A generalized differential method to calculate lumped kinetic triplet of the nth order model for the global one-step heterogeneous reaction using TG data

Computing kinetic triplet is of importance for the process safety of combustion/gasification industries to establish the chemical reaction scheme and to assess the hazardous risk. Few approaches have been capable of calculating lumped kinetic triplet at one time efficiently, which might be attributed to the fact that the analytical solution for the nonlinear ordinary differential equation (NNODE) for the n^th order reaction model has not been found yet. This paper presents an analytical solution of NNODE to compute kinetic triplet. Results showed that the proposed method (mass fraction curve-fitting error ϕ = 1.49%–2.07%) is more efficient to compute kinetic triplet of the n^th order reaction model, comparing to genetic algorithm (GA) optimization (ϕ = 1.43%–1.81%), Coats-Redfern (ϕ = 2.36%–3.16%), peak-shape, and isoconversional methods. A compensation effect between lnA and E_a is observed due to heating rates. Effects of exported data quality and smooth processing on computation of kinetic triplet are discussed. It is the first time that an analytical solution of NNODE (n^th order model) for global one-step heterogeneous reaction is derived for computing kinetic triplet. This work may help to search for analytical solutions of power-law and Avrami-Erofeev models in the future to efficiently calculate kinetic triplet for accelerating and sigmoidal reaction systems.