Premium
Stability and uniqueness of a catalyst particle problem: Parameter optimization in Liapunov functions
Author(s) -
Liou ChingTien,
Lim Henry C.,
Weigand William A.
Publication year - 1973
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690190217
Subject(s) - uniqueness , mathematics , stability (learning theory) , steady state (chemistry) , weighting , mathematical analysis , state (computer science) , matrix (chemical analysis) , chemistry , physics , computer science , algorithm , machine learning , acoustics , chromatography
In the analysis of stability and uniqueness of steady state through the Liapunov functional technique, the Liapunov functional is not unique and different forms can lead to significantly different results. A method is proposed in which the state vector and/or the parameters in the weighting matrix S( x ) are optimized to obtain less conservative results than those reported previously. For the problem of stability and uniqueness of the steady state of a chemical reaction occurring in a catalyst particle with slab geometry, several sufficient conditions for stability have been developed for both cases of unity and nonunity Lewis numbers in terms of the system parameters and steady state profiles, the system parameters and the catalyst center temperature, and the system parameters alone. These conditions are shown to be stronger than the previously reported results (Murphy and Crandall, 1970). Sufficient conditions for uniqueness have also been developed. For unity Lewis number our uniqueness condition is stronger than the previously reported result (Luss and Amundson, 1967), and for non‐unity Lewis number our uniqueness result is new.