Skip to main content
SpringerLink
Log in

Modeling and simulation of bioreactor process dynamics

  • Conference paper
  • First Online:
Bioprocess Parameter Control

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 30))

Abstract

After a brief overview on biochemical reactors and associated processes, relevant model types and modeling approaches are discussed. In addition, a number of simple modeling applications focusing on bioreactor design, interfacial mass transfer and reactor control are reviewed.

In Part 2 published modeling and simulation work on biochemical reactors and reviews of related laboratory investigations are presented. Specifically, simulation case studies for gas-liquid reactors and hollow fiber bioreactors are discussed.

In Part 3, it is concluded that mathematical modeling and computer simulation are supportive tools for laboratory bench-scale investigations and are indispensable for the design, optimization, and control of large-scale bioreactors. However, existing models representing the process dynamics and economics of (research) bioreactors have to be greatly improved before the latter goal can be achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Abbreviations

Ad :

cross-section of the downcomer (cm2)

Ar :

cross-section of the riser (cm2)

B:

biomass concentration (mg l−1)

BA :

dimensionless biomass concentration, B/Y Sf

c:

oxygen concentration in the liquid phase (M mol l−1)

c* :

oxygen concentration in the liquid in equilibrium with air (M mol l−1)

D:

dilution rate (s−1)

D1 :

stoichiometric group, = YsSf/YoxMox (dimensionless)

DG :

oxygen diffusivity in the gas phase (cm2 s−1)

DL :

oxygen diffusivity in the liquid phase (cm2 s−1)

F:

volumetric flow rate (cm3 s−1)

H:

Henry's constant (liter atm/mol)

J:

average volumetric flux density of the mixture (cm s−1)

JG :

gas volumetric flux density (cm s−1)

JL :

liquid volumetric flux density (cm s−1)

K:

dimensionless Michaelis constant, = Km/Sf

Km :

Michaelis constant (mg l−1)

KLa:

volumetric mass transfer coefficient (s−1)

L:

height of the riser (cm)

Ms :

molecular weight of the substrate (g mol−1)

Mox :

molecular weight of the oxygen (g mol−1)

Ptot :

total pressure (atm)

\(P_{o_2 }\) :

oxygen partial pressure (atm)

QL :

liquid volumetric flow rate (l s−1)

QG :

gas volumetric flow rate (l s−1)

R:

reaction group, = LΜ/JL (dimensionless)

rB :

rate of biomass generation (mg l−1 s−1)

rs :

rate of substrate consumption (mg l−1 s−1)

\(r_{o_2 }\) :

rate of oxygen consumption (M mol l−1 s−1)

S:

substrate concentration (mg l−1)

SA :

dimensionless substrate concentration = S/Sf

StG :

Stanton number for the gas phase = (LKLa/JG) (RT/H) (dimensionless)

StL :

Stanton number for the liquid phase = LKLa/JL (dimensionless)

t:

time (s)

T:

temperature (K)

V:

total volume of fermentor (l)

VG :

superficial gas velocity (cm s−1)

VL :

superficial liquid velocity (cm s−1)

VSG :

gas-phase volume of the separator (l)

VSL :

liquid-phase volume of the separator (l)

YS :

stoichiometric coefficient, (g) biomass per (g) substrate

Yox :

stoichiometric coefficient, (g) biomass per (g) oxygen

Y1 :

dimensionless partial pressure of oxygen, \(P_{o_2 } /P_{o_2 o}\)

Y2 :

dimensionless oxygen concentration, C/C*

z:

axial height (cm)

Î’:

ratio of separator volume to total volume (dimensionless)

γ:

ratio of liquid flow rates (dimensionless)

Ï•:

gas hold-up (dimensionless) (fraction of gas volume/total volume)

η:

dimensionless tube length (z/L)

Μ:

specific metabolic rate (s−1)

θ:

dimensionless dilution rate = DL/JL

ξ:

ratio of cross-section of riser to downcomer (dimensionless)

d:

related to the bottom of downcomer

f:

related to the feed

G:

gas phase

s:

related to the gas separator

T:

related to the top of the riser

O:

related to the point of gas injection

L:

liquid phase

T:

310 (K)

Μ:

0.4 (h)−1

Km :

37.5 (mg l−1)

H:

900(atm l−1 mol−1)

Ys :

0.4 (g) biomass per (g) substrate

L:

400–1000 (cm)

Î’:

0.1

JG :

35 (cm s−1)

Sf :

200–775 (mg l−1)

ξ:

4.0

Yox :

