3.3. Response Surface Analysis
It is known that the most important parameters affecting the efficiency of biodiesel production are the molar ratio of alcohol to oil (A), temperature (B), the amount of biocatalyst (C), and reaction time (D). In order to investigate the interaction of independent variables (the overall effect of these factors), the experiments were performed by changing the physical parameters using the experimental design (
Table 2). By applying multiple regression analysis to the obtained data, the experimental results of the factorial central composite design were fitted to a quadratic polynomial equation (1). The resulting adjusted model for the synthesis of isoamyl alcohol esters is given in Equation (2).
where:
Y—transesterification degree, %;
the alcohol-to-oil molar ratio, mol/mol;
temperature, the catalyst (snail shells) amount, °C;
lipase amount, wt. %;
the process duration, h.
Statistical analysis of the model was performed to evaluate the variance (ANOVA) and test the fit of the empirical model. The ANOVA results fitted to the second-order response surface model by the mean-square method are summarized in
Table 4. The coefficients of the response surface model were also estimated as predicted in Equation (2). The significance of each of the coefficients is tested by
p-values (probability of error value), which also indicate the strength of interaction between each parameter. According to the data presented in
Table 4, the
p value of the model is less than 0.0001, which indicates a high significance in predicting the response values and the fitness of the derived model, and there is only a 0.01% chance that such high F values of the models are due to noises (errors, natural scatter). A high F value (F model = 321.38) with a very low probability value (
p < 0.0001) indicates the high significance of the constructed model. Evaluation of the discrepancy of the residual errors compared to the theoretical error (F value 1.97) showed that the discrepancy is insignificant. Significances of all coefficients were determined by
p values and presented in
Table 4.
A higher F value and a lower p value indicate that the respective parameters are significant. p-values “p > F” less than 0.05 mean that the model components are significant. For this model, A, B, C, D, AD, BC, BD, CD, A2, B2, C2, and D2 are statistically significant components of the model. The model can be improved by removing insignificant components from the model and leaving only the significant ones. AB, BD, and D2 components were removed from the model (Equation (3)).
The low value of the coefficient of variation (C.V. = 4.42%) indicates that the results of the fitted model are reliable. The quality of the model fit was assessed by the coefficient of determination (R
2), which was calculated to be 0.9961. This means that 99.61% of the experimental data confirm the agreement with the data predicted by the model. The value of the adjusted coefficient of determination (R
2adj) was 0.9930 and the value of the predicted coefficient of determination (R
2pred) was 0.9844, indicating that the actual results agree with the predicted results (
Figure 2).
This means that the model is accurate and reliable for predicting and analysing the degree of transesterification of biodiesel. The value of the adjusted coefficient of determination (R
2Adj. = 0.9930) is also very high, which confirms the significance of the model. A high value of predicted R
2 (0.9844) indicates that the fitted model is reasonably accurate. The corresponding precision value is 61.803 for the model. This value represents the signal-to-noise ratio. A value greater than 4 is desirable. For this model, the corresponding precision value is more than 15 times the desired value. In this study, a ratio greater than 4 for adequate precision observed in all models validates that the model has an adequate signal, which indicates that the model can be used to navigate the design space. This was further supported by
Figure 2, which shows that all the experimental values were scattered around the predicted values. As shown in
Figure 2, the predicted values of transesterification yield obtained from the model and the actual experimental data were in good agreement.
Based on the data of the initial analysis, three-dimensional (3-D) contour plots were compiled to assess the best conditions for the transesterification degree, as shown in
Figure 3A–D. Each figure examines the patterns of process response (transesterification degree), determining the relationships between the response and independent variables (amount of enzyme, the molar ratio of alcohol to oil, temperature, and duration). The values of the dependent variables are selected in such a way as to obtain the maximum response value, and independent variables are fixed (on the X and Y axes).
Figure 3 shows the effect of the transesterification degree on:
Figure 3A—the molar ratio of alcohol to oil and the amount of the biocatalyst;
Figure 3B—the molar ratio of alcohol to oil and the duration of the reaction;
Figure 3C—temperature and the amount of the biocatalyst;
Figure 3D—the amount of biocatalyst and the duration of the reaction.
