3.2.5. Model Validation

Triplicate reactions were executed at optimum conditions to validate model accuracy. The average yield of 92.0 ± 1.3% was revealed to be comparable with that of predicted value, which was 88.93%. Hence, the model was depicted to be accurate and valid to estimate the response, i.e., yield of biodiesel.

#### 3.2.6. ANOVA for Response Surface Quadratic Models for Biodiesel Production

For biodiesel production catalysed by Fe3O4\_PDA\_Lipase, quadratic model was depicted to be most suitable one with *p*-value < 0.05. The adjusted R<sup>2</sup> value for quadratic model was found to be 0.9840, while the lack of fit value was 0.0531. Insignificant lack of fit test value in addition to R<sup>2</sup> values also suggested/ascertained the fitness of quadratic model for Fe3O4\_PDA\_Lipase catalysed transesterification reactions.

Table 2 presents ANOVA describing selected model significance along with the significance of understudy reaction conditions. Out of the linear terms; A—methanol to oil ratio, B—enzyme concentration, C—reaction temperature and D—reaction time were ascertained to be significant, having *p*-values less than 0.05. While *p*-value i.e., 0.0874 > 0.05 depicted non-significant impact of E—water concentration. The above said factors significantly affected to the response as linear interactions i.e., AB, AC, AD, BD, and BE with *p*-values of 0.0010, 0.0321, 0.0076, 0.0008 and 0.0201 < 0.05, respectively. A2, B<sup>2</sup> and C<sup>2</sup> were found to have significant effect with *p*-values 0.0245, < 0.0001 and < 0.0001, whilst D<sup>2</sup> and E<sup>2</sup> were insignificant quadratic term.

Model equation in terms of coded values is as follow;

$$\begin{aligned} \text{Biodiesel yield} &= +86.03 + 1.97 \text{ A} + 14.73 \text{ B} + 0.97 \text{ C} + 2.24 \text{ D} - 0.68 \text{ E} + 1.45 \text{ AB} - 0.89 \text{ C} \\ \text{AC} - 1.13 \text{ AD} + 0.76 \text{ AE} + 0.51 \text{ BC} + 1.47 \text{ BD} - 0.97 \text{ BE} - 0.57 \text{ CD} + 0.22 \text{ CE} + 0.053 \text{ C} \\ \text{DE} - 3.37 \text{ A}^2 - 11.87 \text{ B}^2 - 8.90 \text{ C}^2 - 1.57 \text{ D}^2 - 1.72 \text{ E}^2 \end{aligned}$$

By the comparison of the factor's coefficients in the equation, the relative impact of each factor on the biodiesel yield can be identified.


**Table 2.** ANOVA for response surface quadratic model for biodiesel yield.

Li and Yan [49] applied three factor RSM for the optimization of transesterification process using immobilized lipase as catalyst, enzyme conc. and temp. were ascertained to be significant linear terms, but methanol to oil ratio was insignificant term with (*p*-value of 0.3083) all quadratic terms were also significant, while no first order interaction term was significant (Table 2). Wu et al. [50] optimized four reaction parameters using RSM, which were (i) lipase concentration, (ii) reaction time, (iii) reaction temperature, and (iv) ethanol to oil molar ratio. Lipase level, temperature and time were revealed to be the significant linear terms that support the present study, while ethanol to oil ratio showed insignificant impact, which might be due to the shorter range (3:1 to 6:1) of alcohol: oil used in that design. (Time × Temperature) was the only significant first order interaction terms. Huang et al. [51] reported a significant quadratic model for the optimization of methyl ester formation. Lipase to oil ratio (x1), ratio of two lipases (x2), t-butanol:oil (x3), methanol:oil (x4) and time (x5) were independent variables chosen for optimization of reaction. Out of that, all the linear terms showed significant effect, while x1x2, x2x3, x3x4, x2x4, x1x4, and x4x5 were significant first order terms and among quadratic terms x3<sup>2</sup> and x4<sup>2</sup> had significant effect on response. Li and Dong [27] selected methanol:oil x1, lipase:oil x2, water content x3, and temperature x4 as independent variables for process optimization of biodiesel production using RSM. All the linear terms were significant in that model as well, which resembles the current study except the water content, which is insignificant in our work. All quadratic and first order interaction terms were also significant, expect for x1x4 and x2x4, and similar first order terms are insignificant in the present work as well. Xia [26] reported methanol:oil, amount of enzyme, time for reaction and amount of hexane (solvent) as significant linear terms, all the quadratic terms showed significant impact/effect on response, while (enzyme × hexane content) was the only significant first order interaction term. The results of ANOVA for the optimization of biodiesel production using immobilized lipase are comparable to the literature; the few variations might be due to different fatty acid profiles, different ranges of selected parameters, different alcohols being used and because of using solvent/solvent free systems.

