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A distributed parameter diffusion-reaction model for the alcoholic fermentation process

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Abstract

A distributed parameter model is developed for the yeast floc in the alcoholic fermentation process. The model takes into consideration the external mass transfer resistances, the mass transfer resistance through the cellular membrane, and the diffusion resistances inside the floc. The two-point boundary value differential equations for the membrane are manipulated analytically, whereas the nonlinear twopoint boundary value differential equations of diffusion and reaction inside the floc have been approximated using the orthogonal collocation technique.

The evaluation of the necessary diffusion coefficients have involved a relatively large number of assumptions because of the present limited knowledge regarding the complex process of diffusion and biochemical reactions in these systems.

The model results have been compared with the experimental results of a laboratory batch fermentor and the results of an industrial fed-batch fermentor. The model simulates reasonably well the experimental results, with the largest deviation being for the concentration of yeast.

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References

  1. Elnashaie, S. S. E. H. and Ibrahim, G. (1988),Appl. Biochem. Biotechnol. 19, 71–101.

    CAS  Google Scholar 

  2. Novak, M., Sterhaiano, P., Moreno, N., and Goma, G. (1981),Biotechnol. Bioeng. 23, 201–211.

    Article  CAS  Google Scholar 

  3. Elnashaie, S. S. E. H. and Ibrahim. G. Paper presented at Cairo International Symposium on Renewable Energy Resources, Cairo, June 13–16,1988.

  4. Dombek, K. M. and Ingram, L. O. (1983),Abstr. Ann. Meet. Soc. Microbiol. 83, (meeting 241).

  5. Carey, V. C. and Ingram, L. O. (1983),J. Bact. 154, 1291.

    CAS  Google Scholar 

  6. Yerushalmi, L. Volesky, B., and Votruba, J. (1986),Biotechnol. Bioeng. 28, 1334–1347.

    Article  CAS  Google Scholar 

  7. Kernevez, J-P. (1976),Proceedings of the International Symposium on Analysis and Control of Immobilized Enzyme Systems, Thomas, D. and Kernevez, J.-P., eds. North Holland/American Elsevier, pp. 199–225.

    Google Scholar 

  8. Ghose, T. K. and Tyagi, R. D. (1979),Biotechnol. Bioeng. 22, 1387–1400.

    Article  Google Scholar 

  9. Holzberg, I., Finn, R. K., and Stienkraus, K. H. (1967),Biotechnol. Bioeng. 9, 413–427.

    Article  CAS  Google Scholar 

  10. Aiba, S., Shoda, M., and Nagatani, M. (1968),Biotechnol. Bioeng. 10, 845–864.

    Article  CAS  Google Scholar 

  11. Egamberdiev, N. B. and Ierusalimskij, N. D. (1969),In Continuous Cultivation of Microorganisms. Vol. I. Malleh, et al. eds., Academic, Praha, pp. 517–527.

    Google Scholar 

  12. Levenspiel, O. (1980),Biotechnol. Bioeng 22, 1671–1687.

    Article  CAS  Google Scholar 

  13. Jobses, I. M. L. and Roels, J. A. (1986),Biotechnol. Bioeng. 28, 554.

    Article  CAS  Google Scholar 

  14. Nagodawithana, T. W. and Steinkrous, K. H. (1976),J. Appl. Environ. Microbiol. 31, 158.

    CAS  Google Scholar 

  15. Thomas, D. S. and Rose, A. H. (1979),Arch. Microbiol. 122, 49.

    Article  CAS  Google Scholar 

  16. Beaven, M. J., Charpentier, C., and Rose, A. H. (1982),J. Gen. Microbiol. 128, 1447.

    CAS  Google Scholar 

  17. Navarro, J. M. and Durand, G. (1978),Ann. Microbiol. (Inst. Pasteur),129B, 215.

    CAS  Google Scholar 

  18. Navarro, J. M., Scherian, A. F., Weiland, P., and Lafferty, R. M. Paper presented at the 7th International Specialized Symposium on Yeast, Valencia, Spain, 1981.

  19. Panchal, J. and Stewart, G. G. (1980),J. Inst. Brew. 86, 207.

    CAS  Google Scholar 

  20. Ghose, T. K. and Tyagi, R. D. (1979),Biotechnol. Bioeng. 22, 1401.

    Article  Google Scholar 

  21. Franz, B. (1961),Die Nahorung 5, 457.

    Article  CAS  Google Scholar 

  22. Pioronti, F. (1979), Ph.D. Thesis, Cornell University, Ithaca, NY.

  23. Egamberdiev, N. B. and Ierusalimskij, N. D. (1968),Microbiologiya 37, 686.

    CAS  Google Scholar 

  24. Ciftci, T. Constantinides, A., and Wang, S. S. (1983),Biotechnol. Bioeng. 25, 2007.

    Article  CAS  Google Scholar 

  25. Cysewski, G. R. and Wilke, C. R. (1978),Biotechnol. Bioeng. 20, 1421.

    Article  CAS  Google Scholar 

  26. Lee, J. M., Pollard, J. F., and Coulman, G. A. (1983),Biotechnol. Bioeng. 25, 497.

    Article  CAS  Google Scholar 

  27. Strehaiano, P. (1973), These Dr. Ing. Toulouse, France.

  28. Guijarro, J. M. and Lagunas, R. (1984),J. Bacteriol. 160(3), 874.

    CAS  Google Scholar 

  29. Benitez, T., Del Castillo, L., Aguilera, A., Conde, J., and Cerda-Omeda, E. (1983),Appl. Environ. Microbiol. 45, 1429.

