Abstract
Nonlinear kinetic parameter estimation plays an essential role in kinetic study in reaction engineering. In the present study, the feasibility and reliability of the simultaneous parameter estimation problem is investigated for a multi-component photocatalytic process. The kinetic model is given by the L-H equation, and the estimation problem is solved by a hybrid genetic-simplex optimization method. Here, the genetic algorithm is applied to find out, roughly, the location of the global optimal point, and the simplex algorithm is subsequently adopted for accurate convergence. In applying this technique to a real system and analyzing its reliability, it is shown that this approach results in a reliable estimation for a rather wide range of parameter value, and that all parameters can be estimated simultaneously. Using this approach, one can estimate kinetic parameters for all components from data measured in only one time experiment.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- ci :
-
concentration of componenti [mol/L]
- cexact(m):
-
the ideal (without error) concentration at the mth instance [mol/L]
- ci,(m):
-
the mth observation of concentration of the component i [mol/L]
- csimulated (m) :
-
the simulated concentration at the mth instance [mol/ L]
- Ĉi(m):
-
the mth simulated concentration of componenti [mol/ L]
- e:
-
the relative error
- Fj :
-
the fitness of jth chromosome
- J:
-
object function
- Ji :
-
object function of componenti
- k :
-
collection of all reaction rate constant
- ki :
-
reaction rate constant of componenti [mol/(L)(s)]
- k ji :
-
the jth possible value of ki
- K :
-
collection of all adsorption equilibrium constants
- Ki :
-
adsorption equilibrium constant of componenti [L/ mol]
- K ji :
-
the jth possible value of Ki
- lk :
-
lower limit of the reaction rate constant
- lK :
-
lower limit of the adsorption equilibrium constant
- Pj :
-
possibility of thejth chromosome
- ri :
-
reaction rate of componenti [mol/(L)(s)]
- uk:
-
upper limit of the reaction rate constant
- UK:
-
upper limit of the adsorption equilibrium constant
- Vi :
-
the ith chromosome
- wi :
-
average weight of componenti
- x:
-
one of estimated reaction rate constants or adsorption equilibrium constants
- x:
-
average of x
- ε(m):
-
random error at the mth instance
References
Alberici, R. M. and Jarditn, W. F., “Photocatalytic Destruction of VOCs in the Gas-Phase Using Titanium Dioxide”,Applied Catlysis B: Environment,14, 55 (1997).
Anpo, M., Matsuoka, M., Hano, K., Mishima, H., Ono, T. and Yamashita, H., “Photocatalytic Decomposition of N2O on Cu+/Y-Zeolite Catalysts Prepared by Ion-Exchange”,Korean J. Chem. Eng.,14, 498 (1997).
Balland, L., Estel, E., Cosmao, J. M. and Mouhab, N., “A Genetic Algorithm with Decimal Coding for Estimation of Kinetic and Energetic Parameter”,Chemometrics and Laboratory Intelligent Systems,50, 121 (2000).
Belohlav, Z., Zamostny, P., Kluson, P. and Volf, J., “Application of Random-Search Algorithm for Regression Analysis of Catalytic Hydrogenations”,Canadian Journal of Chemical Engineering,75, 735 (1997).
Biegler, L. T., Damiano, J. J. and Blau, G. E., “Nonlinear Parameter Estimation: A Case Study Comparison”,AIChE Journal,32, 29 (1986).
Chai, Y. S., Lee, J. C. and Kim, B. W., “Photocatalytic Disinfection ofE. coli in a Suspended TiO2/UV Reactor”,Korean J. Chem. Eng.,17, 633 (2000).
Cheney, W. and Kincaid, D., “Numerical Mathematics and Computing”, Cole Publish Co., New York (1985).
Farza, M., Hammouri, H., Othman, S. and Busawon, K., “Nonlinear Observers for Parameter Estimation in Bioprocesses”,Chemical Engineering Science,52, 4251 (1997).
Fox, M. A. and Dulay, M. T., “Heterogeneous Photocatalysis”,Chemical Review,93, 341 (1993).
Froment, G. F., “The Kinetics of Complex Catalytic Reactions”,Chemical Engineering Science,42, 1073 (1987).
Gen, M. and Cheng, R. W., “Genetic Algorithms and Engineering Design”, Wiley, New York (1997).
Goldberg, D. E., “Genetic Algorithms in Search, Optimization and Machine Learning”, Addison-Welsly, New York (1989).
Herrmann, J. M., “Heterogeneous Photocatalysis: Fundamentals and Application to the Removal of Various Types of Aqueous Pollutants”,Catalysis Today,53, 115 (1999).
Kim, I. W., Liebman, M. J. and Edgar, T F., “Robust Error-in-Variables Estimation using Nonlinear Programming Techniques”,AIChE Journal,36, 985 (1990).
Levenspiel, O., “Chemical Reaction Engineering”, Wiley, New York (1972).
Mehrab, M., William, A. A., Murray, M. Y. and Park, M. R., “Non-linear Parameter Estimation for a Dynamic Model in Photocatalytic Reaction Engineering”,Chemical Engineering Science,55, 4885 (2000).
Michalewicz, Z., “Genetic Algorithm+Data Structure=Evolution Programs (second edition)”, Springer-Verlag, New York (1994).
Oh, S. C., Sohn, S. H., Yeo, Y. K. and Chang, K. S., “A Study on the Prediction of Ozone Formation in Air Pollution”,Korean J. Chem. Eng.,16, 144 (1999).
Ollis, D. F., “Photocatalytic Purification and Remediation of Contaminated Air and Water”,C. R. Acad. Sci. Paris, Se ’rie IIc, Chimie/Chemistry,3, 405(2000).
Park, T. Y. and Froment, G. F., “A Hybrid Genetic Algorithm for the Estimation of Parameters in Detailed Kinetic Models”,Computers in Chemical Engineering,22, 103 (1998).
Press, W H., Flnnery, B. P., Teukolsky, S, A. and Vetterling, W. T., “Nu merical Recipes”, Cambridge University Press, New York (1986).
Sirisuk, A., Hi11Jr, C. G. and Anderson, M. A., “Photocatalytic Degradation of Ethylene over Thin Films of Titania Supported on Glass Rings”,Catalysis Today,54, 159 (1999).
Turchi, C. S. and Rabago, R., “Bench scale Testing of Photocatalytic Oxidation (PCO) to Destroy Volatile Organic Compound (VOC) Emissions”,SEMATECH Technology Transfer Report #95042791A-ENG (1995).
Turchi, C. S., Rabago, R. and Jassal, A., “Destruction of Volatile Organic Compound (VOC) Emissions by Photocatalytic Oxidation (PCO): Field Test Results”,SEMATECH Technology Transfer Report #96083084A-ENG (1996).
Winston, W L., “Introduction to Mathematical Programming: Application & Algorithm”, PWS-Kent, Boston (1991).
Wolf, D. and Moros, R., “Estimation of Rate Constants of Heterogeneous Catalytic Reactions without Supposition of Rate Determining Surface Steps — An Application of a Genetic Algorithm”,Chemical Engineering Science,52, 1189 (1997).
Wolfrum, E. J., Rabago, R. and Jassal, A., “Destruction of Volatile Organic Compound (VOC) Emissions by Photocatalytic Oxidation (PCO): Final Reports”, SEMATECH Technology Transfer Report #97013236A-ENG (1997).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Kim, C.N. On the feasibility and reliability of nonlinear kinetic parameter estimation for a multi-component photocatalytic process. Korean J. Chem. Eng. 18, 652–661 (2001). https://doi.org/10.1007/BF02706382
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02706382