# Study on the Combustion Behavior and Kinetic Characteristics of Semi-Coke from Oil Shale
## 3 Results and Discussion
### Kinetic Analysis
#### 3.2.2 Model-Based Kinetic Function Analysis  
Using TGA data at different heating rates, the fixed conversion temperature (T) points were extracted. Based on the Coats-Redfern equation, the function g(\(\alpha\)) was computed, and its linear relationship with 1/T was plotted. Figure 5 presents the linear fitting results obtained using the Coats-Redfern integral method for oil shale semi-coke combustion at different heating rates. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\alpha\) & \(E_{\alpha}\), kJ/mol & \(A\) (1/s) & \(E_{\alpha}\),avg, kJ/mol & \(A_{avg}\) & \(R_{avg}\)2 \\ \hline  & 0.1 & 145.58 & 6.27 \(\times\) 10\({}^{6}\) & & & \\  & 0.2 & 194.41 & 8.95 \(\times\) 10\({}^{9}\) & & & \\  & 0.3 & 161.96 & 3.72 \(\times\) 10\({}^{7}\) & & & \\  & 0.4 & 132.61 & 2.07 \(\times\) 10\({}^{5}\) & & & \\ OFW & 0.5 & 183.26 & 2.57 \(\times\) 10\({}^{7}\) & 180.80 & 1.04 \(\times\) 10\({}^{9}\) & 0.998 \\  & 0.6 & 205.11 & 1.57 \(\times\) 10\({}^{8}\) & & & \\  & 0.7 & 201.73 & 7.67 \(\times\) 10\({}^{7}\) & & & \\  & 0.8 & 200.39 & 6.01 \(\times\) 10\({}^{7}\) & & & \\  & 0.9 & 202.20 & 7.93 \(\times\) 10\({}^{7}\) & & & \\ \hline  & 0.1 & 145.26 & 5.1 \(\times\) 10\({}^{6}\) & & & \\  & 0.2 & 194.31 & 9.27 \(\times\) 10\({}^{9}\) & & & \\  & 0.3 & 161.82 & 3.35 \(\times\) 10\({}^{7}\) & & & \\  & 0.4 & 132.53 & 1.41 \(\times\) 10\({}^{5}\) & & & \\ KAS & 0.5 & 183.02 & 2.23 \(\times\) 10\({}^{7}\) & 180.81 & 1.07 \(\times\) 10\({}^{9}\) & 0.997 \\  & 0.6 & 204.93 & 1.46 \(\times\) 10\({}^{8}\) & & & \\  & 0.7 & 201.54 & 6.93 \(\times\) 10\({}^{7}\) & & & \\  & 0.8 & 200.19 & 5.36 \(\times\) 10\({}^{7}\) & & & \\  & 0.9 & 201.99 & 7.06 \(\times\) 10\({}^{7}\) & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Kinetic parameters calculated by the OFW method and KAS method at different conversion levels. As shown in Figure 5, the activation energy (\(E_{\alpha}\)) calculated using the Coats-Redfern integral method is 188.75 kJ\(\cdot\)mol\({}^{-1}\), and the pre-exponential factor is 5.86 \(\times\) 10\({}^{7}\). The activation energies obtained by the OFW and KAS methods fall within the range of 180.80-180.81 kJ/mol, which is close to the result from the Coats-Redfern method, indicating that the Coats-Redfern method has a certain degree of applicability. However, because the Coats-Redfern method used in this study is based on the high-temperature range, it fits the combustion process of oil shale semi-coke in the high-temperature stage relatively well, but fits the low-temperature stage poorly. As a result, the overall fit of the combustion process is not ideal and still has certain errors and limitations. It does not adequately describe the full combustion behavior of oil shale semi-coke. Figure 5: The Coats–Redfern linear regression analysis plot. (**a**) Heating rate of 5 \({}^{\circ}\)C/min; (**b**) heating rate of 10 \({}^{\circ}\)C/min; (**c**) heating rate of 15 \({}^{\circ}\)C/min; (**d**) heating rate of 20 \({}^{\circ}\)C/min; (**e**) heating rate of 25 \({}^{\circ}\)C/min. Furthermore, the kinetic fitting results show that a higher reaction order of n = 2 provides a better fit than n = 1. Therefore, second-order reaction models, diffusion models, and nucleation and growth control models are assumed to fit the experimental data, optimize the calculations, and determine the activation energy (\(E_{\alpha}\)) and pre-exponential factor (\(A\)). When the fitting was divided into three stages based on assumed models, the F2-F2-F2 model (second-order reaction across all stages) shows a gradual increase in activation energy from 180 kJ/mol in the first stage to 263 kJ/mol in the third stage. The lowest activation energy in the first stage suggests rapid combustion of volatiles, while the highest in the third stage indicates the dominance of fixed carbon oxidation or mineral decomposition, requiring more energy. The pre-exponential factor increases from 10\({}^{9}\) to 10\({}^{11}\), reflecting the kinetic trend of significantly accelerated reaction rates with the increasing temperature.