Summary

The impact of bioreactor and sparger scale-up on gas transfer properties was investigated using four geometrically similar bioreactors ranging in size from 15-L to 2500-L total volume with the same sintered metal frit (microporous) sparger design.  The mass transfer coefficients for both oxygen and carbon dioxide were measured at each scale at various flow rates.  Scale did not directly affect gas transfer properties, but individual bioreactor properties did. 

The rate of carbon dioxide stripping from sparging in all vessels was much lower that expected based on film diffusion theories.  The rate was limited by the saturation of the sparge gas and the carbon dioxide dissolved in the medium.

The measured surface transfer of carbon dioxide and oxygen decreased directly with available surface area per unit volume.  Thus, cultures that exhibit controlled carbon dioxide levels at small scale (15 L and less) may not have stable carbon dioxide levels at larger scale.

 
Introduction

We investigated the impact of bioreactor and sparger scale-up on gas transfer properties with particular emphasis on carbon dioxide removal.  Microporous spargers are typically frits with holes less than 0.1 mm in diameter. (Aunins 1993)   Previous work has demonstrated that microporous spargers provide gas transfer coefficients several times what is achieved for orifice spargers.(Aunins 1993), (Bovonsombut 1987), (Zhang 1992), (Zhang 1993), (Chisti 1993). However, microporous spargers have been associated with poor carbon dioxide removal. (Gray 1996), (Zhangi 1999), (Kunkel 2000),(Mostafa 2003).

To assess how scale affects microporous spargers, we studied four bioreactors ranging in size from 15-L to 2500-L total volume, with the same sintered metal frit sparger design.  We measured mass transfer coefficients for oxygen and carbon dioxide for the sparger and liquid surface.

Material and Methods

Four Bioreactors were included in the study with nominal total volumes of 15-L, 200-L, 500-L and 2500-L.  The physical dimensions are provided in Table 1.  Sparger dimensions are provided in Table 2.

Table 1: Bioreactor Dimensions

Total                Fill                    Vessel              Impeller

Volume            Volume            Diameter          Diameter

15-L                 8 L                   20 cm               10 cm

200-L               160 L               61 cm               40 cm

500-L               420 L               80 cm               50 cm

2,500-L            2,000 L            150 cm             90 cm  

Table 2: Sparger Dimensions

Bioreactor                    (Number x) Length, Diameter

15 L                             (1x) 5 cm, d = 1.0 cm

200 L                           (4x) 25 cm, d = 1.0 cm

500 L                           (2x) 14cm + (2x) 23 cm, d = 1.4 cm

2,500 L                        (2x) 14cm + (2x) 23 cm, d=3.8 cm

Dissolved oxygen and pH were monitored continuously with in-line probes.  All vessels were filled with purchased DMEM media with 10% Fetal Calf Serum.  The agitation rate was selected to provide a power per unit volume of 2.5 mW/m³. 

Determination of sparger oxygen mass transfer coefficient k_L,Oxa_B

The oxygen transfer rate, d[O₂]/dt, is determined by the oxygen mass transfer coefficient (k_L,Oxa) times the driving force:

Equation 1

d[O₂]/dt = k_L,Oxa([O₂]- [O₂]*)

To determine the sparger oxygen mass transfer coefficient for each bioreactor, nitrogen, air or oxygen was sparged and the k_L,Oxa_B was determined by a linear fit of ln│[O₂]*- [O₂]│vs time. 

Determination of sparger carbon dioxide mass transfer coefficient k_L,COa_B

In many media commonly used for cell culture, the pH is maintained by a carbon dioxide – bicarbonate buffer.  Several reactions are required to fully describe the behavior of this buffer system, but in the pH range 6.5 to 8.0, the reactions can be summarized: (Ho, 1986) 

Equation 2

CO₂ + H₂O <=> H⁺ + HCO₃^-

The equilibrium constant for the above reaction in cell culture media (Gray 1996) is about 8x10^-7.    The rate of carbon dioxide stripping, d[CO₂]/dt is describe by a differential mass balance similar to that for oxygen transfer:

Equation 3

d[CO₂]/dt=-k_L,COa_B[CO₂]

Combining the equilibrium relationship with a mass balance for carbon dioxide, we can show that if no other buffers are present, the bicarbonate level will remain constant during stripping, and the mass transfer coefficient will be directly proportional to the rate of change of the pH.

