Biochemical Engineering Journal 8 (2001) 111–119Volumetric oxygen transfer coefficients (kL a) in batch cultivations 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 l bioreactor has been investigated. Values of the volumetric oxygen transfer coefficient (kL a), obtained at various impeller speeds, air flow rates and at distinct initial substrate concentrations were correlated with operational variables, geometric parameters of the system and physical properties of the broths utilising rigorous techniques in order to obtain a set of reliable and accurate data. An experimental device was constructed for on-line rheological measurements, and the apparent dynamic viscosity was determined from the broth rheograms. In order to measure power requirements, a torque meter was developed and non-Newtonian fluids with rheological characteristics similar to the 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 kL a values. The rigorous methods thus developed allowed adequate evaluation of the oxygen transfer in the cultivations and also permitted good fits of four different traditional correlations for kL a 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 frequently exhibit a pseudoplastic non-Newtonian rheological behaviour, which can be described by the power-law model. This behaviour exerts a profound effect on the bioreactor performance, affecting mixing pattern, power requirement, heat and mass transfer processes [1]. The increase in the broth apparent viscosity (µap ) during aerobic fermentations can be partially compensated by increments in the operating conditions (N and Q), in order to maintain adequate kL a values. Nevertheless, high impeller speeds (N) lead to the formation of high shear zones close to the impellers, with consequent physical damage to the cells and a reduction in the process productivity [2]. Due to the importance of the volumetric oxygen transfer coefficient (kL a) in the performance and scale-up of conventional bioreactors, the literature describing various correlations for kL a in Newtonian fluids is rather extensive. However, particular care should be ∗ Corresponding author. Tel.: +55-11-818-2284; fax: +55-11-211-3020. E-mail addresses:
[email protected] (A.C. Badino Jr.),
[email protected] (W. Schmidell). taken when applying these correlations to non-Newtonian systems containing electrolytes such as fermentation broths [3]. Two types of correlations have been proposed for the volumetric oxygen transfer coefficient (kL a). The first does not make use of any dimensional criterion. In these correlations, kL a is related to the gassed power consumption per unit volume of broth (Pg /V) and the superficial gas velocity (v s ), as originally proposed by Cooper et al. [4]: kL a α Pg V a1 (vs )b1 (1) where the values of the constants a1 and b1 may vary considerably, depending on the system geometry, the range of variables covered and the experimental methodology used. Although initially developed for fluids very distinct from fermentation broths, this type of correlation has been widely used in fermentation systems [3,5–7]. In a more recent work, Montes et al. [8] determined values of kL a in yeast broths (Trigonopsis variabilis) over wide ranges of both impeller speeds and superficial gas velocities in three different mechanically-stirred, sparger-aerated and baffled bioreactors (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: S 1 3 6 9 - 7 0 3 X ( 0 1 ) 0 0 0 9 2 - 4 b2 . a 2 . / Biochemical Engineering Journal 8 (2001) 111–119 Nomenclature a1 . (8) (–) air flow rate (m3 s−1 ) specific oxygen uptake rate (mmol O2 g−1 h−1 ) maximum specific oxygen uptake rate (mmol O2 g−1 h−1 ) global oxygen uptake rate (mmol O2 g−1 h−1 ) correlation coefficient (–) modified Reynolds number (–) substrate concentration (g l−1 ) initial substrate concentration (g l−1 ) (= µap /(ρDO2 )) Schmidt number (–) kL aD2 /DO2 . More recently. The rheology of the xanthan gum solutions was described both in terms of the power-law and the Casson models.112 A.41 and 3. Experimental