## 3 Results and Discussion
### CAF Degradation by Fenton Process
Despite the lower degradation efficiency observed in 5 min intervals, the combination with the adsorption process could potentially yield efficiency akin to that achieved in 60 min Fenton reactions. The attractiveness of the 5 min duration lies in its reduced resource demands, rendering the proposed practice more economically viable. Conversely, the 60 min duration provides insights into the reaction's steady state. Analysis of the results at 15 and 30 min intervals exhibited fluctuations influenced by experimental noise. Therefore, focusing on the analysis of 5 and 60 min durations ensured a more robust and reliable interpretation of the data. The \(\mathrm{C_{F}}\) of caffeine ranged from 0.21 to 7.82 mg L\({}^{-1}\), while caffeine degradation ranged from 58.72% to 98.92%. The second-order models that relate caffeine degradation and caffeine C\({}_{\mathrm{F}}\) as a function of the independent variables for the Fenton reaction times of 5 and 60 min are presented in Equations (16)-(19). \[\mathrm{D_{CAF}\left(5\,\mathrm{min}\right)}=0.365+0.007\;\mathrm{x}-2.070^{-05 }\;\mathrm{x}^{2}+0.142\;\mathrm{y}-0.006\;\mathrm{y}^{2}-0.001\;\mathrm{xy} \tag{16}\]  
\[\mathrm{D_{CAF}\left(60\,\mathrm{min}\right)}=0.358+0.007\;\mathrm{x}-2.027^{-0 5}\;\mathrm{x}^{2}+0.206\;\mathrm{y}-0.020\;\mathrm{y}^{2}-0.001\;\mathrm{xy} \tag{17}\]  
\[\mathrm{C_{F}\left(5\,\mathrm{min}\right)}=12.032-0.129\;\mathrm{x}+0.0004\; \mathrm{x}^{2}-2.696\;\mathrm{y}+0.110\;\mathrm{y}^{2}+0.021\;\mathrm{xy} \tag{18}\]  
\[\mathrm{C_{F}\left(60\,\mathrm{min}\right)}=12.153-0.127\;\mathrm{x}+0.0004\; \mathrm{x}^{2}-3.892\;\mathrm{y}+0.381\;\mathrm{y}^{2}+0.016\;\mathrm{xy} \tag{19}\]  
where \"D\({}_{\mathrm{CAF}}\)\" is the caffeine degradation, \"x\" is the H\({}_{2}\)O\({}_{2}\) concentration, and \"y\" is the FeSO\({}_{4}\)-7H\({}_{2}\)O concentration. The regression coefficients of the models indicate a remarkable similarity in the reactions at both 5 and 60 min intervals. The significance of variables, interactions, and quadratic effects was assessed using ANOVA. Tables 7 and 8 showcase the results obtained specifically for reaction times of 5 and 60 min, respectively. According to Table 8, the interaction term between the concentrations of H\({}_{2}\)O\({}_{2}\) and FeSO\({}_{4}\)-7H\({}_{2}\)O is statistically significant (_p_-value \(<\) 0.05), indicating a significant influence on the caffeine degradation process in the Fenton reaction. This result is corroborated by the F-values, with the calculated F-value being 15.70, only lower than the value corresponding to the interaction term. The linear and quadratic effects of the other variables are not  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **SS R\({}_{\mathrm{CAF}}\)** & **DF** & **F-Value** & _p-Value_ \\ \hline (1) H\({}_{2}\)O\({}_{2}\) (L) & 0.023 & 1 & 13.491 & 0.067 \\ (1) H\({}_{2}\)O\({}_{2}\) (Q) & 0.003 & 1 & 1.907 & 0.301 \\ (2) FeSO\({}_{4}\) 7H\({}_{2}\)O (L) & 0.015 & 1 & 8.577 & 0.100 \\ (2) FeSO\({}_{4}\) 7H\({}_{2}\)O (Q) & 0.0003 & 1 & 0.187 & 0.708 \\
1 by 2 & 0.033 & 1 & 19.279 & 0.048 \\ Error & 0.003 & 2 & & \\statistically significant. Likewise, in Table 9, the linear term of H\({}_{2}\)O\({}_{2}\) concentration is statistically significant within 60 min of the Fenton reaction, evidenced by the \(p\)-value \(<\) 0.05 and calculated F-value of 15.90, inferior only to the term corresponding to this concentration. The other variables do not demonstrate a significant influence, as their F-values are lower than F\({}_{\text{calc}}\). Residual analysis indicated an independent random distribution and normality. The models adjusted for Fenton reaction times of 5 and 60 min presented an R\({}^{2}\) of 96.21% and 96.64%, respectively, indicating a good adaptation to the experimental data.