Reaction Rate Constant Evaluation of Thermal Isomerization of α-Pinene

Abstract

Bayesian inference is applied in this study to evaluate the posterior distribution of rate consents for a thermal isomerization of α-pinene by considering the uncertainty associated with rate constant parameters and kinetic model structural error. The kinetic model of the thermal isomerization of α-pinene is shown to have a mathematically ill-conditioned system that makes it difficult to apply gradient-based optimization methods for rate constant evaluation. The Bayesian inference relates the posterior probability distribution of the rate constants to the likelihood probability of modeled concentration of reaction products meeting the experimentally measured concentration and the prior probability distribution of the parameters. A Markov chain Monte Carlo (MCMC) is used to draw samples from posterior distribution while the Bayesian inference relationship is considered. Multinomial random walk Metropolis-Hastings is applied in this study to construct the histograms of rate constants as well as the confidence intervals and the correlation coefficient matrix. Results showed that the Bayesian approach can successfully apply to estimate the confidence interval of rate constants of reaction model by taking into consideration the uncertainty.