Reutealis Trisperma Oil Esteriﬁcation: Optimization and Kinetic Study

: Reutealis trisperma , due to its high kernel-oil yield ( ± 50%) and long productivity ( ± 70 years), is considered to be a promising feedstock for biodiesel production. In addition, this plant, which can thrive on marginal lands, is classiﬁed as a non-edible oil since it contains a toxin known as eleostearic acid. The present study aimed to optimize the esteriﬁcation step in biodiesel production from R.trisperma oil catalyzed using sulfonic ion exchange resin Lewatit K2640. The optimization step was performed using a response surface methodology through the incorporation of a central composite design. A kinetic study was performed as well, based on the assumption of a pseudo-homogeneous second-order model. Catalyst loading was found to have the most signiﬁcant impact on acid value, followed by temperature and methanol-to-oil molar ratio. The optimal conditions for the esteriﬁcation step were 92 ◦ C temperature, 5.34% catalyst loading, and 5.82:1 methanol-to-oil molar ratio. The acid value and FFA conversion of R.trisperma oil under these conditions were 2.49 mg KOH / g and 91.75%, respectively. The kinetics study revealed that the constructed model could ﬁt the experimental data well with relatively high reliability. The activation energy required for the esteriﬁcation of R.trisperma oil was 33.2 kJ / mol. D-K.K D.-K.K.; Supervision, D.-K.K. and J.-S.L.; Project administration, D.-K.K.; Funding acquisition, D.-K.K. All authors have


Introduction
Our world is highly reliant on a single source of energy, fossil fuel. Cheapness, cost effectiveness, and wide accessibility are some of the recognizable advantages of fossil fuel. These advantages come at a steep price, however, as the excessive exploitation of fossil fuel has released enormous amounts of greenhouse gases into our atmosphere, leading to global warming. As of 2016, CO 2 emissions had reached 32.31 GtCO 2 , almost 2 times greater than the output of the early industrial revolution [1]. In addition, fossil fuel is not a renewable resource, making the need for alternative sources even more urgent.
Whereas the global energy supply is still dominated by fossil fuel, the proportion of renewables has been on the rise, reaching 10.2% of the primary energy supply in the OECD (Organisation for Economic Co-operation and Development) countries by 2017 [1]. This uptrend is projected to continue as numerous other countries race to increase their utilization of renewables. For instance, South Korea released a plan to its renewables proportion from 6% to 20% by 2030. Following South Korea's step is Indonesia, which plans to increase its renewable proportion from 6.2% (2016) to 23% by 2025.
Biodiesel is a product of a transesterification reaction in which triglycerides found in vegetable oils or animal fats combine with alcohol in the presence of a catalyst to produce fatty acid methyl

Preparation of Feedstock
The model oil was synthesized by mixing oleic acid in soybean oil to mimic the average acid value of R.trisperma oil (±30 mg KOH/g). The R.trisperma oil was pretreated with filtration and water removal to remove solid impurities and the moisture content in the feedstock. The properties of the pretreated R.trisperma oil were characterized in terms of the acid value, water content, impurities, metal ions, and phosphorous content.

Optimization of Esterification Reaction
The esterification reactions were performed in a 500 mL stainless steel reactor equipped with thermocouple, agitator, chiller, and sampling port. The catalyst was contained inside a 4-blade propeller covered in a stainless-steel mesh to prevent the blockage of the sampling port by catalys particles. A schematic of the reactor and a photo of the propeller are provided in Figure 1. The optimization reaction was performed according to the response surface methodology (RSM) via a central composite design. RSM was selected, as it is widely used to optimize a system while observing the effects of input variables, along with their interaction, on the response variable. Specifically, RSM is valuable for evaluation of the topography of the response surface and identification of the optimal conditions of a system. Three input variables (temperature, catalyst loading, and methanol-to-oil molar ratio) were selected as the optimization process factors, as shown in Table 1. Each process factor carried three different levels (−1, 0, 1) and two axial points (−1.68 and +1.68), and the effect of each on the response variable (acid value) was evaluated.