data were fitted using the correlation proposed by Cooper et al. Ryu and Humphrey [9] observed the influence of the broth apparent viscosity (µap ) on kL a in penicillin fermentation and proposed the following correlation: kL a α Pg V a2 (vs )b2 (µap )c2 (2) where again.35. the number of blades of the stirrers and the sparger type (ring and disk) in the volumetric oxygen transfer coefficient (kL a). The following equation for kL a was established from a wide variety of experimental data obtained in 20 and 100 m3 stirred tank bioreactors: kL a = 0. respectively. incorporating terms like impeller speed (N) and the fluid apparent viscosity (µap ). Garc´a-Ochoa and Gómez [10] utilised ı this correlation to fit experimental data obtained in a stirred tank reactor of 20 l of working volume. c2 as well as the proportionality constant. a 3 b1 . In the same way. Experiments were performed considering the effect of the number and type of stirrers (paddle or turbine). depend on the geometry of the system. (1). et al. Due to the fact that most of the yeast broths behave as slightly non-coalescent fluid. the constants a2 . c3 C C∗ d3 Di Dt Fr GLA k ke kL a K n nin ˙ nout ˙ N NP P0 Pg Pgi (Pgi /Q)∗ Q QO2 Qmax O2 QO2 X R2 Rem S S0 Sc Sh∗ Si∗ vs V Vi X in YO2 out YO2 out YCO2 constants of Eqs.5 (N )0. [1] have assessed the problem of oxygen transfer in antibiotic broths produced by nine different microorganisms belonging to the actinomycetes and the fungi. (2) and (8) (–) constants of Eqs. Gavrilescu et al. b1 and proportionality constant were 0. the correlation improved the prediction of kL a values with respect to other generic correlations usually developed for strong coalescent and non-coalescent fluids. (2) and (8) (–) dissolved oxygen concentration in the broth in steady-state (mmol O2 l−1 ) dissolved oxygen saturation concentration in the broth (mmol O2 l−1 ) constant of Eq. (10) (–) electrode sensitivity (h−1 or s−1 ) volumetric oxygen transfer coefficient (h−1 or s−1 ) consistency index (Pa sn ) flow behaviour index (–) inlet dry molar gas flow rate (mol O2 h−1 ) outlet dry molar gas flow rate (mol O2 h−1 ) impeller speed (rpm) power number (–) ungassed power consumption (W) gassed power consumption (W) gassed power consumption per impeller (W) (= (Pgi /Q)/(ρ(gvap )2/3 )) dimensionless group of Eq. [4] and the values for the parameters a1 .65 (3) . (2) and (8) (–) constants of Eqs. b3 c2 .025 Pg V 0. modified Sherwood i number (–) dimensionless group in Eq. b2 . (1). Extended forms of this first type of relationship have been proposed in the literature. according to the authors. Badino Jr. For example.5 µap µg 0. (7) (–) (= 4Q/(π Dt2 )) superficial gas velocity (m s−1 ) broth volume (l or m3 ) broth volume per impeller (m3 ) cell concentration (g l−1 ) oxygen molar fraction in inlet gas (–) oxygen molar fraction in outlet gas (–) carbon dioxide molar fraction in outlet gas (–) Greek letters α constant of proportionality φ air specific air flow rate (vvm: air volume per broth volume per minute) (min−1 ) average shear rate (s−1 ) γ av µap apparent dynamic viscosity (Pa s) air viscosity (Pa s) µg µw water viscosity (Pa s) apparent kinematic viscosity (m2 s−1 ) ν ap ρ density (kg m−3 ) σ surface tension of filtrate (N m−1 ) 4 (= σ/(ρ(νap g)1/3 )) Eq. (8) (–) impeller diameter (m) tank diameter (m) (=Di N2 /g) Froude number (–) glucoamylase activity (U l−1 ) constant of Eq.C. 0.4 (vs )0.2 × 10−3 . (8) (–) σ∗ average shear stress (Pa) τ av of the fermentor scale-up on kL a. Garc´a-Ochoa and Gómez [10] ı employed a similar dimensionless equation to fit the set of experimental data of kL a obtained in the same system under operational conditions above specified.0192 Pg V 0. [15]. generally of the same order of magnitude as the annulus. like the rheological properties of the broth and the kL a itself.50 (Sc)0. as well as the tendency of the suspension to become heterogeneous due to settling and particle interaction. particular care should be taken when measuring some variables. Furthermore. they