# Study on the Combustion Behavior and Kinetic Characteristics of Semi-Coke from Oil Shale
## 2 Experimental Section
### Kinetic Model Analysis  
In this study, the combustion kinetics parameters were calculated using both model-free methods (OFW and KAS methods) and model-based methods (Coats-Redfern method based on reaction mechanism functions). The specific procedures were as follows:  
(1) Model-free methods. Under non-isothermal conditions, the reaction rate equation is expressed as:  
\[\frac{d\alpha}{dt}=A\exp(\frac{-E_{a}}{RT})f(\alpha) \tag{1}\]  
Figure 1: Aluminum retort combustion experimental apparatus. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Elemental Composition and Content**} \\ \hline \multirow{3}{*}{Elemental Analysis (wt\%)} & C & 2.23 \\  & H & 0.16 \\  & N & 0.14 \\  & S & 0.08 \\ \hline \multirow{3}{*}{Heating Value Analysis (MJ/kg)} & Dry distillation temperature at 500 \({}^{\circ}\)C \\ \cline{2-3}  & HHV & 8.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Elemental composition and heating value analysis of shale semi-coke. The reaction conversion rate \(\alpha\) can be expressed as:  
\[\alpha=\frac{m_{0}-m_{t}}{m_{0}-m_{\infty}} \tag{2}\]  
where \(\alpha\) is the conversion rate, \(A\) is the pre-exponential factor (with units of min\({}^{-1}\)), \(T\) is the reaction temperature (K), \(R\) is the gas constant (8.314 J/(mol\(\cdot\)K)),  
\(f(\alpha)\) is the mechanism function, \(m_{0}\) is the initial mass of the sample (mg), \(m_{t}\) is the sample mass at a given time (mg), and \(m_{\infty}\) is the sample mass after the reaction is complete (mg). The relationship equation between the reaction rate and activation energy in the OFW method is given as [18]:  
\[\ln(\beta)=\ln\left[\frac{AE_{\alpha}}{RG(\alpha)}\right]-5.331-1.052\left( \frac{E_{\alpha}}{RT}\right) \tag{3}\]  
The KAS (Kissinger-Akahira-Sunose) method is expressed as [19]:  
\[\ln\left(\frac{\beta}{T^{2}}\right)=\ln\left(\frac{AR}{G(\alpha)E_{\alpha}} \right)-\frac{E_{\alpha}}{RT} \tag{4}\]  
where \(\beta\) is the heating rate (\({}^{\circ}\)C/min), \(A\) is the pre-exponential factor (with units of min\({}^{-1}\)), \(R\) is the gas constant (8.314 J/(mol\(\cdot\)K)), Ea is the activation energy at a given conversion rate (kJ/mol), \(G(\alpha)\) is the integral reaction mechanism function, and \(T\) is the reaction temperature at the given conversion rate. (2) Model-based method. The model-based method determines combustion kinetic parameters by assuming a specific reaction mechanism function \(f(\alpha)\) and combining it with thermogravimetric analysis (TGA) data. In this study, the Coats-Redfern method was first applied, where linear fitting of the relevant equations was performed to calculate the activation energy \(E_{\alpha}\) and pre-exponential factor \(A\) based on the slope and intercept. To further optimize the fitting accuracy, different reaction mechanism functions--such as the second-order reaction model, diffusion model, and nucleation and growth control model--were assumed. By comparing the fitting performance, the most suitable reaction mechanism model was identified [20]. Finally, the combustion kinetics of oil shale semi-coke were analyzed using different kinetic mechanism functions. Typical kinetic mechanism functions are shown in Table 3.