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

PP-III-46MATHEMATICAL MODELLING OF A CO-CURRENT REACTORI.S. VerzhbitskayaAl-Farabi Kazakh National University, 71 Al-Farabi st., Almaty 050078, Kazakhstan,fax: +7(727) 247-26-09, e-mail: i_verb@mail.ruThis paper deals with mathematical modeling of a cooled catalytic fixed-bed reactorwhere single exothermic reaction occurs. An important class of reactors is that for which thewall temperature is not constant but varies along reactor length. Such is the case when thecooling tubes and reactor tubes form an integral part of a composite heat exchanger. In thisstudy co-current flow of coolant and reaction mixture is considered. It is assumedinstantaneous heat transfer between the solid catalyst and the reacting gas mixture, constantheat-physical properties and negligible diffusivity inside catalyst pellets. The heat and masstransfer resistance through the packing and gas mixture inside the bed are described by theeffective coefficients of conductivity and diffusivity. Reaction rate varies with temperature byArrhenius law. With these assumptions a two-dimensional pseudo homogeneous model ofheat and mass transfer was used. The partial differential equations (PDE) involve threedecision variables (coolant temperature, gas mixture temperature and concentration), whichvary on time and along two space coordinates.Due to high non-linearity and major number of system parameters of these equations theproblem can only be solved in this form by numerical techniques. In order to obtain a previewof possible dynamics and initial guesses for computations it is necessary to simplify theproblem and give equations which can be solved analytically. For that the set of PDE wasconverted to ordinary differential equations (ODE) by discretization of the spatial derivativeswith finite differences. Then the resultant ODE system (the dynamical system of the 3 rd order)was used for finding steady states and periodic solutions, determining their local stability andbifurcation points. By applying the methods of bifurcation theory [1] the analyticalexpressions for bifurcation diagram and non-unique boundary were obtained. It was foundthat the system can possess from 1 to 3 different equilibrium states. One equilibrium staterepresents a meta-stable and the remaining two states correspond to high- or low-temperatureregime, depending on initial conditions. The stability of steady states was investigated on thebasis of linear approximation of simplified model by applying the 1 st Lyapunov method andRouth-Hurwitz stability criterion [1]. The parametric equations of stability boundaries in theplane «inlet gas temperature»(ϑ 0 ) – «reaction heat»(q) were obtained. These boundariesdivide the parametric plane ϑ 0 ,q into 6 regions with different type of stability and number of389