do not determine all the variables throughout the cultivation. with different geometries. liquid and gas properties and geometry of the tank. the oxygen availability can be the rate-limiting of the fermentation process. In addition. respectively. Although several correlations have been developed for different systems. The main problems are caused by pellet’s size.19 × µap vs σ 0.32 (5) This correlation fitted to the experimental data in a reasonable extent. was used throughout this work. the impeller speed (N) and the apparent viscosity (µap ). (2). it is not considered in the correlations.A. Materials and methods 2. Four classical correlations mentioned previously (Eqs.5 m3 with two and four turbine impellers.C. is considered to be constant throughout the whole cultivation and. is related to the coalescence behaviour of solutions. In recent works. valid for both Newtonian and non-Newtonian fluids. geometrical parameters of the system and physical properties of the broth (apparent viscosity and also surface tension of the filtrated broth).64 (4) × (1 + 2.25 The second type of correlation for kL a is based on dimensional analysis. which correlated quite well the great variety of experimental data. a general dependence of kL a on physico-chemical properties and operating conditions. However. they propose the use of rotational rheometer provided with a helical impeller to obtain reliable and accurate rheological data for filamentous fermentation broths. for instance. most of them are not specific to fermentation broths or. is often unsatisfactory. verified that the use of conventional bench rheometers.23 µap µw µap µw −0. Olsvik and Kristiansen [17] concluded that on-line continuous measurement of broth rheology enables the uniform treatment of the samples and statistically more “correct” measurements. Badino Jr. [16]. were fitted to the experimental values. this equation can be applied to systems with different numbers of impellers and.20X 2 )−0. awamori NRRL 3112. to determine rheological properties of viscous mycelial suspensions.50 (Fr)0.40 × 104 (Fr)0.1.060(Rem )1. the following correlation for kL a incorporating the effect of cell density (X) in oxygen transfer has been proposed: kL a = 0.55 (vs )0. as follows.33 (6) −0. not exactly defined. therefore. therefore. et al. This possibility was verified by Jurecic et al. stored in cryotubes (glycerol 20% v/v) at −20◦ C. awamori in a bench scale fermentor. [13] proposed a relationship among kL a. Li et al. In that way. such as the concentric cylinder. In order to determine the combined effects of the variables. [3]. / Biochemical Engineering Journal 8 (2001) 111–119 113 Additionally. also through dimensional analysis. including the operating conditions. in the development of kL a correlations in cultivations involving filamentous microorganisms. Methodologies for on-line rheological measurements and for determination of both power consumption and kL a have been developed in order to obtain a set of reliable and accurate data. when developed with such a purpose. with maximum deviations of 30 and 80%.58 (7) Zlokarnik [14] suggested. et al. (5) and (8)) for the volumetric oxygen transfer coefficient (kL a). α Pgi Q ∗ a3 (Sc)b3 (σ ∗ )c3 (Si∗ )d3 (8) where the dimensionless variable Si∗ . coli where the cell mass increases up to more than 70 g/l. as follows: kL a Q Vi −1 others since the variable Pgi represents the gassed power consumption per impeller. This approach presents certain advantages because the correlations obtained for a known system can be used to estimate kL a in other systems with different dimensions. (1). respectively: Sh∗ = 5. Shin et al. 2. including operational conditions. investigating submerged cultures of Bacillus licheniforms for bacitracin production in bioreactors of 100 l and 67. Yagi and Yoshida [12] proposed the following correlation. for Newtonian and non-Newtonian fluids. Surface tension of the liquid (σ ). when traditional equipment and methodologies are utilised. as well as Svihla et