**3. Results and Discussion**

#### *3.1. E*ff*ect of Various Heating Processes*

This study compared noncatalytic esterification using microwave irradiation and conventional heating. As demonstrated in Figure 1, conventional heating resulted in low oleic acid conversions (27.13%–67.13%). This finding is consistent with other works in that conventional heating needed long reaction time to achieve a satisfactory reaction conversion [48]. Conventional heating is an inefficient form of heat transfer, because heat is delivered to the reaction solution by convection, radiation, and conduction from the surface of the reactor, causing heat loss [38,39]. To increase the heat transfer and reaction efficiency, microwave approach was employed as a replacement for the reaction. Results indicated that the oleic acid conversion significantly increased and reached high levels (60.61%–90.18%) with microwave irradiation. Remarkably, at a given reaction time, microwave irradiation exhibited significantly higher oleic acid conversion than conventional heating, signifying

that microwave irradiation is preferable to conventional heating for performing the esterification. This result corresponds to the study of Aguilar–Reynosa et al. [49]. Microwave irradiation minimizes loss of heat and additionally provides a nonthermal activation influence on the esterification [50]. Microwaves strongly induce movement, collision, and oscillation of reactant molecules, promoting the reaction efficiency [49,51]. As a result, microwave irradiation is superior than traditional heating regarding to reaction time [43,52]. Therefore, microwave approach was selected for more extensive study.

**Figure 1.** Comparison of esterification using conventional heating and microwave irradiation. Reaction conditions occurred with an ethanol:oleic acid molar ratio of 2:1, temperature of 433 K, and microwave power of 150 W (for microwave irradiation). Vertical bars illustrate the standard deviation of three replicates.

#### *3.2. Influence of Reactant Molar Ratio*

This work investigated the impact of reactant molar ratio on the reaction by undertaking the reaction at 433 K, at a microwave power of 150 W, and at various ethanol:oleic acid molar ratios (1:1–8:1). As demonstrated in Figure 2, the oleic acid conversion was promoted when molar ratios of the reactants were increased from 1:1 to 2:1. Nevertheless, additional increase in ethanol:oleic acid molar ratio resulted in decreased oleic acid conversion. This may be because large quantities of ethanol used to dilute oleic acid, which plays a role as a catalyst for the esterification reaction, may lower the reaction rate [53,54]. This result corresponds to that of the biodiesel production study by Minami and Saka [54].

#### *3.3. Temperature E*ff*ect on Esterification*

The impact of temperature on reaction was evaluated by conducting the reaction at a microwave power of 150 W, an ethanol:oleic acid molar ratio of 2:1, and various temperatures (413–473 K). Figure 3 presents the progress over time of the oleic acid esterification at different temperatures. Results showed that higher temperature provided a greater conversion of oleic acid, with the highest conversion of 97.62% obtained at 473 K and 6 h. This is because high temperature enhances reaction rate [12], increasing the reaction conversion. This finding is similar to those of other works [12,14,55].

**Figure 2.** Influence of molar ratio of ethanol to oleic acid on esterification reaction. Reactions occurred at a temperature of 433 K and with microwave power of 150 W.

**Figure 3.** Influence of temperature on esterification reaction. Reactions occurred at a molar ratio of ethanol to oleic acid of 2:1 and microwave power of 150 W.

#### *3.4. E*ff*ect of Microwave Power on Reaction*

To determine the impact of microwave power on the reaction, the esterification was carried out at different microwave power levels (120–210 W) while maintaining other factors at a constant level. As illustrated in Figure 4, increasing microwave power led to an increase in the oleic acid conversion. This might have been because higher energy generated by higher microwave power resulted in higher activation effects (nonthermal effects), causing faster molecular mobility; therefore, the reaction rate was promoted [50,51]. This result corresponds with that reported for biodiesel production [56] and for pyrolysis of biomass [51].

**Figure 4.** Influence of microwave power on esterification reaction. Reactions occurred at a molar ratio of ethanol to oleic acid of 2:1 and at a temperature of 433 K.

#### *3.5. Kinetic Model Development*

#### 3.5.1. Determination of Reaction Rate Constant

Figures S1–S3 (in the Supplementary Material), respectively, provide a linear plot of ln ⎡ ⎢⎢⎢⎢⎢⎣ <sup>−</sup>1−θ*E*−θ*<sup>D</sup> Ke* +α<sup>2</sup> *X*+2θ*<sup>E</sup>* <sup>−</sup>1−θ*E*−θ*<sup>D</sup> Ke* <sup>−</sup>α<sup>2</sup> *X*+2θ*<sup>E</sup>* ⎤ ⎥⎥⎥⎥⎥⎦ versus <sup>α</sup>2*CA*0*<sup>t</sup>* at different microwave powers, temperatures, and ethanol:oleic