1.0/(1.7/Ys−2.05) (g) biomass per (g) oxygen

a:

inner radius of membrane

A, B:

series solution constants (eigenconstants)

b:

outer radius of membrane

c:

substrate concentration

C:

dimensionless substrate concentration

C:

dimensionless bulk substrate concentration

Cf :

idealized effluent bulk concentration (no diffusional resistance)

D:

diffusion coefficient

h:

membrane mass transfer coefficient

I0 :

modified Bessel function of the first kind, order zero

I1 :

modified Bessel function of the first kind, order one

K0 :

modified Bessel function of the second kind, order zero

K1 :

modified Bessel function of the second kind, order one

Ka, Kb :

membrane partition coefficients

K:

membrane partition coefficient ratio

k:

reaction rate constant

M:

the Kummer function

r:

radial position

X:

dimensionless radial position

z:

axial position

Z:

dimensionless axial position

α:

diffusion coefficient ratio

Î’:

hollow fiber radius ratio

η:

effectiveness factor

λ:

Thiele modulus

λ:

eigenvalues

σ:

overall mass transfer resistance

C0 :

inlet concentration

C3/C0 :

relative concentration

D3 :

effective diffusivity in spongy matrix

k:

first order rate constant

Km :

Michaelis constant

r/b:

relative radius

b:

inner radius of spongy matrix

t:

time

V:

maximum reaction rate

Î’=d/b:

