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.
Highlights
Isomerization of α-pinene is to produce other monoterpene hydrocarbons that have wide application in the cosmetic, perfume, aromatic polymer, and other domestic chemicals industries [1]
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
Reaction modeling consists of two main steps: first is to model the reaction pathways known as a kinetic model that needs an insight understanding of mechanisms in the reaction background and second is to calibrating the kinetic model by using experimental data [4]
Summary
Isomerization of α-pinene is to produce other monoterpene hydrocarbons that have wide application in the cosmetic, perfume, aromatic polymer, and other domestic chemicals industries [1]. Reaction kinetic modeling is a vital tool for the simulation of the thermal isomerization of α-pinene and for industrial reactor design. Kinetic models often involve a number of rate constants to be estimated. The value of these parameters is heavily dependent on the reaction conditions such as temperature, pressure, reaction media, the assumed reaction pathway, and the quantity and quality of the measured experimental data. These are called uncertainty sources and can significantly affect the estimated value of the reaction rates
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