Bifurcation parameters, computational model

In our computational model the strain rate and the equivalence ratio are the natural bifurcation parameters. If we denote either of these parameters by a, then the system of equations in (3.2) can be written in the form... 

To study a class of mechanisms for isothermal heterogeneous catalysis in a CSTR, Morton and Goodman (1981-1) analyzed the stability and bifurcation of simple models. The limit cycle solutions of the governing mass balance equations were shown to exist. An elementary step model with the stoichiometry of CO oxidation was shown to exhibit oscillations at suitable parameter values. By computer simulation limit cycles were obtained. 

Figure 24 Period-doubling bifurcations in the Rossier model, Eqs. [106]. For these simulations (computed using the Runge-Kutta routine DiffEq-3D, with stepsize = 0.1, available through Ref. 18), the following parameters were used a = 0.1 and b = 0.2 with c variable. In (a) c = 2.5 ind the initial values were Xq = -2.98, =... 

When investigating a model of a chemical plant or process, one of the most important tasks is to determine the influence of model parameters like operation conditions or geometric dimensions on performance and dynamics. Because in most cases a large number of parameters has to be examined, an efficient tool for the determination of parameter dependencies is required. Continuation methods in conjunction with the concepts of bifurcation theory have proved to be useful for the analysis of nonlinear systems and are increasingly used in chemical engineering science. They offer the possibility to compute steady states or periodic solutions directly as a function of one or several parameters and to detect changes in the qualitative behaviour of a system like the appearance or disappearance of multiple steady states. In this paper, numerical methods for the continuation of steady states and periodic solutions for large sparse systems with arbitrary structural properties are presented. The application of this methods to models of chemical processes and the problems which arise in this context are discussed for the example of a special type of catalytic fixed bed reactor, the so-called circulation loop reactor. 

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