## 3 Results and Discussion
### Response Surface Process Optimization  
Based on the evidence derived from the severity-based models, solvent effects were pronounced and differentially affected polyphenol recovery from PP. On this ground, response surface optimization was used as a further means of modeling the organosolv treatments, by taking into account time, \(t\), and catalyst (sulfuric acid) concentration, \(C_{\text{SuAc}}\), as the process variables. This approach had the scope to evaluate the effects of \(t\) and \(C_{\text{SuAc}}\) on treatment performance, and to reveal possible synergistic (cross) functions. Model assessment and process optimization were based on analysis of variance (ANOVA) and lack-of-fit tests (Figures 3 and 4), considering the predicted and measured values' proximity (Table 3). Figure 2: Diagrams illustrating the correlations between Y\({}_{\text{TP}}\) values and CSF (**A**), or CSF\({}^{\prime}\) (**B**). Bars indicate standard deviation. CSF, CSF\({}^{\prime}\), and Y\({}_{\text{TP}}\) correspond to combined severity factor, alternative combined severity factor, and the yield in total polyphenols (expressed as chlorogenic acid equivalents—CGAE). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Design**} & \multirow{2}{*}{**Independent Variables**} & \multicolumn{3}{c}{**Response (Y\({}_{\text{TP}}\), mg CGAE g\({}^{-1}\) DM)**} \\ \cline{2-7}  & \(\mathbf{X_{1}}\) **(\(t\))** & \(\mathbf{X_{2}}\) **(\(C_{\text{SuAc}}\))** & \multicolumn{2}{c}{**1-Propanol**} & \multicolumn{2}{c}{**2-Propanol**} \\ \hline  & & & **Measured** & **Predicted** & **Measured** & **Predicted** \\ \hline
1 & \(-1\) & \(-1\) & 17.04 & 17.21 & 9.56 & 9.32 \\
2 & \(-1\) & \(1\) & 19.22 & 19.28 & 12.5 & 12.52 \\
3 & \(1\) & \(-1\) & 17.99 & 17.95 & 13.61 & 13.39 \\
4 & \(1\) & \(1\) & 16.45 & 16.30 & 15.38 & 15.43 \\
5 & \(-1\) & \(0\) & 18.85 & 18.62 & 11.45 & 11.67 \\
6 & \(1\) & \(0\) & 17.31 & 17.50 & 15.00 & 15.17 \\
7 & \(0\) & \(-1\) & 18.02 & 17.87 & 11.88 & 12.34 \\
8 & \(0\) & \(1\) & 18.07 & 18.08 & 15.03 & 14.96 \\
9 & \(0\) & \(0\) & 18.30 & 18.35 & 14.72 & 14.41 \\
10 & \(0\) & \(0\) & 18.22 & 18.35 & 14.01 & 14.41 \\
11 & \(0\) & \(0\) & 18.54 & 18.35 & 14.91 & 14.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The design points included in the response surface optimization, the coded levels of the process (independent) variables, and the actual (measured) and predicted Y\({}_{\text{TP}}\) values for both 1-propanol and 2-propanol-based organosolv treatments. Y\({}_{\text{TP}}\) correspond to a combined severity factor, alternative combined severity factor, and the yield in total polyphenols (expressed as chlorogenic acid equivalents—CGAE). \(C_{\text{SuAc}}\) is the concentration of sulfuric acid in the solvent used for the treatment. Figure 3: Statistical information on response surface optimization of the 1-propanol-based organosolv treatment of PP. Plot (**A**) shows the desirability function, through which prediction of optimized variable values could be made, as well as the estimated maximum Y\({}_{\text{TP}}\). Plot (**B**) shows the correlation of predicted and measured Y\({}_{\text{TP}}\) values of each design point considered for the optimization. Values designated with different colors in the inset tables are statistically different. The models derived were given in the form of equations containing only significant terms (Figures 3 and 4, inset table \"Parameter estimates\"), accompanied by the square correlations coefficients (R\({}^{2}\)), in order to provide a means of the total variability around the mean predicted by the models:  
\[\mathrm{Y_{TP(1-Prop)}=18.34-0.56X_{1}-0.93X_{1}X_{2}-0.37X_{2}^{2}} \tag{11}\]  
\[\mathrm{Y_{TP(2-Prop)}=14.41+1.75X_{1}+1.31X_{2}-0.99X_{1}^{2}-0.76X_{2}^{2}} \tag{12}\]  
Both models found to have R\({}^{2}\) were equal to 0.97 and highly significant \(p\) values for lack-of-fit for a confidence interval of at least 95% (Figures 3B and 4B).