acid molar ratios. As illustrated in Table 1, correlation coefficients (R2) of the regression lines were in the range of 0.972–0.997, indicating the reliability and correction of the second-order reaction model. Table 1 (runs 1–5) shows that rate constants *Ke* and *k*<sup>1</sup> both decreased when the molar ratio of ethanol to oleic acid increased, indicating the negative influence of high ethanol:oleic acid molar ratio on the reaction conversion [53,54]. Nevertheless, the rate constants *Ke* and *k*<sup>1</sup> accelerated with increasing temperature (Table 1, runs 6–9), signifying that the reaction is endothermic [47]. Furthermore, increasing microwave power enhanced the rate constants *Ke* and *k*<sup>1</sup> (Table 1, runs 10–13), which was similar to the results of other studies [51,56]. This result indicated a positive effect from microwave power on the reaction. Notably, at any ethanol:oleic acid molar ratio and temperature, microwave-based reaction had much higher *Ke* and *k*<sup>1</sup> values than the conventional heating-based reaction (see the *Ke* and *k*<sup>1</sup> values for the conventional heating-based reaction in the Table S1 in the Supplementary Material). These results indicated that microwave irradiation enhanced the equilibrium rate constant and forward reaction rate constant. Therefore, microwave irradiation is more efficient than conventional heating for conducting the ethyl oleate synthesis.

#### 3.5.2. Determination of Pre-Exponential Factor and Activation Energy

The influence of temperature on reaction rate constants (*Ke* and *k*1) is represented using the Arrhenius equation [Equations (8) and (9)]. The activation energy, pre-exponential factor, and molar reaction heat of the reaction were calculated using the Arrhenius–van't Hoff plots. As illustrated in Figure 5 and in Table 2, high R2 of the regression lines (0.997 for *k*<sup>1</sup> and 0.985 for *Ke*) were achieved; therefore, the model parameters can be determined from the straight line. Results showed that the activation energy of the forward reaction was 23.59 kJ mol−1, and the molar reaction heat was 65.98 kJ mol<sup>−</sup>1. The pre-exponential factors were calculated to be 2.27 L mol−<sup>1</sup> min−<sup>1</sup> and 9.07 <sup>×</sup> <sup>10</sup><sup>8</sup> for forward and equilibrium reactions, respectively.


**Table 1.** Forward reaction rate constant *k*<sup>1</sup> and equilibrium rate constant *Ke* for esterification under different reaction conditions.

**Figure 5.** Arrhenius–Van't Hoff plot for equilibrium rate constant and forward reaction rate constant of esterification reaction.

**Table 2.** Activation energy, molar reaction heat, and pre-exponential factor for oleic acid esterification with ethanol using microwave approach.


#### 3.5.3. Relation of Microwave Power to Pre-Exponential Factor

The modified Arrhenius equation reported by Su et al. [57] was used to determine the influence of microwave heating on the kinetic model:

$$K\_{\ell} = A\_{\ell} \exp\left(-\frac{\Delta l t}{RT}\right)$$

$$k\_1 = A\_1 \exp\left(-\frac{E\_a}{RT}\right)$$

$$A\_{\ell} = A\_0^{\epsilon} + A\_W^{\epsilon} \cdot W \tag{12}$$

$$A\_1 = A\_0^1 + A\_W^1 \cdot W \tag{13}$$

where *W* is the microwave power; *A<sup>e</sup> <sup>W</sup>* and *<sup>A</sup>*<sup>1</sup> *<sup>W</sup>*, respectively, denote the coefficient for representing the effect of power on the equilibrium and forward reaction; *A<sup>e</sup>* <sup>0</sup> and *<sup>A</sup>*<sup>1</sup> <sup>0</sup>, respectively, denote the constant for representing the effect of power on the equilibrium and forward reaction. The pre-exponential factors (*Ae* and *A*1) were assumed to obey linear functions with the microwave power. Both the constants (*A*<sup>1</sup> <sup>0</sup> and *Ae* <sup>0</sup>) and the coefficients (*A*<sup>1</sup> *<sup>W</sup>* and *Ae <sup>W</sup>*) can therefore be determined by linearly plotting *Ke e*−Δ*h*/*RT* versus microwave power W [Equation (14)] or *<sup>k</sup>*<sup>1</sup> *<sup>e</sup>*−*Ea*/*RT* versus microwave power W [Equation (15)]:

$$\frac{\mathbb{K}\_{\mathfrak{c}}}{\mathfrak{c}^{-\Delta h/RT}} = A\_0^{\mathfrak{c}} + A\_W^{\mathfrak{c}} \cdot \mathcal{W} \tag{14}$$

