# Study on the Combustion Behavior and Kinetic Characteristics of Semi-Coke from Oil Shale
## 3 Results and Discussion
### Kinetic Analysis  
#### 3.2.1 Model-Free Kinetic Analysis  
Based on the core concept of the isoconversional method, there is no need to assume a specific reaction mechanism function. Instead, experimental data from multiple heating rates (\(\beta\)) are used to determine the relationship between \(\beta\) and temperature (\(T\)), and kinetic parameters such as activation energy (\(E_{\alpha}\)) and the pre-exponential factor (\(A\)) are calculated through linear fitting. The model-free fitting results of the non-isothermal combustion kinetics are shown in Figure 4. Both the OFW and KAS methods yield \(R^{2}\) values above 0.996, indicating that these methods are suitable for describing the combustion kinetics of oil shale semi-coke. The kinetic parameters calculated using the OFW and KAS methods are listed in Table 5.  
The activation energy and pre-exponential factor calculated by the OFW and KAS methods are similar, indicating that the model-free method can effectively describe the overall characteristics of the oil shale semi-coke combustion process. Analysis using the isoconversional methods (OFW and KAS) reveals the kinetic behavior of the combustion process. The activation energy increases significantly with the conversion rate, suggesting a clearly staged reaction process. At low conversion rates, the reactions proceed easily, making them suitable for efficient energy release. At higher conversion rates, the reactions are  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Heating Rate/\({}^{\circ}\)C/min** & \(T_{f}\)/\({}^{\circ}\)C & \(T_{p}\)/\({}^{\circ}\)C & \(T_{f}\)/\({}^{\circ}\)C & \(\Delta m\)/\% \\ \hline
5 & 427.94 & 490.83 & 546.53 & 4.29 \\
10 & 453.42 & 510.80 & 564.52 & 5.18 \\
15 & 461.19 & 533.64 & 584.39 & 5.54 \\
20 & 465.38 & 543.61 & 589.62 & 5.82 \\
25 & 475.56 & 549.78 & 599.80 & 6.22 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Combustion characteristics parameters of semi-coke under different heating rates.  
Figure 4: Model-free kinetic fitting curves for non-isothermal combustion.  
hindered by greater energy barriers, requiring the optimization of combustion conditions (e.g., oxygen concentration or combustion temperature) to improve efficiency.  
The gradual increase in activation energy (\(E_{\alpha}\)) with the increasing conversion rate (\(\alpha\)) indicates that, during combustion, the dominant reactions shift from the decomposition of easily volatilized components to the oxidation of more resistant fixed carbon and mineral decomposition. According to the OFW method, in the low conversion range (\(\alpha\) = 0.1-0.3), the activation energy is relatively low (\(E_{\alpha}\), avg = 167.31 kJ/mol), and the reaction is mainly driven by the release of volatiles, with minimal chemical resistance. In the high conversion range (\(\alpha\) = 0.7-0.9), the activation energy increases (\(E_{\alpha}\), avg = 201.44 kJ/mol), and the reaction is dominated by fixed carbon oxidation and mineral decomposition, which are associated with higher energy barriers. This indicates that the combustion reaction proceeds faster and more easily at low conversion rates (\(\alpha\) = 0.1-0.3), while at high conversion rates (\(\alpha\) = 0.7-0.9), the reaction slows down due to the high energy required for carbon and mineral decomposition [24].  
The average activation energy calculated by the OFW and KAS methods (180.80-180.81 kJ/mol) falls within the range reported by previous studies on semi-coke and low-grade coals [25,26]. Compared with the results of [PERSON] et al. [27], who reported a lower value (\(\sim\)150 kJ/mol) for retorted oil shale, the slightly higher activation energy in this study suggests a greater thermal stability of the semi-coke used, likely due to its residual carbon content and mineral matrix.