A New Thiele's Modulus for the Monod Biofilm Model

Abstract

Abstract: A new Thiele's modulus,φ_F,was developed to provide a gradual transition between zero and the first order of kinetics,and to accurately calculate the mass transfer flux and the effectiveness factor for the Monod biofilm.Values of the effectiveness factor,calculated using the new Thiele's modulus,were compared with those obtained from numerical solutions and from other published moduli and empirical formulae.The comparison indicated that the new Thiele's modulus was the best modulus for the Monod biofilm model.In addition,another Thiele's modulus,φ_G,was developed for a Monod biofilm,covered with an external water layer.The overall effectiveness factor can also be calculated by using both moduli φ_F and φ_G.The criteria that were proposed for identification were based on the values of φ_F andφ_G,the limiting processes for biomass growth,and substrate conversion. Developed from φ_F,a new parameterψwas related uniquely to such features as the depth and shallowness of the generalized substrate concentration profiles inside a Monod biofilm.Criteria were developed to identify the types of concentration distribution inside a Monod biofilm.These methods were used to estimate the substrate flux and the concentration distribution of the biofilms defined in the first benchmark problem(BM1),by a task group of the International Water Association on Biofilm Modeling.

Key words: Monod biofilm, kinetic model, effectiveness factor, Thieles modulus, generalized concentration profiles

摘要： A new Thiele's modulus,φ_F,was developed to provide a gradual transition between zero and the first order of kinetics,and to accurately calculate the mass transfer flux and the effectiveness factor for the Monod biofilm.Values of the effectiveness factor,calculated using the new Thiele's modulus,were compared with those obtained from numerical solutions and from other published moduli and empirical formulae.The comparison indicated that the new Thiele's modulus was the best modulus for the Monod biofilm model.In addition,another Thiele's modulus,φ_G,was developed for a Monod biofilm,covered with an external water layer.The overall effectiveness factor can also be calculated by using both moduli φ_F and φ_G.The criteria that were proposed for identification were based on the values of φ_F andφ_G,the limiting processes for biomass growth,and substrate conversion. Developed from φ_F,a new parameterψwas related uniquely to such features as the depth and shallowness of the generalized substrate concentration profiles inside a Monod biofilm.Criteria were developed to identify the types of concentration distribution inside a Monod biofilm.These methods were used to estimate the substrate flux and the concentration distribution of the biofilms defined in the first benchmark problem(BM1),by a task group of the International Water Association on Biofilm Modeling.

关键词: Monod biofilm, kinetic model, effectiveness factor, Thieles modulus, generalized concentration profiles

FANG Yuanxiang, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. , 2008, 16(2): 277-286.

方元祥, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. , 2008, 16(2): 277-286.

