Mass Transfer and Mixing Across the Scales in Animal Cell Culture

Abstract

As in all aerobic bioprocesses, the oxygen transfer rate is a critical parameter that needs to be met for the satisfactory cultivation of animal cells. Oxygen in solution has to be continuously provided because of its low solubility in aqueous solution which is continually being utilised by the growing cells (at the current time, reaching a cell density of ~10⁷ cells mL⁻¹ in bioreactors up to 25 m³). Such a process requires a certain specific power input (or mean specific energy dissipation rate) to be used, which also has to provide a satisfactory level of other mixing parameters. However, though for animal cells, the specific power required is relatively low (typically < ~0.05 W/kg), because of the lack of a cell wall, there is still a perception that ‘shear damage’ may occur. Another aspect of oxygen mass transfer is the need to provide a continual inflow of oxygen into the bioreactor, typically by sparging (rates < ~0.01 vvm). However, especially at large scale, sparging may lead to excessive foaming requiring the use of antifoam to control it; and bursting bubbles damage cells unless protective agents are used. Both these additives negatively affect the rate of mass transfer. Another critical aspect directly linked to oxygen transfer is the molar equivalent production of carbon dioxide by the cells. Stripping of CO₂ is essential to prevent physiologically damaging levels of pCO₂ being produced as well as issues associated with pH and osmolality. Essentially, oxygen transfer, carbon dioxide stripping and mixing parameters are all intimately connected and need to be considered in an integrated way. In this chapter, oxygen mass transfer and carbon dioxide stripping theory and practice are considered in detail including non-stirred and single use bioreactors. In addition, other mixing parameters such as blending, heat transfer and scale-up/scale-down in stirred bioreactors are briefly considered as these are used commercially from the 15 mL ambr^TM to the 25 m³ scale. Because the perceived ‘shear-sensitivity’ of animal cells to stirring and bubbling has impacted on how aeration and stripping have been addressed in practice, these topics too are worthy of consideration in any integrated approach. Finally, some recommendations regarding sparger selection and impeller choice are also made.

Nomenclature

a

Specific area of bubbles, m⁻¹

A

Dimensional constant in Eq. 5.23

AR

Aspect ratio, H/T

C _L

Concentration in the liquid phase, mol m⁻³

d ₃₂

Sauter mean diameter, m

D

Agitator diameter, m

D _L

Diffusion coefficient, m² s⁻¹

g

Gravitational constant, 9.81 m s⁻²

H

Bioreactor fill level, m; or Henry’s law constant, atm. m³ mol⁻¹

H _G

Height of aerated liquid, m

J

Rate of mass transfer, mol s⁻¹

k _g

Gas film mass transfer coefficient, mol s⁻¹ m⁻² atm⁻¹

k _L

Liquid film mass transfer coefficient, m s⁻¹

k _L a

Specific mass transfer coefficient, s⁻¹ or h⁻¹

M

Mass of media, kg

N

Agitator speed, s⁻¹ or rpm; or specific rate of mass transfer, mol m⁻³ s⁻¹

OD

Oxygen demand, mol m⁻³ s⁻¹

OTR

Oxygen transfer rate, mol m⁻³ s⁻¹

OUR

Oxygen uptake rate, mol m⁻³ s⁻¹

p

Partial pressure, atm

P

Power, W; or total pressure, atm

P _g

Total pressure, atm

Po

Power number, dimensionless

Q _G

Air flow rate, m³ s⁻¹

Q _H

Heat evolution rate, W m⁻³

R

Gas constant, m³ atm K⁻¹ mol⁻¹

Re

Reynolds number, dimensionless

SOD

Specific oxygen demand, mol s⁻¹ cell⁻¹

t

Temperature, °C; or time, s

T

Bioreactor diameter, m; or absolute temperature, K

v _S

Superficial gas velocity, m s⁻¹

VVM

Specific volumetric flow rate, (min⁻¹)

V

Volume of media, m³

y

Mol fraction, dimensionless

X

Cell density, cells m⁻³; or % dO₂

Greek Letters

α,β

Exponents

ΔC

Concentration driving force, mol m⁻³

ε _G

Hold-up, dimensionless

ε _T

Local specific energy dissipation rate, W kg⁻¹

${\overline{\varepsilon}}_T$

Mean specific energy dissipation rate, W kg⁻¹

λ _K

Kolmogoroff turbulence scale, m

μ

Viscosity, Pa s

ν

Kinematic viscosity_, m² s⁻¹

ρ

Liquid density, kg m⁻³

τ _p

Time constant of the oxygen probe, s

θ _m

Mixing time, s

Subscripts

CO ₂

Carbon dioxide

Crit

Critical oxygen concentration

I

At the interface

In

Entering at the sparger

G

When air is sparged; or in the gas phase

Max

Maximum

Out

At the exit

O ₂

Oxygen

Superscript

*

At equilibrium