Ultrasound–Assisted Biodiesel Production Using Heterogeneous Base
3.3 Results and discussion
3.3.4 Kinetic modelling and Arrhenius analysis
conversion in the validation experiment was 92.35 ± 1.08%, which is very close to the triglyceride conversion of 92.03% predicted by the model.
(A) (B)
(C)
Figure 3.5: Contour plots depicting interactions among parameters for statistical optimization of transesterification process (A) molar ratio vs catalyst loading; (B) temperature vs catalyst loading and (C) molar ratio vs temperature
Figure 3.6: 1H NMR spectra of mixed oil transesterification reaction at optimum conditions in presence of ultrasound
Table 3.5: Kinetic rate constants (min–1) for different steps of transesterification process at 332 K
Rate constants (min–1)
Control experiment (with mechanical agitation)
Test experiment (with sonication)
k1 7.1910–3 4.4210–3
k2 4.3610–2 5.6010–2
k3 4.9210–2 6.2410–2
k4 5.2610–2 7.3810–2
k5 6.6410–2 8.1710–2
k6 8.4810–2 1.0210–1
k7 2.4210–1 2.7810–1
Cumulative error 2.8510–2 4.0510–2
The experimental profiles of FAME or biodiesel yield were fitted to Eley–
Rideal model as shown in Fig. 3.7. As mentioned earlier, for Activation energy (Ea) determination, the transesterification reaction (both test and control) were conducted at two different temperatures (other than optimum temperature) 327 and 322 K with same molar ratio (11.68:1) and catalyst loading (7% w/w).
(A) (B)
Figure 3.7: Fitting of experimental and model predicted data for biodiesel yield (A) with mechanical agitation and (B) with ultrasound treatment
Table 3.6: Kinetic rate constants (min–1) and activation energies (kJ/mol) for the three reaction steps and overall transesterification reaction
(A) With mechanical agitation Transesterification
reaction (MA)
332 K 327 K 322 K Ea
(kJ/mol) R2 Step 1 (rate expression =
r2, kinetic constant = k2) 4.3610–2 3.8610–2 3.1410–2 29.09 0.98 Step 2 (rate expression =
r3, kinetic constant = k3) 4.9210–2 4.2510–2 3.8510–2 21.80 0.99 Step 3 (rate expression =
r4, kinetic constant = k4) 5.2610–2 4.7910–2 4.5010–2 13.80 0.98 Overall transesterification
reaction (k) 1.9710–2 1.0710–2 4.3010–3 135.40 0.99 (B) With ultrasound system
Transesterification reaction (US)
332 K 327 K 322 K Ea
(kJ/mol)
R2 Step 1 (rate expression =
r2, kinetic constant = k2) 5.6010–2 4.8510–2 4.3510–2 22.40 0.99 Step 2 (rate expression =
r3, kinetic constant = k3) 6.2410–2 5.5910–2 5.2810–2 14.81 0.96 Step 3 (rate expression =
r4, kinetic constant = k4) 7.3810–2 6.9010–2 6.6410–2 9.42 0.97 Overall transesterification
reaction (k) 3.9110–2 1.5110–2 9.7010–3 123.65 0.95 For calculating the activation energy of overall transesterification process, the kinetic constants determined at three reaction temperatures were used, whereas kinetic constants of three individual reaction steps were used for determining the activation
energy of these steps. All rate constants are tabulated in Tables 3.6 (A) and (B).
Activation energies calculated using Arrhenius plots (ln k vs 1/T, shown in Fig. 3.8) are also listed in Tables 3.6 (A) and (B).
(A) (B)
Figure 3.8: Arrhenius plots of individual reaction steps and overall transesterification process (A) with mechanical agitation; (B) with ultrasound
The kinetic and Arrhenius analyses showed some interesting trends and revealed facts of transesterification reaction and the role of ultrasound in transesterification reaction. These findings are as follows:
The simulated FAME or biodiesel yield profile was compared with the experimental data. A good match between the simulated results and experimental data could be seen from Fig. 3.7, which validated the selected kinetic model.
It could be seen from Table 3.5, that the rate constants k2 – k7 showed 25–50%
enhancement, as mechanical agitation is replaced by ultrasound, while the rate constant k1 shows ~ 50% reduction when mechanical agitation is replaced by ultrasound.
Among all the rate constants the value of k1 is ~ 10–100 times smaller than other rate constants, which indicated that the adsorption of methanol on the catalyst surface is the slowest or rate limiting step in transesterification process.
The sum of activation energies of three individual reaction steps (r2, r3, r4) was significantly smaller than the activation energy of overall transesterification process in both test and control conditions. For the test experiments, the total activation energy for three reactions steps was 46.63 kJ/mol, with overall activation energy of transesterification was 123.65 kJ/mol. While for the control experiments, the total activation energy for three reactions steps was 64.69 kJ/mol, with overall activation energy of transesterification was 135.40 kJ/mol.
The activation energies of three individual reaction steps showed the trend: r2 > r3
> r4, for both the test and control conditions, which means that successive transformation of tri–, di– and mono– glycerides to biodiesel requires less activation energy.
A marginal reduction (~ 9%) in overall activation energy of transesterification process was observed with application of ultrasound, which is in concurrence with observation of Choudhury et al [28]. But, the reduction in activation energies of three individual reaction steps is remarkable (~ 30%), when mechanical agitation was replaced with ultrasound as listed in Table 3.6.
Plausible explanations to these trends, which may help in identifying the mechanistic role of ultrasound in transesterification reaction, are as follows:
1. The lowest value of methanol adsorption rate constant (k1) results in less adsorption of methanol on catalyst active sites/surface. The probable reason is high reaction temperature, which is close to boiling point of methanol, and does not favour adsorption process. The rate of adsorption of methanol in test experiments is further reduced, due to the shock waves generated by transient cavitation that cause desorption of adsorbed species [29,30]. These phenomena are essentially manifested in terms of reduction in value of k1. Moreover, this speculation can also
be proven from the increase in the values of kinetic rate constants k5, k6, and k7, in test experiments when compared to the control experiments. The desorption rate of intermediates and by–product glycerol enhanced significantly in the test experiments in presence of sonication.
2. The enhancement in rate constants of individual reaction steps with application of sonication could be attributed to intense mixing between the two phases (oil and methanol). The micro–convection generated by sonication causes fine emulsification of the phases and reduction in the interfacial tension and consequently, the activation energies.
3. The reduction in activation energies of three individual reaction steps (i.e. r2 > r3 >
r4) is again a mass transfer effect. Successive conversion of triglyceride to diglyceride, results in lower interfacial tension and enhanced mixing with methanol phase. Similarly, this effect is more prominent with conversion of diglyceride to monoglcyeride. This effect was also demonstrated by Bhoi et al. [31]. Thus, the activation energies of the individual reaction steps decreased from r2 to r4.
4. The marginal reduction in activation energy of overall transesterification process in presence of sonication demonstrates influence of mass transfer in transesterification reaction with heterogeneous catalyst. This result is further corroborated by comparing the difference between the sum of activation energies of three individual reaction steps and the overall activation energy in both control and test experiments.
For mechanically agitated system, the overall activation energy was 135.40 kJ/mol, whereas for ultrasound–assisted system the overall activation energy was 123.65 kJ/mol. However, the sum of activation energies for three reactions steps in control and test experiments were 64.69 and 46.63 kJ/mol, respectively. The discrepancy between the overall activation energy and sum of activation energies of three
reaction steps is attributed to mass transfer limitation of the process. Notably, this discrepancy is higher for ultrasound–assisted experiments, which demonstrates greater control of mass transfer limitation on the transesterification reaction.