## 3 Results and Discussion  
### Effect of Process Conditions on TPC  
Phenolic compounds are a very wide and divergent group. Therefore, an accurate evaluation of their content via HPLC methods would be very toilsome. As a result, the most common method of evaluating their content, a spectrophotometric test using Folin-Ciocalteu reagent, was used. The selectivity of this test is low: the presence of thiols, proteins, and some inorganic ions can lead to overestimating the result [34]; however, in the investigated system, the polarity of extraction medium was too low to co-extract significant amounts of such compounds. The results are listed in Table 1.  
RSM (Response Surface Methodology) was selected as a mathematical method of optimization [35]. The yield of phenolic compounds was connected with the process parameters using the equation (Equation (1)):  
\[Y=\mathrm{a}_{0}+\mathrm{a}_{1}X_{1}+\mathrm{a}_{2}X_{2}+\mathrm{a}_{3}X_{3}+ \mathrm{a}_{11}{X_{1}}^{2}+\mathrm{a}_{22}{X_{2}}^{2}+\mathrm{a}_{33}{X_{3}}^{ 2}+\mathrm{a}_{12}X_{1}X_{2}+\mathrm{a}_{13}X_{1}X_{3}+\mathrm{a}_{23}X_{2}X_{3} \tag{1}\]  
where: \(Y\) = the yield of the extraction, \(X_{i}\) = normalized process parameters (as in Table 1), and \(\mathrm{a}_{i}\) = model constants. The values of the model constants obtained during the optimization are presented in Table 2 along with a statistical analysis of their significance. Amongst the process parameters and their combinations, three significantly (at \(p\leq 0.05\)) affected the yield of the extraction: \(X_{1}\), \(X_{2}\), and \(X_{3}\). Broadening the significance level to \(p\leq 0.10\) revealed that \({X_{1}}^{2}\) and \(X_{1}X_{2}\) also influenced the outcome of the process. An increase in the recovery of phenolic compounds was obtained by minimizing the extraction temperature, and maximizing the addition of ethanol and pressure. The highest yield (1.52 g per 100 g of pomace) was acquired at 35 \({}^{\circ}\)C, 10 MPa, and 80% m/m ethanol addition. The calculations showed that better results (1.78 g per 100 g of pomace) would be acquired for 35 \({}^{\circ}\)C, 12.5 MPa and 80% m/m of ethyl alcohol (parameter set not tested due to using the Box-Behnken approach). A graphical representation of the results is shown in Figure 1.  
The values of the yield obtained by model computations were comparable with the empirical data. As an illustration, at 35 \({}^{\circ}\)C, 10 MPa, and 80% m/m ethanol addition, the computed yield (1.54 g per 100 g) was only about 1% higher than the result of the experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Constant** & **Value** & **Significance (\(p\)-Value)** \\ \hline a\({}_{0}\) & 731.60 & - \\ a\({}_{1}\) & \(-\)285.19 & 0.0007 \\ a\({}_{2}\) & 297.38 & 0.0006 \\ a\({}_{3}\) & 226.76 & 0.0011 \\ a\({}_{11}\) & 171.19 & 0.0587 \\ a\({}_{22}\) & \(-\)85.59 & 0.1424 \\ a\({}_{33}\) & 16.59 & 0.7920 \\ a\({}_{12}\) & \(-\)95.95 & 0.0908 \\ a\({}_{13}\) & \(-\)24.68 & 0.7144 \\ a\({}_{23}\) & 39.85 & 0.6036 \\ Model \(F\)-Value & 15.229 & 0.0038 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of three-parameter optimization of the extraction process. The presented approach allowed good modelling of empirical data, however, it was not able to explain clearly what mechanisms were responsible for the results, for e.g., is the effect of pressure connected with an increase of density? To test the hypothesis about the impact of solvent density, the computations were repeated using the density of CO\({}_{2}\) instead of the temperature and pressure. The yield of phenolic compounds was connected with the process parameters using the equation (Equation (2), symbols as above):  
\[Y=\mathrm{a}_{0}+\mathrm{a}_{3}X_{3}+\mathrm{a}_{4}X_{4}+\mathrm{a}_{33}{X_{3} }^{2}+\mathrm{a}_{44}{X_{4}}^{2}+\mathrm{a}_{34}X_{3}X_{4} \tag{2}\]  
The values of the model constants acquired and their significance are presented in Table 3. Two of the process parameters were significant: \(X_{3}\) and \(X_{4}\).