Stability analysis of steady-state solutions for porous catalytic pellets: Influence of the shape of the pellet

✍ Scribed by Andrzej Burghardt; Marek Berezowski

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 593 KB
• Volume: 50
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(94)00248-p

✦ Synopsis

Based on the established method of Berezowski and Burghardt (1993, Chem. Engng Sci. 48, 1517-1534) for analysing the bifurcation to oscillatory solutions, the effect of the pellet shape on the occurrence of oscillatory destabilization is studied. A linear analysis of the dynamics of the system studied led to a relation between the critical values of the Lewis number (i.e. those above which an oscillatory destabilization becomes possible) and the parameters of the system (?, //*, 00). The nonlinear analysis confirmed fully the results of the linear approach. An approximate analysis of the system of differential equations describing the process enabled analytical relations to be determined between the parameters of the system which define the limits of the oscillatory instability (Hopf bifurcation), limits of saddle-type instability and an approximate formula to determine the critical values of the Lewis number. The results of extensive calculations reveal a considerable increase in the critical value of the Lewis number when the pellet shape is changed from the infinite slab to infinite cylinder to sphere. It may therefore be concluded that the infinite slab and sphere represent the limiting dynamic characteristics with respect to the bifurcation to oscillatory solutions. The susceptibility of other shapes to oscillatory destabilization should lie between these two limiting dynamic characteristics corresponding to the sphere and infinite slab.