# 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
However, fitting all stages with a second-order model overlooks mass transfer limitations such as ash layer coverage. Therefore, the F2-D4-F2 model (a mixed diffusion + second-order reaction model) and the F2-R3-F2 model (interface reaction + second-order reaction model) were introduced for further analysis. In the F2-D4-F2 model, a sharp 50 kJ/mol drop in activation energy in the second stage is mainly due to enhanced diffusion control, as reduced oxygen transfer resistance lowers the apparent activation energy. The key feature of the F2-R3-F2 model is the use of the R3 model in the second stage, which reflects interface-controlled shrinking reactions. This results in a lower activation energy during this stage, as intermediate products (e.g., opened coke pores) promote the reaction. The third stage becomes the dominant one, contributing up to 58.3%, with a high activation energy of 203 kJ/mol, corresponding to dense carbon layer oxidation--consistent with fundamental combustion kinetics. When fitting the reaction in two stages, the A2-F2 model (nucleation and growth + second-order reaction) stands out. Its second stage contributes 64.9%, with an activation energy of 221 kJ/mol, which is associated with nucleation and growth mechanisms, reflecting phase transitions and sintering behaviors of ash-forming minerals. In summary, although the F2-F2-F2 model shows a high degree of fit and general applicability, with activation energy increasing alongside conversion--matching the typical multi-stage characteristics of oil shale semi-coke combustion (volatiles \(\rightarrow\) fixed carbon \(\rightarrow\) minerals)--its simple mechanism tends to overestimate reaction rates in diffusion-limited stages. The combustion of oil shale semi-coke exhibits clear multi-stage kinetic behavior, so model selection must balance mechanistic rationality and data fitting accuracy. Among the tested models, the F2-R3-F2 model, with its segmented mechanism (interface reaction + second-order reaction), better reflects the physicochemical changes during semi-coke combustion. It also has a more reasonable distribution of contribution rates. Moreover, pore structure evolution and mineral phase transitions observed via in situ characterization (SEM, XRD) support the mechanism, making the F2-R3-F2 model the most suitable. The detailed kinetic parameters of each model are listed in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & F2-F2-F2 & & & F2-F2 & \\ \hline  & stage I & Stage II & Stage II & stage I & Stage II \\ \(E_{\alpha}/\)KJ-mol\({}^{-1}\) & 180.130 & 249.799 & 263.730 & 170.646 & 277.451 \\ \(A/\)S\({}^{-1}\) & \(3.93\times 10^{9}\) & \(4.58\times 10^{10}\) & \(1.35\times 10^{11}\) & \(8.04\times 10^{8}\) & \(4.73\times 10^{11}\) \\ Contribution & 0.395 & 0.278 & 0.355 & 0.431 & 0.596 \\ \(E_{\alpha,avg}/\)KJ-mol\({}^{-1}\) & & 231.22 & & & 224.05 & \\ \(R^{2}\) & & 0.98 & & 0.97 & \\ \(f(\alpha)\) & \((1-\alpha)^{2}\) & \((1-\alpha)^{2}\) & \((1-\alpha)^{2}\) & \((1-\alpha)^{2}\) & \((1-\alpha)^{2}\) & \((1-\alpha)^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Calculated kinetic parameters for each mode.