*2.7. Statistical Analysis*

The experimental data obtained from experimental design were analyzed by RSM [29,30]. A mathematical model, following a second-order polynomial equation, was developed to describe the relationships between the predicted response variable (selectivity or viscosity) and the independent variables of reaction conditions, as shown in Equation (1), where y is the predicted response variable; *β<sup>0</sup>*, *βi*, *βii*, *βij* are the intercept, linear, quadratic and interaction constant coefficients of the model, respectively; *Xi*, *Xj* (*i* = 1, 3; *j* = 1, 3; *i* = *j*) represent the coded independent variables (reaction conditions):

$$y = \ \beta\_0 + \sum\_{i=1}^{3} \beta\_i X\_i + \sum\_{i=1}^{3} \beta\_{ii} X\_i^2 + \sum\_{i$$

Response surface plots were developed using the fitted quadratic polynomial equation obtained from regression analysis, holding one of the independent variables at constant values corresponding to the stationary point and changing the order two variables. The quality of the fit of the polynomial model equation was evaluated by the coefficient of determination R2. Likewise, its regression coefficient significance was checked with F-test. Confirmatory experiments were carried out to validate the model, using combinations of independent variables which were not part of the original experimental design, but included in the experimental region.

## **3. Results and Discussions**

#### *3.1. Immobilization of the Commercial Biocatalyst Lipozyme RM IM on an Inorganic Support*

Table 2 shows the conversion and selectivity values obtained in the ethanolysis reaction with the Lipozyme RM IM over all the different supports here studied, as well as the viscosity of the biofuel synthesized.

**Table 2.** Ethanolysis reactions with Lipozyme RM IM immobilized on different inorganic supports, under the standard experimental reaction conditions: 12 mL of sunflower oil, 3.5 mL of absolute ethanol, at a temperature of 35 ◦C, 25 μL of 10 N aqueous solution of NaOH, 0.01 g of Lipozyme RM IM, 2 h reaction times and an agitation of 700 rpm, and the indicated amounts of support.


1 The two initial phases of the reaction mixture (oil and ethanol) are kept separate, an unambiguous sign of inactivity in the reaction.

As can be seen, the covalent immobilization of the Lipozyme RM IM on Sepiolite support, independently on the procedure employed, produce its complete deactivation. It seems that the presence of functional groups that make possible the covalent immobilization of the lipase, cause the deactivation of its active site somehow. Likewise, the adsorption of the Lipozyme on the demineralized sepiolite also caused the deactivation of the lipase. However, if the Lipozyme is physically adsorbed on silica-gel, reasonably good results are obtained. This immobilization would be well-founded by a physical interaction between the microporous anion exchange resins, in which the lipases is already immobilized, and the silica support. Thus, the interaction allowed increase the low density of the organic polymer without affect the actives sites of the lipase. In order to corroborate the economic feasibility of the lipase immobilization procedure, the performance of the lipase after different reuses must be evaluated. Figure 3 shows the conversion, selectivity and the viscosity of the biofuel obtained, after 15 successive reactions, over the Lipo-silica biocatalyst. As can be seen, the stability of the Lipo-silica is outstanding. In fact, even after the 15th reuse, the conversion and the selectivity are pretty similar to that obtained after the first use. Furthermore, the viscosity of the biofuel obtained is the same for every reaction (10.5 ± 0.5 cSt). These results are very encouraging, above all if we compare it with those obtained with the Lipozyme without immobilize, with which only six reuses before a total loss of the activity is observed [26]. Furthermore, considering the operative aspects at plant scale, the Lipo-silica catalyst only requires that the product of the reaction be extracted from the reactor and then, a new charge of reactants can be added for starting the subsequent reaction. For its part, the Lipozyme without immobilization requires a centrifugation process, much more difficult from an operational point of view.

**Figure 3.** Reuse of the *Rhizomucor miehei* system of Novozyme (Lipozyme RM IM) immobilized with silica gel (Lipo-silica), by simple physical attraction, operating under the standard conditions indicated in Table 2.

#### *3.2. Analysis of Variance (ANOVA) and Optimization of the Reaction Parameters by RSM*

Given the good behavior of the Lipo-silica biocatalytic system in the Ecodiesel production, a multilevel factorial experimental design has been carried out in order to analyze the effects of experimental parameters in the enzymatic selective ethanolysis reaction of sunflower oil. In this sense, on the basis of previous researches [27], the weight of Lipo-silica, the oil/ethanol volume ratio

and the amount of 10 N NaOH have been selected as the most relevant parameters. To evaluate the magnitude of these parameters on the selectivity of the partial ethanolysis reaction of sunflower oil, some limits have been set for each variable, as indicated in Table 1. It is also intended to determine the influence of these variables on the kinematic viscosity of the final mixture, given that the viscosity is the parameter which determines whether the biofuel obtained can be employed in current engines. Therefore, the experimental design consists of 18 experiments (runs) carried out in duplicate and in a random way to minimize possible errors. The sequence of the performed experiments is shown in Table 3.


**Table 3.** Experiments matrix of factorial design and the response obtained for viscosity and selectivity.

From these data, we are able to determine the correlation between the experimental variables here studied with the output variables (selectivity and kinematic viscosity), by using the Statgraphics software and a multivariate statistical analysis (ANOVA). As can be seen in Tables 4 and 5, the quadratic polynomial model was highly significant, allowing us to understand which variables have a greater impact on the selectivity and kinematic viscosity.


**Table 4.** Analysis of variance (ANOVA) for selectivity.

R<sup>2</sup> = 0.849; R2(Adj.) = 0.805.

**Table 5.** Analysis of variance (ANOVA) for viscosity.


R<sup>2</sup> = 0.936; R2(Adj.) = 0.917.

The correlation coefficients values, R2, were 0.849 and 0.936 for selectivity and kinematic viscosity, respectively. These results imply a good fit between models and experimental data in Pareto graphics (Figure 4). Furthermore, the adjusted correlation coefficients R2(Adj) were 0.805 for selectivity and 0.917 for selectivity and kinematic viscosity (Tables 4 and 5). The results here collected pointed out that all the parameters studied has an important influence on the selectivity of the process, specially the oil/ethanol ratio (*v*/*v*) and. However, according to the kinematic viscosity, the most relevant parameters are the oil/ethanol ratio (*v*/*v*) and the amount of 10 N NaOH employed (*p* < 0.05).

**Figure 4.** Pareto graphics: (**a**) for selectivity and (**b**) for viscosity.

Likewise, if we represent the influence of the different factors on selectivity and kinematic viscosity (Figure 5), it is easy to deduce that the higher the positive slope, the higher the effect of the factor. Thus, it can be seen in Figure 5a,b, how the oil/ethanol ratio is the parameter with the highest statistical significance not only on the selectivity but also on the kinematic viscosity.

**Figure 5.** Graphical representation of the different factors on: (**a**) selectivity; (**b**) on the viscosity.

Furthermore, the software also allows obtaining equations, after the elimination of non-influent parameters in the model, for selectivity and kinematic viscosity, whose R<sup>2</sup> values were 0,741 and 0.873, respectively. The equations obtained were quite simpler as compared to initial ones. These equations describe the created model and gives solutions for the dependent variable based on the independent variable combinations, whether they are or not significant in the response. Thus, considering that R is the Oil/Ethanol ratio (*v*/*v*); N is the amount of 10 N NaOH in μL and A, amount of Lipozyme RM, we have the following equations:

$$\text{Selectivity} = 50.1194 + 7.39722\text{R} + 0.1625\text{RN} - 1.30417\text{A}^2 \tag{2}$$

$$\text{Viscosity} = 10.1458 + 0.107917 \text{A} - 0.698611 \text{R} + 0.65125 \text{A}^2 \tag{3}$$

The surface plots described by the regression model were drawn to display the effects of the independent variables on selectivity and kinematic viscosity, Figure 6. This model shows that the optimum values for the parameters to maximize selectivity were: low lipase amount (0.012 g), high oil/ethanol molar ratio (1/6) and high 10 N NaOH amount (50 μL). Regarding the optimum values to maximize the viscosity: lipase amount (0.017 g), which is a bit higher than that for selectivity, oil/ethanol molar ratio (1/6) and amount of 10 N NaOH (50 μL). Thus, a selectivity value around 66% and viscosity around 9.5 cSt can be achieved under these conditions. The biofuel obtained at these conditions is feasible to be employed in a mix with diesel fuel in blends of 50%, or even more, falling within the acceptance limits of the EN 14214.

To validate the proposed models, a serie of experiments, whose conditions are among the range of the studied variables, has been carried out. Thus, the experimental values of selectivity and kinematic viscosity have been collected in Table 6. Furthermore, a comparison between the experimental values and the theoretical ones has been also compiled. As can be seen in Figure 7, a good adjustment of the model, with values of R<sup>2</sup> of 84.955%, for Selectivity and 93.649% for Viscosity, has been obtained, corroborating the good correlation between the experimental values and those predicted by the model.

**Figure 6.** Graphic representation of the different factors on: (**a**) selectivity; (**b**) viscosity.

**Figure 7.** Probability graphs of (**a**) Selectivity and (**b**) Viscosity.

Therefore, it can be concluded that the model created to correlate the reaction parameters (amount of lipase, ratio oil/ethanol and amount of NaOH 10N aqueous solution) with the selectivity and the kinematic viscosity is acceptable, since it is able to explain the variability produced in these experimental parameters.


**Table 6.** Experiments matrix of factorial design and the response obtained for selectivity and viscosity. Experimental values obtained for each reaction of the experimental design for the Selectivity and Kinematic Viscosity at 40 ◦C, collected in Table 3, compared to the values obtained when applying the theoretical model proposed.