From the data presented, it can be seen that the content of the biocatalyst had a positive effect on transesterification degree (
Figure 3A). With an increase in the amount of biocatalyst to 11%, the transesterification degree increased. With a further increase in the amount of biocatalyst, it was noted that the transesterification degree decreases. This could be explained by the fact that the higher amount of immobilised enzyme increased the viscosity of the reaction medium it and therefore created conditions for the less effective transfer of the substrate to the active sites of enzyme particles [
33]. The catalytic performance of lipase is affected by the effective interfacial area [
34]. In the case when accession of substrates to the active sites of the excess enzymes, the interfacial area was reduced and transesterification degree was decreased, despite the fact that more immobilized enzyme was added. The results given in
Figure 3 show that, when assessing the transesterification degree depending on the reaction time, temperature, and molar ratio, the maximum yield is always obtained at a concentration of about 11% of the lipase from the oil content. This is unlike Marín-Suárez et al., who studied the use of fish oil transesterification with ethanol using three commercial immobilized enzymes: Lipozyme
® RM IM, Lipozyme
® TL IM, and Novozym
® 435 [
13]. They received a maximum biodiesel yield of around 75% at a Lipozyme
® RM IM content of 50% [
13]. Ramakrishnan et al. studied the transesterification of salmon oil with methanol and obtained the highest biodiesel yield using 15% Novozym
® 435 (immobilized lipase from Candida antartica) [
18].
Figure 3B shows the effect of the molar ratio of alcohol to oil and the duration of the reaction on the transesterification degree. The molar ratio of oil to alcohol is essential for obtaining high amount of alkyl esters [
35]. As scientists observed, the amount of alcohol used for the conversion to biodiesel should be slightly higher than the stoichiometric content, equal to the number of fatty acids in the oil, to compensate for thermodynamic or kinetic restrictions, i.e., a higher alcohol content is used to push the balance to the right in order to obtain a higher yield of alkyl esters. From the data presented, it can be seen that the molar ratio of isoamyl alcohol to salmon oil has a significant influence on the transesterification degree (
p < 0.0001 (
Table 4)). With an increase in the molar ratio of alcohol to oil from 3:1 to 6:1, the transesterification degree increases. This ratio also depends on the type of raw material used [
18,
35,
36]. However, with an increase in the molar ratio higher than 6:1, the transesterification degree slightly decreased. This could be explained by the fact that an excess of isoamyl alcohol can inhibit the activity of the enzyme [
37].
The reaction temperature affects the activity and stability of enzymes, as well as influences the transesterification reaction rate. In addition, any increase in the solubility of the substrate depends on temperature, which can lead to an increase in the interaction of the enzyme and the substrate [
37]. Foreign scientists have found that the optimum temperature for the synthesis of biodiesel using various lipases is from 30 to 55 °C [
18,
21,
38]. At this temperature, lipases have an activity of more than 90% [
30]. The results of our tests at a temperature of 30–50 °C confirm this observation. In the
Figure 3C, presented data show that, by increasing the temperature from 30 °C to 45 °C, the transesterification degree increases. A higher temperature has a negative effect, since the efficiency of transesterification is reduced. This result can be explained by the low resistance of the biocatalyst to high temperatures. Using the enzyme preparation Lipozyme
® RM IM, other scientists have noticed that the most effective temperatures for this enzyme are 40–45 °C [
37,
39]. The research results showed that high temperatures lead to the denaturation of lipase.
A longer duration of the reaction increased the transesterification degree of salmon oil with isoamyl alcohol (3-d). In this study, the duration of the process ranged from 4 h to 24 h. The observed trend indicates that a high transesterification degree is obtained at the maximum duration of the process. The results obtained by other scientists for the influence of duration on the ester yield are contradictory. Some claim that the process rate is relatively high. Moreira et al. [
30] studied the transesterification of babassu oil (residual babassu oil) (
Orbignya sp.) with ethanol, using the enzyme preparation Novozym
® 435, and found that the maximum yield of biodiesel is obtained in 2 h. Meanwhile, researchers Park et al. [
32] in the salmon oil transesterification with methanol reaction using lipase Lipozyme
® RM IM reached their peak biodiesel yield in 6 h, while scientists Ramakrishnan et al. [
18], in the salmon oil methanolysis reaction using Novozym
® 435 as a catalyst, reached their highest biodiesel yield in 16 h. Deng et al. [
40], for sunflower oil transesterification with ethanol, propanol, and butanol, used the same catalyst Lipozyme
® RM IM and reached the maximum biodiesel yield in 24 h, while researchers Amin et al. [
41], in the methanolysis reaction of sweet basil seed oil using the biocatalyst Novozym
® 435, reached the highest biodiesel yield in 72 h.