STABILITY ANALYSIS OF STEADY-STATE SOLUTIONS FOR POROUS CATALYTIC PELLETS - INFLUENCE OF THE SHAPE OF THE PELLET

Based on the established method of Berezowski and Burghardt (1993, Che m. Engng Sci. 48, 1517-1534) for analysing the bifurcation to oscillat ory solutions, the effect of the pellet shape on the occurrence of osc illatory destabilization is studied. A linear analysis of the dynamics of the system studied led to a relation between the critical values o f the Lewis number (i.e. those above which an oscillatory destabilizat ion becomes possible) and the parameters of the system (gamma, beta, theta(o)). The nonlinear analysis confirmed fully the results of the l inear approach. An approximate analysis of the system of differential equations describing the process enabled analytical relations to be de termined between the parameters of the system which define the limits of the oscillatory instability (Hopf bifurcation), limits of saddle-ty pe instability and an approximate formula to determine the critical va lues of the Lewis number. The results of extensive calculations reveal a considerable increase in the critical value of the Lewis number whe n the pellet shape is changed from the infinite slab to infinite cylin der to sphere. It may therefore be concluded that the infinite slab an d sphere represent the limiting dynamic characteristics with respect t o the bifurcation to oscillatory solutions. The susceptibility of othe r shapes to oscillatory destabilization should lie between these two l imiting dynamic characteristics corresponding to the sphere and infini te slab.