References

1 Ottengraf, S.P.P., van den Oever, A.H.C., “Kinetics of organic compound removal from waste gases with a biological filter”, Biotechnol. Bioeng., 25, 3089-3102 (1983).
2 Muslu, Y., “Substrate removal in microbial film reactors (I) Mathematical-model”, J. Dispersion Sci. Technol., 14 (2), 135-149 (1993).
3 Muslu, Y., Kinaci, C., Tuna, M., “A new approach to the biological filtration (II) Experimental confirmation”, J. Dispersion Sci. Technol., 14 (2), 191-203 (1993).
4 Riefler, R.G., Smets, B.F., “Comparison of a type curve and a least-squared errors method to estimate biofilm kinetic parameters”, Water Res., 37, 3279-3285 (2003).
5 Atkinson, B., Daoud, I.S., “The analogy between micro-biological ‘reactions’ and heterogeneous catalysis”, Trans. Instn. Chem. Engrs., 46, 19-24 (1968).
6 Atkinson, B., Davies, I.J., “The overall rate of substrate uptake (reaction) by microbial film: Part I-A biological rate equation”, Trans. Inst. Chem. Engrs., 52, 248-259 (1974).
7 Tan, C.S., Lai, C.C., “Semianalytical expression of effectiveness factor for michaelis-menten kinetics”, AIChE J., 34 (10), 1757-1759 (1988).
8 Williamson, K.J., McCarty, P.L., “A model for substrate utilization by bacterial biofilm”, J. Water Pollut. Control Federation, 48, 9-24 (1976).
9 Rittmann, B.E., McCarty, P.L., “Model of steady-state-biofilm kinetics”, Biotechnol. Bioeng., 22, 2343-2357 (1980).
10 Rittmann, B.E., McCarty, P.L., “Substrate flux into biofilms of any thickness”, J. Environ. Eng., 107 (4), 831-849 (1981).
11 Suidan, M.T., Wang, Y.T., “Unified analysis of biofilm kinetics”, J. Environ. Eng., 111 (5), 634-646 (1985).
12 Kim, B.R., Suidan, M.T., “Approximate algebraic solution for a biofilm model with the monod kinetic expression”, Water Res., 23 (12), 1491-1498 (1989).
13 Saez, P.B., Rittmann, B.E., “Improved pseudoanalytical solution for steady-state biofilm kinetics”, Biotechnol. Bioeng., 32 (3), 379-385 (1988).
14 Saez, P.B., Rittmann, B.E., “Accurate pseudoanalytical solution for steady-state biofilms”, Biotechnol. Bioeng., 39, 790-793 (1992).
15 Chaudhry, M.A.S., Beg, S.A., “A review on the mathematical modeling of biofilm processes: Advances in fundamentals of biofilm modeling”, Chem. Eng. Technol., 21 (9), 701-710 (1998).
16 Grady, C.P.L.J., Daigger, G.T., Lim, H.C., Biological Wastewater Treatment, 2nd ed., Marcel Dekker, New York (1999).
17 Froment, G.F., Bischof, K.B., Chemical Reactor Analysis and Design, 2nd ed., Wiley, New York (1990).
18 Henze, M., Marremoes, P., Jansen, J.l.C., Arvin, E., Wastewater Treatment: Biological and Chemical Processes, 2nd ed., Springer, Berlin (1997).
19 Noguera, D.R., Morgenroth, E., “Introduction to the IWA task group on biofilm modeling”, Water Sci. Technol., 49 (11/12), 131-136 (2004).
20 Morgenroth, E., Eberl, H.J., van Loosdrecht, M.C.M., Noguera, D.R., Pizarro, G.E., Picioreanu, C., Rittmann, B.E., Schwarz, A.O., Wanner, O., “Comparing biofilm models for a single species biofilm system”, Water Sci. Technol., 49 (11/12), 145-154 (2004).
21 Wanner, O., Reichert, P., “Mathematical modeling of mixed-culture biofilms”, Biotechnol. Bioeng., 49 (2), 172-184 (1996).
22 Eberl, H.J., Picioreanu, C., Heijnen, J.J., van Loosdrecht, M.C.M., “A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms”, Chem. Eng. Sci., 55 (24), 6209-6222 (2000).
23 Pizarro, G., Griffeath, D., Noguera, D.R., “Quantitative cellular automaton model for biofilms”, J. Environ. Eng., 127 (9), 782-789 (2001).
24 Suidan, M.T., Rittmann, B.E., Traegner, U.K., “Criteria establishing biofilm-kinetic types”, Water Res., 21 (4), 491 (1987).
25 Saez, P.B., Rittmann, B.E., “Error analysis of limiting-case solutions to the steady-state-biofilm model”, Water Res., 24 (10), 1181 (1990).
26 Levenspiel, O., Chemical Reaction Engineering, 3rd ed., Wiley, New York, 688 (1998).
27 Levenspiel, O., The Chemical Reactor Omnibook, Oregon State University Book Stores Inc., Oregon (1993).
28 Golla, P.S., Overcamp, T.J., “Simple solutions for steady-state biofilm reactors”, J. Environ. Eng., 116 (5), 829-836 (1990).
29 Gantzer, C.J., Ritmann, B.E., Herricks, E.E., “Mass transport to streambed biofilms”, Water Res., 22 (6), 709-722 (1988).
30 Rittmann, B.E., McCarty, P.L., “Variable-order model of bacterial-film kinetics”, J. Environ. Eng., 107, 889-900 (1978).
31 Kato, M., Kiuchi, T., “Biological rate equation for microbiol films”, Chem. Eng. J., 44, B87-B90 (1990).
32 Kobayashi, T.K., Ohmiya, K., Shimizu, S., “Approximate expression of effectiveness factor for immobilized enzymes with michaelis-menten kinetics”, J. Ferment. Technol., 54, 162 (1976).
33 Moo-Young, M., Kobayashi, T., “Effectiveness factors for immobilized-enzyme reactions”, Can. J. Chem. Eng., 50, 162 (1972).
34 Atkinson, B., Howell, J.A., “Slime holdup, influent BOD, and mass transfer in trickling filters”, J. Environ. Eng., 101 (EE4), 585-605 (1975).

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