Materials
R.trisperma oil was kindly provided from Indonesia via air mail. Due to the limited availability of feedstock with the same acid value, however, experiments for the optimization of esterification of FFA and methanol were performed with a model oil made up of oleic acid (99.5%; Samchun Pure Chemical, Korea) and soybean oil (99.99%; Daesang, Korea) and synthesized to mimic the average acid value of R.trisperma oil (30 mg KOH/g). Methanol (dried, GR grade) was obtained from Duksan Pure Chemical in Korea. KOH (95%, flake) was acquired from OCI Chemical in Korea. Benzene (99.5%) and ethanol (95%) were supplied by Samchun Pure Chemical. Methyl heptadecanoate was obtained from Sigma Aldrich (St. Louis, Missouri, USA). Catalyst (Lewatit K2640) was purchased from LANXESS Deutschland GmbH.

Preparation of Feedstock
The model oil was synthesized by mixing oleic acid in soybean oil to mimic the average acid value of R.trisperma oil (±30 mg KOH/g). The R.trisperma oil was pretreated with filtration and water removal to remove solid impurities and the moisture content in the feedstock. The properties of the pretreated R.trisperma oil were characterized in terms of the acid value, water content, impurities, metal ions, and phosphorous content.

Optimization of Esterification Reaction
The esterification reactions were performed in a 500 mL stainless steel reactor equipped with thermocouple, agitator, chiller, and sampling port. The catalyst was contained inside a 4-blade propeller covered in a stainless-steel mesh to prevent the blockage of the sampling port by catalyst particles. A schematic of the reactor and a photo of the propeller are provided in Figure 1. The optimization reaction was performed according to the response surface methodology (RSM) via a central composite design. RSM was selected, as it is widely used to optimize a system while observing the effects of input variables, along with their interaction, on the response variable. Specifically, RSM is valuable for evaluation of the topography of the response surface and identification of the optimal conditions of a system. Three input variables (temperature, catalyst loading, and methanol-to-oil molar ratio) were selected as the optimization process factors, as shown in Table 1. Each process factor carried three different levels (−1, 0, 1) and two axial points (−1.68 and +1.68), and the effect of each on the response variable (acid value) was evaluated.
agitator, (7) reactor vessel, (8) low-temperature sampling port, (9) high-temperature sampling port; (b) 4-blade propeller. The esterification reactions were performed with 200 mL of oil as feedstock. A specific amount of catalyst was put into the propeller blade and heated alongside the feedstock under constant stirring of 300 rpm. The heating process was continued for 30 min before the addition of methanol to the reactor. The experiments were conducted in a randomized manner, as shown in Table 2. The analysis was performed with the help of statistical software Minitab 17 (Minitab, LLC., Pennsylvania, USA). A second-order polynomial equation was constructed based on the experimental data and used as the basis of the optimization step.
where y represents the response variable (acid value); A, B, and C are the input variables, and b 0 , b i , b ii , b ij , b ij , b ijk (i = 1,2,3; j > i and k > j) are the regression coefficients respectively. An analysis of variance (ANOVA) was also performed to identify the significance of each factor to the response variable and the fit of the developed model to the experimental data. The optimal conditions were obtained by solving the model equation.

Kinetics of Esterification Reaction
A pseudo-homogeneous model was adapted for the evaluation of the kinetics of the R.trisperma oil esterification. This model was selected as it has been widely used in the study of esterification kinetics [16,17]. The assumptions held in the development of a pseudo-homogeneous model are as follows [17]: The methanol concentration is high enough to ensure a constant concentration of methanol throughout the reaction; • Backward reaction is neglected.
Based on these assumptions, a second order pseudo-homogeneous model was developed for the evaluation of the R.trisperma oil esterification. The derivation of the reaction rate equation was performed as follows. The terms A, B, and C refer to FFA, methanol, and catalyst, respectively. The terms k, W, X, and C represent the kinetics constant, weight, conversion, and concentration, respectively. By substituting C A = C A0 (1 -X A ) and C B = C B0 -C A0 X A , Equation (4) can be rearranged in terms of the conversion of A to construct a linearized equation, as shown in Equation (5). The term M refers to C B0 /C A0 .

