A New and Simple Method to Estimate f(E) and k0(E) in the Distributed Activation Energy Model from Three Sets of Experimental Data

Complex reactions such as coal pyrolysis reaction are often analyzed using the distributed activation energy model, in which the reactions are assumed to consist of a set of irreversible first-order reactions that have different activation energies and a constant frequency factor. The difference in the activation energies has been usually represented by a Gaussian distribution a priori. In this paper, a simple method is presented for estimating both the distribution curve of the activation energy, f(E), and the activation energy dependent frequency factor, k 0 (E), without any a priori assumptions for f(E) and k 0 (E). Only three sets of experimental data obtained under different heating profiles are required to obtain both f(E) and k 0 (E). The presented method was applied to estimate f(E) and k 0 (E) for the pyrolysis of three kinds of coals. f(E) was different significantly among the coals. It had a maximum at E = 240-260 kJ/mol and was spread over 150-400 kJ/mol. Estimated k 0 vs E relationship was little dependent on coal types, and k 0 increased from 10 11 to 10 26 s -1 as E increased from 150-400 kJ/mol. The applicability of the presented method to single reactions is also discussed.