- Open Access
Correlation between mass transfer coefficient kLa and relevant operating parameters in cylindrical disposable shaken bioreactors on a bench-to-pilot scale
© Klöckner et al.; licensee BioMed Central Ltd. 2013
- Received: 23 May 2013
- Accepted: 4 November 2013
- Published: 2 December 2013
Among disposable bioreactor systems, cylindrical orbitally shaken bioreactors show important advantages. They provide a well-defined hydrodynamic flow combined with excellent mixing and oxygen transfer for mammalian and plant cell cultivations. Since there is no known universal correlation between the volumetric mass transfer coefficient for oxygen kLa and relevant operating parameters in such bioreactor systems, the aim of this current study is to experimentally determine a universal kLa correlation.
A Respiration Activity Monitoring System (RAMOS) was used to measure kLa values in cylindrical disposable shaken bioreactors and Buckingham’s π-Theorem was applied to define a dimensionless equation for kLa. In this way, a scale- and volume-independent kLa correlation was developed and validated in bioreactors with volumes from 2 L to 200 L. The final correlation was used to calculate cultivation parameters at different scales to allow a sufficient oxygen supply of tobacco BY-2 cell suspension cultures.
The resulting equation can be universally applied to calculate the mass transfer coefficient for any of seven relevant cultivation parameters such as the reactor diameter, the shaking frequency, the filling volume, the viscosity, the oxygen diffusion coefficient, the gravitational acceleration or the shaking diameter within an accuracy range of +/− 30%. To our knowledge, this is the first kLa correlation that has been defined and validated for the cited bioreactor system on a bench-to-pilot scale.
- Dimensional analysis
- Maximum oxygen transfer capacity
- Orbitally shaken
- Plant cell suspension cultures
- Volumetric mass transfer coefficient
The success of new biopharmaceuticals highly depends on their potential to compete with established products. Parameters such as a fast time to market, cost effectiveness and manufacturing flexibility are key issues that need to be considered while maintaining product quality . Using disposable equipment can help reduce investment costs and increase flexibility and process safety  ultimately leading to enhanced competitiveness of the products. Consequently, disposable bioreactors are increasingly being used in biotechnological production processes within the past ten years .
Today, one of the most popular disposable bioreactors is the WAVE cultivation system that was first described in 1976 [4, 5]. Since then, various other types of disposable cultivation systems for different applications have been developed. A wide range of different reactor sizes, starting with disposable screening systems in microliter scale, up to bioreactors with capacities of several cubic meters are on the market . Available cultivation systems and their applications are described in several review articles [2, 3, 6, 7].
Despite the increasing usage of disposable cultivation systems, only few scientific publications have reported about their characterization with respect to power input, oxygen transfer and mixing performance . By contrast, stirred stainless steel bioreactors have been extensively characterized and optimized over the past 60 years . A direct design transfer from stainless steel to stirred disposable bioreactor systems is not feasible because of different properties of the applied materials. For instance, it is not possible to keep geometric similarity between a stirrer made of stainless steel and a disposable stirrer, due to the reduced strength and rigidity of the disposable polymer material. New agitation concepts for disposable bioreactors are desired to simplify their design and make them more cost-efficient . Surface aerated reactors without complex built-in components fulfil the requirement for a cost-efficient reactor design . In these systems, oxygen transfer and power input are either introduced by a wave, rocking or shaking motion of the bioreactor . Orbitally shaken bioreactors are advantageous due to their well-defined liquid distribution that allows a precise characterization of power input and oxygen transfer. The magnitude of volumetric power input in these systems is comparable to that of conventional stirred tank reactors [10, 11], indicating excellent mixing characteristics also for liquids at elevated viscosity.
In the 50 mL scale, the orbitally shaken TubeSpin Bioreactor was developed and tested as a high throughput system for mammalian cell cultivation [12, 13]. On a larger scale, different studies reported about power input [10, 11, 14, 15], mixing properties  and scale-up performance [15, 17–20] of disposable orbitally shaken reactors. In several studies the volumetric mass transfer coefficient kLa was identified as one of the main parameters for successful scale-up and transfer of cultivation conditions from stirred tank to disposable shaken reactors [13, 18, 21, 22]. Zhang et al.  also described a helical track attached on the inner reactor wall as a potential means to increase the mass transfer coefficient. However, a scale- and volume-independent kLa correlation for cylindrical orbitally shaken bioreactors has not been described so far. Thus, the aim of this current study is to experimentally determine such a kLa correlation in cylindrical disposable shaken bioreactors with volumes from 2 L up to 200 L and apply it to the cultivation of suspended plant cells.
