Numerical solution of differential and integral equations
The dynamic model of the reaction under study together with the conditions [1]: Z + ZO + ZCO + (Z$_{v}$OZ) + (Z$_{v}$OZ)O + (Z$_{v}$OZ)CO = 10$^{15}$ particles/cm$^{2} $ Z$_{v}$ + (Z$_{v}$OZ) + (Z$_{v}$OZ)O + (Z$_{v}$OZ)CO = 10$^{15}$ particles/cm$^{2}$ . oindent is presented in the following mathematical form: oindent dx$_{1}$/dt = 2k$_{1}$P(O$_{2})$(1 -- x$_{1} $-- x$_{2} $-- x$_{3}$ -- x$_{4 }$-- x$_{5})^{2}$ -- k$_{4}$x$_{1}$x$_{2}$ -- k$_{5}$x$_{1}$(1 -- x$_{3}$ -- x$_{4} $-- x$_{5})$ oindent dx$_{2}$/dt = k$_{2}$P(CO)(1 -- x$_{1} $-- x$_{2} $-- x$_{3}$ -- x$_{4} $-- x$_{5})$ -- k$_{3}$x$_{2}$ -- k$_{4}$x$_{1}$x$_{2} $-- k$_{11}$x$_{2}$ x$_{4 }$-- k$_{12}$x$_{2}$x$_{3}$ (1) oindent dx$_{3}$/dt = k$_{5}$x$_{1}$(1 -- x$_{3}$ -- x$_{4} $-- x$_{5})$ -- 2k$_{6}$P(O$_{2})$ x$_{3}^{2}$ -- k$_{7}$P(CO) x$_{3}$ + k$_{8}$x$_{5}$ + 2k$_{9}$x$_{4}$x$_{5}$ + k$_{11}$x$_{2}$ x$_{4}$ -- k$_{12}$x$_{2}$x$_{3}$ oindent dx$_{4}$/dt = 2k$_{6}$P(O$_{2})$ x$_{3}^{2}$ -- k$_{9}$x$_{4}$x$_{5}$ -- k$_{11}$x$_{2}$ x$_{4}$ oindent dx$_{5}$/dt = k$_{7}$P(CO)x$_{3}$ -- k$_{8}$x$_{5}$ -- k$_{9}$x$_{4}$x$_{5}$ -- k$_{10}$x$_{5}$ Here P(O$_{2})$, P(CO) are the partial pressures of O$_{2}$ and CO, respectively; x$_{i}$, i=1,ldots 5 are the dimensionless concentrations of intermediates ZO, ZCO, (Z$_{v}$OZ), (Z$_{v}$OZ)O, (Z$_{v}$OZ)CO, respectively; k$_{j}$, j=1,ldots 12 are the rate coefficients of elementary steps of the investigating mechanism.
Numerical study of the model (1) has been carried out by means of a software package STEP [2] elaborated in Sobolev Institute of Mathematics, SB RAS. Software package STEP is oriented to the qualitative analysis (construction of bifurcation diagrams, determination of stability, solution multiplicity, etc.) of the autonomous dynamic systems of ordinary differential equations (ODE): dx/dt = f(x,$alpha )$, where $alpha $ is one of the model parameters.
The results of physicochemical and numerical experiments lead to the conclusion that the basic peculiarities of the reaction kinetics under study are connected with the changing of the ratio ``IS/SO'' at the variation of the reaction conditions. It has been shown that SO effect the reaction dynamics mainly at high P(O$_{2})$/P(CO) ratio whereas at relatively low temperature and low P(O$_{2})$/P(CO) ratio the reaction of CO$_{2}$ formation proceed predominantly on the active centers of IS of iridium. The increasing of temperature and P(O$_{2})$/P(CO) ratio leads to the appearance of reaction rate hysteresis and changing of its shape. The numerical analysis of the model shows the possibility of the existence of the parameter regions with five steady states and with limit cycles. The dynamic properties of the iridium surface determine the main kinetic regularities of the carbon monoxide oxidation reaction. Only taking into account the influence of the reaction media on the catalytic surface (in our case the formation of the subsurface oxygen and changing of the properties of the surface layer) permit to construct the detailed reaction mechanism that can clarify the observed kinetic behavior.
[1] Elokhin V.I. and Boronin A.I. Dynamics of surface processes over iridium in carbon monoxide oxidation reaction.//Proc. of the First Soviet-Chinese Seminar on Catalysis, Novosibirsk, Russia, 1991, 5-20. [2] Fadeev S.I., Pokrovskaya S.A., Berezin A.Yu. and Gainova I.A. The software package STEP for numerical studying of nonlinear systems of equations and autonomous systems of the general form. Description how to use the package STEP by the example of the learning tasks from the university course ``Engineering chemistry of catalytic processes''. Manual, NSU, 1998.
Note. Abstracts are published in author's edition
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