Stability analysis of steady-state solutions for porous catalytic pellets

Abstract

Stability analysis of steady-state solutions has been performed for a model which describes transport phenomena and chemical reaction in a porous catalyst pellet. The model equations have been derived based on the assumption that the resistance to heat transfer is concentrated in a boundary layer around the pellet, while the resistance to mass transfer occurs only inside the pellet. The model, employed in previous publications by the authors, revealed some very interesting new features of the structure of steady-state solutions. In the present work only the stability of stationary solutions with respect to static bifurcation is analysed. Applying Liapunov's indirect method, a local stability condition has been derived in which the kinetics of chemical reaction is represented by the function defining the effectiveness factor of a catalyst pellet. In order to determine the size of the neighbourhood in which a given stationary point remains asymptotically stable, a global stability analysis has been performed based on Popov's frequency method. An analytical condition for the global stability has been derived. The analysis of the stochastic model of the process led to the condition for the asymptotic stochastic stability, which determines the region of asymptotic stability with probability one. This region is smaller than that found for the deterministic model.