A kLa identification technique for a dynamic model of the coupled system: Air-lift fermenter — oxygen probes

The time delay of oxygen probe response to the signal from a fermenter makes identification of the volumetric oxygen transfer coefficient k_La by the dynamic method more complicated. A coupled model involving the transient-state oxygen balance of the fermenter together with the dynamic model of the oxygen probe must be then formulated, solved and identified. In this paper two simple models of air-lift loop fermenters have been proposed and a coupled mathematical model of the fermenter – oxygen probe system has been developed. The identification procedure was used to estimate k_La values in the fermenter with internal circulation flow on the basis of experimental measurements. A comparison of evaluated and experimental indications of the probes placed at various heights of the column proves that the model presented gives a possibility of the first-step approximation of k_La in loop fermenters.     

On-line estimation of kLa by an analog computer

A new method was developed for estimating the volumetric oxygen transfer coefficient, k_La, in a fermentor. Various methods were investigated for the on-line estimation of k_La with an analog computer employing a steepest-descent calculation technique. The method by which k_La is estimated (by minimizing the error residue of the model) was found to be very applicable. A method for the simultaneous estimation of the volumetric oxygen transfer coefficient and respiration rate in biological systems is also presented.     

Desorption of carbon dioxide from fermentation broth

Rates of CO₂ desorption from fermentation broths under actual operating conditions were determined by measuring the CO₂ partial pressure in the exit gas. The concentrations of CO₂ physically dissolved in the broths were measured by the so-called tubing method. Values of k_La for CO₂ desorption calculated from these values agreed well with the k_La values for oxygen absorption corrected for the difference in gas diffusivities. The dissolved CO₂ concentration in the broth, which seems to bean important operating parameter, can easily be estimated from the CO₂ partial pressure in the exit gas, a more easily measurable quantity, if the k_La value is known. For a given value of k_La, assumption of perfect mixing or plug flow in the gas phase made little difference in the calculated values of the dissolved CO₂ concentration, indicating that the gas phase was probably in between perfect mixing and plug flow. In industrial fermentors, the CO₂ partial pressure in the exit gas can practically be assumed to be in equilibrium with the dissolved CO₂ concentration.     

Vergleich von Messungen des kLa-Wertes nach der stationären und der dynamischen Methode bei der Fermentation von L-Lysin und Turimycin

The calculation and scale-up of fermentation processes need k_La as one of the most important engineering data. There are two methods to determine k_La depending on power input, aeration rate and the properties of the fermentation broth: static with a balance between air supply and exit, dynamic gassing out with following the changes of dissolved oxygen concentration during periods of air off and a following air on. Within early intervals of fermentation time the data from both methods agree well, while for later time intervals the dynamic method always gives much lower values for k_La than static. The only explanations for this phenomenon are quick changes in the oxygen metabolism or an enzymatic storage of oxygen. For both gassing out and saturation period it is possible to calculate the same absolute amounts of this additional oxygen.     

Oxygen transfer in Streptomyces fermentation broths

The oxygen transfer coefficient has been investigated in S. noursci and S. lavendulae fermentation broths obtained from fermentors of different operating volumes (61., 30001., 20,0001.). Fermentors had K_La_s values ranging from 1.0 to 17.0 min^?1, calculated from sulphite oxidation rates. The dynamic measurement of the volumetric oxygen transfer coefficient. (K_La) has been performed in the different fermenting systems. As the fermentation progressed, especially in the first stages, K_La values have decreased in both fermentations and in each system of fermentors. In order to characterise the whole fermenting system an average K_La_s was calculated from the obtained K_La values. The average K_La grew with increasing K_La_s values and ranged from 0.03 to 3.72 min^?l. Some factors possibly having an influence on the, change of K_La have been studied. The oxygen transfer coefficients of the broths have been measured in falling films and ranged from 0.05 to 0.4 cm min^?1. The flow conditions have been characterized by Reynolds numbers of broths varying between 1.0 and 60.0. The average thickness of the falling films have been measured and plotted against Reynolds number. The Re⁺ which is the breaking-point of the plot increased as the fermentation proceeded. In the region of Re⁺ the values of the oxygen transfer coefficient increased rapidly. An approximate correlation could be established between the Re⁺ and the physical properties of fermentation broth.     

