Optimization of Kinetic Parameters for an Aftertreatment Catalyst 2014-01-2814
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.  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®,  a commercial aftertreatment model. The genetic algorithm was developed and expanded from the code presented by Michalewicz et al.  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.