Equation 4

k_L,COa_B=2.303 dpH/dt

To determine the sparger carbon dioxide mass transfer coefficient (k_L,COa_B), the pH was reduced to between 7.00 and 7.20 by sparging with CO₂.  Nitrogen, air, or oxygen was then sparged until a pH change of at least 0.04 units was observed.  The stripping rate, d(pH)/dt, was determined by a linear fit of pH vs time and the mass transfer coefficient was then calculated directly from k_L,COa_B =2.303 d(pH)/dt.  

Determination of surface oxygen mass transfer coefficient k_L,Oxa_S and surface carbon dioxide mass transfer coefficient k_L,COa_s

To determine the surface mass transfer coefficients for each reactor, nitrogen was first sparged to reduce the dissolved oxygen to less than 10% and the pH was reduced to between 7.00 and 7.20 by sparging with CO₂.  Air was sent to the headspace at 0.05 vvm, and the [O₂] and pH was monitored for several hours. The k_L,Oxa_B was determined by the slope of the least squares fit of ln│[O₂]*- [O₂]│vs time, and stripping rate,  and d(pH)/dt, was determined by a linear fit to pH vs time.   The surface carbon dioxide mass transfer coefficient was calculated directly from k_L,COa_S =2.303 d(pH)/dt.  

Results and Discussion

No statistically significant differences were found between determinations made by sparging with air, nitrogen or oxygen.  As can be seen in Table 3, there is no trend with bioreactor scale in the oxygen or carbon dioxide sparger mass transfer coefficients under typical operating conditions. 

Table 3: Gas transfer coefficients (1/hr) at 0.005 vvm with scale

Bioreactor        k_L,Oxa_B             k_L,COa_B

15-L                 3.4                  0.46    

200-L               9.3                  0.65    

500-L               3.0                  0.28    

2,500-L            3.7                  0.42    

The observed ratio of the carbon dioxide to the oxygen mass transfer coefficient is much lower than would be expected based on film diffusion based theories. (Aunins 1993), (Ho 1986), (Ho 1988).  Gray proposed that the shrinking of bubbles as they traveled to the surface would reduce the stripping of CO₂.(Gray 1996)   However, we observed no significant differences in the CO₂ stripping rates for nitrogen, air or oxygen, so this mechanism does not explain these results.

An explanation that fits our results well is that the sparge gas is saturating with CO₂ prior to reaching the headspace.  Using Henry's law, the ideal gas law, and  the volume of sparger gas per bioreactor volume per minute (vvm), we can derive an apparent maximum gas transfer coefficient,  (k_L,COa)_SAT.

Equation 5

 (k_L,COa)_SAT = (H/RT)(60)(vvm)  

For CO₂ in media at 37 ^oC, the Henry's Law constant, H,  is ~40 atm-L/mol (Onda 1970), (Yagi 1977) and (k_L,COa)SAT  will be ~94 vvm  or 0.47 at 0.005 vvm.  The saturation value is consistent with the measured values in table 3. 

To avoid accumulation, CO₂ must be removed by another mechanism such as surface stripping.  We confirmed that the surface gas mass transfer coefficients were proportional to the available surface area to volume ratio, consistent the problem of carbon dioxide accumulation with scale-up.  For the smallest bioreactor, the k_L,COa_B was about 0.15/hr.  For typical cell culture conditions  (10% dissolved CO₂ ), the rate of carbon dioxide  removal through the surface would be 0.38 mmoles/L-hr, or equivalent to the carbon dioxide produced by cellular respiration when the OUR is about 2.5% per minute.  For the largest reactor, the k_L,COa_B is about 0.03/hr and could only remove the carbon dioxide produced by cellular respiration when the OUR is about 0.5% per minute.   

Conclusions

The oxygen gas transfer coefficient of the sparger, was not dependent on scale.  Of the four bioreactors investigated, only the 200 L had statistically significantly different (higher) values for the oxygen transfer coefficient at the operating condition of 0.005 vvm.   The carbon dioxide transfer coefficient was nearly the same for the four bioreactors and was not dependent on sparge gas.  The measured values were much lower than what would be expected based on film diffusion theories.  The values were consistent with the saturation of sparge gas with carbon dioxide.

As expected, the surface stripping of carbon dioxide decreased directly with the available surface area per unit volume.  With this sparger design, cultures that exhibit balanced carbon dioxide levels at small scale (15-L and less) may not have stable CO₂ levels at larger scale.   (Aunins 1993) Aunins, J. G.; Henzler H.-J. In Biotechnology: A Multi-Volume Comprehensive Treatise; Stephanopoulos, G., Rehm, H.-J., Reed, G., Puhier, A., Stadler, P. J. W., Eds.; VCH Verlag: Weinheim, 1993; Vol. 3.

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