al. for the standard six-bladed turbine in standard configuration in a vessel of 0. [11] verified that in high cell density cultures of fast-growing aerobes such as recombinant E. between experimental and calculated Sh∗ values. for fermentation broths of Aureobasidium pullulans and Xanthomonas campestris in 100 l fermentor. Microorganism and culture media A spore suspension (2×107 spores per millilitre) of A.25 m diameter: Sh∗ = 0. this correlation presents a feature not found in the . Thus. respectively. Badino Jr.32 × 103 (Fr)0.60 NDi vs 0.12X + 0.45 Sh∗ = 3. The aim of this work is to investigate the influence of operating conditions on the rheological properties of the fermented broth and on the oxygen transfer during batch cultivations of A. The average shear rate. Fermentation equipment and cultivation procedure Nine batch cultivations were conducted at 35◦ C and pH 5. in order to provide adequate mixing and oxygen supply to the cells. 1. respectively. utilising the experimental device constructed and calibrated by Badino Jr.4.91N and τ av = 10530T . E40-7-2.0 in a 10 l Microferm MF-14 fermentor (New Brunswick Sci. 7. Fig. E40-5-2. Na2 HPO4 ·12H2 O. a rotational helical ribbon impeller was connected to Brookfield rheometers. each holding 200 ml of growth medium. The ranges of impeller speed (300 < N < 700 rpm) and specific air flow rate (0. bearing a 0. The first had the same composition as the growth medium and the second had initial TRS concentration (S0 ) of 40. Inc.0. Substrate concentration (S) was determined as equivalent glucose utilising Glucose Autoanalyser II (Bran-Luebbe). The experimental apparatus is shown in Fig. τ av .. models LV-DVIII and RV-DVIII (Brookfield Eng. Analytical determinations and surface tension measurement Cell concentration (X) was evaluated as dry matter obtained after vacuum filtration and drying at 85◦ C for 6 h. Flasks were inoculated with 1 ml of the spore suspension from the cryotubes and inoculated in a rotary shaker (New Brunswick Sci.3. Badino Jr.2 < φ air < 1. et al. around the impeller were calculated from the calibration equations. USA). Co.3 vvm. E40-5-6. 0. KH2 PO4 .0254 mm thick FEP (fluorinated ethylene propylene) membrane. for instance.2. (NH4 )2 SO4 . 20. specifies the following experimental conditions: S0 = 20 g/l.) for 24 h at 35◦ C and 300 rpm. N = 700 rpm and φ air = 0.0 g/l. and the average shear stress.0 vvm) are frequently utilised during filamentous fungal cultivations in bench-scale bioreactors.56. Two fermentation media with different compositions were utilised. γ av = 28. ring tensionmeter. 2. Liquid surface tension of the filtrated broth (σ ) was measured with a Fisher Scientific Co. which measured the impeller torque (T) at different rotational impeller speeds (N). Rheological properties Continuous on-line rheological measurements were recorded every 2 h of cultivation. Experimental apparatus. MgSO4 ·7H2 O. γ av . The assays were designated as follows: E20-7-3. performing a total of 10 l of fermentation broth. . The cultivations were carried out at different operational conditions.114 A. 1. USA) provided with four baffles in order to favour turbulence and to prevent vortex formation. The label E20-7-3.C.0. 1. et al.2.0. The contents of the flasks were transferred to the fermentor with 9 l of fermentation medium.08 ml/l) to both. E40-5-10. Lab. Readings of the oxygen (YO2 ) and carbon dioxide (YCO2 ) molar fractions in the outlet gas were furnished by gas analysers produced by Beckman Industrial (model 755) and Fuji Electric (model IR-730). E20-7-9. yeast extract. Dissolved oxygen concentration was measured by a sterilisable galvanic electrode (Mettler-Toledo InPro6000 Series). spores were initially germinated in five 1 l Erlenmeyer flasks. with addition of silicone antifoam (0. respectively. [15] based upon the original reports of Kemblowski and Kristiansen [19]. 2. after the polysaccharide in the sample had previously been converted to glucose through an enzymatic hydrolysis [18]. 