Numerical Calculation and 3-D Imaging of the Arrhenius Temperature Integral

The Arrhenius temperature integral is typically used in non-isothermal kinetic analysis, which is widely applied in gas–solid reactions in separation processes. In previous studies, researchers provided various methods to solve the temperature integral, but the error usually became significant when the value of x (x = Ea/RT) was too large or too small. In this paper, we present a new series method and design a computer program to calculate the temperature integral. According to the precise calculation of the temperature integral, we first reveal the relationship among the integral, the temperature, and the activation energy, and we find an interesting phenomenon in which the 3-D image of the temperature integral is of self-similarity according to fractal theory. The work is useful for mechanism and theoretical studies of non-isothermal kinetics.