relative radius of which there is no substrate concentration gradient

References

  1. Aiba, S., Humphrey, A. E., Millis, N. F.: Biochemical Engineering, 2nd edit. Tokyo: Univ. of Tokyo Press 1973

    Google Scholar 

  2. Allen, B. R. et al.: Biotech. Bioeng. 21, 689 (1979)

    Google Scholar 

  3. Andrews, G. F.: ibid. 24, 2013 (1982)

    Google Scholar 

  4. Bailey, J. E.: Chem. Eng. Sci. 35, 1854 (1980)

    Google Scholar 

  5. Bailey, J. E.: Personal Communication 1981

    Google Scholar 

  6. Bailey, J. E., Ollis, D. F.: Biochemical Engineering Fundamentals. New York: McGraw-Hill 1977

    Google Scholar 

  7. Begovich, J. H., Watson, J. S.: In: Fluidization, Cambridge University Press 1978

    Google Scholar 

  8. Belfort, G.: In: Course Notes, Advanced Biochemical Engineering, Troy: Rensselaer Polytechnic Institute (Summer 1982)

    Google Scholar 

  9. Blanch, H. W., Bhavaraju, S. M.: Biotech. Bioeng. 18, 745 (1976)

    Google Scholar 

  10. Blenke, H.: Adv. Biochem. Eng. 13 (1979)

    Google Scholar 

  11. Bowski, L. et al.: Presented at 182nd ACS Meeting, New York City, Aug. 23–28, 1981

    Google Scholar 

  12. Box, G. E., Jenkins, G. M.: Time Series Analysis; Forecasting and Control, Holden-Day 1976

    Google Scholar 

  13. Brauer, H.: Adv. Biochem. Eng. 13 (1979)

    Google Scholar 

  14. Bravard, J. P. et al.: Biotech. Bioeng. 21, 1239 (1979)

    Google Scholar 

  15. Brodkey, R. S.: Chem. Eng. Commun. 8, 1 (1981)

    Google Scholar 

  16. Bryant, J.: Adv. Biochem. Eng. 5 (1977)

    Google Scholar 

  17. Buhr, H. O., Andrews, J. F.: Water Research 11, 129 (1977)

    Google Scholar 

  18. Bungay, H. R.: In: Enzyme engineering (Kendall Pye, Weetal, eds.), Vol. 3, Plenum Publishing Company 1978

    Google Scholar 

  19. Bungay, H. R.: Jour. Amer. Oil Chem. Soc. 59, 270A (1982)

    Google Scholar 

  20. Calderbank, P. H.: Trans. Inst. Chem. Eng. 37, 173 (1959)

    Google Scholar 

  21. Chang, H.-C.: AIChE J. 28, 208 (1982)

    Google Scholar 

  22. Chang, M. M. et al.: Adv. Biochem. Eng. 20, 15 (1982)

    Google Scholar 

  23. Charm, S. E., Wong, B. L.: Biotech. Bioeng. 20, 451 (1978)

    Google Scholar 

  24. Christensen, D. R., McCarty, P. L.: J. W. P.C.F. 47, 2652 (1975)

    Google Scholar 

  25. Cichy, P. T. et al.: Ind. Eng. Chem. 61, 6 (1969)

    Google Scholar 

  26. Cohen, A. et al.: Water Research 13, 571 (1979)

    Google Scholar 

  27. Collins, A. S., Gilliland, B. E.: J. Environ. Eng. Div., Proc. ASCE, 100, No. EE2, 487 (1974)

    Google Scholar 

  28. Cooney, C. L.: Science 219, 728 (1983)

    Google Scholar 

  29. Danckwerts, P. V.: Gas-Liquid Reactions. McGraw-Hill 1970

    Google Scholar 

  30. Danielsson, B. et al.: Biotech. Bioeng. 21, 1749 (1979)

    Google Scholar 

  31. Deckwer, W.-D.: Intl. Chem. Eng. 19, 21 (1979)

    Google Scholar 

  32. Deckwer, W.-D.: Chem. Eng. Sci. 35, 1341 (1980)

    Google Scholar 

  33. Deckwer, W.-D. et al.: Biotech. Bioeng. 24, 461 (1982)

    Google Scholar 

  34. Do, D. D., Weiland, R. H.: ibid. 23, 691 (1981)

    Google Scholar 

  35. Emery, A. N., Cardoso, J. P.: ibid. 20, 1903 (1978)

    Google Scholar 

  36. Erickson, L. E., Deshpande: ibid. 24 (1982)

    Google Scholar 

  37. Fan, L.-S., Hwang, S.-J., Matsuura, A.: Proc. AIChE Annual Mtg. Washington D.C., Nov. 1983

    Google Scholar 

  38. Fan, L.-S., Long, T.-R., Fujie, K.: Proc. AIChE Annual Mtg. San Francisco, CA, Nov. 1984

    Google Scholar 

  39. Friedmann, M. R., Gaden, E. L.: ibid. 12, 961 (1970)

    Google Scholar 

  40. Goldberg, I. et al.: ibid. 18, 1657 (1976)

    Google Scholar 

  41. Graef, S. P., Andrews, J. F.: AIChE Symp. Ser., 70. No. 136. 101 (1973)

    Google Scholar 

  42. Gregor, H. P.: Proc. 3rd Annual Biomass Energy Syst. Conf., Golden, Colorado. June 5–7, 1979

    Google Scholar 

  43. Gregor, H. P., Jeffries, T. W.: In: Biochemical Engineering (Vieth et al., eds.), Vol. 326, New York: New York Academy of Sciences 1979

    Google Scholar 

  44. Guilbault, G.: In: Biochemical Engineering (Vieth et al., eds.), Vol. 326, New York: New York Academy of Sciences 1979

    Google Scholar 

  45. Hamilton, B. K. et al.: J. theor. Biol. 41, 547 (1973)

    Google Scholar 

  46. Hampel, W.: Adv. Biochem. Eng. 13 (1979)

    Google Scholar 

  47. Hatch, R. T.: Ph. D. Thesis, M.I.T., Cambridge 1973

    Google Scholar 

  48. Hatch, R. T., Wang, D. I. C.: Presented at the 1st Chemical Congress of the North American Continent, Mexico City, December 1975

    Google Scholar 

  49. Herbert, D.: Proc. 6th Intl. Symp. Continuous Culture of Microorganisms, Chichester: Ellis Horwood 1976

    Google Scholar 

  50. Hikuma, M. et al.: Biotech. Bioeng. 21, 1845 (1979)

    Google Scholar 

  51. Hills, J. H.: Chem. Eng. J. 12, 89 (1976)

    Google Scholar 

  52. Ho, C. S. et al.: Biotech. Bioeng. 19, 1503 (1977)

    Google Scholar 

  53. Hsu, H. W.: In Biotechnology and Bioengineering Symp. (Scott, ed.) No. 8, 1, 1978

    Google Scholar 

  54. Huffman-Reichenbach, L. M., Harper, W. J.: J. Dairy Sc. 65, 887 (1982)

    Google Scholar 

  55. Inloes, D. S. et al.: Biotech. Bioeng., to be published (1983a)

    Google Scholar 

  56. Inloes, D. S. et al.: Applied Env. Microbiol. (1983b)

    Google Scholar 

  57. Kim, S. S., Cooney, D. O.: Chem. Eng. Sci. 31, 289 (1976)

    Google Scholar 

  58. Kiparissides, C., MacGregor, M.: Presented at the 182nd ACS Meeting, New York: Amer. Chem. Soc., Aug. 23–28, 1981

    Google Scholar 

  59. Klein, J., Vorlop, K.-D.: In: Foundations of Biochemical Engineering (Blanch et al. eds.), Symp. Ser. No. 207, New York: Amer. Chem. Soc. 1983

