Applied Microbiology and Biotechnology

, Volume 29, Issue 2–3, pp 107–112

Estimation of oxygen penetration depth in immobilized cells

  • Ho Nam Chang
  • Murray Moo-Young
Biotechnology

Summary

A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 μ and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 μ. Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.

Nomenclature

as

specific area of a support (cm)

Bi

Biot number

\(\frac{{k_{eff} d_p }}{{2D_{eff} }}\)

dimensionless

Cb

oxygen concentration in the bulk liquid (mM)

Cb

Cb*-Ccr (mM)

Cb*

bulk oxygen concentration in equilibrium with air (mM)

Ccr

critical oxygen concentration (mM)

Cs

oxygen concentration in the solid phase (mM)

dp

diameter or thickness of a support (cm)

Deff

effective diffusivity of oxygen in the solid phase (cm2/s)

km

membrane permeability of oxygen (cm/s)

km*

Deffm

kLaL

liquid phase mass transfer rate coefficient (1/s)

ksas

solid phase mass transfer rate coefficient (1/s)

(OUR)v

volumetric oxygen uptake rate (mmol O2/l)

p

geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere

Pd

oxygen penetration depth (cm)

Pd

oxygen penetration depth in the absence of external diffusion limitation (cm)

Q

volumetric oxygen uptake rate,\(Q_{O_2 } X\) (mmol O2/l·h)

\(Q_{O_2 } \)

specific oxygen uptake rate (mmol O2gm biomass (dry)·h)

r

length coordinate (cm)

rc

oxygen penetration depth for sphere (cm)

rc

rc in the absence of external diffusion limitation (cm)

rc*

oxygen penetration depth for cylinder (cm)

rc*

rc*in the absence of external diffusion limitation (cm)

rcom

combined mass transfer rate resistance (s)

rd

location where Cs becomes zero or Ccr (cm)

ri

radius of cylinder or sphere, half thickness of slab (cm)

Usg

superficial gas velocity (cm/s)

X

cell concentration (g/l)

Greek letters

ϕ

Thiele modulus, dimensionless

φL, φs

liquid and solid phase volume fraction, respectively, dimensionless

η

effectiveness factor

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References

  1. Atkinson B, Mavituna F (1983) Biochemical Engineering and Biotechnology Handbook p. 734, The Nature Press, NY, USAGoogle Scholar
  2. Altshuler GL, Dziewulski DM, Sowek JA, Belfort G (1986) Continuous hybridoma growth and monoclonal antibody production in hollow fiber reactors-separators. Biotechnol Bioeng 28:646–658Google Scholar
  3. Brodelius P (1983) Immobilized plant cells. In immobilized cells and organelles, Vol. I, Mattiasson, B (ed) CRC Press, Boca Raton, Fl., USAGoogle Scholar
  4. Chibata I, Wingard LB Jr (1983) Immobilized microbial cells (Applied Biochemistry Bioeng Series, vol 4) Academic Press, NY, USAGoogle Scholar
  5. Chang HN, Chung BH, Kim IH (1986) Dual hollow fiber bioreactors for biochemicals production. In: Asenjo JA, Hong J (eds) Separation, recovery and purification in biotechnology: recent advances and mathematical modelling. ACS Symp Series 314:32–42Google Scholar
  6. Chang HN, Moo-Young M (1988) Analysis of oxygen transport in immobilized cells and enzymes. Moo-Young M (ed) Elsevier (in press)Google Scholar
  7. Dean JF, Webb C (1986) Oxygen mass transfer and particle circulation in an immobilized cell bioreactor. In: International Conference on Bioreactor Fluid Dynamics. Cambridge, England: 15–17 April, 1986. BHRA, The Fluid Engineering Centre, Cranfield, Bedford MK43 OAJ, England, pp 1–16Google Scholar
  8. Deckwer WD (1981) Physical transport phenomena in bubble column bioreactors. II. Liquid-solid mass transfer, mixing and heat transfer. In: Moo-Young M, Robinson CW, Venzia C (eds) Adv in biotech Vol. I. pp 471–476, Pergamon PressGoogle Scholar
  9. Duff RG (1985) Microencapsulation technology: a novel method for monoclonal antibody production. Trends in biotech 3:167–170Google Scholar
  10. Gosman B, Rehm HJ (1986) Oxygen uptake of microorganisms entrapped in Ca-alginate. Appl Microbiol Biotechnol 23:163–167Google Scholar
  11. Hopkinson J (1985) Hollow fiber cell culture systems for economical cell-product manufacturing. Bio/Technology 3:226–230Google Scholar
  12. Horitsu H, Adachi S, Takahashi Y, Kawai K, Kawano Y (1985) Production of citric acid byAspergillus Niger immobilized in polyacrylamide gels. Appl Microbiol Biotechnol 22:8–12Google Scholar
  13. Huang MY, Bungay HR (1973) Microbe measurements of oxygen concentrations in mycelial pellets. Biotechnol Bioeng 15:1193–1197Google Scholar
  14. Knazek RA, Gullino PM, Kohler PL, Dedrick RL (1972) Cell culture on artificial capillaries: an approach to tissue growth in vitro. Science 178:65–67Google Scholar
  15. Kobayashi T, Van Dedem G, Moo-Young M (1973) Oxygen transfer into mycelial pellets. Biotechnol Bioeng 15:27–45Google Scholar
  16. Linko P, Linko YY (1984) Industrial applications of immobilized cells. CRC Crit Rev in Biotech 1:289–338Google Scholar
  17. Margaritis A, Merchant FJA (1984) Advances in ethanol production using immobilized cell systems. CRC Crit Rev Biotech 1:339–393Google Scholar
  18. Mattiasson B (1983) Immobilized cells and organelles. Vol I, CRC Press, Boca Raton, FI, USAGoogle Scholar
  19. Mogensen AO, Vieth WR (1973) Mass transfer and biochemical reaction with semipermeable microcapsules. Biotechnol Bioeng 15:467–481Google Scholar
  20. Shah YT (1979) Gas-liquid-soilid reactor design. McGraw-Hill, USAGoogle Scholar
  21. Shah YT, Kelkan BG, Godbole SP, Deckwer WD (1982) Design parameters estimations for bubble column reactors. AIChE J 28:353–379Google Scholar
  22. Sinskey AJ, Fleischaker RJ, Tyo MA, Giard DJ, Wang DIC (1981) Production of cell-derived products: virus and interferon. Ann NY Acad Sci 369:47–59Google Scholar
  23. Tharakan JP, Chau PC (1986) A radial flow hollow fiber bioreactor for the large-scale culture of mammalian cells. Biotechnol Bioeng 28:329–342Google Scholar
  24. White MW (1974) Viscous fluid flow. McGraw-Hill, USA p 136Google Scholar
  25. Wittler R, Baumgartl H, Lubbers DW, Schugerl K (1986) Investigations of oxygen transfer intoPenicillium chrysogenum pellets by microbe measurements. Biotechnol Bioeng 28:1024–1036Google Scholar
  26. Yano T, Kodama T, Yamada K (1961) Fundamental studies on the aerobic fermentation (VIII) O2 transfer. Agr Biol Chem 25:580–584Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Ho Nam Chang
    • 1
  • Murray Moo-Young
    • 1
  1. 1.Department of Chemical EngineeringUniversity of WaterlooWaterlooCanada

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