Mixing time and oxygen transfer characteristics of double draft tube airlift fermentor

Despite the increasing importance of airlift fermentors, very little published information is available on how the geometric configurations of the draft tubes and the air-sparging system affect the mixing and oxygen transfer characteristics of the fermentor. A 14-L air-lift fermentor was designed and build with a fixed liquid height to diameter ratio of 1.5 utilizing four equally spaced air jets at the bottom. Two jet orifice sizes were used, 1.27 and 3.81 mm i.d., and for each jet size the following four geometric configurations were used: Single inner concentric draft tube, single outer concentric draft tube, two concentric draft tubes, and no draft tubes where the fermentor was operated as a shallow bubble column. It was found that the presence of draft tubes stabilized liquid circulation patterns and gave systemically higher mixing times than those obtained in the absence of draft tubes. In addition, the double draft tube geometry resulted in higher mixing times than the single draft tubes. For the power unit volume range 20 to about 250 W/m³ the larger 3.81-mm orifices gave systemically higher k_L a values than the smaller 1.27-mm i.d. orifices. At 200 W/m³ the use of a single outer draft tube with the 3.81-mm orifices resulted in 94% increase in k_L a values over that obtained with no draft tubes. However, the effect of draft tube geometry on k_L a values when the 1.27-mm orifices were used was not significant. The air bubble formation characteristics at the jet orifices were found to be different, which reflected the differences observed in mass transfer and mixing characteristics. The power economy for oxygen transfer was found to be depend strongly on the orifice size and less on the geometric configuration of draft tubes.     

Using CFD simulations and statistical analysis to correlate oxygen mass transfer coefficient to both geometrical parameters and operating conditions in a stirred-tank bioreactor

Optimization of a bioreactor design can be an especially challenging process. For instance, testing different bioreactor vessel geometries and different impeller and sparger types, locations, and dimensions can lead to an exceedingly large number of configurations and necessary experiments. Computational fluid dynamics (CFD), therefore, has been widely used to model multiphase flow in stirred-tank bioreactors to minimize the number of optimization experiments. In this study, a multiphase CFD model with population balance equations are used to model gas–liquid mixing, as well as gas bubble distribution, in a 50 L single-use bioreactor vessel. The vessel is the larger chamber in an early prototype of a multichamber bioreactor for mammalian cell culture. The model results are validated with oxygen mass transfer coefficient (k_La) measurements within the prototype. The validated model is projected to predict the effect of using ring or pipe spargers of different sizes and the effect of varying the impeller diameter on k_La. The simulations show that ring spargers result in a superior k_La compared to pipe spargers, with an optimum sparger-to-impeller diameter ratio of 0.8. In addition, larger impellers are shown to improve k_La. A correlation of k_La is presented as a function of both the reactor geometry (i.e., sparger-to-impeller diameter ratio and impeller-to-vessel diameter ratio) and operating conditions (i.e., Reynolds number and gas flow rate). The resulting correlation can be used to predict k_La in a bioreactor and to optimize its design, geometry, and operating conditions.     

High density cultivation of plant cells in a new aeration-agitation type fermentor,maxblend fermentor®

The applicability of a new aeration-agitation type fermentor with a grid-paddle type impeller and a spiral-sparger, Maxblend Fermentor® (MBF) for high density cultivation of plant cells, was investigated. The MBF showed a high capacity for oxygen supply and extremely low hydrodynamic stress in aeration and mixing compared with a conventional fermentor (CF). When Oryza sativa cells were cultivated at a k_La of 20 h⁻¹, a high cell density cultivation of about 30 g dry cell weight per liter was accomplished in both fermentors and there were few differences in culture performance between the two. On the contrary, considerable differences were observed when Catharanthus roseus cells, which seemed to be sensitive to physical stress, were cultivated at a k_La of 20 h⁻¹ in both fermentors. The MBF exhibited excellent cell growth characteristics, achieving about 19 g dry cell weight per liter, because of its superior oxygen supply and low hydrodynamic stress in aeration and mixing in highly viscous cultures containing high density cells. In CF only about 9.5 g dry cell weight per liter was achieved because of its high hydrodynamic stress.     

kLa of stirred tank bioreactors revisited

By means of improved feedback control k_La measurements become possible at a precision and reproducibility that now allow a closer look at the influences of power input and aeration rate on the oxygen mass transfer. These measurements are performed online during running fermentations without a notable impact on the biochemical conversion processes. A closer inspection of the mass transfer during cultivations showed that at least the number of impellers influences mass transfer and mixing: On the laboratory scale, two hollow blade impellers clearly showed a larger k_La than the usually employed three impeller versions when operated at the same agitation power and aeration rate. Hollow blade impellers are preferable under most operational conditions because of their perfect gas handling capacity. Mixing time studies showed that these two impeller systems are also preferable with respect to mixing. Furthermore the widths of the baffle bars depict a significant influence on the k_La. All this clearly supports the fact that it is not only the integral power density that finally determines k_La.     

