# Biodiesel and Biolubricant Production from Waste Cooking Oil: Transesterification Reactor Modeling
## 2 Materials and Methods
### Biodiesel and Biolubricant Characterization  
Regarding WCO-FAME and WCO-TMP characterizations, Table 2 shows the main analyses carried out for each sample. The characterization methods were detailed in previous research, including the most representative characteristics of biodiesel and biolubricants [37]. It should be noted that most of the analyses were performed on both samples, with some exceptions, such as the FAME content and cold filter plugging points, typical tests applied to biodiesel. In any case, previous work and standards, such as those included in the table, have proven the suitability of these tests on both kinds of samples. Regarding the FAME content, the gas chromatography method was applied to measure the fatty acid methyl esters included in the WCO-FAMEs [40]. For this purpose, a VARIAN 3900 gas chromatograph coupled to a flame ionization detector was used. A polyethylene glycol column (Zebron ZB-WAX PLUS, Phenomenex, Torrance, CA, USA, length: 30 m, film thickness: 0.5 um, and i.d. : 0.32 mm) was selected, using different standards (methyl oleate, palmitate, linoleic, and linolenate) and methyl heptadecanoate as the internal standard, with heptane as a solvent. Viscosity was determined using an Ostwald viscometer at 40 \({}^{\circ}\)C [40], whereas density was measured using a pycnometer (Pobel, Madrid, Spain). Concerning the cold filter plugging point (CFPP), specific equipment included in the standard was used [46], whereas flash and combustion point measurements were carried out according to the Cleveland open-cup method [45]. Finally, the oxidation stability was calculated through the Rancimat method [43; 47]. Three grams of the sample was placed in a test tube, heating it at 110 \({}^{\circ}\)C and bubbling synthetic air (at 10 L-h\({}^{-1}\)). The resulting stream bubbled 50 mL of distilled water, increasing \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline WCO FAME/TMP ratio & 3 \\ Catalyst concentration, \% & 0.3–1.0 \\ Reaction time, min & 120 \\ Reaction temperature, \({}^{\circ}\)C & 80–140 \\ Stirring rate, rpm & 350 \\ Working pressure, mmHg & 210–760 \\ \hline \end{tabular}
\end{table} 
Table 1: Operating conditions for biolubricant production from WCO. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **WCO-FAME** & **WCO-TMP** & **Details** \\ \hline FAME content & Yes & No & [40] \\ Viscosity & Yes & Yes & [41] \\ Density & Yes & Yes & [42] \\ Oxidation stability & Yes & Yes & [43] \\ Acidity value & Yes & Yes & [44] \\ Flash and combustion points & Yes & Yes & [45] \\ Cold filter plugging point & Yes & No & [46] \\ \hline \end{tabular}
\end{table} 
Table 2: WCO-FAME and WCO-TMP characterizations, including references to the corresponding standards. the sample's conductivity because of the dilution of the byproducts generated during oxidation. This value was measured using a conductivity meter. The induction point (or oxidation stability) was the time when the conductivity abruptly increased, which is normally expressed in minutes. FT-IR analysis of the final biolubricant was carried out using specific equipment (PerkinElmer Spectrum 3F-IR, Waltham, MA, USA) and measuring between 4000 and 650 cm\({}^{-1}\). Also, TG and DTG analyses were carried out using a thermobalance (STA449F3, QMS403D, VERTEX70, Netzsch-Bruker, Billerica, MA, USA). A certain mass of the biolubricant was heated at a constant heating rate (10 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)). The carrier gas was nitrogen (100 mL\(\cdot\)min\({}^{-1}\)). TGA and DTG curves were obtained by monitoring the weight loss at various temperatures. The conversion of FAMEs during the second transesterification with TMP was calculated through the FAME content decrease (using gas chromatography, as previously explained) according to Equation (1). Also, for kinetic studies, the decrease in the FAME content was used for the corresponding calculations, as explained in further subsections.