## 3 Results
### Torrefaction Kinetics Using PSO Algorithm  
Global and individual parameters were obtained from the experimental results to compare their suitability, as shown in Table 4. The global parameter fitted is 99.99996887%, indicating an acceptable fit of the sixteen experimental data points to the two-step kinetic model. This means there is good predictive behavior for the torrefaction process at 250, 300, and 325 \({}^{\circ}\)C. However, for 275 \({}^{\circ}\)C, a major error is found, as shown in Figure 7a. For individual parameters, the error decreases significantly, as shown in Figure 7b; the fit is 99.99996187%, 98.07280000%, 99.99999997%, and 99.99048931% for 250, 275, 300, and 325 \({}^{\circ}\)C, respectively. Therefore, there is a better fit for individual Arrhenius parameters than for the global ones. However, the cumulative error when combining the individual parameters could be greater than that of the global one.  
Figure 5: Van Krevelen diagram of torrefied biomass.  
Figure 6: The energy density of wheat straw at different torrefaction temperatures.  
The model is validated by correlating the calculated torrefied mass with the experimental data, as shown in Figure 8. The global parameters maintained an R\({}^{2}\) of 0.9998. For the individual parameters, an R\({}^{2}\) of 0.9963 is obtained. This indicates that the correlation between the predicted weight loss and the experimental data provides better results for the global parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm PSO**} & \multirow{2}{*}{**Temperatures (\({}^{\circ}\)C)**} & \multirow{2}{*}{**Arrhenius Constants (s\({}^{-1}\))**} & \multicolumn{2}{c}{**Arrhenius Parameters**} & \multirow{2}{*}{**Fit (\%)**} \\ \cline{4-5}  & & & **A (s\({}^{-1}\))** & **Ea (kJ mol\({}^{-1}\))** & \\ \hline \multirow{4}{*}{Global Parameters} & \multirow{4}{*}{250, 275, 300, and 325} & k\({}_{1}\) & \(1.141\times 10^{11}\) & \(1.310\times 10^{5}\) & \\  & & k\({}_{V1}\) & \(9.789\times 10^{5}\) & \(8.087\times 10^{4}\) & \\  & & k\({}_{2}\) & \(9.724\times 10^{6}\) & \(9.762\times 10^{4}\) & \\  & & k\({}_{V2}\) & \(6.763\times 10^{5}\) & \(8.557\times 10^{4}\) & \\ \hline \multirow{4}{*}{Individual Parameters} & \multirow{4}{*}{250} & k\({}_{1}\) & \(2.401\times 10^{11}\) & \(1.350\times 10^{5}\) & \\  & & k\({}_{V1}\) & \(9.199\times 10^{5}\) & \(8.066\times 10^{4}\) & \\  & & k\({}_{2}\) & \(4.426\times 10^{7}\) & \(1.036\times 10^{5}\) & \\  & & k\({}_{V2}\) & \(7.338\times 10^{7}\) & \(1.075\times 10^{5}\) & \\ \cline{2-5}  & & k\({}_{1}\) & \(9.058\times 10^{10}\) & \(1.432\times 10^{5}\) & \\  & & k\({}_{V1}\) & \(2.785\times 10^{3}\) & \(5.713\times 10^{4}\) & \\  & & k\({}_{2}\) & \(9.706\times 10^{4}\) & \(8.003\times 10^{4}\) & \\  & & k\({}_{V2}\) & \(4.218\times 10^{4}\) & \(9.595\times 10^{4}\) & \\ \hline \multirow{4}{*}{300} & \multirow{4}{*}{325} & k\({}_{1}\) & \(5.178\times 10^{10}\) & \(1.289\times 10^{5}\) & \\  & & k\({}_{V1}\) & \(5.490\times 10^{4}\) & \(6.870\times 10^{4}\) & \\ \cline{1-1}  & & k\({}_{2}\) & \(3.770\times 10^{9}\) & \(1.297\times 10^{5}\) & \\ \cline{1-1}  & & k\({}_{V2}\) & \(2.222\times 10^{4}\) & \(7.035\times 10^{4}\) & \\ \hline \multirow{4}{*}{325} & \multirow{4}{*}{325} & k\({}_{1}\) & \(9.283\times 10^{5}\) & \(7.746\times 10^{4}\) & \\  & & k\({}_{V1}\) & \(2.651\times 10^{5}\) & \(7.451\times 10^{4}\) & \\ \cline{1-1}  & & k\({}_{2}\) & \(7.643\times 10^{7}\) & \(1.104\times 10^{5}\) & \\ \cline{1-1}  & & k\({}_{V2}\) & \(1.603\times 10^{2}\) & \(4.830\times 10^{4}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Global and individual Arrhenius kinetic parameters obtained from PSO.  
Figure 7: Solid yield prediction curves and normalized solid yield experimental data of wheat straw at different study temperatures under the schemes of (**a**) global parameters and (**b**) individual parameters.