Mechanistic analysis of ultrasound–assisted biodiesel synthesis with Cu 2 O catalyst and
2.4 Results and Discussion
2.4.3 Kinetic and Arrhenius analysis of transesterification reaction
(predicted). A confirmation experiment has been performed at the optimum conditions predicted by the model. The triglyceride conversion in the confirmation experiment is 89.95 ± 0.78%, which confirms validity of the statistical experimental design, as the experimental triglyceride conversion matches closely with the triglyceride conversion predicted by the model.
(A) (B) (C)
(D) (E) (F)
Figure 2.4: Contour plots depicting interactions among parameters for statistical optimization of transesterification process in packed bed reactor. (A) Catalyst packing height vs Molar ratio; (B) Residence time vs Catalyst packing height; (C) Residence time vs Molar ratio; (D) Molar ratio vs Temperature; (E) Catalyst packing height vs Temperature and (F) Residence time vs Temperature.
reactor at the optimum conditions predicted by the statistical experimental design using packed bed reactor. These conditions are: molar ratio = 10.6, temperature = 335.5 K, catalyst = 7.25% (w/w) oil (corresponding to packed bed height of 35.61 mm, with steady–state hold–up of 100 mL oil/methanol mixture). Greater details of the calculations of catalyst concentration at steady–state operation of packed bed reactor are provided in Annexure C.
The reactions in batch mode have been conducted in 25 mL two–neck round bottom flask (15 mL reaction mixture) fitted with reflux condenser. For control reactions, the mechanical agitation of reaction mixture at 400 rpm was provided using magnetic stirrer (Tarson–spinot digital model MC–02). In case of test reaction, the reaction flask was immersed in ultrasound bath at the same location as the packed bed reactor. The reaction mixture composition in batch experiments (as per the optimum conditions stated above) was as follows: mixed oil feedstock = 10.46 mL, methanol = 4.54 mL, catalyst = 0.76 g. The reaction was conducted for 1 h and samples from reaction mixture were withdrawn at the successive interval of 10 min and analysed using 1H NMR to determine the gross conversion of the triglyceride.
Fig. 2.5 A and B shows the representative 1H NMR spectra of organic layers of transesterification product, which contain FAME and unreacted triglycerides in oil feedstock for reactions conducted with sonication at optimum conditions in packed bed and slurry reactor.
(A)
(B)
Figure 2.5: 1H NMR spectra of organic layer of the product of transesterification reaction conducted at optimum conditions with sonication. (A) packed bed reactor (B) slurry batch reactor
The results of fitting of kinetic model to experimental profiles of triglyceride, glycerol and FAME are shown in Fig. 2.6 (A) and (B), for control and test experiments, respectively. It could be inferred from Fig. 2.6 that experimental and model predicted
profiles of reactants and product shows reasonable match. The kinetic rate constants (i.e. model parameters) for the control and test experiment have been listed in Table 2.5. It could be inferred from Table 2.5 that all kinetic constants except k1 shows almost 2-fold enhancement, as mechanical agitation is replaced with sonication. The rate constant for methanol adsorption (k1), however, shows moderate reduction with sonication. Moreover, the value of k1 is 2 to 3 order of magnitude smaller than all other kinetic constants. Thus, methanol adsorption on catalyst essentially becomes the rate limiting step of transesterification process. This is attributed to high temperature of the transesterification process (335.5 K), which is close to the boiling point of methanol.
Adsorption, being as exothermic process, is not favoured at high temperature.
Table 2.5: Kinetic rate constants for different steps of transesterification process in batch mode at 335.5 K
Rate constants (s–1)
Control experiment (with mechanical shaking)
Test experiment (with sonication)
k1 1.3210–4 1.0410–4
k2 1.2410–2 5.8410–2
k3 2.1110–2 4.1010–2
k4 5.9710–1 9.8810–1
k5 3.5510–2 7.2610–2
k6 1.4510–1 1.0110–1
k7 1.5810–2 2.8210–2
Cumulative error 8.0110–2 2.6110–1
Moreover, it is also noteworthy that intense turbulence generated by ultrasound/
cavitation is not able to overcome the adverse thermal effect on adsorption. In fact, the micro–turbulence generated by ultrasound/ cavitation creates hindrance to adsorption of methanol, which is manifested in reduction in value of k1, in test experiments. The probable cause leading to this effect is generation of discrete and intermittent shock waves by transient cavitation bubbles [29]. Random motion of the catalyst particles in these shock waves can cause desorption of the adsorbed molecules, as demonstrated in
our previous work [30,31]. This conjecture is further supported by rise in kinetic constants of k5, k6, k7, in test experiments (with sonication) which corresponds to desorption of the intermediates (di– and mono–glyceride) and final by-product (glycerol) of the transesterification process from catalyst surface.
