Understanding complex chemical kinetics with computational singular perturbation

Abstract

A moderately complex hydrogen-oxygen reaction system is used to demonstrate the application of the Computational Singular Perturbation (CSP) technique. Most of the “insights” normally clained by theoreticians after a successful convenient singular perturbation analysis on “tractable” problems can be obtained for highly complex problems using data generated by CSP, including simplified multi-step reaction models . The basic idea of CSP is that the large number of physically meaningful elementary reactions in a complex reaciion system can be grouped into separate reaction groups each identified with a single characteristic time scale. CSP theory provides an exact algorithm for the determination of this grouping and the reaction rates of earch of the groups, requiring no experience or intuition about the reaction system from the invetigator. terms representing fast reaction groups can simply be discarded when they are exhausted to yield simplified models of the reaction system as a function of time. Examples are given to show how physically meaningful information about the reaction system can be derived when relevant CSP data are available. Sample calculations are performed for the hydrogen-oxygen reaction system at 16]]° K and low pressure CSP. Examination of the CSP data suggests that, when [H], [O], [OH], [H 2 O], and [HO 2 ] are present initially only in trace amounts, the reaction system can be represented reasonably accurately by a single set of 5 reaction groups (two extremely fast, two moderately fast, and one extremely slow) over an extended time period. Depending on the interest of the invetigator, different simplified multi-step reaction models can be derived to represent the full kinetics formulation.