(263d) Sparger and Surface Gas Transfer for Cell Culture Bioreactors

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.  
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