Enhancement of oxygen absorption into sodium sulfite solutions

Oxygen absorption enhancement in a sodium sulfite solution was studied in the absence and presence of copper catalyst both for absorption across the liquid surface in a stirred cell and for absorption from individual bubbles rising through a turbulent liquid. The enhancement factor was determined from the ratio of oxygen and argon mass transfer coefficients, measured under identical experimental conditions in the same batch of liquid. It has been found that the oxygen absorption is not chemically enhanced, as long as the mass transfer coefficient, k_L⁰, is high enough, i.e., higher than the value 1.4 × 10^?4 m sec^?1 for the sulfite solution we used. An analysis of our data as well as literature data indicates that the sulfite system is poorly suited for studies of the volumetric mass transfer coefficient of physical absorption (k_L⁰a) in fermentors, inasmuch as oxygen absorption can be chemically enhanced while the degree of enhancement depends on the operating conditions of batch aeration, as well as on the concentration of trace impurities with catalytic effects upon the sulfite solution used.     

Enhancement factor for oxygen absorption into fermentation broth

Values of the enhancement factor for oxygen absorption into fermentation broth, i.e., the ratio of the liquid phase mass transfer coefficients for oxygen absorption for both cases with and without respiration of microorganisms were predicted theoretically on the assumption of various cell concentration distributions. Calculations indicate that in the usual case the enhancement factor is only slightly or negligibly larger than unity, even when accumulation of microorganisms at or near the gas-liquid interface is assumed. Results of experiments with sparged-stirred fermentors on oxygen absorption into fermentation broths containing resting and growing cells of Candida tropicalis confirmed the theoretical prediction. Except for extreme cases, the effect of respiration of microorganisms on k_La, values can practically be ignored.     

Comparison of oxygen mass transfer coefficient in simple and extractive fermentation systems

Aeration and agitation are important variables to ensure effective oxygen transfer rate during aerobic bioprocesses; therefore, the knowledge of the volumetric mass transfer coefficient (k_La) is required. In view of selecting the optimum oxygen requirements for extractive fermentation in aqueous two-phase system (ATPS), the k_La values in a typical ATPS medium were compared in this work with those in distilled water and in a simple fermentation medium, in the absence of biomass. Aeration and agitation were selected as the independent variables using a 2² full factorial design. Both variables showed statistically significant effects on k_La, and the highest values of this parameter in both media for simple fermentation (241 s⁻¹) and extractive fermentation with ATPS (70.3 s⁻¹) were observed at the highest levels of aeration (5 vvm) and agitation (1200 rpm). The k_La values were then used to establish mathematical correlations of this response as a function of the process variables. The exponents of the power number (N³D²) and superficial gas velocity (V_s) determined in distilled water (α = 0.39 and β = 0.47, respectively) were in reasonable agreement with the ones reported in the literature for several aqueous systems and close to those determined for a simple fermentation medium (α = 0.38 and β = 0.41). On the other hand, as expected by the increased viscosity in the presence of polyethylene glycol, their values were remarkably higher in a typical medium for extractive fermentation (α = 0.50 and β = 1.0). A reasonable agreement was found between the experimental data of k_La for the three selected systems and the values predicted by the theoretical models, under a wide range of operational conditions.     

The optimization of L-lysine fermentation and a mass transfer model

The efficiency of L-lysine biosynthesis is essentially determined by the power input and aeration ratio in the stirred fermenter. A mass transfer model was developed by means of the results of lysine fermentations in four geometrically similar fermenters with working volumes of 10 1, 50 1, 100 1 and 2500 1 which allows the optimization of lysine fermentation from the energetical point of view. The usefullness of this k_La-model is demonstrated with an example where the power input for an unknown fermenter is calculated.     

