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

PP-I-26FIVE-PHASIC OSCILLATORS IN HETEROGENEOUS CATALYSISO.V. Dimitrieva and N.I. KoltsovChuvash State University, Moskovskii pr. 15, Cheboksary, Russia,Tel.: (+78352)452468, Fax: (+78352) 428090, E-mail: koltsovni@mail.ruIn works [1,2] for the description of self-oscillations in kinetics of catalytic reactionsthree-and four-stage schemes have been used. It is known [3] that the increase in number ofstages in mechanisms of catalytic reactions results in complication of their kinetic behaviourand allows to describe self-oscillations by schemes with smaller molecularity making stages.It proves to be true results of research of four-stage schemes and their comparison to results ofthe analysis of three- stage schemes. In the given message the possibility of the description ofself-oscillatory regimes in heterogeneous catalytic reactions with the help five-stagebimolecular on intermediate substances of the schemes is investigated.Let's consider any one-routing heterogeneous catalytic reaction consisting of a stage+ie Ae+ +−aijX j = aijX j + ∑−∑ν ∑ ∑ νieAe, di,i,j = 1,..., n;e = 1,..., s,(1)ejje+ −+ −where А е and X j – the basic and intermediate substances, ν , and a , – stoichiometriccoefficient (∑j+ =∑a ij aj−ij), d i > 0 – stoichiometric numbers of stages. In conditions of anisothermal differential reactor the non-stationary behaviour of reaction is described by system− +x& j = ( aij− aij)( ri− r−i ) ≡ ϕ j(2)∑i∑where x j – concentration of substances Х j ( x = 1,x ≥ 0 ); r i , r -i ≥0 – rates of a stage in thedirect and return directions± i =ν ie∏ C±e± ie∏jjj∏=+aiji i x j r− i = ω−ijjr−aijjω , x ,k ±iω k – frequencies of stages, – constants of stage rates; С е – concentration ofbasic substances А e .For kinetic model (2) we shall enter a characteristic multinominaln−1n−2λ λ σ λ + + σ =(3)( ) 0+ 1−... n 1one of which λ roots is equal to zero in view of validity for heterogeneous catalytic reactionsof the law of preservation =1. Coefficients of characteristic multinominal (3) can becalculated as:∑ x jj∂ϕj⎛ ∂ϕ⎞σ 1 = −∑ ,j ∂∑⎜j ∂ϕ∂ϕk j ∂ϕkσ 2 = −− ⎟ ,… (4)xjj