GB: gas balancing for kLa determination).

118 A.C. Badino Jr. et al. / Biochemical Engineering Journal 8 (2001) 111–119

Fig. 9. Comparison of the experimental data with those calculated usingthe correlation proposed by Zlokarnik [14] (DM: dynamic method, GB:gas balancing for kLa determination).

unit volume (Pg/V) and the superficial gas velocity (vs) onkLa, fitted the data less well than those correlations thatconsider the effects of the physical properties of the brothon kLa. Despite its simplicity, the correlation proposed byRyu and Humphrey [9] gave also a good fit, practically asgood as the more complex correlations proposed by Yagiand Yoshida [12] and by Zlokarnik [14] that need the knowl-edge of additional variables of the broth, such as apparentviscosity (µap) and surface tension (σ ), for convenient ap-plication. However, if we intend to use a kLa correlation inthe design or scaling-up of conventional bioreactors, it ismore convenient to use more complex correlations, such asthose proposed by Yagi and Yoshida [12] and by Zlokarnik[14], which relate dimensionless variables.

In addition, it should be observed that the parametersestimated by the regressions are very close to the valuesfound in the literature. The parameters of the correlationproposed by Cooper et al. [4], a1 = 0.47 and b1 = 0.39,respectively, are within the ranges of values mentioned byKawase and Moo-Young [29] for non-Newtonian systems,which are 0.37 < a1 < 0.80 and 0.20 < b1 < 0.84. Thevalue obtained for the constant c2 of the correlation pro-posed by Ryu and Humphrey [9] (c2 = −0.12) is verydifferent from that obtained in the original work (c2 =−0.86). However, it should be pointed out that the brothsstudied had different physicochemical properties and thediscrepancy may be due to the fact that different equationshave been used to calculate the apparent viscosities (µap)of the fermentation media: while the power law modelhas been used in this work to describe the non-Newtonianbehaviour of Aspergillus fermentation broths, Ryu andHumphrey [9] employed the Bingham plastic model. How-ever, as expected, both of the values for the constant c2were coherently negative, indicating an inverse proportion-ality between kLa and µap. The values obtained for theparameters from the correlation of Yagi and Yoshida [12]could not be compared with values found in the literature,because no published work has been found that appliesthis correlation to non-Newtonian fermentation broths. The

parameters obtained from the correlation of Zlokarnik [14],presented values similar to those obtained by Jurecic et al.[3], employing non-Newtonian fermentation broths of B.licheniformis in pilot and industrial scales (a3 = 0.35, b3 =−0.30 and c3 = −0.50). Also, it should be emphasised thatalthough a lot of correlations for kLa include dimensionlessterms, in the literature investigated no works have beenfound that present measurements of parameters such as thesurface tension of the filtrate (σ ) during cultivation.

4. Conclusions

The main objective of this work was to investigate theinfluence of operating conditions on the rheological prop-erties of the broth and on the oxygen transfer during batchcultivations of A. awamori in a bench scale fermentor. Fourclassical correlations found in the literature, which correlatethe volumetric oxygen transfer coefficient (kLa) with theprocess operational variables (N, Q and Pg) and the geomet-ric parameters of the system has been utilised. In particular,in some of these correlations, kLa is also correlated withthe physical properties of the broth (apparent viscosity andliquid surface tension), which are time dependent duringthe fermentation process.

Good fits were obtained for all the correlations tested,considering experimental data obtained with Aspergillus cul-tivation in quite distinct operational conditions, observingthat the fit was even better for the more complex correla-tions, which take into account the physical properties of thebroth. It is obvious, however, that the utilisation of such cor-relations means the necessity of more complex analyticaldeterminations, which is not always possible.

Finally, it should be pointed out that the good fits obtainedare a consequence of the quality and accuracy of the gen-erated experimental values, which are a result of carefullyelaborated methodologies implemented in the cultivations.

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