Hs. Sidhu et al., ANALYSIS OF THE UNIFIED THERMAL AND CHAIN-BRANCHING MODEL OF HYDROCARBON OXIDATION, Proceedings - Royal Society. Mathematical and physical sciences, 449(1937), 1995, pp. 493-514
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.