7. / Biochemical Engineering Journal 8 (2001) 111–119 Growth medium was composed of (in g/l): total reducing sugars (TRS) from cassava flour and assayed as glucose. Inc. 2. In order to determine flow curves of fermentation broths. E20-5-6.0. pH 5. Samples were withdrawn each 3 h for analytical determinations.0.. E40-7-6 and E40-7-10. 10. For each fermentation. by using traditional reference curves and correlations to interpret data from a purpose-built torque meter based on flat strain gauges of 120 resistance. all fermentation broths at different cultivation times.2% of its final value when exposed to a step change in oxygen concentration. the K value decreases suddenly. . 3. the fermentation broth was pumped out of the bioreactor through silicone rubber tubing and into the impeller rheometer by a peristaltic pump. n The power law model (τav = Kγav ) was fitted to on-line experimental data and the rheological properties. non-Newtonian fluids of similar rheological characteristics to the fermentation broths were used [20]. without causing particle settling or even disturbing the performance of the cultivation. consistency index (K) and flow behaviour index (n). immediately after the carbon source is exhausted (∼27 h). were estimated. in order to allow good measurements.4. as proposed by Metzner et al. every hour during cultivation. to avoid frictional losses in the mechanical seal. behaved as non-Newtonian pseudoplastic fluids. obtained for the experimental system used in cultivations: Pg = 0. [21] for non-Newtonian pseudoplastic fluids.832 2 P0 ND3 i Q0. After each cultivation the electrode sensitivity (ke ) was determined in triplicate assays utilising xanthan gum solution 0. showing that on-line rheological measurement is a consistent and reliable technique for mycelial cultivations. Rheological behaviour of fermentation broths Rem = (10) where k = 11. [23]. proposed by Michel and Miller [22]. The new device was connected to the stirrer shaft inside the fermentor. based on the traditional dynamic method taking into consideration the electrode sensitivity (ke ) [24]. Aseptic conditions were ensured by introducing sterile air through the glass tubing next to the head of the vessel.3 and 0. Significant changes in the rheological parameters. from the mass balance for dissolved oxygen as follows: kL a = QO2 X C∗ − C (14) where C is the dissolved oxygen concentration in the broth at the steady-state given by the galvanic electrode and C∗ is the dissolved oxygen saturation concentration in the broth estimated by the method proposed by Schumpe et al. 2. especially when measurements are taken frequently. 3. NP = P0 ρN 3 Di5 ρN 2−n Di2 K(k n−1 ) (9) The inlet molar gas flow rate (nin ) was measured utilis˙ ing a mass flowmeter model 5811-N (Brooks Instrument Division). an added feature of the on-line technique was its ability to accurately anticipate the instant at which the culture medium is depleted of carbon source.5. probably as a consequence of both hyphae fragmentation and lysis. The electrode sensitivity (ke ) is defined as the inverse of the time taken for the electrode to reach 63. Good fits between the power law model and the experimental data were achieved.C. were observed as the fermentations proceeded: K increased rapidly while n decreased to values between 0. and the outlet molar gas flow rate (nout ) was ˙ calculated from the nitrogen mass balance in the gas phase by the following equation: nout = ˙ 0.96 to 72.A. Ungassed power consumption (P0 ) was obtained through a graph of power number (NP ) as a function of modified Reynolds number (Rem ). Interestingly. et al. 3 for the run E40-7-6. In order to obtain the reference curves and correlations.79nin ˙ out out 1 − YO2 − YCO2 (13) The volumetric oxygen transfer coefficient (kL a) could be calculated for the steady-state condition. By the gas balancing method. Oxygen transfer Global oxygen uptake rate (QO2 X) as well as the volumetric oxygen transfer coefficient (kL a) were obtained by both steady-state and dynamic methods. fluid consistency index (K) and flow behaviour index (n) as depicted the Fig. Fig. QO2 X was determined from an oxygen mass balance in the gas phase by the following expression: QO2 X = out nin YO2 − nout YO2 ˙ int ˙ V (12) With the average shear rate (γ av ) ranging from 0.4% w/v at 35◦ C to simulate the fermentation broth.5. As can be observed in Fig. / Biochemical Engineering Journal 8 (2001) 111–119 115 For these continuous on-line rheological measurements. Badino Jr.56 0.1. Gassed power consumption (Pg ) was estimated through a traditional correlation. Power consumption Ungassed and gassed power consumptions were estimated under the previously mentioned different operating conditions (N and Q). 2 illustrates typical flow curves (rheograms) obtained at different times for the run E40-7-6. The volumetric oxygen transfer coefficient (kL a) was also evaluated through an alternative method.27 s−1 .44 (11) 2. under the conditions considered. The average residence time in the loop was fixed at 90 s. Results and discussion 3.6. The outlet of the impeller shaft in the rheometer was provided with a rotating labyrinth seal. dynamic methods for determinations of kL a are useful only when the dissolved oxygen concentration is fairly above the critical value (Ccrit ).5 mmol O2 g−1 h−1 . utilising glucose as the main carbon source. the simultaneous use of the two measuring methods allowed reliable determinations of kL a over a wide range (60. / Biochemical Engineering Journal 8 (2001) 111–119 Fig.39 ).2. Characteristics of oxygen uptake and oxygen transfer Typical time course profiles of specific oxygen uptake rate (QO2 ) and of dissolved oxygen concentration (C) obtained during an experiment with oxygen limitation (E40-5-2) is shown in Fig. should be used in a complementary manner: while the gas balancing method provides accurate measurements mainly after the cell concentration reaches higher values.257 Pa s and the estimated maximum value of ungassed power consumption (P0 ) was 187 W.837γav 0. It is known that besides the agitation (N) and aeration (Q) conditions. in Fig. which agrees very well with the present results. 5. The relative surface tension of the filtrated broth presented an ascendant behaviour. Nevertheless. Badino Jr.04. Fig. Influence of apparent viscosity (µap ) and relative surface tension of filtrated broth (σ /σ w ) on the kL a during run E40-5-10 (γ av = 95 s−1 ). for lower values. when the differences in oxygen composition between inlet and outlet gas are quite small and the levels of dissolved oxygen concentration are very high. 4. et al. 3. both cultivating Aspergillus niger strains. Typical flow curves obtained at different times of the run E40-7-6 0. Considering all runs. the alternative dynamic method is particularly useful to evaluate kL a at the beginning of the fermentation. 4. the maximum values of specific oxygen uptake rate (Qmax ) ranged from 2. found Qmax O2 values in the range 3–4 mmol O2 g−1 h−1 .261γav .60 0. Metwally et al. Values of apparent viscosity (µap ) varied between 0. 22 h: τav = 0. 5 the time course of the relative surface tension of the filtrated broth (σ /σ w ) is depicted.8 to O2 4. varying from 0.43 0.1–768 h−1 ) showing that the gas balancing and the alternative dynamic method taking into account the electrode response time.897 to 0. where σ w = 7.257 Pa s in the time interval from 0 to 37 h of cultivation. the gas balancing method would be more appropriate [24].554γav Fig.47 (10 h: τav = 0. . 16 h: τav = 0. In addition. It can be observed that kL a decreased from 381 to 124 h−1 when µap increased from 0. a variable that negatively affects kL a is the broth apparent viscosity (µap ). 3. Variation in substrate concentration (S) and rheological parameters K and n during run E40-7-6. Time profiles of specific oxygen uptake rate (QO2 ) and of dissolved oxygen concentration (C) for the experiment E40-5-2.013 and 0. With respect to kL a determinations.943 for the same time period considered before. The strong influence of the broth apparent viscosity (µap ) on the volumetric oxygen transfer coefficient (kL a) during experiment E40-5-10 is shown in Fig. 5.019γav . Such variation is relatively modest and it is probably due to the consumption Fig. as well as Shuler and Kargi [26]. 