$$\frac{k\_1}{e^{-E\_x/RT}} = A\_0^1 + A\_W^1 \cdot \mathcal{W} \tag{15}$$

Figure 6a,b, respectively, represents a linear relationship between *Ke <sup>e</sup>*−Δ*h*/*RT* and W and *<sup>k</sup>*<sup>1</sup> *e*−*Ea*/*RT* and *W* for the equilibrium reaction and forward reaction. The high R2 value of the regression line (0.951–0.997) signified that the developed model is reliable, and the assumption is correct. The coefficients (*A<sup>e</sup> <sup>W</sup>* and *<sup>A</sup>*<sup>0</sup> *<sup>W</sup>*) and constants (*A<sup>e</sup>* <sup>0</sup> and *<sup>A</sup>*<sup>1</sup> <sup>0</sup>) could therefore be determined from the slope and intercept of each regression line. The value of *A<sup>e</sup> <sup>W</sup>* and *Ae* <sup>0</sup> for the equilibrium reaction was 4.11 × 106 <sup>W</sup>−<sup>1</sup> and 3.69 <sup>×</sup> 108, respectively (Table 3). For the forward reaction, the values of *<sup>A</sup>*<sup>1</sup> *<sup>W</sup>* and *<sup>A</sup>*<sup>1</sup> <sup>0</sup> were respectively determined to be 4.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> L mol–1 min–1 <sup>W</sup>–1 and 1.5282 L mol–1 min–1.

**Figure 6.** Linear regression of the experimental data for determining microwave power constants and coefficients for forward reaction (**a**) and equilibrium reaction (**b**).


**Table 3.** Constants and power coefficients for describing the relationship between microwave power and pre-exponential factors.

*3.6. Comparison with Other Works*

Table 4 illustrates the comparison of reaction conditions for oleic acid esterification using various processes. The esterification was mainly conducted using a liquid acid catalyst (e.g., H2SO4) [16]. This process provides a high conversion yield (99.9%), but it severely corrodes equipment, requires a complicated process for catalyst removal from the reaction solution, and pollutes the environment [16,17]. To avoid the complications associated with homogeneous catalysts, Vieira et al. [20] used HZSM-5 as a solid catalyst for the reaction. Nevertheless, the heterogeneous catalyst demonstrated low catalytic activity, thus requiring large quantities of catalyst (20%) and a long reaction time (7 h), and lowering reaction conversion (80%) [20]. Enzymatic esterification is proposed as a substitute for chemically catalyzed esterification to facilitate environmentally friendly biodiesel production. Nguyen et al. [24] successfully esterified oleic acid with methanol using Eversa Transform lipase for producing biodiesel. Although this process showed high reaction conversion (96.73%), the high cost of enzymes limits its industrial application. Tsai et al. [29] developed another green process called the noncatalytic process using supercritical methanol for oleic acid esterification to eliminate the problems associated with both enzyme- and chemical-catalyzed methods. This efficiently converted oleic acid to esters (97%) within a short reaction time (15 min), but the reaction proceeded at a high temperature (593 K) and high pressure (25 MPa) [29]; it thus required expensive reactors and extensive safety precautions. Melo–Júnior et al. [58] proposed a noncatalytic esterification of fatty acid using microwave irradiation. However, the reaction conversion obtained in their study was low (only 35%), because microwave power was not maintained in their study, leading to lack of microwave-induced nonthermal effect for promotion of the reaction rate [59]. Therefore, the microwave irradiation used in their study is similar to conventional heating. In this study, we proposed another noncatalytic method using microwave irradiation for the oleic acid esterification with ethanol under constant microwave powers to enhance the reaction conversion. The result was a high reaction conversion of 97.62%. The use of microwave irradiation for esterification was more efficient and rapid than conventional heating-based esterification, reducing energy consumption and reaction time. In the reaction mixture, oleic acid and ethanol exist under molecular cage with hydrogen bonding [60]. With the application of microwaves, oleic acid and ethanol absorb the energy from the electromagnetic field, which consequently induces the oscillation of reaction molecule and hydrogen bond variation between ethanol and oleic acid [59]. Resonance is subsequently generated and causes the hydrogen bonds breakage and formation of free small molecules due to reactant molecules escaping from the molecular cage. Consequently, the number of activation molecules is promoted, enhancing the reaction rate [60]. This work signifies that microwave-assisted noncatalytic esterification can be an ecofriendly and efficient process to produce biodiesel.


**Table 4.** Oleic acid esterification using different methods for producing biodiesel.

The potential applications of microwave approach in the large-scale biodiesel production have been widely discussed in literatures [61,62]. Although microwave is superior to conventional heating in the terms of energy consumption and reaction time, the use of microwave for industrial application has several limitations regarding to the control of temperature and safety of the pressurized vessel [61,62]. To address these concerns, the design of microwave reactor is crucial. Studies have showed that the design of microwave reactor for enhancing the temperature and pressure monitoring, safety features, and cooling features is possible [61]. In addition, microwave-based process has been successfully implemented in many industries such as polymers processing, minerals processing, and powder processing [61]. Therefore, the microwave process has a potential application for industrial biodiesel production. However, microwave process has not been used commercially for biodiesel production yet. Further studies are consequently required to evaluate the application of microwave in large-scale biodiesel production.
