# Biodiesel and Biolubricant Production from Waste Cooking Oil: Transesterification Reactor Modeling
## 3 Results and Discussion
### Industrial Equipment, Reactor Design, and Economic Feasibility Study
#### 3.5.3 Reactor Design  
In the case of the reactor, it was designed according to the characteristics included in Table 5. The first and second transesterification reactions were designed to be developed sequentially in the same reactor. Therefore, the effective reactor volume that is required for both reactions was calculated. Because of the available amount of WCO in a medium-sized city, like Badajoz, and considering the expected demand of the biolubricant, these two steps could take place in the same reactor to ensure the desired annual amount of product without requiring two reactors, which would increase the initial costs of the plant. \begin{table}
\begin{tabular}{c c c} \hline
**Equipment** & **Size** & **Details** \\ \hline WCO & Volume = 2 m\({}^{3}\); heigh = 2.8 m; & The container (stainless steel) is \\ container & diameter = 1.15 m; & oversized to ensure WCO collection. \\  & wall thickness = 1.2 mm & HDPE containers, a smaller container \\ Methanol & Volume = 0.6 m\({}^{3}\); & (V = 0.3 m\({}^{3}\)), is used for the collection of \\ container & size = 1.2 \(\times\) 0.8 \(\times\) 1 m & methanol after vacuum filtration. \\ Sodium methoxide & Volume = 0.3 m\({}^{3}\); & HDPE container to supply 100 L of \\ container & size = 1.2 \(\times\) 0.8 \(\times\) 1 m & catalyst on a daily basis. \\ Glycerol & Volume = 0.6 m\({}^{3}\); & HDPE container to store 495 kg of \\ container & size = 1.2 \(\times\) 0.8 \(\times\) 1 m & glycerol obtained as a byproduct. \\ TMP & Volume = 0.3 m\({}^{3}\); & Stainless-steel container to provide TMP. \\ container & height = 1.7 m; diameter = 0.74 m; & Stainless-steel container to store \\  & wall thickness = 1 mm & WCO-TMP and to include TBHQ. \\  & height = 2.9 m; diameter = 1.15 m; & A cooling and temperature control \\  & wall thickness = 1.2 mm & system is included. \\ TBHQ & Volume = 150 L; & HDPE container to store and supply TBHQ \\ container & height = 0.975 m; & when necessary. \\  & diameter = 0.48 m & \\ \hline \end{tabular}
\end{table} 
Table 7: Details about the main containers included in this study. \begin{table}
\begin{tabular}{c c c} \hline
**Condition** & **First Reaction** & **Second Reaction** \\ \hline Initial temperature, \({}^{\circ}\)C & 15 & 60 \\ Final (reaction) temperature, \({}^{\circ}\)C & 60 & 120 \\ Heating time, min & 35 & 40 \\ Saturated steam, kg & 136.1 & 112.5 \\ Flow, kg\(\cdot\)min\({}^{-1}\) & 3.9 & 2.82 \\ \hline \end{tabular}
\end{table} 
Table 8: Steam requirements for the first and second transesterification reactions. Equation (19) for the first transesterification with excess methanol and Equation (20) for the second transesterification were considered. \[WCO+6\;CH_{3}OH\;\leftrightarrow 3\;FAMEs+Glycerol \tag{19}\]  
\[FAMEs+\frac{1}{3}\;TMP\;\leftrightarrow\frac{1}{3}\;Biolubricant+CH_{3}OH \tag{20}\]  
According to the WCO supply observed in Table 5 (206.03 kg\(\cdot\)h\({}^{-1}\)) and by considering the stoichiometry of the process, the density and molecular weight of each reagent, the daily inlet mass flow, and the reactor size could be obtained for a working day (see Table 9). A total inlet volume of 2.32 m\({}^{3}\) to the reactor was found if the first transesterification is considered. On the other hand, according to the second transesterification, glycerol is first removed, and the remaining reagent (in this case, TMP) is added along with the catalyst (sodium methoxide). Considering the reaction included in Equation (24), the main inlet flows for the second transesterification are shown in Table 10 to determine the total volume of the reactor. Under these circumstances, the total inlet volume was 2.02 m\({}^{3}\). Comparing both total volumes, it can be observed that the first transesterification required a higher volume, which will be selected for the reactor design so that both reactions can take place in the same reactor in successive steps. Finally, considering an oversize of 20%, the real volume for the reactor was 3 m\({}^{3}\).