This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Optimization of Kinetic Parameters for an Aftertreatment Catalyst
Technical Paper
2014-01-2814
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
Mathematical modelling has become an essential tool in the design of modern catalytic systems. Emissions legislation is becoming increasingly stringent, and so mathematical models of aftertreatment systems must become more accurate in order to provide confidence that a catalyst will convert pollutants over the required range of conditions.
Automotive catalytic converter models contain several sub-models that represent processes such as mass and heat transfer, and the rates at which the reactions proceed on the surface of the precious metal. Of these sub-models, the prediction of the surface reaction rates is by far the most challenging due to the complexity of the reaction system and the large number of gas species involved. The reaction rate sub-model uses global reaction kinetics to describe the surface reaction rate of the gas species and is based on the Langmuir Hinshelwood equation further developed by Voltz et al. [1] The reactions can be modelled using the pre-exponential and activation energies of the Arrhenius equations and the inhibition terms.
The reaction kinetic parameters of aftertreatment models are found from experimental data, where a measured light-off curve is compared against a predicted curve produced by a mathematical model. The kinetic parameters are usually manually tuned to minimize the error between the measured and predicted data. This process is most commonly long, laborious and prone to misinterpretation due to the large number of parameters and the risk of multiple sets of parameters giving acceptable fits. Moreover, the number of coefficients increases greatly with the number of reactions. Therefore, with the growing number of reactions, the task of manually tuning the coefficients is becoming increasingly challenging.
In the presented work, the authors have developed and implemented a multi-objective genetic algorithm to automatically optimize reaction parameters in AxiSuite®, [2] a commercial aftertreatment model. The genetic algorithm was developed and expanded from the code presented by Michalewicz et al. [3] and was linked to AxiSuite using the Simulink add-on for Matlab.
The default kinetic values stored within the AxiSuite model were used to generate a series of light-off curves under rich conditions for a number of gas species, including CO, NO, C3H8 and C3H6. These light-off curves were used to generate an objective function.
This objective function was used to generate a measure of fit for the kinetic parameters. The multi-objective genetic algorithm was subsequently used to search between specified limits to attempt to match the objective function. In total the pre-exponential factors and activation energies of ten reactions were simultaneously optimized.
The results reported here demonstrate that, given accurate experimental data, the optimization algorithm is successful and robust in defining the correct kinetic parameters of a global kinetic model describing aftertreatment processes.
Recommended Content
Authors
Citation
Pedlow, A., McCullough, G., Goguet, A., and Hansen, K., "Optimization of Kinetic Parameters for an Aftertreatment Catalyst," SAE Technical Paper 2014-01-2814, 2014, https://doi.org/10.4271/2014-01-2814.Also In
References
- Voltz , Se , Morgan , C.R. , Liederma , D. , and Jacob , S.M. 1973 Kinetic study of carbon-monoxide and propylene oxidation on platinum catalysts Industrial & Engineering Chemistry Product Research and Development 12 4 294 301
- Exothermia , S. A. Axisuite version 2013A user guide, 2012A
- Michalewicz , Z. 1999 Genetic algorithms + data structures = evolution programs 3rd Springer-Verlag
- Olsson , L. , and Andersson , B. 2004 Kinetic modelling in automotive catalysis Topics in Catalysis 28 1-4 APR 89 98
- Stewart , J. , Douglas , R. , Goguet , A. , and Glover , L. Limitations of Global Kinetic Parameters for Automotive Application SAE Technical Paper 2012-01-1638 2012 10.4271/2012-01-1638
- Lapidus L , Amundson N Chemisorption kinetics and equilibria Chemical reactor theory 1977 160 164
- Khajehzadeh , Mohammad , Taha Mohd Raihan , El-Shafie Ahmed , and Eslami Mahdiyeh 2011 A survey on meta-heuristic global optimization algorithms Research Journal of Applied Sciences, Engineering and Technology 3 6 569 78
- Terry , D. B. , Bader J. L. , and Messina M. 1999 Simulated annealing search algorithm for the determination of activation energies and Arrhenius prefactors from limited experimental kinetic data Journal of Chemical Information and Computer Sciences 39 6 1204 10
- Da Silva , Leite Armando M. , Manso Da Fonseca , De Resende Leonidas C. , and Rezende Leandro S. 2008 Tabu search applied to transmission expansion planning considering losses and interruption costs 10th International Conference on Probabilistic Methods Applied to Power Systems, PMAPS 2008 May 25 2008 May 29
- Elliott , L. , Ingham , D. B. , Kyne , A. G. , Mera , N. S. , Pourkashanian , M. , and Wilson , C. W. 2004 A novel approach to the optimization of reaction rate parameters for methane combustion using multi-objective genetic algorithms Journal of Engineering for Gas Turbines and Power 126 3 455 64
- Pontikakis , G. , and Stamatelos A. 2001 Mathematical modelling of catalytic exhaust systems for EURO-3 and EURO-4 emissions standards Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 215 9 1005 15
- Pontikakis , G. N. , and Stamatelos A. M. 2004 Identification of catalytic converter kinetic model using a genetic algorithm approach Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 218 12 1455 72
- Ling , Chen , Hai-Ying Sun , and Shu Wang 2012 A parallel ant colony algorithm on massively parallel processors and its convergence analysis for the travelling salesman problem Information Sciences 199 31 42
- Kennedy , J. , and Eberhart R. 1995 Particle swarm optimization Proceedings of ICNN'95 - International Conference on Neural Networks
- Di , Zhou , Jun Sun , and Wen-bo Xu 2011 Quantum-behaved particle swarm optimization algorithm with cooperative approach Control and Decision 26 4 582 6
- Chuang , Yao-Chen , and Chen Chyi-Tsong 2011 A study on real-coded genetic algorithm for process optimization using ranking selection, direction-based crossover and dynamic mutation 2011 IEEE Congress of Evolutionary Computation, CEC 2011 June 5 2011 June 8
- Falkenauer , E. 1998 Genetic algorithms and grouping problems John Wiley & Sons
- Ding , Chao , Cheng Ye , and He Miao 2007 Two-level genetic algorithm for clustered traveling salesman problem with application in large-scale TSPs Tsinghua Science and Technology 12 4 459 65
- Li , Wang , Li Bi , and Zhang Qiansheng 2012 Genetic algorithm with geographic speciation 2012 8th International Conference on Natural Computation, ICNC 2012 May 29 2012 May 31
- Lee , Cheol-Gyun , Cho Dong-Hyeok , and Jung Hyun-Kyo 1999 Niching genetic algorithm with restricted competition selection for multimodal function optimization IEEE Transactions on Magnetics 35 3 1722 5
- Sareni , B. , and Krahenbuhl L. 1998 Fitness sharing and niching methods revisited IEEE Transactions on Evolutionary Computation 2 3 97 106
- Della Cioppa , Antonio , De Stefano Claudio , and Marcelli Angelo 2007 Where are the niches? dynamic fitness sharing IEEE Transactions on Evolutionary Computation 11 4 453 65
- Mc Ginley , Brian , Maher John , O'Riordan Colm , and Morgan Fearghal 2011 Maintaining healthy population diversity using adaptive crossover, mutation, and selection IEEE Transactions on Evolutionary Computation 15 5 692 714