Acid Value Analysis
The acid value analysis procedure was adapted from the EN ISO 66 standard. Approximately 1 mL of oil sample was mixed with 1 mL of distilled water inside a 2 mL micro tube followed by centrifugation. Around 0.5 g of the washed oil was mixed with 20 mL of benzene and ethanol mixture (1:1 v/v). The solution was titrated with KOH as the titrant and phenolphthalein as the indicator of the end point of titration. The calculation of the acid value was performed according to Equation (6) shown below. The terms V, C, and m represent the volume of KOH (mL), the concentration of KOH (g/mol), and the mass of oil (g), respectively.

Optimization of Esterification Reaction
The experimental data obtained are shown in Table 3. A response equation was constructed based on the experimental data by fitting it to a second order polynomial equation through a multiple regression analysis. The quality of the developed model was analyzed based on several parameters including p-value, F-value, coefficient of determination (R 2 ), and lack of fit. It can be seen in the table that the acid value of the esterified oil was in the range of 1.239-19.534 mg KOH/g. In order to understand the impact of each input variable on the response variable, an ANOVA was performed, the results of which are shown in Table 4.
The significance of a factor can be represented statistically by its p-value with a p-value < 0.05 indicating high significance and a p-value > 0.1 indicating low significance or irrelevance of that factor. Based on our ANOVA results, it was clear that the developed model has a high F-value (111.29) and a low p-value (0.000), both of which are indicative of a high fit with the experimental data. This is further backed up by the high value of R 2 (0.9901), which means that up to only 0.99% of the variation in the acid value of the esterified model oil could not be explained by the constructed model. The high value of the predicted R 2 (0.9337) also supports this claim. The low lack of fit F-value (3.86) relative to the model F-value (111.29) and the high p-value of the lack of fit (0.086) also imply that the model had a good fit with the experimental data.  The relationship of the predicted and actual acid values of the esterified model oil, which is shown in Figure 2, exhibited a good fit as well, thus also supporting the good fit of the developed model to the experimental data.
According to the ANOVA results, all of the individual factors of the input variables had a significant impact on the acid value of the esterified model oil with a confidence level of 95%. This was inferred from the p-values of the individual factors, all of which were lower than 0.05. Among these factors, catalyst loading was found to have the most dominant impact on the acid value of the esterified oil, followed by temperature and methanol-to-oil molar ratio respectively (from highest F-value to lowest). The two-way interaction of the individual factors, however, was found to have no significant According to the ANOVA results, all of the individual factors of the input variables had a significant impact on the acid value of the esterified model oil with a confidence level of 95%. This was inferred from the p-values of the individual factors, all of which were lower than 0.05. Among these factors, catalyst loading was found to have the most dominant impact on the acid value of the esterified oil, followed by temperature and methanol-to-oil molar ratio respectively (from highest Fvalue to lowest). The two-way interaction of the individual factors, however, was found to have no significant impact on the acid value of the esterified model oil as the p-value was higher than 0.01 for all of the variations.
The impacts the input variables had on the response variable can be seen in Figure 2b,c,d. An increase in reaction temperature led to a decrease of acid value. This phenomenon could be observed for all of the different catalyst loading inputs (Figure 2b) and different methanol-to-oil molar ratios (Figure 2c). One study performed with palm kernel oil revealed that the increase of temperature reaction from 40 to 60 °C led to a decrease of acid value, especially at a lower catalyst amount [18]. In the present study, the synergistic impact of either catalyst loading or methanol-to-oil molar ratio with temperature to the acid value of the esterified oil could not be determined. In fact, based on the ANOVA result, the two-way interaction of temperature with either catalyst loading or the methanolto-oil molar ratio was determined to be a statistically insignificant factor.
The impact the catalyst loading had on the acid value of the esterified model oil can be seen in Figure 2b,d. It can be inferred from both figures that the impact was significant. A higher amount of catalyst available in the system increased the active surface area available for reaction, thereby increasing the possibility of a catalytic reaction to occur, the occurrence of which decreased the acid The impacts the input variables had on the response variable can be seen in Figure 2b,c,d. An increase in reaction temperature led to a decrease of acid value. This phenomenon could be observed for all of the different catalyst loading inputs (Figure 2b) and different methanol-to-oil molar ratios (Figure 2c). One study performed with palm kernel oil revealed that the increase of temperature reaction from 40 to 60 • C led to a decrease of acid value, especially at a lower catalyst amount [18]. In the present study, the synergistic impact of either catalyst loading or methanol-to-oil molar ratio with temperature to the acid value of the esterified oil could not be determined. In fact, based on the ANOVA result, the two-way interaction of temperature with either catalyst loading or the methanol-to-oil molar ratio was determined to be a statistically insignificant factor.
