Slow Invariant Manifold and its approximations in kinetics of catalytic reactions

Equations of chemical kinetics typically include several distinct time scales. There exist many methods which allow to exclude fast variables and reduce equations to the slow manifold. In this thesis, we start by studying the background of the quasi equilibrium approximation, main approaches to this approximation, its consequences and other related topics. We present the general formalism of the quasi equilibrium (QE) approximation with the proof of the persistence of entropy production in the QE approximation. We demonstrate how to apply this formalism to chemical kinetics and describe the difference between QE and quasi steady state (QSS) approximations. In 1913 Michaelis and Menten used the QE assumption that all intermediate complexes are in fast equilibrium with free substrates and enzymes. Similar approach was developed by Stuekelberg (1952) for the Boltzmann kinetics. Following them, we combine the QE (fast equilibria) and the QSS (small amounts) approaches and study the general kinetics with fast intermediates present in small amounts. We prove the representation of the rate of an elementary reaction as a product of the Boltzmann factor (purely thermodynamic) and the kinetic factor, and find the basic relations between kinetic factors. In the practice of modeling, a kinetic model may initially not respect thermodynamic conditions. For these cases, we solved a problem: is it possible to deform (linearly) the entropy and provide agreement with the given kinetic model and deformed thermodynamics ? We demonstrate how to modify the QE approximation for stiffness removal in an example of the CO oxidation on Pt. QSSA was applied in order to get an approximation to the One dimensional Invariant Grid for oxidation of CO over Pt. The method of intrinsic low dimension manifold (ILDM) was implemented over the same example (CO oxidation on Pt) in order to automate the process of reduction and provide more accurate simplified mechanism (for one-dimension), yet at the cost of a significantly more complicated implementation.