This set of dimensionless numbers was also proposed by Henzler and Schedel  to develop a scale-independent correlation for the mass transfer coefficient in shake flasks. The applied numbers for surface aerated bioreactors differ from dimensionless numbers that are commonly used to describe the mass transfer in bubble aerated bioreactors because the principle of mass transfer differs fundamentally in both systems. In contrast to surface aerated orbitally shaken bioreactors, mass transfer in bubble aerated bioreactors depends on the amount, size, break-up and coalescence of gas bubbles. The characteristics of gas bubbles are strongly influenced by the volumetric power input, which is therefore commonly used as a parameter for kLa correlations for bubble aerated bioreactors. These aspects are not relevant for the utilized surface aerated bioreactors that are operated without bubble aeration.
Each exponent in Eq. 1 has to be determined separately by empirically varying the corresponding dimensionless number.
Influence of the critical circulation frequency
According to Eq. 2, the critical circulating frequency Nc is a function of the inner reactor diameter d, the filling volume VL and the acceleration of gravity g.
Out-of-phase operation in orbitally shaken bioreactors
The transition from in-phase to out-of-phase operation in orbitally shaken bioreactors is accompanied by a strong decrease in power input and oxygen transfer [30–32]. Liquids with high viscosities in systems with low shaking diameters are prone to out-of-phase operation as described in several studies for shake flasks [32, 33]. Thus, a minimum value for the ratio of shaking diameter (d0) to reactor diameter (d), expressed by the Geometric number, is required to avoid an undesired out-of-phase operation in cylindrical orbitally shaken bioreactors.
Defining the kLa correlation
Oxygen solubility, diffusion coefficient and kinematic viscosity for the applied solutions at 25°C
Composition of the solution
Solubility (LO2) [mol/(m3∙bar)]
Diffusion coefficient for oxygen () [m2/s]
Kinematic viscosity (ν) [m2/s]
2.14 · 10-9
0.89 · 10-6
0.5 mol/L Na2SO3
1.897 · 10-9
1.10 · 10-6
1 · 10-7 mol/L CoSO4
0.012 mol/L phosphate buffer (pH 8)
1 mol/L Na2SO3
1.688 · 10-9
1.48 · 10-6
1 · 10-7 mol/L CoSO4
0.012 mol/L phosphate buffer (pH 8)
An exponent of 2.03 for the influence of the reactor diameter d and 1 for the influence of the shaking frequency n were specified in Eq. 5 for shake flasks. Different characteristics with respect to the oxygen transfer are based on differences in the shape of the reactor systems. The conical shape of the shake flask wall prevents a strong expansion of the liquid surface with increasing shaking frequency and vessel size. This is not the case in cylindrical orbitally shaken bioreactors, resulting in higher exponents for the corresponding variables n and d.
The application of dimensionless numbers requires geometrical similarity. The utilized reactor systems for determining the exponents in Eq. 4 had a cylindrical reactor wall with flat bottom geometry. Thus, Eq. 4 is only applicable for such cylindrical bioreactors. The developed kLa correlation can be used to calculate suitable shaking parameters for a sufficient oxygen supply by calculating the maximum oxygen transfer capacity (OTRmax) according to Eq. 10. To avoid an oxygen limitation during scale-up it is essential to select shaking parameters where the OTRmax is higher than the oxygen uptake of the culture.
A similar trend of the OTR signal was achieved at a shaking frequency of n = 160 rpm in the 10 L reactor system compared to the 250 mL shake flask. A plateau of the OTR signal, as it usually appears during cultivations with oxygen limitation , was not observed.
A universally applicable equation was defined for calculating the mass transfer coefficient kLa in disposable cylindrical bioreactors with volumes ranging from 2 L to 200 L. Important parameters as the critical circulation frequency for the induction of liquid motion as well as in-phase operation conditions were considered during the experiments and the data evaluation. It was demonstrated that the final kLa equation can be applied to determine the OTRmax of cylindrical bioreactors and, in this way, enables the identification of suitable cultivation conditions such as for plant cell suspension cultures. As a result, the derived kLa equation is an essential tool for the correct application of cylindrical disposable shaken bioreactors on a bench- to pilot-scale.
Cultivation and agitation systems
Properties of the utilized disposable reactor systems
Reactor diameter (d)
Ncfor VL = 20% (Eq.2)
Corning roller bottle, 850 cm2, easy grip vent cap
Nalgene 10 L Clearboy
Kühner SR 200-X Pilot-Shaker
Nalgene 20 L Carboy
Kühner SR 200-X Pilot-Shaker
Nalgene 50 L Carboy
Kühner SR 200-X Pilot-Shaker
Sartorius 200 L CultiBag ORB
Kühner SB 200-X OrbShake
Model for the gas/liquid oxygen transfer
Values for the mass transfer coefficient kLa were calculated from the measured OTRmax signal according to Eq. 11.
