Over the last decades the method of proper orthogonal decomposition (POD) has been successfully employed for reduced order modelling (ROM) in many applications, including distributed parameter models of chemical reactors. Nevertheless, there are still a number of issues that need further investigation. Among them, the policy of the collection of representative ensemble of experimental or simulation data, being a starting and perhaps most crucial point of the POD-based model reduction procedure. This paper summarises the theoretical background of the POD method and briefly discusses the sampling issue. Next, the reduction procedure is applied to an idealised model of circulating fluidised bed combustor (CFBC). Results obtained confirm that a proper choice of the sampling strategy is essential for the modes convergence however, even low number of observations can be sufficient for the determination of the faithful dynamical ROM.

Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control.

The work concerns the dynamic behaviour of a porous, isothermal catalyst pellet in which a simultaneous chemical reaction, diffusion and adsorption take place. The impact of the reactant adsorption onto the pellet dynamics was evaluated. A linear isotherm and a non-linear Freundlich isotherm were considered. Responses of the pellet to sinusoidal variations of the reactant concentration in a bulk gas were examined. It was demonstrated that the dynamics of the pellet is significantly affected both by accounting for the adsorption and by the frequency of the bulk concentration variations. The sorption phenomenon causes damping of the concentration oscillations inside the pellet and damping of its effectiveness factor oscillations. Depending on the frequency of the concentration oscillations in the bulk, the remarkable oscillations can involve an entire volume of the pellet or its portion in the vicinity of the external surface.