## Results and Discussions
### Desorption Isotherms Analysis  
In general, adsorption behavior occurs simultaneously along with desorption behavior and their reaction rates are equivalent at equilibrium. Therefore, some adsorption models can be applied to the desorption system of FTWR. In this study, the Langmuir and Freundlich models were used to fit the equilibrium data in the FTWR desorption process. The relevant equations are as follows [37]. \[\mathrm{q_{e}} =\mathrm{q_{m}}\mathrm{k_{L}}\frac{C_{e}}{1+\mathrm{k_{L}}C_{e}} \tag{4}\] \[\mathrm{q_{e}} =k_{L\mathrm{F}}C_{e}^{1/\mathrm{n}} \tag{5}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Objective** & **Lower Limit** & **Upper Limit** \\ \hline Temperature (\({}^{\circ}\)C) & In range & 25 & 80 \\ Retention time (h) & In range & 0.5 & 4 \\ Liquid–solid ratio (mL/g) & In range & 10 & 30 \\ Extracted wax yield (wt\%) & Maximum & 20.66 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Independent variables and response as constraints for optimization. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Run** & **Temperature (\({}^{\circ}\)C)** & **Retention Time (h)** &
\begin{tabular}{c} **Liquid–Solid** \\ **Ratio (mL/g)** \\ \end{tabular} & \multicolumn{2}{c}{**RFTW Yield (wt \%)**} & \multirow{2}{*}{**Error (\%)**} \\ \cline{3-3}
1 & 80 & 4 & 24 & 83.54 & 82.28 & 1.51 \\
2 & 80 & 4 & 24 & 84.12 & 82.28 & 2.19 \\
3 & 80 & 4 & 24 & 83.41 & 82.28 & 1.35 \\ Average & - & - & - & 83.69 & 82.28 & 1.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental and predicted values of RFTW yield at optimum condition. Figure 2: (**a**) Response surface of the influence of B and C on the RFTW yield, (**b**) contours of the influence of B and C on the RFTW yield. where \(\rm q_{m}\) and \(\rm k_{L}\) are Langmuir constants of maximal uptake (mg/g\({}^{-1}\)) and desorption coefficient (g/mL), \(\rm k_{LF}\) and n are two Freundlich isotherm constants. The fitted isotherms of Langmuir and Freundlich models are presented in Figure 3, and the isotherm correlated parameters are shown in Table 8. The correlation coefficients \(\rm R^{2}\) fitted by [PERSON] and Freundlich equations were all less than 0.99, which means that the fitting effect was not ideal. In addition, the amount of desorption when the Langmuir model reached equilibrium is less than the experimental value, while B is the opposite. Both [PERSON] and Freundlich isotherm models assume that the adsorbent surface is a uniform monolayer adsorption, which is contrary to the pore structure and non-uniform surface of FTC. Therefore, the Langmuir and Freundlich equations are not suitable for simulating the desorption process of FTWR. In order to study the desorption process of FTWR better, this research continued to study the nature of the pores in FTWR based on the N\({}_{2}\) adsorption-desorption analysis. It could be seen from Figure 4 that the average pore diameter of Fresh FTWR was almost 0 and the pore volume is negative, which means that almost no pores were exposed in Fresh FTWR, that is, FTW almost blocked all the pore structure of FTC. As the solvent residence time increases, the average pore diameter changes from larger to smaller, and the cumulative pore volume gradually increases. The average pore size gradually increased to 32 nm in the first 1 h, and then slightly decreased for 1-4 h, the average pore size was 29 nm at 4 h. This means that during the desorption process, pores with larger pore diameters were desorbed first; then more small pores were exposed, resulting in a gradual decrease in the average pore diameter. Figure 5 showed the nitrogen adsorption and desorption curve. The shape of the adsorption equilibrium isotherm was related to the pore structure of the material. The amount of desorbed gas decreased with the decrease of component partial pressure. The downward trend of the curve indicated that the desorption rate was faster in the early stage, which is due to the lower desorption heat of the multi-molecular layer.