Calculation of the activation energy

The activation energy was calculated using the Coats–Redfern integral method. Here, the coal–oxygen combustion reaction was viewed as a first-order reaction. According to the Arrhenius law, the reaction rate of coal combustion can be calculated based on the following equation:

where k denotes the coal–oxygen reaction rate constant, A denotes the frequency factor, E denotes the activation energy (kJ/mol), T denotes the reaction temperature (K), and R denotes the gas constant (R = 8.314 J/(mol⋅K)).

The mass conversion rate during the coal–oxygen reaction process was calculated as follows:

where α denotes the mass conversion rate during the coal combustion process, m₀ is the mass of the coal sample at the start of the TGA experiment, m_t is the mass of the coal sample in the reaction equipment at moment t (after the start of the TGA experiment), and m_∞ is the mass of the coal sample in the reaction equipment at the end of the TGA experiment. The reaction rate was calculated as follows:

where k denotes the chemical reaction rate and t is the time.

Then, an integral operation was performed with the Coats–Redfern approximation, yielding the following equations:

Considering the general reaction temperature range and the activation energy (E), the E/RT was ≥ 1, and 1–2RT/E ~ 1. For n = 1, Eq. (⁸) could be rewritten as follows:

The above equation was employed to calculate the kinetic parameters of the coal–oxygen reaction in the coal samples. A diagram was generated considering 1n[ − 1n(1 − α)/T²] for the vertical axis and 1/T for the horizontal axis. A linear fitting was then performed on the diagram, and the activation energy was determined according to the slope of the fitting line.