Model for oxygen transfer in a shake flask

The shake flask is a very common and useful tool for the study of submerged fermentations on a small scale. However, the oxygen supply may easily become a limiting factor. A model for the aeration in shake flasks is presented that enables one to predict whether in the course of an experiment the oxygen supply is becoming a growth-limiting factor or not. The results of measurements of the transfer coefficient of a cotton plug and the oxygen mass-transfer coefficient k_la are also given.     

The volumetric oxygen mass transfer coefficient in antibiotic biosynthesis liquids

This paper approaches the problem of oxygen mass transfer. This transfer is in antibiotic biosynthesis liquids produced by microorganisms belonging to the actinomycete and fungi classes, which exhibit a shear thinning non-Newtonian rheological behaviour. The volumetric oxygen mass transfer coefficients in these liquids (k_L a_b) change during biosynthesis processes. The change is mainly due to rheological parameter modifications, such as increasing the consistency index (K) and decreasing the flow behaviour index (n). The values of k_L a_b were 3.0–6.5 times lower than those recorded in water, and their decreasing depended on the k_L a values obtained without biological liquid and on the nature of fermentation broths, as well. Starting from experimental data, two correlations were established between k_L a_b and P/V,υ_SG and P/V,υ_SG, N, respectively. These correlations contain a dimensionless factor (η_am/η_g), which takes into account the rheological properties of the liquid phase and offers the possibility for a fast and sufficiently accurate estimation of k_L a_b. The empirical correlations developed in the paper correspond reasonably well with the relatively wide variety of experimental data, as in the model proposed by PEREZ and SANDALL , and allow for the comparison of the fermentation batches of the same or different microorganisms; also, they may be applied to the workings of design, scale-up, control and monitoring of bioreactors.     

Gas–liquid mass transfer in an up-flow cocurrent packed-bed biofilm reactor

Gas–liquid mass transfer was investigated in an up-flow cocurrent packed-bed biofilm reactor. In aerobic processes gas–liquid mass transfer can be considered as a key operational parameter as well as in reactor scale-up. The present paper investigates the influence of the liquid phase mixing in the determination of the volumetric gas–liquid mass transfer coefficient (k_La) coefficient. Residence time distribution (RTD) experiments were performed in the reactor to determine the flow pattern of the liquid phase and to model mathematically the liquid phase mixing. The mathematical model derived from RTD experiments was used to evaluate the influence of the liquid mixing on the experimental estimation of the (k_La) in this reactor type. The methods used to estimate the k_La coefficient were: (i) dynamic gassing-out, (ii) sulphite method, and (iii) in-process estimation through biological conversion obtained in the reactor. The use of standard chemical engineering correlations to determine the k_La in this type of bioreactors is assessed. Experimental and modelling results show how relevant can be to take into consideration the liquid phase mixing in the calculations of the most-used methods for the estimation of k_La coefficient. k_La coefficient was found to be strongly heterogeneous along the reactor vertical axis. The value of the k_La coefficient for the packed-bed section ranged 0.01–0.12 s⁻¹. A preliminary correlation was established for up-flow cocurrent packed-bed biofilm reactors as a function of gas superficial velocity.     

Oxygen mass-transfer performance of low viscosity gas-liquid-solid system in a split-cylinder airlift bioreactor

The O₂ mass-transfer coefficient, k _L a, decreased by 20% when the viscosity of a simulated broth increased from 1.38 × 10^–3 to 3.43 × 10^–3 Pa s in a split-cylinder airlift bioreactor with a broth volume of 41 l. When the paper pulp concentration was below 10 g l^–1, k _L a hardly changed. While at 30 g l^–1, k _L a decreased by 56%. C₂O₄ ^2– and Na⁺ were found to have some effect on the k _L a value.     

Effects of hydrocarbon additions on gas-liquid mass transfer coefficients in biphasic bioreactors

The effects of aliphatic hydrocarbons (n-hexadecane andn-dodecane) on the volumetric oxygen mass transfer coefficient (k _L a) were studied in flat alveolar airlift reactor and continuous stirred tank reactors (CSTRs). In the flat alveolar airlift reactor, high aeration rates (>2 vvm) were required in order to obtain efficient organic-aqueous phase dispersion and reliablek _L a measurements. Addition of 1% (v/v)n-hexadecane orn-dodecane increased thek _l a 1.55-and 1.33-fold, respectively, compared to the control (superficial velocity: 25.8×10⁻³ m/s, sparger orifice diameter: 0.5 mm). Analysis of the gas-liquid interfacial areaa and the liquid film mass transfer coefficientk _L suggests that the observedk _L a increase was a function of the media's liquid film mass transfer. Addition of 1% (v/v)n-hexadecane orn-dodecane to analogous setups using CSTRs led to ak _L a increase by a factor of 1.68 and 1.36, respectively (superficial velocity: 2.1×10⁻³ m/s, stirring rate: 250 rpm). These results propose that low-concentration addition of oxygen-vectors to aerobic microbial cultures has additional benefit relative to incubation in purely aqueous media.     