The sulfite reaction system
Different reaction rates of the sodium sulfite oxidation reaction can be adjusted by varying the cobalt concentration. A non-accelerated reaction rate with a Hatta number (Ha) of Ha < 0.3 is required for kLa measurements . In this range, the sulfite reaction is able to reduce the dissolved oxygen concentration (CL) to values close to zero. An increase in the oxygen transfer rate leads to a slight increase in CL as described by Maier et al. . Thus, CL needs to be considered during measurements with high oxygen transfer rates, as they are usually reached in bubble aerated stirred tank reactors . As comparatively low oxygen transfer rates of less than 16 mmol/(L∙h) were achieved with the disposable reactor systems in the present work, the assumption of (CL ≈ 0 mol/L) is, in this case, applicable for the determination of kLa values.
Sodium sulfite (Roth, Karlsruhe, Germany, purity < 98%) dissolved in deionized water and catalyzed with cobalt sulfate (Fluka, Neu-Ulm, Germany) was used for the oxidation reaction in the liquid phase. Two different sulfite concentrations of 0.5 mol/L and 1 mol/L were used to vary the diffusion coefficient for oxygen in the liquid phase. Both solutions were buffered with 12 mmol Na2HPO4/NaH2PO4 buffer, and a pH value of 8 was adjusted with 30% (w/w) sulfuric acid. The oxygen solubility of the solutions were calculated according to Weisenberger and Schumpe  and oxygen diffusion coefficients according to Akita . A ratio of = 0.886 was determined for the 0.5 mol/L sulfite solution and a ratio of = 0.788 was found for the 1 mol/L sulfite solution in agreement with values calculated by Linek and Vacek  using the same model proposed by Akita . The viscosity was measured with an Anton Paar MCR 301 rheometer (Anton Paar GmbH, Graz, Austria). Values for the oxygen solubility, diffusion coefficients and liquid viscosity are listed in Table 1.
Adaption of the Respiration Activity Monitoring System (RAMOS)
Aeration of the 2 L Corning roller bottle reactor
The Corning roller bottle reactor (Corning Inc., Acton, MA, USA) with vent cap is equipped with a 0.2 μm membrane that is integrated in the cap to allow a sufficient aeration during cultivation. A method developed by Anderlei et al.  for determining the mass transfer resistance of shake flask closures was applied to measure the diffusive mass transfer through the membrane of the cultivation system. A volume flow rate of 9 mL/min was determined with open ports at 25°C. This value was used for the active aeration with a Brooks 5850 TR mass flow controller (Brooks Instrument, Ede, The Netherlands) in the RAMOS as pictured in Figure 11. An oxygen sensor was placed on top of the reactor systems to measure the oxygen partial pressure in the gas phase. No further changes of the RAMOS for shake flasks were required to measure the OTRmax of the Corning roller bottle cultivation system.
Aeration of cylindrical orbitally shaken bioreactors with volumes from 10 L to 200 L
The settings of the air flow rate for the active headspace aeration of the cylindrical shaken bioreactors was transferred from the RAMOS device for shake flasks and adjusted according to the nominal reactor volume. A volume flow rate of 10 mL/min is usually applied in the RAMOS device for 250 mL shake flasks to mimic the oxygen transfer through a conventional cotton plug of shake flasks with a narrow neck. Consequently, an air flow rate of 400 mL/min was used for a volume of 10 L, 800 mL/min for 20 L, 2 L/min for 50 L and 8 L/min for 200 L bioreactors, respectively. For reactor volumes from 2–50 L, the flow rate was adjusted with a Brooks 5850-E mass flow controller (Brooks Instrument) in the RAMOS as illustrated in Figure 11. A manual air flow meter was used for the dynamic gassing-out method in the 200 L reactor system. The air flow rates in different scales were high enough to keep the absolute headspace concentration of oxygen, measured with the oxygen partial pressure sensor, above 20% during all OTR measurements.
