Boreskov Institute of Catalysis of the Siberian Branch of Russian ...

PP-II-3exist around the steady state – a stable and an unstable ones. If a steady state is located farfrom the borders of the unstable part of the thermal isoclinal line, so soft birth of selfoscillations(limit cycle) takes place. In this case the amplitude of self-oscillations is growingsmoothly. The solution of the non-steady problem has confirmed the detected mechanisms ofthe birth/death of self-oscillations.Consecutive reactions. For CSTR with a two-step consecutive reaction (both stagesbeing exothermal first-order processes), analysis of the multiplicity of the steady states andthe mechanism of birth/death of self-oscillations have been carried out. A region of fivesteady states was discovered for the first time. Its evolution with the change of the ratio of theactivation energy of the first stage to that of the second stage has been investigated. It wasshown that this region arises within the region of three steady states. With the growth of theabove ratio, it is elongated and partly oversteps the limits of the region of three steady states.This part of the domain contains just only three stationary states.For a definite set of kinetic parameters in the parametric space Semenov criterion –Damköhler criterion, a region of the existence of self-oscillations was found. For the regionof one steady state, it was shown that at the lower border of the self-oscillation region (smallvalues of Semenov parameter) their birth occurs by a soft way. The steady state becomesunstable and gives rise to a stable limit cycle. At the upper border of the self-oscillationregion (large values of Semenov parameter), stiff death of self-oscillations takes place: astable limit cycle is joined with an unstable limit cycle. The unstable limit cycle arises at thechange of the steady state stability.For the region of three steady states it was demonstrated that at lower border of the selfoscillationregion, the oscillation arise by a stiff way, by the mechanism of a loop formation.This work was supported by the Russian Foundation of Fundamental Researches, thegrant No. 06–03–32053–a.Reference1. D.A. Vaganov, N.G. Samoilenko, V.G. Abramov, Periodic Regimes of Continuous Stirred Tank Reactors,Chem. Eng. Science, Vol. 33, pp. 1133-1140 (1978).278