Analysis of the unified thermal and chain-branching model of hydrocarbon oxidation

H. S. Sidhu, L. K. Forbes, Brian Gray

Research output: Contribution to journalArticlepeer-review


This paper investigates in detail the Gray-Yang model of hydrocarbon oxidation. The model incorporates initiation, branching and termination processes, and the rate of the branching and one of the termination processes are governed by Arrhenius kinetics with different activation energies. It is also shown in this paper that the basic model is applicable to two different situations, one of which involves a reservoir of initial reagent, and the other pertains to flow and conditions in a continuously stirred tank reactor (CSTR), although the parameters have different physical interpretations in each case. The mathematical equations governing the system are coupled and highly nonlinear. The solutions to these equations yield the temperature in the vessel and the concentration of the intermediate chemical species. Under certain circumstances, these solutions can exhibit oscillatory behaviour.

In this paper we present a rigorous mathematical and numerical analysis of the system. We show that depending on the parameters used, there are three different behaviour types, which also depend on the overall heat release rate at the steady state. Steady-state solutions are examined, and the Hopf condition for the emergence of limit cycles is given. Results of extensive numerical investigation for the different behaviour types are presented. The presence of multiple limit cycles is detected and discussed in detail. We show that oscillatory behaviour is confined only to a certain region of the parameter space and that the system always has a stable attractor for certain parameter values.

Original languageEnglish
Pages (from-to)493-514
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1937
Publication statusPublished - 8 Jun 1995
Externally publishedYes



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