According to Chai et al. (2014), UAE was carried out with the help of sulfuric acid (10%, w/w H₂SO₄/free fatty acid) as the catalyst, which was dissolved in methanol (methanol/free fatty acid molar ratio of 40). The said ingredients were mixed for 5 minutes. In conforming with the American Oil Chemists’ Society (AOCS) Official Method (Ca 5a-40), the free fatty acid of olive oil is 2.36%, which can increase to 2.5, 5.0, and 10.0% by pure oleic acid (AOCS, 2000). The sulfuric acid-methanol solution was mixed with 100 g of inedible olive oil which contained high amounts of free fatty acid. The reaction lasted for 30 minutes using an ultrasonic probe (Bandelin HD 3200, Bandelin Electronics, Berlin, Germany). Distilled water was used as a temperature regulator by circulating in the jacketed vessel. A high grade titanium tip (TT13, 13 mm diameter) assisted in sonicating the substrates with an unchanging horn depth of 2 cm. Also, the hot plate mixer operated at 60 ºC, for 120 minutes, and at 600 rpm as the traditional-assisted esterification method. At the end of the reaction time, the reaction mixture was immediately cooled down to room temperature. The water-soluble components were separated from the product in a separatory funnel. Esterification yield was calculated in conformity with a method used previously by Chai et al. (2014).

UAT was optimized including the methanol/oil mole ratio (3, 9, and 15), KOH catalyst concentration (0.5, 1.0, and 1.5 %), power level (30, 90, and 150 W), reaction time (15, 30, and, 45 min), and reaction temperature (45, 55, and 65 ºC). Each factor was optimized by considering an intermediate value (central point) of other factors.

The catalyst-methanol solution was mixed with 100 g esterified inedible olive oil. Then, the reaction took place with the help of an ultrasonic probe. A hot plate mixer operated at 60 ºC for 120 minutes and at 600 rpm as TAT.

At the end of the reaction, fatty acid methyl esters were refined chemically according to a method used previously by Dehghan et al., 2019. Methyl margarate was added to the crude biodiesel as an internal standard (Atapour and Kariminia, 2011). The purity of biodiesel was determined using the GC/FID in conformity with the method reported by Golmakani et al., 2012a, 2012b. The weight of yield, purity, and final yield were determined according to methods reported by Atapour and Kariminia, 2011; Hsiao et al., 2010.

The power level of the ultrasound affected the yield indices of the produced biodiesel (Figure 1a). By increasing the ultrasound power level from 30 to 90 W, the final yield was enhanced from 76.10 to 92.69%. This positive effect can be attributed to broader acoustic streaming and more cavitation bubbles. The increase in the mentioned factors can cause enhancements in the dispersion and mass transferal effects of the ultrasound, while allowing the two immiscible reaction layers to be thoroughly emulsified (Joshi et al., 2018; Korkut and Bayramoglu, 2018). However, the final yield decreased from 92.69 to 80.62% when the ultrasound power was further increased from 90 to 150 W. In fact, high levels of power can make the tip of the horn overpopulated with bubbles, thereby resulting in bubble coalescence and acoustic decoupling. These criteria act to reduce the number of active cavitation bubbles (Korkut and Bayramoglu, 2018). The ultrasound power of 90 W proved to be high enough to obtain a purity of 98.95% and a final yield of 92.69%, under the studied conditions. These findings are in accordance with the results of Korkut and Bayramoglu (2018) who evaluated the UAT of canola oil. They reported that by raising the ultrasound power to 40 W an increase in the reaction yield by up to 99.4% was observed; whereas higher levels of ultrasound power reduced the reaction yield.

As shown in Figure 1b, the methanol/oil mole ratio affected the yield indices. Rising the mole ratio from 3 to 9, significantly increased the yield indices. However, as the mole ratio increased from 9 to 15, a downward trend was recorded for the yield indices. When the methanol/oil mole ratio measured 9, the results corresponded with the highest weight of yield, purity, and final yield (93.68, 98.95, and 92.69%, respectively). Since transesterification is an equilibrium reaction, larger amounts of methanol can modify the reaction to make the equilibrium favorable to the formation of fatty acid methyl esters, The stoichiometric mole ratio of triacylglycerol to methanol for the occurrence of transesterification is 1:3 and, in fact, an excess amount of methanol is preferable for the completion of the reaction (Ho et al., 2016). At high methanol/oil mole ratios, the lower concentration of oil causes a decrease in the interaction between triacylglycerol molecules and catalytic active sites, thereby reducing the reaction kinetics and the reaction yield. Moreover, freeing the reaction mixture from unnecessary methanol requires more energy (Korkut and Bayramoglu, 2018). Ultrasound radiation rapidly generates tiny methanol droplets and, as a result, the emulsion forms easily and quickly in the oil phase. When the solution is rich in methanol, the droplets tend to become larger in the emulsion. In such circumstances, larger droplets are created as a result of the frequent encounters among small-size droplets of methanol, compared to when methanol is not abundantly present in the solution. As large droplets become more common, the transesterification reaction could then take on a slower rate (Thanh et al., 2010). Similarly, Yin et al. (2017) studied how different mole ratios of methanol to soybean oil (4-12) can affect UAT yield. They showed that the UAT yield significantly increased by rising the mole ratio from 4 to 8. Then, by rising the mole ratio from 8 to 10, the yield did not increase significantly. By its further increase to 12, the UAT yield decreased to an extent that was lower than the amount obtained when there was a mole ratio of 8.

