Dynamic and Steady-State Bifurcation for Modeling Chemical Reaction Systems

Citation

Lyberatos, Gerasimos (1984) Dynamic and Steady-State Bifurcation for Modeling Chemical Reaction Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/bspw-np07. https://resolver.caltech.edu/CaltechETD:etd-01112007-103406

Abstract

Chemical reaction systems often exhibit nonlinear dynamic phenomena such as multiple steady states and different types of nonlinear oscillations. Furthermore, nonlinear dynamic models are essential for control and input optimization of chemical reactors. Methods of bifurcation theory are used for analysis of the nonlinear behavior of chemical reaction systems and for chemical reactor model discrimination and identification. The latter objective is attained by forcing "tame" chemical systems to bifurcate and provide valuable information about the nonlinear system nature. Discrimination between rival kinetic models is demonstrated and a strategy for accurate parameter estimation is developed. The problem of steady-state bifurcation to multiple steady states in the event that the original model equations are not reducible to a single algebraic equation is attacked using the simple geometrical method of Newton Polyhedra. This method is particularly useful for analysis of feedback induced steady-state bifurcations. The theory of normal forms is used to illustrate that systems when close to bifurcation exhibit even locally their non-linear characteristics. The most common types of bifurcation phenomena are discussed and the minimum number of feedback (or system) parameters that must be varied to attain the various bifurcational structures is determined. Systems that are easily reducible to normal forms (simpler locally equivalent polynomial systems) are identified with distinctive advantages for the study of steady state and eigenvalue structure close to bifurcation. The analogy between some chemical systems and a particle's motion in a potential field is exploited to gain special insights into the chemical systems' dynamics. Chemical examples include nitrous oxide decomposition on NiO catalyst, consecutive-competitive reaction systems in a CSTR, parallel nonisothermal reactions of arbitrary order in a CSTR, reactions between adsorbed chemical species, coupled oscillating autocatalytic CSTRs and a class of feedback regulated enzymatic reaction systems.

Thesis Files