Estimation of the distribution of reactivity for powdered cellulose pyrolysis in isothermal experimental conditions using the Bayesian inference

Abstract

Bayesian inference was used to test the powdered cellulose pyrolysis, under the isothermal experimental conditions. A completely new procedure that was based on obtaining the reliable distribution functions of the effective (apparent) activation energy (E a ) values by the statistical derivation of prior and posterior functions was introduced. It has been found that the pyrolysis of the powdered cellulose can be described by the kinetics, which differs from the first-order model. It was established that the apparent activation energy value presented as average magnitude in the conversion fraction range of 0.20 ≤ α ≤ 0.65 does not represent the “lumped” kinetic parameter, so in indicated conversion range, the pyrolysis process can be described through single-step reaction model with six-eighths-order (n * = 0.75) kinetics. Based on the presented Bayesian inference results, it was assumed that mechanism of pyrolysis takes place through the decomposition reactions which start from the cellulose chains. From the main characteristics of the prior distribution, relationship between the ingredients of Bayesian inference and the cellulose characteristic energy constant (c) [which is related to the rigidity angle (ψ) as a measure of tenseness of the cellulose chains] has been established in this paper. Based on evaluated prior and posterior distributions and their characteristics, it was found that the pyrolysis process of powdered cellulose takes place probably through formation of levoglucosan, where depolymerization represents the primary reaction path. Bayesian approach can be applied to highly structured reaction systems and complex physico-chemical processes, which include the reactivity distribution of various energy counterparts, which has been often un-tractable by traditional statistical access.