Mathematical Modelling of Structured Reactors with Emphasis on Catalytic Combustion Reactions

by Papadias, Dennis

Investigations with specific emphasis on geometrical aspects in the mathematical modelling of structured reactors for catalytic combustion reactions are presented in this thesis. Focus has been on addressing the implications of geometry and on investigating the potential of model reductions. Furthermore, mathematical modelling as a tool for characterising chemical reactors has also been used for the development and design of structured reactors for kinetic measurements. The thesis is a summary of five papers and is divided into three main parts. The first part is an introductory text to the field of catalytic combustion. The concept and status of this technology in applications for gas turbine power generation are briefly summarised. Mathematical modelling and its application to catalytic combustors are furthermore addressed, emphasising the principles in the development of mathematical models. The second part is concerned with simplification in the mathematical treatment of reaction and diffusion in irregular geometries of monolithic coatings. A simplified method is developed where the two-dimensional geometry of the washcoat is reduced to a series of one-dimensional particles. The main idea is that the washcoat may be considered as a set of particles side by side on the monolith wall and that for each particle the effect of reaction and diffusion may be calculated individually by a simple formula or algorithm. The simplified method is compared with multidimensional models using the finite element method for different geometries and kinetic values showing a good agreement in most cases. The method is investigated for cases of two- and three-dimensional concentration fields with a significant reduction in the computational labour compared to the full set of washcoat equations. The last part is concerned with the development of a structured annular reactor for kinetic measurements under large flow and high temperature conditions. One of the major benefits of this reactor is that it offers almost isothermal conditions of the catalyst phase, which allows for an easier interpretation of kinetic data in highly exothermic combustion reactions. However, due to deformation problems, a high degree of eccentricity may exist between the tubes of the annular reactor, which strongly increases the effect of external mass-transfer resistances. A comparison between 3D and 1D models showed that lumped models might not be adequate for properly quantifying mass-transfer effects and hence analysing kinetic data in eccentric reactors unless the reactor is nearly concentric. As a consequence of the model analysis, an annular reactor was designed with the goal of keeping the eccentricity within narrow limits, close to a concentric tube. A characterisation of the reactor was performed through a combination of mathematical modelling and experiments, verifying that the reactor was closely concentric under reaction conditions.