The transesterification reaction is commonly affected by the concentration of the catalyst. This factor was observed to have significant effects on the yield indices (Figure 1c). The lowest values for biodiesel purity (1.17%) and its final yield (0.97%) were recorded when the catalyst concentration was 0.5%. An insufficient catalyst concentration could not contribute adequately to the conversion of inedible olive oil to biodiesel. The yield indices of biodiesel increased as the catalyst concentration rose to 1.0% in terms of adequacy. This correlation is natural since a higher concentration of catalysts is associated with more of their active sites, and thus the conversion of reactants is better facilitated for the reaction to be pushed forward. The transesterification reaction begins with the carbonyl carbon atoms of monoacylglycerol, diacylglycerol, and triacylglycerol reacting with methoxide ions (CH₃O^-). Dissolving KOH in methanol produces CH₃O^- according to the following reaction: OH^- + CH₃OH → CH₃O^- + H₂O. Since KOH is a strong alkaline, it has a large “dissociation constant” in methanol. Therefore, the concentration of CH₃O^- depends only on the concentration of the KOH catalyst. The result is that a higher concentration of KOH encourages a faster procession in the reaction (Ho et al., 2016; Thanh et al., 2010). Raising the catalyst concentration from 1.0 to 1.5% reduced the production of biodiesel. Several disadvantages usually discourage researchers from using catalysts excessively when experimenting with transesterification reactions. Large amounts of catalyst tend to increase the extent of how soluble fatty acid methyl esters can be in glycerol, thereby causing residual levels of fatty acid methyl ester after glycerol has been separated. Decreasing the fatty acid methyl ester content would reduce the purity and yield of biodiesel as well, (Thanh et al., 2010). Furthermore, higher concentrations of catalysts usually increase the viscosity of the reaction mixture, and this acts as a hindrance to glycerol separation (Korkut and Bayramoglu, 2018). The high concentrations of catalysts can lead to prolific levels of soap formation which then cause difficulties in the separating step of emulsification. This chain of events ultimately concludes with a lower biodiesel yield (Yin et al., 2017). As a consequence, the optimal amount of KOH in this study was 1.0%, as far as the relevant treatments are concerned. Similarly, Deshmane and Adewuyi (2013), produced biodiesel from soybean oil using UAT at different catalyst concentrations (0.6-1.4%). They reported that the biodiesel yield was improved by raising the catalyst concentration from 0.6 to 1%. However, further increases in the concentration amounted to almost no change or even a slight decrease in the reaction rate.

The duration of the reaction time had notable effects on the yield indices of biodiesel (Figure 1d). Prolonging the reaction time from 15 to 30 min caused an increase in the yield indices of biodiesel. At the early stages of the reaction, the provision of an insufficient contact time between the reaction mixtures led to lower levels of purity and yield. The highest values pertaining to the weight of yield, purity, and the final yield were obtained during a total reaction time of 30 min (93.68, 98.95, and 92.69%, respectively). The reversible nature of the transesterification reaction is a reason for the decrease in yield indices when reactions take longer than 30 min. This reduction could be due to the solubility of fatty acid methyl ester in the glycerol and also because of other unwanted reactions that can negatively affect the yield and purity (Badday et al., 2013). Similar observations were also reported (Badday et al., 2013) when the ultrasound method was used for transesterified crude Jatropha oil. In the mentioned research, an increase in biodiesel yield was observed when the reaction time was prolonged from 10 to 60 min, but it started to decrease if the reaction took more than 60 min.

