Article pubs.acs.org/IECR
Production of Biodiesel by Esterification of Stearic Acid over Aminophosphonic Acid Resin D418 Wen Chen, Ping Yin,* Hou Chen,* and Zhi Wang School of Chemistry and Materials Science, Ludong University, Yantai 264025, P. R. China S Supporting Information *
ABSTRACT: Biodiesel production has become a very intense research field because of its environmental benefits and the growing interest in finding new resources and alternatives for conventional fuels. In the present work, biodiesel production from the esterification of the free fatty acid stearic acid with ethanol over aminophosphonic acid resin D418 was studied. The effects of experimental factors such as the amount of D418, reaction temperature, and molar ratio of ethanol to stearic acid on the conversion ratio were evaluated. Process optimization using response surface methodology (RSM) was performed, and the interactions between the operating variables were elucidated. The optimum values for maximum esterification percentage were obtained by using a Box−Behnken center-united design with a minimum of experimental work. Moreover, the kinetics of the esterification catalyzed by D418 was studied, and the pseudohomogeneous (PH) model was used to simulate the experimental data.
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INTRODUCTION Because of the heavy consumption of fossil fuels, particular focus has been paid to global warming and the exhaustion of nonrenewable resources. Biodiesel production has become a very intense research field because of its environmental benefits and the growing interest in finding new resources and alternatives for conventional fuels. Compared to fossil-based fuels, biodiesel has many advantages, such as cleaner engine emissions, biodegradability, renewability, and superior lubricating properties. Therefore, increasing research is now being directed toward the use of alternative renewable fuels that are capable of fulfilling an increasing energy demand.1 Methyl and ethyl esters derived from vegetable oil or animal fat, known as biodiesel, have good potential as alternative diesel fuels. Biodiesel is produced by chemically reacting a triglyceride (vegetable oil or animal fat) with a short-chain alcohol such as methanol or ethanol. However, some oils include significant amounts of free fatty acids (FFAs), for example, inedible oils, animal fats and oils, recycled or waste oil, and byproducts of the refining of vegetable oils, such as crude mahua oil, which contains about 20% FFAs.2 Animal and vegetable oils contain several kinds of free fatty acids, so the study of the esterification reactions of free fatty acids has a significant effect on the production of biodiesel. The current technology utilizes homogeneous catalysts such as concentrated sulfuric acid, and the main drawbacks in this production process are its high corrosiveness to equipment, the large amount of water required, and the harmfulness of the discharged wastewater to the environment. Comparared with homogeneous catalysts, heterogeneous catalysts for the production of biodiesel are friendly to the environment, less corrosive to reactors, less toxic, and easily separated from reaction mixtures. Despite the problems of longer esterification reaction times and higher reaction temperatures required, solid acid catalysts utilized in esterification reactions are extremely important in developing © 2012 American Chemical Society
cleaner and economically improved processes. They offer significant advantages in eliminating separation, corrosion, toxicity, and environmental problems, and therefore, they have recently attracted considerable attention.3−6 To improve the conversion of acid and the efficiency of the process, response surface methodology (RSM) is usually presented to optimize operating parameters for the relative synthesis process. RSM is an effective statistical technique for optimizing multifactor experiments, building models, and evaluating the effects of several factors for desirable responses. The advantage of RSM is that it allows the user to gather large amounts of information from a small number of experiments, and it also provides the possibility of observing the effects of individual variables and their combinations of interactions on the response.7 So far, several papers have reported on the subject of optimization and RSM applied to biodiesel production.8−10 On the other hand, the kinetics of the esterification catalyzed by various catalysts has been studied in recent years.11−14 For example, Oliveira et al.11 studied the kinetics of the esterification of oleic acid with ethanol using a free or immobilized lipase as the catalyst and found that the reaction follows Michaelis−Menten kinetics; they also evaluated the kinetic constants. However, studies on the kinetics of esterification with solid acid catalysts have been little reported so far. In this work, the esterification of the free fatty acid stearic acid with ethanol over D418 catalyst was investigated, and the effects of experimental factors such as the amount of D418, reaction temperature, and molar ratio of ethanol to stearic acid on the conversion ratio were evaluated. Response surface methodology (RSM) was employed to optimize the catalyst Received: Revised: Accepted: Published: 5402
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amount, molar ratio of ethanol to acid, and temperature. Moreover, a kinetic model was proposed, and kinetic parameters were determined by fitting the model to the experimental results.
Y = λ0 +
4
3
4
∑ λixi + ∑ λiixi 2 + ∑ ∑ i=1
i=1
i=1 j=i+1
λ ijxixj (3)
where λ0, λi, λii, and λij are regression coefficients (λ0 is the constant term, λi is the linear effect term, λii is the squared effect term, and λij is the interaction effect term) and Y is the predicted response value.
