ANALYSIS OF THE UNIFIED THERMAL AND CHAIN-BRANCHING MODEL OF HYDROCARBON OXIDATION

This paper investigates in detail the Gray-Yang model of hydrocarbon o xidation. The model incorporates initiation, branching and termination processes, and the rate of the branching and one of the termination p rocesses are governed by Arrhenius kinetics with different activation energies. It is also shown in this paper that the basic model is appli cable to two different situations, one of which involves a reservoir o f 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 equ ations governing the system are coupled and highly nonlinear. The solu tions to these equations yield the temperature in the vessel and the c oncentration of the intermediate chemical species. Under certain circu mstances, these solutions can exhibit oscillatory behaviour. In this p aper 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 rele ase rate at the steady state. Steady-state solutions are examined, and the Hopf condition for the emergence of limit cycles is given. Result s of extensive numerical investigation for the different behaviour typ es are presented. The presence of multiple limit cycles is detected an d discussed in detail. We show that oscillatory behaviour is confined only to a certain region of the parameter space and that the system al ways has a stable attractor for certain parameter values.