Necessary conditions for steady-state multiplicity for (m,n)-th order reactions and analysis of multiplicity patterns for a class of single reactions in perfectly mixed reactors
✍ Scribed by L.H. Hosten
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 971 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0009-2509
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✦ Synopsis
The first part of the paper presents exact necessary conditions for steady-state multiplicity for a general (m,n)-th order reaction as considered by Lin (1980, Chem. Engng Sci. 35. 1537-1543). The effect of changes in the various parameters on the location of the cusp point is investigated. The second part presents an analysis of multiplicity patterns for a class of single reactions described by rate equations of the type r = kcpe -EIRT /( 1 + Kc)~, as considered by Tsotsis et al. (1982, Chem. Engng Sci. 37, 1235-1243), and which may exhibit up to five steady states. The construction of the hysteresis and double limit varieties allows the parameter space to be subdivided into subregions corresponding to all possible multiplicity patterns, 1,1-3-l, 1-3-1-3-1, l-3-5-3-1, and within the latter pattern corresponding to the four possible different bifurcation diagrams. Exact necessary and sufficient conditions are presented for all these types of hysteresis behaviour. Some numerical data are given which should be helpful in gaining some insight into this phenomenon. 1. INTRODUmION