Statistical foundations of heterogeneous kinetics

Abstract

A mathematical analysis of the correlation between Weibull and gamma distributions is presented. On this basis, processes obeying the relation Qt/Q∞ = 1 − e−btn (Qt/Q∞ being the fractional yield of an interface reaction at time t) can be explained better. Selected values of n, found experimentally, reflect the specific rate dependence of the distribution of the surface potential on active sites. By using the corresponding gamma distribution functions we show that most of these processes obey either directly or indirectly the normal distribution of the activity of reacting sites.

Historical Perspective on the Maturation of Modeling Coal and Kerogen Pyrolysis

“…The Weibull distribution was first proposed for modeling chemical reactivity distributions by Dorko et al 27 in 1974, a year before the Gaussian model of Anthony et al, 8 and again in 1975 by Kolar-Anic et al, 28 including a comparison to the gamma distribution in a following paper. 29 It was first suggested for coal pyrolysis by Burnham et al 11 as an alternative to a nth-order Gaussian model and subsequently used for coal and kerogen pyrolysis by Laksmanan et al 30 It is one of the models provided in Kinetics2015 31 and predecessors, 32 but for sparse data that appear to have a substantial and asymmetric reactivity distribution, my experience is that a nth-order Gaussian E distribution has a more robust convergence. One final issue is how to accurately integrate the reaction rate when a reactivity distribution is involved.…”