Value-Based Numerical Identification and Analysis of Critical States of Chemical Reaction Systems

A value-based method for the numerical identification and analysis of critical (limiting) states in chemical reaction systems is described. The extreme behavior of the reaction system, in which its behavior changes qualitatively with small changes in the initial parameters, is proposed to use when evaluating the critical states of reactions. The problem of the calculus of variations with the target condition is solved using the Pontryagin maximum principle. The value-based approach, which consists in the Hamiltonian systematization of kinetic equations of multistep reactions, is distinguished by the relative simplicity of the calculation procedures and makes it possible to determine the values, i.e., the kinetic significances of the individual chemical steps and chemical components of the reaction. According to the pressure–temperature ( P – T ) diagrams, three known self-ignition limits are described using the kinetic model of a reacting mixture of hydrogen and oxygen as an example, which includes forty two separate steps and eight chemical components. The existence of the fourth new degenerate limit in the H 2 /O 2 reaction system is predicted. The limiting phenomena are chemically interpreted by identifying the value-based numerical subordination of chemical components and individual steps of the kinetic mechanism of the reaction of hydrogen with oxygen.