The impact the catalyst loading had on the acid value of the esterified model oil can be seen in Figure 2b,d. It can be inferred from both figures that the impact was significant. A higher amount of catalyst available in the system increased the active surface area available for reaction, thereby increasing the possibility of a catalytic reaction to occur, the occurrence of which decreased the acid value of the esterified oil. The impact of catalyst loading on the acid value of the esterified oil was independent of both temperature and methanol-to-oil ratio, which was confirmed statistically by the ANOVA result. The esterification of waste cooking oil with Amberlyst-15 (Rohm & Haas, USA) in an Energies 2020, 13, 1513 8 of 12 earlier study showed a similar trend, the acid value of the esterified oil decreasing as the Amberlyst-15 concentration was increased to 3% [19].
Based on stoichiometric analysis, the minimum FFA-to-methanol ratio required for the esterification reaction is 1:1. Hence, to favor the conversion of FFA to FAME, an excess amount of methanol is usually used in a reaction. The esterification of oleic acid with methanol catalyzed using Amberlyst-46 (Rohm & Haas, USA) revealed that a higher methanol concentration could increase the FAME concentration only to a certain level and that the conversion would decrease beyond that optimal concentration [20]. It is thought that an excessively high methanol concentration can inhibit the contact of methanol and oleic acid due to the formation of a biphasic system. In the present study, the increase of the methanol-to-oil molar ratio to the maximum level led to a decrease of FFA. In other words, the effect of the methanol-to-oil molar ratio was independent of temperature and catalyst loading.
The optimal conditions for the esterification reaction of the model oil were evaluated by means of Equation (7), obtained through Minitab 17 by minimizing the response target (Y). The optimal conditions obtained ( Table 5) were then used to conduct another set of experiments with the model oil and R.trisperma oil for comparison purposes. The acid value profile for both the model oil and the R.trisperma oil system is shown in Figure 3a. For the model oil system, the final acid value was 1.08 mg KOH/g with 95.65 of FFA conversion achieved. In the R.trisperma oil system however, the final acid value was 2.49 mg KOH/g with 91.75% conversion achieved. The higher acid value in the R.trisperma oil system was considered to have been caused by the higher impurities and metal ions present in the R.trisperma oil. It was concluded that these impurities had poisoned the catalyst, leading thereby to a decrease in catalytic activity. Indeed, this phenomenon can be seen in Figure 3a. The acid value for both systems was quite similar up to 1 h of reaction time; thereafter, from 1.5 h, it started to differ, the value for the R.trisperma oil system staying higher to the end of the reaction, indicative of a reduction in catalytic activity. value of the esterified oil. The impact of catalyst loading on the acid value of the esterified oil was independent of both temperature and methanol-to-oil ratio, which was confirmed statistically by the ANOVA result. The esterification of waste cooking oil with Amberlyst-15 (Rohm & Haas, USA) in an earlier study showed a similar trend, the acid value of the esterified oil decreasing as the Amberlyst-15 concentration was increased to 3% [19]. Based on stoichiometric analysis, the minimum FFA-to-methanol ratio required for the esterification reaction is 1:1. Hence, to favor the conversion of FFA to FAME, an excess amount of methanol is usually used in a reaction. The esterification of oleic acid with methanol catalyzed using Amberlyst-46 (Rohm & Haas, USA) revealed that a higher methanol concentration could increase the FAME concentration only to a certain level and that the conversion would decrease beyond that optimal concentration [20]. It is thought that an excessively high methanol concentration can inhibit the contact of methanol and oleic acid due to the formation of a biphasic system. In the present study, the increase of the methanol-to-oil molar ratio to the maximum level led to a decrease of FFA. In other words, the effect of the methanol-to-oil molar ratio was independent of temperature and catalyst loading.  The optimal conditions for the esterification reaction of the model oil were evaluated by means of Equation (7), obtained through Minitab 17 by minimizing the response target (Y). The optimal conditions obtained ( Table 5) were then used to conduct another set of experiments with the model oil and R.trisperma oil for comparison purposes. The acid value profile for both the model oil and the R.trisperma oil system is shown in Figure 3a. For the model oil system, the final acid value was 1.08 mg KOH/g with 95.65 of FFA conversion achieved. In the R.trisperma oil system however, the final acid value was 2.49 mg KOH/g with 91.75% conversion achieved. The higher acid value in the R.trisperma oil system was considered to have been caused by the higher impurities and metal ions present in the R.trisperma oil. It was concluded that these impurities had poisoned the catalyst, leading thereby to a decrease in catalytic activity. Indeed, this phenomenon can be seen in Figure 3a. The acid value for both systems was quite similar up to 1 h of reaction time; thereafter, from 1.5 h, it started to differ, the value for the R.trisperma oil system staying higher to the end of the reaction, indicative of a reduction in catalytic activity.

