# Parameter estimation in heterogeneous catalysis

[Doktorsavhandling]

The detailed modelling of heterogeneous catalytic systems is challenging due to the unknown nature of new catalytic materials as well as the often required transient nature of the resulting models. Thus, this thesis deals with the methodologies involved in the kinetic modelling of heterogeneous catalysis and in particular NOx reduction systems. The methods presented increase the understanding of the interplay between model parameters and also decrease the number of necessary laboratory experiments. The effect of more efficient parameter estimation methods should result in faster model development which is required in any process development but especially for catalytic emission control. In the first paper, injection parameters for an engine rig with a NOx Storage and Reduction (NSR) system were optimised using different experimental designs at different load points. The optimised settings were used as a map for a control strategy complying with a European Transient Cycle (ETC). In the second paper, we developed a method that copes with the large number of unknown model parameters by applying a Latent Variable (LV) model to the Jacobian matrix in the fitting procedure. The LV model results in a low-dimensional approximation of the Jacobian with reduced parameter correlation and enables improved efficiency in parameter estimation. In the third paper, Experimental design for precise parameter estimation was performed in a batch-sequential way using D-optimality as the objective function. A screening methodology similar to that used for drug discovery in the pharmaceutical industry was applied for a large number of simulated candidate experiments. By applying an LV model to the Jacobian of all these experiments, a reduced parameter correlation was obtained and the number of necessary experiments was reduced. The results from the second and third paper pinpoint a number of benefits of using LV models including: 1) the determination of the effective rank, i.e. the number of independent phenomena present in the data at hand, 2) the analysis of the correlation structure which is useful in the parameter assessment and 3) the linear approximation in few dimensions enables more efficient computations. In the fourth paper, a detailed model for the Selective Catalytic Reduction of NOx using Hydrocarbon as a reducing agent (HC-SCR) over silver alumina (Ag-Al2O3) was developed. By applying an experimental design to the steady state levels and also selecting the run order, improved fitting properties were obtained due to the increased parameter sensitivity enabled by the transient experiments. This thesis also contains a description of the modelling techniques and challenges encountered during this thesis project. An assessment of the importance as well as the parameter correlation is given. This demonstrates the intimate interplay between model assumptions and the stipulated model parameters and exemplifies a thorough assessment of the whole modelling chain from initial experiments to model validation.

**Nyckelord: **Parameter estimation, Jacobian, Latent Variable models, Experimental design, Design of experiments, microkinetic modelling, heterogeneous catalysis, sensitivity analysis

Denna post skapades 2009-04-22. Senast ändrad 2014-09-17.

CPL Pubid: 92706