    CAS  Google Scholar 

  30. Bajpai, P. and Margaritis, A. (1986),Biotechnol. Bioeng. 28, 283.

    Article  CAS  Google Scholar 

  31. Mill, P. J. (1964),J. Gen. Microbiol. 35, 61.

    CAS  Google Scholar 

  32. Atkinson, B. and Ur-Rahman, F. (1970),Biotechnol. Bioeng. 21, 221.

    Article  Google Scholar 

  33. Stein, W. D. (1967),The Movement of Molecules Across Cell Membranes, Academic, New York, London.

    Google Scholar 

  34. Weeks, M. G., Munro, P. A., and Speeding, P. L. (1983),Biotechnol. Bioeng. 25, 687.

    Article  CAS  Google Scholar 

  35. Weeks, M. G., Munro, P. A., and Speeding, P. L. (1983),Biotechnol. Bioeng. 25, 699.

    Article  CAS  Google Scholar 

  36. Atkinson, B. and Daoud, I. S. (1976),Advances in Biochemical Engineering, vol. 4, Ghosh, T. K., Fiechter, A., Blakeborough, N., eds. Springer-Verlag, Berlin.

    Google Scholar 

  37. Eddy, A. A. (1955),J. Inst. Brew. 61, 313.

    Google Scholar 

  38. Baker, D. A. and Kirsop, B. H. (1972),J. Inst. Brew. 78, 454.

    CAS  Google Scholar 

  39. Rainbow, C. (1966),Process Biochem. 1, 489.

    CAS  Google Scholar 

  40. Mandelbrot, B. B. (1983),The Fractal Geometry of Nature, Freeman, N.Y.

    Google Scholar 

  41. Davis, R. H. and Hunt, T. P. (1986),Biotechnol. Progress 2, 91–97.

    Article  Google Scholar 

  42. Villadsen, J. V. and Stewart, W. E. (1967),Chem. Eng. Sci. 22, 1483.

    Article  Google Scholar 

  43. Loureiro, V. and Ferreira, H. G. (1983),Biotechnol. Bioeng. 25, 2263.

    Article  CAS  Google Scholar 

  44. Calderbank, P. H. (1967),Biochemical and Biological Engineering Science, Blake Borough, N., ed., vol. 1, p. 102, Academic Press, New York.

    Google Scholar 

  45. Kollerup, F. and Daugulls, A. J. (1985),Biotechnol. Bioeng. 27.

  46. Perry, R. H. and Green, D. (1984),Perry's Chemical Engineer's Handbook, 6th Ed. pp. 251–254.

  47. Kendall and Monroe, (1917),J. Am. Chem. Soc. 39, 1787.

    Article  CAS  Google Scholar 

  48. Kendall and Honoe, (1921),J. Am. Chem. Soc. 43, 115.

    Article  CAS  Google Scholar 

  49. Bailey, J. E. and Ollis, D. F. (1986), Biochemical Eng. Fundamentals, 2nd Ed., McGraw-Hill, New York.

    Google Scholar 

  50. Wilke, C. R. and Chang, P. (1955),AIChEJ,1, 264.

    Article  CAS  Google Scholar 

  51. Avakyants, S. P. (1979),Proceedings of Papers Concerning Biosynthesis and Metabolism of Lipids on Microorganisms, Second All-Union Conference (in Russian), Nauka, Moscow, p. 133.

    Google Scholar 

  52. James, S., Rha, C., and Sinskey, A. J. (1986),Biotechnol. Bioeng. 28, 769.

    Article  Google Scholar 

  53. Sullivan, K. H., Hegemann, G. D., and Cords, C. H. (1979),J. of Bacteriol. 138, 133.

    CAS  Google Scholar 

  54. Van Stevenincek, J. and Rothstein, A. (1965),J. Ge. Physiol. 49, 325.

    Google Scholar 

  55. Van Uden, N. (1967),Arch. Mikrobiol. 58, 155.

    Article  Google Scholar 

  56. Bisson, L. F. and Fraenkel, D. G. (1983),Proc. Natl. Acad. Sci. 80, 1730.

    Article  CAS  Google Scholar 

  57. Suzuki, S. and Karube, I. (1979),Am. Chem. Soc. Symp. Series 106, 59.

    CAS  Google Scholar 

  58. D'Souza, S. F. and Nadkarni, G. B. (1980),Biotechnol. Bioeng. 22, 2191.

    Article  Google Scholar 

  59. Onuma, M., Omura, T., Umita, T., and Aizawa, J. (1985),Biotechnol. Bioeng. 27, 1533.

    Article  CAS  Google Scholar 

  60. Cooney, C. L., Wang, H. Y., and Daniel, I. C. (1977),Biotechnol. Bioeng. 21, 55.

    Article  Google Scholar 

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Authors and Affiliations

  1. Chemical Engineering Department-College of Engineering, King Saud University, P.O. Box 800, Riyadh, Saudi Arabia

    S. S. E. H. Elnashaie

  2. Faculty of Engineering-Menoufia University, Menoufia, Egypt

    G. Ibrahim

  3. Chemical Engineering Dept., Cairo University, Cairo, Egypt

    S. S. E. H. Elnashaie

Authors
  1. S. S. E. H. Elnashaie
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  2. G. Ibrahim
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Elnashaie, S.S.E.H., Ibrahim, G. A distributed parameter diffusion-reaction model for the alcoholic fermentation process. Appl Biochem Biotechnol 30, 339–360 (1991). https://doi.org/10.1007/BF02922037

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