(A) (B)
(C) (D)
Figure 2.6: Experimental and simulated profiles (using Eley-Rideal kinetic model) of triglyceride (T), glycerol (G) and FAME (or biodiesel, F) in transesterification process in slurry reactor (batch) mode under different conditions. (A) transesterification with mechanical shaking at 335.5 K; (B) transesterification with sonication at 335.5 K; (C) transesterification with sonication at 325.5 K; (D) transesterification with sonication at 315.5 K.
As noted earlier, for determination of Arrhenius parameters of activation energy, experiments have been conducted at two more temperatures (in addition to the
reactants and products have been fitted to Eley–Rideal kinetic model to obtain the kinetic constants of three reaction steps (r2, r3, r4) in the transesterification process, which have been listed in Table 2.6. The model predicted and experimental profiles of the reactant and products for batch transesterification at 325.5 K and 315.5 K have been depicted in Figs. 2.6 (C) and (D). The kinetic constants of the overall transesterification process at the three temperatures of 315.5, 325.5 and 335.5 K have also been determined using pseudo–1st order kinetic model and listed in Table 2.6.
Table 2.6: Arrhenius analysis of transesterification process: kinetic rate constants (s-1) and activation energies (kJ/mol) for the three steps and overall reaction of transesterification
Transesterification reaction 315.5 K 325.5 K 335.5 K Activation energy
R2
Step 1 (rate expression = r2,
kinetic constant = k2) 3.8510–2 4.3810–2 5.8410–2 18.21 0.95 Step 2 (rate expression = r3,
kinetic constant = k3) 2.9810–2 3.3210–2 4.1010–2 13.97 0.96 Step 3 (rate expression = r4,
kinetic constant = k4) 8.0810–1 8.7410–1 9.8810–1 8.80 0.98 Overall transesterification
reaction (k) 1.0910–2 4.0410–2 8.4110–2 90.14 0.98
(A) (B)
Figure 2.7: Arrhenius plots for transesterification process using Cu2O catalyst in slurry reactor configuration (A) individual reaction steps of transesterification process and (B) overall transesterification reaction
The Arrhenius plots (ln k vs 1/T) for the three reaction steps of transesterification process and the overall transesterification process have been shown in Fig. 2.7 (A) and (B). The activation energies determined from these plots and are
listed in Table 2.6. The activation energies for three reaction steps show the trend: r2 >
r3 > r4. This essentially means that the activation energies reduce with successive transesterification of triglyceride to di– and mono–glycerides. Moreover, the activation energy of all three reaction steps is significantly smaller than the overall activation energy. The sum total of the activation energies of all three reaction steps (40.98 kJ/mol) is less than half of the activation energy of 90.14 kJ/mol for overall process. A possible explanation for these results can be given as follows:
1. The extent of emulsification between methanol and oil phase, and the overall mass transfer resistance of the system depends on interfacial tension between oil and methanol. Successive transformation of triglyceride to di– and mono– glyceride results in reduction of the interfacial tension and rise in miscibility of the phases, as demonstrated by Bhoi et al. (2014). This essentially results in reduction in mass transfer barriers and also activation energy.
2. The smallest value of kinetic constant k1 indicates low adsorption of methanol on catalytic sites. Thus, it is the rate determining step in the process. The reaction kinetics varies proportionally with temperature and this effect is further augmented by sonication. The adsorption of methanol on catalytic sites has to precede the commencement of the transesterification process. Thus, the overall transesterification essentially remains a mass transfer controlled process, even in presence of sonication.
This facet is also reflected in the values of the activation energy, in that the sum total of the activation energies of all three reaction steps is less than half of the activation energy for the overall transesterification process. These results reveal an important mechanistic facet of ultrasound–assisted transesterification process with solid Cu2O catalyst in that contribution of sonication towards intensification of process is more in
terms of boosting of the reaction kinetics than the adsorptive mass transfer, which is offset due to high reaction temperature.