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EXPERIMENTAL SECTION Materials and Instruments. Aminophosphonic acid resin D418 was obtained from Tianjin Bohong Resin Science & Technology Limited Company, Tianjin, China. The other chemicals were of AR grade and were used without further purification. The number of strong acid sites on the catalyst was measured by means of titration, according to Kang.15 The X-ray diffraction (XRD) pattern of D418 resin was obtained using a Rigaku D/max2500VPC instrument. Thermogravimetric analysis (TGA) was recorded on a Netzsch STA 409 apparatus, under the following test conditions: type of crucible, DTA/TG crucible Al2O3; atmosphere, nitrogen; flow rate, 30 mL/min; heating rate, 10 K/min. Esterification Reaction. Biodiesel production from the free fatty acid stearic acid with ethanol was investigated in the presence of D418. Esterification reactions were carried out under batch reaction conditions using a 250 mL flask fitted with a stirrer, a thermometer, and a water divider. A typical reaction mixture in the reactor contained stearic acid, ethanol, and the catalyst, and the process was similar with that described in ref 16. The esterification reaction between stearic acid and alcohol can be represented as follows
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RESULTS AND DISCUSSION Effect of Catalyst Amount on the Esterification Reaction. D418 with aminophosphonic acid functional groups can provide H+ species and protonate the carboxylic moiety of stearic acid, increasing the electrophilicity of the carbonyl carbon atom and facilitating the following step of the nuclephilic attack of ethanol. Figure 1 shows the relationships
stearic acid (A) + alcohol (B) catalyst
←⎯⎯⎯→ ethyl stearate (C) + water (D)
(1)
Figure 1. Effect of catalyst amount (A, 7%; B, 8%; C, 9%; D, 10%; and E, 11%) on the etherification reaction at 95 °C and an alcohol/acid molar ratio of 12:1.
The conversion of stearic acid can be calculated according to the equation x = (1 − AV1/AV0) × 100%
(2)
between the conversion ratio and the reaction time at various catalyst amounts with an ethanol/stearic acid molar ratio of 12:1 and a temperature of 95 °C. The effect of the catalyst amount was examined from 7% to 11% of D418. As seen in Figure 1, the reactions had higher rates initially than later in the reaction and reached steady state at a stirring time of about 3 h. The conversion ratio increased with increasing catalyst amount, which can be attributed to the fact that more D418 catalyst would provide more active reaction sites. Moreover, it is clear that the conversion ratio continuously improved with more water being generated; therefore, the activity of D418 catalyst was not obviously affected by water produced during the esterification process for its organophonic acid function groups. The conversion ratios in 10 h for catalyst amounts of 7%, 8%, 9%, 10%, and 11% were 77.34%, 79.58%, 90.08%, 82.36%, and 84.60%, respectively. The esterification reaction is a reversible reaction and reached steady state at different times under different conditions, and the conversion ratio at the reaction time of 10 h reached the highest value. To facilitate comparison and analysis, 10 h was chosen for the subsequent experiments. It is clear that the conversion ratio for 10 h had a maximum value at a catalyst amount of 9%, and more catalyst might lead to a decrease of the conversion ratio and the wasting of the catalyst. The results, presented in Figure 1, confirm that the reaction was catalyst-amount-limited, and increasing the catalyst amount increased the reaction rate and consequently
where AV0 and AV1 are the acid values of feed and products, respectively, and the relative acid value was determined by the titration method. Experimental Design and Optimization by RSM. Factors considered included the amount of D418 (9−11%, wt/wt), the ethanol-to-acid molar ratio (6:1−14:1), and the reaction temperature (75−95 °C). Response surface methodology (RSM) was employed to analyze the operating conditions of esterification to obtain high-percentage conversion. The experimental design was carried out by choosing three independent process variables at three levels, and the studied factors included catalyst amount, ethanol-to-acid molar ratio, and temperature. For each factor, the experimental range and the central point are listed in Table S1 (Supporting Information). Minitab software was used for designing and analyzing the experimental data. The independent variables (factors) and their levels, real values, and coded values are presented in Table S1 (Supporting Information). The percentage conversion of stearic acid was the response of the experimental design. The model equation was used to predict the optimum value and subsequently to elucidate the interactions between the factors. The quadratic equation model for predicting the optimal point was expressed as17 5403
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reduced the time required to achieve a high conversion ratio. However, excessive catalyst could adsorb reactants or products and result in a lower conversion ratio because of poor mass transfer. Effect of the Molar Ratio of Alcohol to Acid on the Esterification Reaction. The esterification reaction is a reversible reaction, so the amount of ethanol must be in excess to force the reaction toward the formation of ethyl stearate. Figure 2 presents the relationships between the conversion
Figure 3. Effect of temperature (A, 75; B, 85; C, 95; and D, 105 °C) on the esterification reaction with a catalyst amount of 9% and an alcohol/acid molar ratio of 12:1.
