## 3 Results and Discussion
The optimized parameters are presented in Table 5 with the middle points (line 1 in Table 1) of the plan matrix. In both reactor systems, the optimized parameters provided an increase of the FAEE yield. Using the MX-mixer, the mass fraction of FAEE could be raised from 68.1% to 84.9%. With the T-mixer the yield of FAEE could be increased from 61.8% to 90.8%. Increased flow rate had a great positive impact on reaction yields in the system with the T-mixer. The optimized parameters were applied to the experiments in the batch reactor and compared for soybean oil, original cooking and waste cooking oil (Table 6). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dimension Specific Coefficient** & **MX-Mixer** & **T-Mixer** \\ \hline b\({}_{0}\) & 44.9 & 7.0 \\ b\({}_{1}\) & 3.1 & 4.1 \\ b\({}_{2}\) & –2.8 & 9.8 \\ b\({}_{3}\) & 12.9 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dimension specific coefficients for MX- and T-mixer. Figure 4: Graphical presentation of the regression equations for different reactor systems as a dependency of the molar ethanol/oil ratio. All experimental results are shown in Table 7. The FAEE yield with soybean oil at ethanol-oil-ratio = 11:1 and 12:1 in the batch reactor is illustrated in Figure 6. For a molar ethanol/oil ratio = 11:1, a maximum yield = 94.8% FAEE was detected after a reaction time of 8 min. The product yield remained nearly constant after a reaction time of 5 min, indicating that the reaction was practically finished. At the ethanol/oil ratio = 12:1 the maximum FAEE yield of 96.7% was detected after 8 min. The product yield of the experiment with the molar ethanol/oil ratio = 11:1 is exceeded, showing that a higher excess of ethanol has a positive effect on the reaction. Figure 7 shows the reaction results of the experiment with the original cooking oil at molar ethanol/oil ratios = 11:1 and 12:1. The maximum yield = 96.6% for the ethanol-oil-ratio = 11:1 was detected after 8 min. It can be assumed that this value could be further increased by a longer reaction time. The highest yield in the reaction with the molar ethanol/oil ratio = 12:1 could be detected at 8.5 min. A higher amount of ethanol leads to higher yields indicating a need for high alcohol excess. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Oil** & \multicolumn{2}{c}{**Soybean**} & \multicolumn{2}{c}{**Cooking**} & \multicolumn{2}{c}{**Waste**} \\ \hline nEtOH/noil & 11:1 & 12:1 & 11:1 & 12:1 & 11:1 & 12:1 \\ max. wFAEE [\%] & 94.8 & 96.7 & 96.6 & 97.9 & 82.1 & 97.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental parameters for the ethanolysis at 50 \({}^{\circ}\)C and KOH = 0.86 wt.-% in a batch reactor. Figure 5: Graphical presentation of the regression equations for different reactor systems as a dependency of the flow rate. The same conclusion can be provided from the experimental results obtained with waste cooking oil (Figure 8). The effect of ethanol excess on the FAEE yield is very significant. The product analysis \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**t[min]**} & **Soybean** & **Original** & **Waste** & **Soybean** & **Original** & **Waste** \\  & **Oil** & **Cooking Oil** & **Cooking Oil** & **Oil** & **Cooking Oil** & **Cooking Oil** \\ \hline
**11:1** & **11:1** & **11:1** & **11:1** & **12:1** & **12:1** & **12:1** \\ \hline
0.7 & 66.8 & 78.1 & 73.1 & 64.0 & 68.8 & 56.6 \\
1 & 70.5 & 80.7 & 74.8 & 71.1 & 73.9 & 83.0 \\
2 & 75.6 & 85.2 & 77.8 & 78.8 & 87.4 & 89.9 \\
5 & 94.3 & 93.1 & 80.1 & 85.9 & 96.9 & 93.3 \\
8 & 94.8 & 96.6 & 82.1 & 96.7 & 97.9 & 97.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: FAEE yields (w\({}_{\text{FAEE}}\) [%]) in a batch reactor by ethanolysis reaction of soybean oil, original cooking and waste cooking oil. Figure 6: FAEE yields in the batch reactor at molar ethanol/oil ratios = 11:1 and 12:1 with soybean oil. Figure 7: FAEE yields in the batch reactor at molar ethanol/oil ratios = 11:1 and 12:1 with original cooking oil.