2. because it offers resistance to the oxygen transfer from the gaseous to the liquid phase.013 to 0.116 A.10−2 N m−1 is the surface tension of water at 35◦ C [27].C. a situation at which the gas balancing and other methodologies are often inadequate. [25]. and 30 h: τav = 1. and Pg ). 6.12 µap vs −0. 6–9 illustrate the quality of the fits. as described by Cooper et al.45(Rem )0. [4] Ryu and Humphrey [9] Yagi and Yoshida [12] Zlokarnik [14] Regression coefficient (R2 ) 0. it can also be observed that the more complex is the correlation.20 (σ ∗ )−0.92 0. No convergence problems were found in non-linear regression and all confidence intervals.74 σ vs Pgi ∗ 0. The fitted correlations.45 (Sc)−0. The simultaneous use of the two methods. GB: gas balancing for kL a determination). GB: gas balancing for kL a determination). GB: gas balancing for kL a determination). four classical correlations have been utilised to correlate the volumetric oxygen transfer coefficient (kL a) with the operation variables (N. indicating that any of the adjusted models can be used to estimate.90 0. also the better is the quality of the fit (higher R2 values). show that good fits were obtained for all the correlations.25 of the dissolved nutrients from the original culture medium as the fermentation proceeds. Yagi and Yoshida [12] and Zlokarnik [14]. [4]. are presented in Table 1. . 8.94 0.C.43 (µap )−0. as well as the figures.44(Pg /V )0. with the obtention of similar values in the same operating conditions. et al.96 117 Experimental values 286 305 316 318 −0. The correlations were fitted to the experimental values and the parameters were estimated through Marquardt’s procedure that utilises the least squares non-linear regression [28].A. were below 25% of the estimated values. with good precision. Fig. 3. computed for the 95% of probability. Q. However.89(Pg /V )0.53 Q −1 kL a = 1.43 (Fr)0.47 (vs )0. Badino Jr.02 NDi Sh∗ = 1. Ryu and Humphrey [9]. the volumetric oxygen transfer coefficient (kL a) in these cultivations. The data in Table 1. / Biochemical Engineering Journal 8 (2001) 111–119 Table 1 Correlations for the volumetric oxygen transfer coefficient (kL a) Correlation kL a = 41. 7. allowed a great number of kL a values to be obtained as previously discussed. Comparison of the experimental data with those calculated using the correlation proposed by Cooper et al. Figs.3. being less complex because it only considers the effects of the gassed power consumption per Fig.53 (vs )0. The criterion for the best fit and parameter optimisation was the sum of squares of residuals (SSR). together with the respective correlation coefficients (R2 ) and numbers of experimental values used in the regressions. for instance. Correlations for kL a As mentioned before. Comparison of the experimental data with those calculated using the correlation proposed by Ryu and Humphrey [9] (DM: dynamic method.39 kL a = 19.83 (Sc)0. Fig. [4]. [4] (DM: dynamic method. The correlation proposed by Cooper et al. geometric parameters of the system (V and Di ) and physical properties of the broths (µap and σ ). gas balancing (GB) and dynamic method (DM). Comparison of the experimental data with those calculated using the correlation proposed by Yagi and Yoshida [12] (DM: dynamic method.40 Vi Q Reference Cooper et al. in: Proceedings of the 2nd International Conference on Bioreactor Fluid Dynamics. Four classical correlations found in the literature.80 and 0. R. kL a is also correlated with the physical properties of the broth (apparent viscosity and liquid surface tension). 62 (1984) 334. that the utilisation of such correlations means the necessity of more complex analytical determinations. In particular.A. Advances in Bioprocess Engineering. J. 157. [2] J. Badino Jr. Badino Jr. Shin. Catalan. [7] A. observing that the fit was even better for the more complex correlations. Also. Jurecic. are within the ranges of values mentioned by Kawase and Moo-Young [29] for non-Newtonian systems. Fernstrom. 