Simulation of Chemical Reactors

This thesis consists basically of two parts. They are, however, interrelated by the fact that both parts concerns modelling of catalytic reaction systems and also by the fact that in both parts, spectral methods are used for simulation. The first part describes the numerical treatment of the dispersion model. The model is used to simulate a packed-bed reactor producing formaldehyde from methanol with an iron/ molybdenum catalyst. The self-adjoint partial differential operators involved in the model can, based on the Spectral theorem, be used to obtain infinite series of ordinary differential equations. After solving these equations, the solution to the original equation is obtained by summation. An advantage of the solution method is the possibility to obtain information regarding system behaviour, before actually simulating the system. This information can be extracted from the spectra of eigenvalues obtained after resolving the self- adjoint operators. The second part describes the simulation of heterogeneous/homogeneous combustion where the catalyst is located at the solid wall in contact whith a reactive gas flow. The full equation system, describing compressible fluid flow and chemical reactions, is solved. The numerical solution includes handling of non-linear differential operators which makes the simulation much more difficult than the one performed in part I. The impact of the convective/diffusive operators involved in the simulations become differently important in different areas in space, i.e. in areas far from the solid phase, the convective part will dominate whereas the diffusive part will dominate close to the solid. In order to resolve each contribution efficiently, a fractional step method was used whereby the equation systen was divided into hyperbolic, parabolic and reaction steps. The different steps were then calculated with spectral methods suitable for each specific type of equation system.