## 3 Results
### Design of Experiments (DoE) and Process Optimization
\[\text{CFA}(\%)\ =\ -3.08*[\text{MeOH}]\ +\ 0.29*[\text{MeOH}]^{2}-0.93*[\text{Q}] \ +\ 0.194*[\text{Q}]^{2}-0.091*[\text{MeOH}]*[\text{Q}]\ +\ 8.49 \tag{4}\]  
where: CFA(%): Caffeic Acid Recovery; [MeOH]: Methanol concentration (%); [Q]: CO2 flow rate (g/min). Figure 1: Pareto chart of effects for both responses of the optimization study for the SFE of potato peels: TPR (**a**) and CFA recovery (**b**). For both models, the F-calculated values (12.41 and 9.04) is greater than the F-tabulated value (5.05), which implies that the mathematical model is valid to describe the extraction with confidence. Additionally, the models can be deemed reliable, given their high R\({}^{2}\) values (TPR: 0.925, CFA: 0.90), and low errors. Thus being, the response surface plots for TPR and CFA recovery are illustrated in Figure 1(a) and 1(b), respectively. They show the correlation between the recoveries versus the independent variables _MeOH_% and _qCO2_. In both graphs, it can be seen that the optimum conditions for the process are located near the top region of the plot, i.e., where the _MeOH_% and _qCO2_ are at their highest. The optimized conditions, found by calculating the global maxima of the graphs, were pinpointed at a temperature of 80 \({}^{\circ}\)C, pressure of 350 bar, 21% of MeOH, at 20 g/min of CO\({}_{2}\) flow rate. These conditions were tested in triplicates and the results found were compared with those predicted by the model. Under these conditions, for TPR, the result obtained was 25.2%, while the model predicted a value of 44.2%. For CFA, a 45.0% recovery was obtained, while the model predicted a result of 92.7%. As observed, the predicted responses of the model did not match experimental values. A common consensus in optimization studies via DoE is that for a model to be deemed predictive, the F\({}_{\text{calc}}\) value must be at least 3-fold higher than the F\({}_{\text{tab}}\) value, which was not the case for either model. Therefore, the model validated in this work can be considered descriptive, but not predictive, i.e., it is only valid for values that fall within the boundaries tested, but it cannot be used for extrapolation purposes. In practical terms, this reinforces the trend that was already observed in the screening runs: Increasing _MeOH_% and _qCO2_ concurrently increases TPR and CFA up to a certain point, before they start decreasing. From a model standpoint (Figure 2), however, increasing both variables outside the range \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Response**} & **ANOVA** & **Square Sum** & **Degrees of Freedom** & **Mean Square** & **F-Value** & _p-Value (\%)_ & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{**Total phenolic recovery (TPR)**} & Regression & 1227.5 & 5 & 245.50 & \multirow{4}{*}{12.41} & \multirow{4}{*}{5} & \multirow{4}{*}{0.925} \\ \cline{2-2} \cline{5-8}  & Residual & 98.9 & 5 & 19.78 & & & \\ \cline{1-1} \cline{2-2} \cline{5-8}  & Total & 1326.4 & 10 & & & & \\ \cline{1-1} \cline{2-2} \cline{5-8}  & F\({}_{\text{tab}}\) (95\%) & & & & 5.05 & & \\ \hline \multirow{4}{*}{**Caffeic acid (CFA) recovery**} & Regression & 5806.8 & 5 & 1161.4 & \multirow{4}{*}{9.04} & \multirow{4}{*}{5} & \multirow{4}{*}{0.90} \\ \cline{1-1} \cline{2-2} \cline{5-8}  & Residual & 642.3 & 5 & 128.5 & & & \\ \cline{1-1} \cline{2-2} \cline{5-8}  & Total & 6449.1 & 10 & - & & \\ \cline{1-1} \cline{2-2} \cline{5-8}  & F\({}_{\text{tab}}\) (95\%) & & & & 5.05 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of variance of the models generated for TPR and CFA recovery. Figure 2: Response surfaces of _MeOH_% vs. _qCO2_ of the models generated for (**a**) TPR and (**b**) CFA recovery of potato peels by SFE. tested would result in even higher recoveries. Nevertheless, using an excessive amount of co-solvent is not desirable, because apart from not bringing any further polarity gains to the main solvent [38], this approach would probably impart extra extraction costs.