Kinetics of Esterification Reaction
For comparison purposes, the aforementioned kinetics study was performed for both the model oil and the R.trisperma oil. The operating conditions were the same as the optimal conditions shown in Table 5. The catalyst loading and methanol-to-oil molar ratio were set as fixed parameters, while the temperature was varied for the kinetics observation ( Table 6). The experimental data obtained were processed according the assumption of pseudo-homogeneous kinetics and the equation elaborated in Section 2 (Equation 3). The experimental data are shown in Figure 4.

Kinetics of Esterification Reaction
For comparison purposes, the aforementioned kinetics study was performed for both the model oil and the R.trisperma oil. The operating conditions were the same as the optimal conditions shown in Table 5. The catalyst loading and methanol-to-oil molar ratio were set as fixed parameters, while the temperature was varied for the kinetics observation ( Table 6). The experimental data obtained were processed according the assumption of pseudo-homogeneous kinetics and the equation elaborated in Section 2 (Equation 3). The experimental data are shown in Figure 4.  At the same temperature, the R.trisperma oil system yielded a lower acid value than that of the model oil system. The lowest acid value was achieved at 95 °C for both systems, 0.40 mg KOH/g for  At the same temperature, the R.trisperma oil system yielded a lower acid value than that of the model oil system. The lowest acid value was achieved at 95 • C for both systems, 0.40 mg KOH/g for the model oil system, and 1.95 mg KOH/g for the R.trisperma oil system. As previously explained, this difference is thought to have been caused by the impurities of the R.trisperma oil. The linearized experimental data of the two systems are shown in Figure 4c and 4d, respectively. It is clearly apparent that the experimental data fit the developed equation well with a high reliability (high R 2 ), indicating that the developed model could represent the experimental data well and confirming that the esterification reaction followed pseudo-homogenous kinetics. The values of the kinetics constants for both systems are shown in Table 7. The kinetics constants for the model oil system were higher than those for R.trisperma at all temperatures, which served to further confirm the catalytic activity reduction in the R.trisperma oil system. The activation energy required for the esterification reaction of both systems was derived from an Arrhenius plot, as shown in Figure 5.  Figure 4c and 4d, respectively. It is clearly apparent that the experimental data fit the developed equation well with a high reliability (high R 2 ), indicating that the developed model could represent the experimental data well and confirming that the esterification reaction followed pseudo-homogenous kinetics. The values of the kinetics constants for both systems are shown in Table 7. The kinetics constants for the model oil system were higher than those for R.trisperma at all temperatures, which served to further confirm the catalytic activity reduction in the R.trisperma oil system. The activation energy required for the esterification reaction of both systems was derived from an Arrhenius plot, as shown in Figure 5.  The activation energy required for the model oil system was revealed to be 40.8 kJ/mol. The esterification of oleic acid with ethanol as catalyzed using a sulfonated ion exchange resin at a 47% catalyst loading in a previous study had an activation energy of 24.80 kJ/mol [21], which is much lower than the values determined in the present study. This could be due to the different types of alcohol used (methanol vs. ethanol) as well as the catalyst concentration difference (5.34% vs. 47%). In addition, the catalyst used in that study had a higher surface area (46 m 2 /g) than the one utilized in the present study (33 m 2 /g). Furthermore, the earlier study used pure oleic acid as the feedstock, while this study used a mixture of soybean oil and oleic acid.