    Google Scholar 

  60. Kleinstreuer, C., Belfort, G.: In: Synthetic Membrane Processes (Belfort, ed.), New York: Academic Press 1984

    Google Scholar 

  61. Kleinstreuer, C. et al.: Comp. Biomed. Res. 16, 29 (1983)

    Google Scholar 

  62. Kleinstreuer, C. et al.: Proc. AIChE Annual Mtg., San Francisco, CA, Nov. 1984

    Google Scholar 

  63. Kleinstreuer, C., Poweigha, T.: Biotech. Bioeng. 24, 1941 (1982)

    Google Scholar 

  64. Kuraishi, M. et al.: In: Microbial Growth on C1-Compounds, p. 231, Osaka: Soc. Ferment. Technol., 1975

    Google Scholar 

  65. Lee, G. K. et al.: Biotech. Bioeng. 23, 487 (1981)

    Google Scholar 

  66. Luttmann, R. et al.: ibid. 24, 817 (1982); 24, 1851 (1982)

    Google Scholar 

  67. Luttmann, R. et al.: Comp. Chem. Eng. 7, 43 (1983); 7, 51 (1983)

    Google Scholar 

  68. Maiorella, B., Wilke, C. R.: Biotech. Bioeng. 22, 1749 (1980)

    Google Scholar 

  69. Margaritis, A., Sheppard, J. D.: ibid. 23, 2117 (1981)

    Google Scholar 

  70. Margaritis, A., Zajic, J. E.: ibid. 20, 939 (1978)

    Google Scholar 

  71. Mattiasson, B., Ramstorp, M.: Biotechnol. Lett. 3, 561 (1981)

    Google Scholar 

  72. Merchuk, J. C., Stein, Y.: Biotech. Bioeng. 23, 1309 (1981)

    Google Scholar 

  73. Merchuk, J. C., Stein, Y.: AIChE J. 27 (1981)

    Google Scholar 

  74. Merchuk, J. C. et al.: ibid. 22, 1189 (1980)

    Google Scholar 

  75. Messing, R. A. (Ed.): Immobilized Enzymes for Industrial Reactors, Academic Press 1975

    Google Scholar 

  76. Metz, B. el al.: Adv. Biochem. Eng. 11 (1979)

    Google Scholar 

  77. Michaels, A. S.: Desalination 35, 329 (1980)

    Google Scholar 

  78. Moo-Young, M., Blanch, H. W.: Adv. Biochem. Eng. 19 (1981)

    Google Scholar 

  79. Moo-Young, M., Blanch, H. W.: In: Foundations of Biochemical Engineering (Blanch et al. eds.), Symp. Ser. No. 207, New York: Amer. Chem. Soc. 1983

    Google Scholar 

  80. Nauman, E. B., Buffham, B. A.: Mixing in Continuous Flow Systems, New York: Wiley Interscience 1983

    Google Scholar 

  81. Orazem, M. E., Erickson, L. E.: Biotech. Bioeng. 21, 69 (1979)

    Google Scholar 

  82. Ovano, A. C.: In: Advances in Chromatography (Giddings et al., eds.), Vol. 15, Marcel Dekker 1979

    Google Scholar 

  83. Patterson, G. K.: Chem. Eng. Commun. 8, 25 (1981)

    Google Scholar 

  84. Prokop, A.: Int. J. General Syst. 8, 7 (1982)

    Google Scholar 

  85. Prokop, A.: In: Foundations of Biochemical Engineering (Blanch et al. eds.), Symp. Ser. No. 207, New York: Amer. Chem. Soc. 1983

