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A bibliographic review of mathematical models of packed-bed biological reactors (PBR)
Modelos matemáticos para reactores biológicos de lecho empacado (PBR): una revisión bibliográfica
DOI:
https://doi.org/10.15446/ing.investig.v25n3.14664Keywords:
packed-bed reactor, bioreactor, immobilised cells, modelling, simulation (en)reactor empacado, biorreactor, células inmovilizadas, modelamiento, simulación (es)
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Several authors have subjected packed-bed biological reactors to mathematical and theoretical analysis. They have taken reaction kinetics and single-dimensional, homogeneous, pseudo-homogeneous and heterogeneous models into account. Numerical methods have provided the set of equations so developed. The effect of physically important process variables in terms of design and operation have been investigated (i.e. residence time, operating-flow, substrate conversion, bio-film area and film thickness).
El modelo matemático y análisis teórico de reactores biológicos de lecho empacado (PBR) ha sido estudiado por diferentes autores, quienes tuvieron en cuenta variedad de cinéticas de reacción, modelos unidimensionales, homogéneos, pseudohomogéneos y heterogéneos. Las ecuaciones resultantes del modelo fueron solucionadas, en su gran mayoría, por sistemas de métodos numéricos. Se ha analizado en estos el efecto de variables de proceso de importancia física con respecto a parámetros de diseño y operación, como tiempos de residencia, flujos de operación, conversiones de sustrato, área y superficie del biofilm, entre otros.
References
Aris, Routherform, Elementary chemical reaction analysis, Prentice-Hall, N.J., 1969.
Bales, V., Acai, P, Mathematical analysis of the performance of a packed bioreactor with immobilised cells”, Recent Progress en Genierdes Procedes, 13, 71, 335-342, 1999.
Beg S.A., Hassan M., “Effects of inhibitors on nitrification in a packed bed biological flow reactor”, Water Res., 21, 191-198,1987. DOI: https://doi.org/10.1016/0043-1354(87)90048-0
Beg, S.A.; Hassan, M., “Nitrification studies in Bubble aerated packed bed reactor”, J. Environ. Sci. Health, Part A, 20, 315-336, 1985. DOI: https://doi.org/10.1080/10934528509375228
Beg, S.A.; Hassam, M.M., “A Bio-film model for packed-bed reactors considering diffusion resistance and back-mixing effects”, Chem. Engineer Journal, 30, B1-B8, 1985. DOI: https://doi.org/10.1016/0300-9467(85)80009-5
Beg, S.A.; Hassam, M.M.; Jamal, N.A., “Modelling the effects of enzyme activation on the performance of a packed bed biological reactor”, J. Environm. Sci. Health, A28, (7), 1519-1543, 1993. DOI: https://doi.org/10.1080/10934529309375959
Beg, S.A.; Hassan, M.M.; Chaudry, S.A., “Response of a packed bed biological reactor to perturbation teed concentration and temperature”, Intern. J. Envirom. Studies, 49, 31-52,1995. DOI: https://doi.org/10.1080/00207239508711007
Bird, R B.; Stewart, W.E.; Lightfoot, E.N., Transport Phenomena, Wiley and sons, N.Y, 1960.
Caicedo, L.A., “Estudio comparativo de generación de CO2 en fermentaciones con células libres e inmovilizadas de Zymomonas mobilis”, Ingeniería e Investigación, 34, 23-26,1996. DOI: https://doi.org/10.15446/ing.investig.n34.24816
Caicedo, L.A.; Torres, J.; Vargas, G.; “Principios para el diseño de reactores bioquímicos de células inmovilizadas”, Universidad Nacional de Colombia, chapter 4, 1987.
Carberry, J.J.; Wendel, M.M., “Computer model of the fixed catalytic reactor”, A.I.Ch.E. Journal, 9, 129-133, 1963. DOI: https://doi.org/10.1002/aic.690090128
Conde, A.; Boyacá A.; “Reactores trifásicos de lecho fijo”, Universidad Nacional de Colombia, 1994.
Elmaleh, S.; Labaquere; Ben Aim, R., “Title”, Water Res., 12, 41, 1980.
Finlayson, B.A., The method of weighted residuals and variation principles, Academic Press, N.Y.,1972.
Froment, G.; Bischoff, K., Chemical Reactor Analysis and Design, John Wiley and Sons, chapter 3, 1990.
Gencer, M.; Mutharasan, R., “Ethanol fermentation in a yeast immobilised column fermentor”, Advances in Biotechnology Proc. Int. Ferm. Symp., 97, 627, 633, 1980. DOI: https://doi.org/10.1016/B978-0-08-025383-1.50104-1
Gerald, C.T., Applied numerical analysis, Addison Wesley, N.Y.,1970.