The R.trisperma oil system had an activation energy of 33.2 kJ/mol, which is lower than that of the model oil system. This could be explained by the difference in the fatty acid compositions of the feedstocks. The model oil system contained only oleic acid (C18), while the R.trisperma oil was comprised of several fatty acids ranging from palmitic acid (C16) to docosanoic acid (C22). Additionally, the fatty acid chain length was found to have an impact on the activation energy of the FFA esterification reaction, a longer chain requiring higher activation energy (Table 8) [22]. Table 8. Effect of fatty acid chain length on activation energy of esterification reaction [22]. The activation energy required for the model oil system was revealed to be 40.8 kJ/mol. The esterification of oleic acid with ethanol as catalyzed using a sulfonated ion exchange resin at a 47% catalyst loading in a previous study had an activation energy of 24.80 kJ/mol [21], which is much lower than the values determined in the present study. This could be due to the different types of alcohol used (methanol vs. ethanol) as well as the catalyst concentration difference (5.34% vs. 47%). In addition, the catalyst used in that study had a higher surface area (46 m 2 /g) than the one utilized in the present study (33 m 2 /g). Furthermore, the earlier study used pure oleic acid as the feedstock, while this study used a mixture of soybean oil and oleic acid.
The R.trisperma oil system had an activation energy of 33.2 kJ/mol, which is lower than that of the model oil system. This could be explained by the difference in the fatty acid compositions of the feedstocks. The model oil system contained only oleic acid (C18), while the R.trisperma oil was comprised of several fatty acids ranging from palmitic acid (C16) to docosanoic acid (C22). Additionally, the fatty acid chain length was found to have an impact on the activation energy of the FFA esterification reaction, a longer chain requiring higher activation energy (Table 8) [22]. Table 8. Effect of fatty acid chain length on activation energy of esterification reaction [22].

Conclusions
The esterification of R.trisperma oil was evaluated and optimized statistically using a response surface methodology via a central composite design with a model oil for optimization of esterification reaction conditions. It was revealed that all of the individual factors (temperature, catalyst loading, and methanol-to-oil molar ratio) observed in this study had a significant impact on the acid value of the esterified oil, catalyst loading having the most significant impact, followed by temperature and methanol-to-oil molar ratio, respectively. The two-way interaction of the individual factors did not have any impact on the acid value of the esterified oil. The developed model could represent the experimental data well with high reliability. Based on the optimization process, the optimal conditions for the esterification reaction of R.trisperma oil were 92 • C temperature, 5.34 wt% catalyst loading, and 5.82:1 methanol-to-oil molar ratio, with a final acid value of 2.49 mg KOH/g and an achieved FFA conversion of 91.75%.
The kinetics of R.trisperma were investigated under the assumption of pseudo-homogeneous second-order kinetics. It was discovered that the experimental data could fit the developed reaction rate equation well and with high reliability, indicating that the kinetics of R.trisperma oil esterification followed a pseudo-homogeneous second-order reaction under the specified conditions. The activation energy required for the esterification of R.trisperma oil was 33.2 kJ/mol.