Application of the dynamic gassing-out method for kLa measurements with water
A defined and constant headspace volume is required for OTRmax measurements with RAMOS . This could not be provided in the flexible 200 L bag reactor system. Thus, the dynamic gassing-out method, first described by Bandyopadhyay et al. , was used for kLa measurements in the 200 L scale. Nitrogen was used to replace the dissolved oxygen in the liquid phase, and deionized water was used as medium. Oxygen-sensitive spots (type SP-PSt3-YAU-D5-YOP) from PreSens (PreSens GmbH, Regensburg, Germany) were applied to measure the dissolved oxygen tension (DOT) in the liquid phase. An electrochemical sensor (MAX-250B, Maxtec, Salt Lake City, UT, USA) was additionally used to measure the oxygen concentration in the headspace of the reactor. The reactor system was filled with deionized water according to the desired filling volume. Then, the headspace of the system was filled with nitrogen, and the reactor was shaken at 80 rpm until the DOT reached a value below 1%. Subsequently, the shaker was stopped, and the gas volume in the headspace was replaced with air until the relative oxygen concentration in the headspace reached a value above 98%. The shaker was then immediately started with the designated shaking frequency, and the DOT was recorded over time. During the required time to replace the nitrogen in the headspace with air, the diffusion of oxygen from the gas phase to the liquid phase could cause small oxygen concentration differences in the liquid phase. Therefore, measured DOT values during the first 60 s were not considered for the calculation of the mass transfer coefficient (kLa) to ensure a sufficient mixing of the liquid phase. According to Tissot et al. , a mixing time of 60 s can be regarded as sufficient for a 200 L reactor system using liquids with water-like viscosity and shaking frequencies above 60 rpm. During all measurements the DOT signal after the 60 s mixing step was below 4%, indicating that only small amounts of oxygen were transferred to the liquid phase during the time needed to replace the gas in the headspace. Values for kLa were calculated from the recorded DOT signal over time as described by Van Suijdam et al.  and recently summarized by Suresh et al. .
Cultivation of Nicotiana tabacum cv. BY-2 plant cell suspension cultures
For evaluation of the kLa correlation the transgenic N. tabacum cv. Bright Yellow-2 (BY-2) MTAD cell line producing the human antibody M12 was used. The generation of the transgenic BY-2 cell line is described by Raven et al. . BY-2 plant cell suspension cultures were cultivated at 26°C in the dark using Murashige and Skoog media  with minimal organics (# M6899, Sigma Aldrich, Saint Louis, MO, USA) supplemented with 30 g/L sucrose, 0.2 g/L KH2PO4, 0.6 mg/L thiamine-HCl, 0.2 mg/L 2.4-Dichlorophenoxyacetic acid (2.4-D) and, where stated, additional 100 mmol/L KNO3. The pH of the culture medium was adjusted to 5.8 with 1 mol/L KOH before autoclaving for 21 min at 121°C. Plant cell suspensions cultures were sub-cultivated weekly for cell maintenance in 250 mL Erlenmeyer flasks, filled with 50 ml cell suspension, sealed with a cotton plug and shaken at 180 rpm and 26°C in the dark. Inoculation was conducted by adding 5% (V/V) of a seven day old culture to fresh medium.
Oxygen transfer rate measurements in shake flasks
The OTR signals in 250 mL Erlenmeyer flasks were measured with a Respiration Activity Monitoring System (RAMOS). A detailed description of the device and its applications is provided by Anderlei et al. 2004  and Anderlei and Büchs 2001 . The non-invasive measuring system allows online monitoring of the OTR, CTR and RQ without changing the culture conditions compared to conventional 250 mL shake flasks . Conventional Erlenmeyer flasks were used in addition to the RAMOS flasks to take samples during the cultivations.
Determination of fresh and dry cell weight
An electronic precision balance (SBC 31, Scaltec, Göttingen, Germany) was used to determine fresh and dry cell weight. Fresh cell weight was determined by vacuum filtration of 10 ml cell suspension for 3 min using Whatman filter paper grade 3 (# 1003–055, 55 mm diameter, Fisher Scientific GmbH, Schwerte, Germany). Prior to the filtration step the filter paper was weighted dry and after wetting with purified water. The fresh cell weight was determined from the difference in weight of the membrane with cells directly after filtration and the wet membrane without cells. The membrane with cells was dried at 105°C until the mass remained constant. The dry cell weight was determined from the difference in weight of the dried membrane with and without cells.
Determination of osmolality, dissolved oxygen tension and pH
Osmolality was determined in the supernatant with a Gonotec Osmomat 030 (Gonotec GmbH, Berlin, Germany). The device was calibrated with a two point calibration prior to each measurement. The pH value was determined with a pH510 pH meter (Eutech, Fisher Scientific GmbH, Schwerte, Germany). The dissolved oxygen tension (DOT) was measured by using oxygen sensitive sensor spots (type SP-PSt3-YAU-D5-YOP) from PreSens (PreSens GmbH, Regensburg, Germany).
The authors thank the company Kühner AG for their helpful support with equipment and materials. This work has been financed within the EU Project CoMoFarm (grant agreement no.: 227420).
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