The yield indices of biodiesel were affected by the temperature at which the ultrasound operated (Figure 1e). Rising the reaction temperature from 45 to 55 °C caused significant increases in biodiesel yield indices. These findings are logical to obtain because KOH has an enhanced solubility, while there is a thorough contact between the components of the reaction mixture, leading to a higher biodiesel yield (Maddikeri et al., 2013). However, an extra increase in the reaction temperature from 55 to 65 °C can begin to reduce the yield indices which can be attributed to the overheating of the reaction mixture. This could result in the loss of methanol and energy, along with a lower level of cavitational effects. Also, due to the lower thermal stability of fatty acid methyl esters under extreme conditions and the decomposition of the fatty acid methyl esters (especially the polyunsaturated ones) which can further produce by-products, temperatures higher than 55 °C have adverse effects on fatty acid methyl esters (Maddikeri et al., 2013). Therefore, the reaction temperature of 55 °C is considered the most suitable temperature for the production of biodiesel from inedible olive oil. Similarly, Maddikeri et al., 2013 showed how different temperatures (i.e. 30-50 °C) affected the UAT yield of waste cooking oil. They stated that an increase in temperature from 30 to 40 °C caused an increase of 10% (from 78 to 88%) in the biodiesel yield, whereas another 10 °C increase (from 40 to 50 °C) in the reaction temperature only made a negligible improvement (from 88 to 93%) in the biodiesel yield (Maddikeri et al., 2013).

According to the findings, the optimal state for the operation of UAT can be described as a set of circumstances which include a power level of 90 W, a methanol/oil mole ratio of 9, a catalyst concentration of 1.0%, a reaction time of 30 min, and a reaction temperature of 55 °C. Figure 2 compares the optimum conditions of UAT and TAT. The weight of yield, purity, and final yield of UAT were higher (93.68, 98.95, and 92.69%, respectively) compared to those obtained by TAT (88.66, 87.17, and 77.28%, respectively). The cavitation and its physical effects can lead to this improved performance. Furthermore, there are related features such as the liquid micro-circulation (acoustic streaming), local turbulence and micro-emulsion formation. These features increase the interactions that are necessary for the reaction. An external, mass transfer barrier existed between the oil and the methanol phase. Since micro-emulsions joined the two phases that participated as reactants, an enormous increase was observed in the areas where the reactants collide, thereby accelerating the reaction rates. In the case of TAT, the reactants receive energy exclusively as heat, and this occurs by the mechanisms of conduction and convention. These two mechanisms do not contribute to the establishment of a sufficient contact between the reactants. Accordingly, the UAT is capable of reducing the reaction time significantly, as compared to the duration required by the TAT. The UAT can achieve higher levels of purity and more yield. These findings are in accordance with the results of Maddikeri et al. (2013), who produced biodiesel from waste cooking oil by using the UAT operation. A higher biodiesel yield was reported (90%) when using UAT compared to TAT (70%).

No considerable differences were observed between the profiles of fatty acids when using the UAT and TAT. Accordingly, different transesterification methods had no selectivity on the transesterification of different fatty acids (i.e. with various saturation degrees and chain length). Nonetheless, the UAT created a biodiesel that showed higher values for density and L* value, but lower values for a* value, b* value, kinematic viscosity, and refractive index. These differences can be due to the higher amount of final yield obtained by transesterification when using the UAT compared to the TAT. The UAT produced a biodiesel that showed higher levels of purity than those produced by TAT. Accordingly, the application of UAT can yield a biodiesel which exhibits a higher brightness value (L* value), and thus the purification steps can be reduced.

As shown in Table 3, no significant differences were observed between the UAT and TAT, including their flash point, fire point, and cloud point. In conformity with the ASTM D6751 Official Method, the flash point, cloud point, and pour point of biodiesel must be at least 130 °C, -3 to 12 °C, and -15 to 10 °C, respectively. In this research, the biodiesel became a product that fell into the standard ASTM range. In conformity with the findings of the pour point, the biodiesel that had been produced by UAT eventually showed less viscosity which allowed it to be pumped at more efficient rates.

Table 3 shows energy consumptions by UAT and TAT during the transesterification step and further through all of the steps of biodiesel purification. The percentages of energy consumption during the transesterification step were 20.74 and 61.52% for UAT and TAT, respectively. The amount of energy that was consumed during the transesterification step in TAT was 0.227 kWh, which is at least five-fold compared to that of the UAT (0.045 kWh). However, during their purification steps, the energy consumptions for both UAT and TAT were equal. TAT requires 4.775 kWh/kg to produce 1 kg biodiesel. This amount was at least 2 times higher than that required by the UAT (2.170 kWh/kg). It can be concluded that UAT can significantly increase the final yield, shorten the reaction time and reduce the energy consumption (Motasemi and Ani, 2012). The main production costs of biodiesel strongly depend on energy consumption during the transesterification step in addition to the cost of feedstock. Processing inedible olive oil by UAT has many advantages for biodiesel production. These advantages are primarily a lower energy consumption and a lower feedstock cost.