Xylitol Production from D‐Xylose at Different Oxygen Transfer Coefficients in a Batch Bioreactor

Conversion of D‐xylose to xylitol by Candida boidinii NRRL Y‐17213 was studied under anaerobic and oxygen limited conditions by varying the oxygen transfer coefficient k_La. Shake flask experiments were used to provide the preliminary information required to perform experiments in a bioreactor. The yeast did not grow under fully anaerobic conditions, but anaerobic formations of xylitol, ethanol, ribitol, and glycerol were observed as well as D‐xylose assimilation of 11 %. In shake flasks, with an initial D‐xylose concentration of 50 g/L, an increase in k_La from 8 to 46 h^–1 resulted in a faster growth, higher rate of substrate uptake and lower yields of products. The highest xylitol productivity (0.052 g/L h) was attained at k_La = 8 h^–1. At k_La = 46 h^–1, 98.6 % of D‐xylose was consumed and mainly converted to biomass. Using 130 g/L D‐xylose, k_La was varied in the fermenter from 26 to 78 h^–1. The percentage of consumed D‐xylose increased from 31 % at k_La = 26 h^–1 to 93–94 % at all other aeration levels. Biomass yield increased with k_La, whereas ethanol, ribitol, and glycerol yields exhibited an opposite dependence on the oxygenation level. The most favorable oxygen transfer coefficient for xylitol formation, in the fermenter, was k_La = 47 h^–1 when its concentration (57.5 g/L) surpassed ethanol accumulation by 3.6‐fold, and the glycerol plus ribitol by 10‐fold. Concurrently, xylitol yield and productivity reached 0.45 g/g and 0.26 g/L h, respectively. The volumetric xylitol productivity was affected more by changes in the aeration than the corresponding yield.     

A new dynamic model for highly efficient mass transfer in aerated bioreactors and consequences for kLa identification

Gas–liquid mass transfer is often rate‐limiting in laboratory and industrial cultures of aerobic or autotrophic organisms. The volumetric mass transfer coefficient k_La is a crucial characteristic for comparing, optimizing, and upscaling mass transfer efficiency of bioreactors. Reliable dynamic models and resulting methods for parameter identification are needed for quantitative modeling of microbial growth dynamics. We describe a laboratory‐scale stirred tank reactor (STR) with a highly efficient aeration system (k_La ≈ 570 h^?1). The reactor can sustain yeast culture with high cell density and high oxygen uptake rate, leading to a significant drop in gas concentration from inflow to outflow (by 21%). Standard models fail to predict the observed mass transfer dynamics and to identify k_La correctly. In order to capture the concentration gradient in the gas phase, we refine a standard ordinary differential equation (ODE) model and obtain a system of partial integro‐differential equations (PIDE), for which we derive an approximate analytical solution. Specific reactor configurations, in particular a relatively short bubble residence time, allow a quasi steady‐state approximation of the PIDE system by a simpler ODE model which still accounts for the concentration gradient. Moreover, we perform an appropriate scaling of all variables and parameters. In particular, we introduce the dimensionless overall efficiency κ, which is more informative than k_La since it combines the effects of gas inflow, exchange, and solution. Current standard models of mass transfer in laboratory‐scale aerated STRs neglect the gradient in the gas concentration, which arises from highly efficient bubbling systems and high cellular exchange rates. The resulting error in the identification of κ (and hence k_La) increases dramatically with increasing mass transfer efficiency. Notably, the error differs between cell‐free and culture‐based methods of parameter identification, potentially confounding the determination of the “biological enhancement” of mass transfer. Our new model provides an improved theoretical framework that can be readily applied to aerated bioreactors in research and biotechnology. Biotechnol. Bioeng. 2012; 109: 2997–3006. © 2012 Wiley Periodicals, Inc.