Predicted vs. actual plot (Figure 8) of % biodiesel yield for the design, depict the fitness of the quadratic model, the difference between the predicted and the actual values are very small, as presented in Figure 8, which confirms the fitness of quadratic model. Our findings are comparable to the previous reports [27,51].

**Figure 8.** Predicted vs. actual values plot.

3.2.7. Response Surface (RS) Plots of Interacting Terms

RS plots of the significant first order interaction terms are presented in Figure 9. Figure 9a is the RS plot for biocatalyst (Fe3O4\_PDA\_Lipase) concentration and methanol to oil ratio. 3D plot revealed that the biodiesel yield increases with the increase in biocatalyst concentration and the content of methanol

as the highest biodiesel yield is obtained at a biocatalyst concentration of 10% and 6:1 methanol to oil ratio, with further increase in the methanol content the yield starts to decrease, which might be due to deactivation of the enzyme by excess methanol. Figure 9b indicates the e ffect of methanol to oil ratio and reaction temperature interaction. The highest response value at the centre shows that the yield increases with temperature and methanol to oil ratio till the optimum points, then increase in temperature and methanol content results in decreased in biodiesel yield. Figure 9c 3D plot describes the influence of reaction time and methanol: oil ratio on response. Figure 9d is the response surface plot of enzyme concentration (%) and reaction time (h). The highest response at the inner corner presents that the biodiesel yield increases with both reaction time and the biocatalyst concentration, as the highest yield is obtained at 10% biocatalyst concentration and 30 h of reaction time. BE (enzyme conc. × water content) is another significant interaction term. The enzyme activity and structure are affected by the water content, which is clearly indicated by Figure 9e, which predicts that the biodiesel yield decreases by reduced enzyme activity as the water percentage deviates from optimum value.

**Figure 9.** Response surface graphs of significant first order interaction terms (**a**) A × B, (**b**) A × C, (**c**) A × D, (**d**) B × D and (**e**) B × E.

3.2.8. Recovery and Reusability of Nano-Biocatalyst

At reaction completion, Fe3O4\_PDA\_Lipase was recovered by using magnetic decantation. Afterwards, lipase assay was carried out to find out the activity of immobilized lipase after recovery. No change in the activity of lipase was detected after first use, i.e., 17.83 U/mg/min. Therefore, these recovered Fe3O4 magnetic nanoparticles were reused several times for the biodiesel production and after the completion of each reaction the lipase activity assay was performed, which showed that lipase activity started decreasing after four uses, and after seven uses the activity declined to 4.6 U/mg/min. The biodiesel conversion rate decreased after four uses (Figure 10), which was clearly due to a decrease in the activity of immobilized lipase. This reduction in activity may be due to the exposure of nano-biocatalyst to organic solvents present in the reaction mixture or repeated exposure to heat, which may have resulted in the decrease of lipase activity. Similar studies have also been reported by Dumri and Hung [23].

**Figure 10.** Re-usability of lipase immobilized Fe3O4 nanoparticles.

#### 3.2.9. Physical Properties of Biodiesel

Fuel properties of produced biodiesel are presented in Table 3. The fuel properties meet the biodiesel standards set by ASTMD.


**Table 3.** Properties of WCO based biodiesel.

For the complete combustion of biodiesel, optimum fuel to air ratio is required, which is obtained at specific levels of density. Kinematic viscosity is a measure of restriction between the two layers of a liquid, and quality of combustion is recognized to be affected by kinematic viscosity. The ignition point of fuel on exposure to the spark is called the flash point. High flash points of the biodiesel make it easy to store. Pour point and cloud point are important for cold flow properties. Furthermore, suitability of biodiesel for the use in engine can also be evaluated by these properties. Previous studies have revealed comparable results for the biodiesel produced from WCO. Few variations in the observed fuel characteristics may be attributed to different source and composition of feedstock oil [33].