13 (1993) 59. However.O.V. Montes. Hokka. presented values similar to those obtained by Jurecic et al. Ryu. Acta Biotechnol. M. Kluwer Academic Publishers.A. T. GB: gas balancing for kL a determination). Biochem. Berovic. unit volume (Pg /V) and the superficial gas velocity (v s ) on kL a.J. Dunn.R. Despite its simplicity. 10 (1996) 679. I. 35 (1990) 1011.84. V.C. V. which is not always possible.S. 4. et al. Bioeng. Ferment. considering experimental data obtained with Aspergillus cultivation in quite distinct operational conditions. [8] F.J. 1988.30 and c3 = −0. awamori in a bench scale fermentor. Eng.C. M. S. 35 (1990) 1034. which are 0. licheniformis in pilot and industrial scales (a3 = 0. in the literature investigated no works have been found that present measurements of parameters such as the surface tension of the filtrate (σ ) during cultivation. Biotechnol. / Biochemical Engineering Journal 8 (2001) 111–119 parameters obtained from the correlation of Zlokarnik [14]. Technol.12) is very different from that obtained in the original work (c2 = −0.50). in some of these correlations. which relate dimensionless variables. Miller. Chem. Hong. Gavrilescu. it should be observed that the parameters estimated by the regressions are very close to the values found in the literature. such as those proposed by Yagi and Yoshida [12] and by Zlokarnik [14]. which are time dependent during the fermentation process. a1 = 0. R. . Steiner. M. Conclusions Fig. respectively.20 < b1 < 0. [4] C.47 and b1 = 0. Biochem. 1994. Griot. the correlation proposed by Ryu and Humphrey [9] gave also a good fit. Biotechnol. however. it is more convenient to use more complex correlations. J. However. Eng. for convenient application. E. Goméz. The The main objective of this work was to investigate the influence of operating conditions on the rheological properties of the broth and on the oxygen transfer during batch cultivations of A. W. because no published work has been found that applies this correlation to non-Newtonian fermentation broths. Ind. [5] M. both of the values for the constant c2 were coherently negative. Heinzle.M. It is obvious. Fox. p. [9] D.S. employing non-Newtonian fermentation broths of B. practically as good as the more complex correlations proposed by Yagi and Yoshida [12] and by Zlokarnik [14] that need the knowledge of additional variables of the broth.Y. J. Chem. Galan. Biotechnol.86). Ryu and Humphrey [9] employed the Bingham plastic model.37 < a1 < 0. which are a result of carefully elaborated methodologies implemented in the cultivations. Linek. 34 (1999) 549. ı [11] C. 17.D. J. M. fitted the data less well than those correlations that consider the effects of the physical properties of the broth on kL a. which correlate the volumetric oxygen transfer coefficient (kL a) with the process operational variables (N.. References [1] M. J. Q and Pg ) and the geometric parameters of the system has been utilised. J. However. as expected. such as apparent viscosity (µap ) and surface tension (σ ). Sinkule.118 A. Bourne. Good fits were obtained for all the correlations tested.39. Comparison of the experimental data with those calculated using the correlation proposed by Zlokarnik [14] (DM: dynamic method. E. [6] V. Technol. In addition.35. The parameters of the correlation proposed by Cooper et al. indicating an inverse proportionality between kL a and µap . C. [3]. b3 = −0. A. The Can. M. The values obtained for the parameters from the correlation of Yagi and Yoshida [12] could not be compared with values found in the literature. [10] F. Humphrey. Roman. Cooper. p. 50 (1972) 424. J. Smith. Saner. Eng. [4].A. Finally. Lee. The Netherlands. Efimov. Lilly. [3] R. if we intend to use a kL a correlation in the design or scaling-up of conventional bioreactors. 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