Guota, S.K.; Chand, S.; “Bioconversion of sugars in an immobilised cell packed bed bioreactor; dynamic response to perturbations in process parameters”, The Chem. Eng. Journal, 43, B1-B12, 1990. DOI: https://doi.org/10.1016/0300-9467(90)80046-F
Hassam, M. M.; Atiqullah, M.; Beg, S.A., “Analysis of non-isothermal tubular reactor packed with immobilized enzyme systems”, The Chem. Enginner. Journal, 58, 275-283,1995. DOI: https://doi.org/10.1016/0923-0467(95)06097-9
Hassam, M.M.; Beg, S.A., “Theoretical analysis of a packed-bed biological reactor for various reaction kinetics”, The Chem. Engineer Journal, 36, B15-B27, 1987. DOI: https://doi.org/10.1016/0300-9467(87)80051-5
Hannoun, B.J.; Stephanopoulos, G., “Title,” Biotechnol. Prog., 6, 349-356, 1990.
Hannoun, B.J.; Stephanopoulos, G., “Growth and fermentation model for alginate-entrapped Sacharomyces cervisiae”, Biotechnol. Prog., 6, 349-356 (1990) DOI: https://doi.org/10.1021/bp00005a006
Haug, R.T.; McCarty, PL., “Nitrification with the submerged filter”, J. Water Poll. Control Fed., 41, 2086-2098, 1972.
Jennings, P; Snoeyink, V.; Chain, s., “Theoretical model for a submerged biological filter”, Biotechnol. Bioeng., 18, 1249-1273, 1976. DOI: https://doi.org/10.1002/bit.260180906
Keller, H.B.A.; Bramble, J., Numerical solutions of partial differential equations, Academic Press, N.Y., 1972.
Klesser, I.; Oertzen, G.A.; Bauer, W. “Title”, Chem. Eng. Technol, 13, 20, 1990. DOI: https://doi.org/10.1002/ceat.270130105
Krishna, R.; Ramachandran, PA., “Title”, J. Appl. Chem. Biotechnol., 25, 623-640,1975. DOI: https://doi.org/10.1002/jctb.5020250809
Laca, A.; Quirós, C.; García, L., Díaz, M., “Modelling and description of internal profiles in immobilised cell systems”, Biochemical Engineering Journal, 1, 225-232, 1988. DOI: https://doi.org/10.1016/S1369-703X(98)00005-9
Mulcahy, L.; Shieih, W.; La Motta, E., “Title”, Prog. Water Technol., 12, 41, 1978. DOI: https://doi.org/10.1016/0043-1354(78)90194-X
Petersen, E.E., Chemical reaction analysis, Prentice-Hall, N.J,1965.
Quirós, C.; Rendueles, M.; García, L.A., “Diffusion of micro-organism in calcium alginate beads”, Biotechnol. Tech., 9, (11), 809-814, 1995. DOI: https://doi.org/10.1007/BF00159406
Rittman, B.E., “Comparative performance of bio-film reactor types”, Biotechnol. Bioeng., 24,1341-1370, 1982. DOI: https://doi.org/10.1002/bit.260240609
Rittman, B.E.; Mc Carty, PL., “Model of steady state biofilm kinetics”, Biotechnol. Bioeng., 22, 2343-2357, 1980. DOI: https://doi.org/10.1002/bit.260221110
Rittman, B.E.; Mc Carty, PL., “Substrate flux into biofilm of any thickness”, J. Environ. Eng. Div. (A.S.C.E.), 107, 831-849, 1981. DOI: https://doi.org/10.1061/JEEGAV.0001202
Rittman, B.E.; Strubler, C.E.; Ruzicka, T., “Anaerobic filter pre-treatment kinetics”, J. Environ. Eng. Div. (Am. Soc. Civ. Eng.), 108, 900-912, 1982. DOI: https://doi.org/10.1061/JEEGAV.0001350
Sarraut, P; Cheruy, A; Lenoel, M.; Shingleton, M.; Ruhaut, L.; “Hydrodynamic modelling of a packed bed bioreactor used in brewing industry with a view to process control”, Automatic Control of Food and Biological Process Development in Food Science, 36, 243-249, 1994.
Skowlun, C.C.T.; Kimse, D.W., “The simplified models for packed-bed bio-film reactors”, Biotechnol. Bioeng., 33, 164-172, 1989. DOI: https://doi.org/10.1002/bit.260330205
Webb C., “The role of cell immobilisation un fermentation technology”, Aust. J. Biotechnol., 3, 50-62, 1989. DOI: https://doi.org/10.1016/S0269-915X(89)80110-7
Wijffels, R.H.; Gooijer, C.D.; Scheper, A.W.; Beuling, E.E.; Maleé, L.T., “Dynamic modelling of immobilised Nitrosomonas europea: implementation of diffusion limitation over expanding micro-colonies”, Enzyme Microb. Technol., 17, 225-232, 1998.
Young J.C.; Mc Carty, PL., “The anaerobic filter for waste treatment”, J. Water Poll. Control Fed., 41, R160-173 (1969).
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Copyright (c) 2005 Deisy Corredor, Luis Alfonso Caicedo
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