Mathematical treatment of transient kinetic data: Combination of parameter estimation with solving the related partial differential equations

To exploit the full potential of transient techniques modelling is required such that reaction rate constants of elementary reaction steps may be obtained. Such a model is characterised by a set of coupled partial differential equations (PDEs). The numerical method of lines has been employed here to solve the PDEs. The principle of this method is approximation of spatial derivatives reducing the PDEs to a set of coupled ordinary differential equations (ODEs). Several robust numerical methods for solving coupled ODEs are discussed. The unknown reaction parameters are estimated by coupling the PDE solving method to a method which minimises the difference between the model and the experimental data. Several numerical minimisation methods are discussed. Three examples are given which show the potential of this procedure in heterogeneous catalysis.