Consistency of a Reaction Dataset

Abstract

The understanding of a variety of natural phenomena and industrial processes is reliant on knowledge of the chemical reaction mechanisms and kinetics. Endeavors in such cases begin with identification of the underlying reaction pathways and fundamental mechanisms. When sufficient data accumulate, the interest often shifts to practical applications, motivating the development of mechanistic models. The “textbook” approach to the development of mechanistic reaction models consists of conjecturing the reaction mechanism, expressing it in a suitable mathematical form, and comparing the predictions of the constructed model to available experimental observations. Typically, such comparisons result in mixed outcomes: some show a reasonably close agreement and some do not. In the latter case, the apparent inconsistency obtained between the model and the experiment is argued to imply either that the model is inadequate or that the experiment (or, rather, its interpretation) is incorrect. In some areas, such as heterogeneous catalysis and biochemical systems, the fundamental reaction mechanisms are largely unknown and establishing them form the challenge of the current research. Yet, in other fields, such as atmospheric chemistry and the combustion of small hydrocarbons such as methane, there is a broad consensus in regard to the reaction pathways underlying the mechanisms. Thus, any inadequacy of the kinetic models essentially rests in their parameter values. In the following discussion, we assume the latter situation. If the kinetic parameters of such a “known” mechanism were known exactly, then a direct comparison of model prediction with a given experiment, within its uncertainties, would decisively indicate whether that experiment is consistent or inconsistent with the model. In reality, however, the model parameters themselves have uncertainties that must be included in the analysis. In principle, the parameter identification of chemical kinetic models can be posed as a classical statistical inference: 1-3 given a mathematical model and a set of experimental observations for the model responses, determine the best-fit parameter values, usually those that produce the smallest deviations of the model predictions from the measurements. The validity of the model and the identification of outliers is then determined using analysis of variance. The difficulty involved in the application of standard statistical methods lies in the fact that chemical kinetics models are stated in the form of differential equations that do not possess a closed-form solution. Further complications result from the highly “ill-structured” character of the best-fit objective function, with long and narrow valleys and multiple local minima, resulting in an ill-conditioned optimization that lacks a unique solution. 2,4