    Google Scholar 

  86. Rajagopalan, R., Tien: AIChE J. 22, 523 (1976)

    Google Scholar 

  87. Ramachandran, P. A.: Biotech. Bioeng. 17, 211 (1975)

    Google Scholar 

  88. Reuss, M., Buchholz, K.: ibid. 21, 2061 (1979)

    Google Scholar 

  89. Rony, P. R.: ibid. 13, 431 (1971)

    Google Scholar 

  90. Roy, T. B. V. et al.: Biotech. Letters 4, 483 (1982)

    Google Scholar 

  91. Russell, T. W. F. et al.: Biotech. Bioeng. 16, 1261 (1974)

    Google Scholar 

  92. Schaftlein, R. W., Russell, T. W. F.: Ind. Eng. Chem. 60, 12 (1968)

    Google Scholar 

  93. Schügerl, K.: Chem. Ing.-Tech., 52, Nr. 12, s. 951 (1980)

    Google Scholar 

  94. Schügerl, K. et al.: Adv. Biochem. Eng. 8 (1978)

    Google Scholar 

  95. Schügerl, K.: ibid. 19 (1981)

    Google Scholar 

  96. Schügerl, K.: ibid. 22 (1982)

    Google Scholar 

  97. Scott, C. D., Hancher, C. W.: Biotech. Bioeng. 18, 1393 (1976)

    Google Scholar 

  98. Shah, Y. T. et al.: AIChE J. 28, 353 (1982)

    Google Scholar 

  99. Shuler, M. L. et al.: J. theor. Biol. 35, 67 (1972)

    Google Scholar 

  100. Shuler, M. L. et al.: ibid. 41, 347 (1973)

    Google Scholar 

  101. Shuler, M. L., Domach, M. M.: In: Foundations of Biochemical Engineering (Blanch et al. eds.), Symp. Ser. No. 207, New York: Amer. Chem. Soc. 1983

    Google Scholar 

  102. Smith, J. M.: Chemical Engineering Kinetics, McGraw-Hill 1981

    Google Scholar 

  103. Stephanopoulos, G., San, K.-Y.: Presented at the 182nd ACS Meeting, New York City, Aug. 23–28, 1981

    Google Scholar 

  104. Taguchi, H.: Adv. Bioehem. Eng. 1 (1971)

    Google Scholar 

  105. Tanaka, H. et al.: Biotech. Bioeng. 23, 1683 (1981)

    Google Scholar 

  106. Thoenes, D.: Chem. Eng. Sc. 35, 1840 (1980)

    Google Scholar 

  107. Tirrell, M., Middleman, S.: Biotech. Bioeng. 17, 299 (1975)

    Google Scholar 

  108. Trevan, M. D.: Immobilized Enzymes, John Wiley 1980

    Google Scholar 

  109. Tsao, G. T., Lee, Y. H.: In: Annual Reports on Fermentation Processes (Pearlman, ed.), Vol. 1, New York: Academic Press 1977

    Google Scholar 

  110. U.S. Dept. of Energy: Contact: K. W. Koch, JPL, Pasadena, CA 91109 (1983)

    Google Scholar 

  111. Van Keulen, M. A. et al.: Biotech. Bioeng. 23, 1437 (1981)

    Google Scholar 

  112. Vemuri, V.: Modeling of Complex Systems, New York: Academic Press 1978

    Google Scholar 

  113. Vemuri, V., Karplus: Digital Computer Treatment of Partial differential Equations, Prentice-Hall 1981

    Google Scholar 

  114. Venkatsubramanian, K. (Ed.): Immobilized Microbial Cells, Symp. Series 106, Amer. Chem. Soc. 1979

    Google Scholar 

  115. Verhoff, F. H., Schlager, S. T.: Biotech. Bioeng. 23, 41 (1981)

    Google Scholar 

  116. Wang, D. I. C. et al.: Fermentation and Enzyme Technology, John Wiley 1979

    Google Scholar 

  117. Wang, H. Y. et al.: Biotech. Bioeng. 21, 975 (1979)

    Google Scholar 

  118. Waterland, L. R. et al.: AIChE J. 20, 50 (1974)

    Google Scholar 

  119. Webster, I. A., Shuler, M. L.: Biotech. Bioeng. 20, 1541 (1978)

    Google Scholar 

  120. Webster, I. A. et al.: ibid. 23, 447 (1981)

    Google Scholar 

  121. Webster, I. A. et al.: ibid. 21, 1725 (1979)

    Google Scholar 

  122. Yau, W. W. et al.: Modern Size-Exclusion Liquid Chromatography — Practice of Gel Permeation and Gel Filtration Chromatography, John Wiley 1979

    Google Scholar 

  123. Zeigler, B. P. et al. (eds.): Methodology in Systems Modeling and Simulation, North-Holland Publishing Company 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical and Environmental Engineering, Rensselaer Polytechnic Institute, 12181, Troy, N.Y., USA

    C. Kleinstreuer & T. Poweigha

  2. School of Engineering, NC State University, 27650, Raleigh, NC

    C. Kleinstreuer

Authors
  1. C. Kleinstreuer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Poweigha
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Kleinstreuer, C., Poweigha, T. (1984). Modeling and simulation of bioreactor process dynamics. In: Bioprocess Parameter Control. Advances in Biochemical Engineering/Biotechnology, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006381

Download citation

  • DOI: https://doi.org/10.1007/BFb0006381

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13539-5

  • Online ISBN: 978-3-540-39004-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation