A BBREVIATIONS
Scheme 2.5: Scheme 2.5: Simultaneous esterification and transesterification by heterogeneous acid catalyst
3.3 Results and Discussion
3.3.3 Experimental results and statistical analysis
The result of each experiment in the Box–Behnken statistical design is given Table 3.2A. The average FAME yield in each experiment is given along with standard deviation of the three trial runs in each experiment. A quadratic regression model (given in equation 3.1) was fitted to the results using coded values for the experimental parameters (Minitab 15 software, trial version). The fitted model is as follows:
2 2 2
75.028 21.686 9.522 20.341 16.918 24.078 22.369 6.062 3.818 7.606 Y= + T− M+ C− T − M − C − T×M− M×C+ T×C
(3.6)
Notation: T – temperature, M – molar ratio and C – catalyst loading. The significant of each coefficient in the model equation was determined by standard t–test and p–values, also
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indicated in Table 3.4A. It should be noted that the fitted model equation 3.6 is for the coded values of parameters (i.e. +1, 0 and –1), and not for the actual or absolute values of the parameters. Therefore, the regression coefficients of fitted model are only mathematical parameters and their significance is to be judged only the basis of F-value and p-value [39, 40]. A high F-value and p-value less than 0.05 indicate the significance level of the coefficient. For example, the coefficients for parameters M, C and (M × C) indicate the individual influence of molar ratio, catalyst concentration and the interaction between these two parameters. The p-value of all three regression coefficients is 0.0, as indicated in Table 3.4A and the F-value of the regression coefficients, as given in Table 3.4B, is 8412.22 for overall model, 15582.11 for linear coefficients and 872.62 for interaction coefficient. This essentially means that the individual influence of molar ratio and catalyst concentration is relatively more significant than the interaction effect. The physical meaning of these values is that both molar ratio and catalyst concentration affect the transesterification yield, but these are rather independent parameters, in that there is no inter-link between the mechanisms of effects of these parameters. Values of FAME yield calculated using this model matched very well with the experimental results. The significance of regression is indicated by the coefficient of determination (R2) which was 99.95%. This essentially means that 99.95% of the effect on the yield for CaO catalyst was explained by the variation in process variables.
Table 3.4B shows the (analysis of variance) ANOVA for the quadratic model. The Lack of Fit F–value of 2.55 and p-value of 0.073 implies that Lack of fit is not significant as compared to the pure error.
The response surface 3–D plots indicating effect of interaction between any two variables (temperature–molar ratio or catalyst loading–temperature or molar ratio–catalyst loading), while holding the third parameter of its center point are shown in Fig. 3.5.
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Figure 3.4: 1H NMR spectrum of fatty acid methyl esters (FAME) of soybean oil
Table 3.4: Statistical analysis of experimental results (A) Estimated Regression Coefficients for % FAME yield
Term Coefficients SE coeff t–Stat p–value
Constant (β) 75.028 0.2358 318.179 0.
Temperature (T) 21.686 0.1444 150.182 0.
Molar ratio (M) –9.522 0.1444 –65.940 0.
Catalyst (C) 20.341 0.1444 140.868 0.
Temperature × Temperature (T2) –16.918 0.2126 –79.593 0.
Molar ratio × Molar ratio (M2) –24.078 0.2126 –113.283 0.
Catalyst × Catalyst (C2) –22.369 0.2126 –105.242 0.
Temperature × Molar ratio (TM) –6.062 0.2042 –29.683 0.
Temperature × Catalyst (TC) 7.606 0.2042 37.245 0.
Molar ratio × Catalyst (MC) –3.818 0.2042 –18.698 0.
Fig. 3.5A indicates that the FAME yield shows a maximum for catalyst concentration &
molar ratio, especially for medium values of molar ratios. For lower molar ratios, however, the yield monotonically increases with catalyst concentration.
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Table 3.4: Statistical analysis of experimental results (continued….)
(B) Analysis of variance (ANOVA) for transesterification of soybean oil using ultrasound
Source DF Sq SS Adj SS Adj MS F p–value
Regression 9 37887.6 37887.6 4209.74 8412.22 0.
Linear 3 23393.3 23393.3 7797.78 15582.11 0.
Square 3 13184.2 13184.2 4394.75 8781.92 0.
Interaction 3 1310.1 1310.1 436.69 872.62 0.
Residual Error 35 17.5 17.5 0.50 –– ––
Lack–of–Fit 3 3.4 3.4 1.13 2.55 0.073
Pure Error 32 14.1 14.1 0.44 –– ––
Total 44 37905.2 –– ––
R2 = 99.95%; R2 (adj) = 99.94%
(C) Analysis of surface plots
(Values of variable parameters for maximum yield for center point value of third parameter) Fixed Parameter
(Center point value) Variable parameter FAME
Yield (%) Catalyst loading =
4 wt%
Temperature = 61.2oC Molar ratio = 10.3 83.89%
Temperature = 52.5oC
Molar ratio = 10.6 Catalyst loading = 5.4 wt% 80.98%
Molar ratio = 12:1 Temperature = 62.2 oC Catalyst loading = 5.8 wt% 89.36%
Similar behaviour is also seen for the variables temperature and molar ratios as evident from surface plot shown in Fig. 3.5B. However, for lower molar ratios, the FAME yield monotonically increases with temperature. The values of variables in Fig. 3.6A and 3.6B for which maximum in yield occurs is seen are listed in Table 3.4C, along with the value of the yield as predicted by the model. For combination of catalyst concentration (or loading) and temperature as variable (Fig. 3.5C), however, we do not see any maxima.
Again the values of catalyst loading and temperature for which maximum yield is seen for center point molar ratio of 12:1 are given in Table 3.4C. The FAME yield increases monotonically for all reaction temperature with increasing catalyst concentration.
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0 20 40 60 80 100
6 8
10 12
14 16
18
2 1 4 3
6 5 7
% FAME
Molar ratio Catalyst
(A)
0 20 40 60 80 100
6 8
10 12
14 16
18
40 45 50 55 60
% FAME
Molar ratio Temperature
(B)
-40 -20 0 20 40 60 80 100
40 45
50 55
60 65
1 2 3 5 4
6
% FAME
Tem perature
Catalyst
(C)
Figure 3.5: Response surface plots for % FAME yield as a function of reaction temperature, catalyst loading and methanol-to-oil molar ratio.
Results given in Table 3.4C clearly indicate that temperature is a dominant variable of the process, followed by catalyst loading and molar ratio. The highest yield of 89.36% is seen for high value of molar ratio of 12:1, high temperature of 62.2oC and catalyst loading of 5.8%.
An important observation is that no plateau is observed in any of the surface plots (the plateau is essentially indicative of nullification of interactive effect of variables on the FAME yield). The p–values of the ANOVA corroborate this result. Zero p–values of all individual
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(linear and quadratic) as well as interaction coefficients indicate that all parameters have strong influence on the FAME yield; and moreover the influence of these parameters is strongly inter–related.