conversion ratio of stearic acid with ethanol to produce ethyl stearate with three reaction parameters: amount of catalyst, ethanol/stearic acid molar ratio, and reaction temperature. A Box−Behnken center-united design was employed to design the experiments, and the results obtained after running the 15 trials for the statistical design are reported in Table S2 (Supporting Information). The best-fitting models were determined by multiregression and backward elimination. Table S2 (Supporting Information) also presents the experimental and fitting values of stearic acid conversion, and the results indicate a good fit. Table S3 (Supporting Information) lists the significant regression coefficients of the established model equation. The linear coefficients of catalyst amount and ethanol-to-acid molar ratio, all of the quadratic terms, and the cross-product coefficients except X1X3 were highly significant. One quadratic term (reaction temperature) and the cross-product coefficient X1X3 were very insignificant (P > 0.5). The values of the coefficients and the analysis of variance (ANOVA) are also presented in Table S3 (Supporting Information). According to the results of ANOVA, R2, which means the fraction of the variation of the response explained by the model, and Q2, which indicates the fraction of the variation of the response predicted by the model, are 0.9839 and 0.9549, respectively. In this case, the R2 value indicates that the model can explain 98.39% of the variability. As a result, well-fitting models for the esterification were successfully established. The polynomial model for the conversion of stearic acid was regressed by considering the significant terms, and the following equation was obtained
Figure 2. Effect of the alcohol/acid molar ratio (A, 6:1; B, 8:1; C, 10:1; D, 12:1; E, 14:1) on the esterification reaction at 95 °C and with a catalyst amount of 9%.
ratio and the reaction time at 95 °C and various ethanol/stearic acid molar ratios with 9 wt % D418 catalyst to stearic acid under stirring conditions. It can be seen that the conversion ratio depends largely on the ethanol/stearic acid molar ratio, and the conversion ratios in 10 h at ethanol/stearic acid molar ratios of 6:1, 8:1, 10:1, 12:1, and 14:1 were 88.15%, 81.99%, 84.56%, 90.08%, and 83.86%, respectively. The conversion ratio increased as the ethanol/acid molar ratio increased from 8:1 to 12:1; however, with an increase of the ethanol/acid molar ratio from 12:1 to 14:1, the conversion ratio decreased. Shu et al. also found a similar trend in their work, in that the conversion of FFA increased as the methanol/acid molar ratio increased from 10.6 to 16.8, and it decreased as the molar ratio increased from 16.8 to 21.0.4 Effect of Temperature on the Esterification Reaction. The free fatty acid (FFA) stearic acid initially requires the activation of its carbonyl function by protonation under acidcatalyzed conditions to start the reaction, and temperature is an important variable for acid-catalyzed esterification because the rate of reaction is strongly influenced by the reaction temperature. The effect of the reaction temperature was examined from 75 to 105 °C at an ethanol/stearic acid molar ratio of 12:1 and a D418 catalyst loading of 9% is shown in Figure 3. It can be seen that the conversion ratio increased with increasing temperature, and it reached a maximum value at 95 °C. In addition, the time for the conversion ratio to reach the steady state tended to become shorter with the increase in temperature. RSM Experiments and Model Fitting. Response surface methodology (RSM) is an efficient statistical technique for optimizing multiple experimental variables to predict the best performance conditions with the minimum number of synthesis experiments. Therefore, RSM was applied to model the
Y = 91.2167 + 0.1775X1 + 0.5563X 2 − 0.6008X12 − 1.6233X 2 2 + 0.2917X32 + 1.6325X1X 2 − 0.4150X 2X3
(4)
where Y is the conversion ratio of stearic acid (%), X1 is the catalyst amount (%), X2 is the ethanol-to-acid molar ratio, and X3 is the reaction temperature (°C). Effects of Process Variables on Stearic Acid Conversion. The response surfaces of the above-mentioned model for the free fatty acid stearic acid conversion (eq 4) were used to evaluate the relationships of parameters. Three-dimensional response surface plots are displayed in Figure 4 and show the stearic acid conversion as a function of two variables while 5404
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keeping other variables at the zero level. Figure 4a depicts the effects of ethanol-to-acid molar ratio, catalyst amount, and their reciprocal interaction on oleic acid conversion. As can be seen from the figure, enhancing amounts of D418 could bring about high conversion ratio. However, excess amounts of catalyst would lead to a decline of the conversion ratio. Moreover, the conversion ratio of stearic acid increased with the molar ratio of ethnol to stearic acid to about 12:1 and then decreased thereafter. This result can be attributed to the saturation of the catalytic surface with ethanol or prevention of nucleophilic attack by sheilding protonated ethanol, which confirmed Eley− Rideal mechanism with chemisorption on the Brønsted acid sites. The effects of different reaction temperatures and catalyst amounts on the conversion ratio are shown in Figure 4b, which indicates that the interactions of reaction temperature and catalyst amount are not obvious. Figure 4c represents the effects of the reaction temperature and ethanol-to-acid molar ratio on stearic acid conversion. It is evident that the stearic acid conversion increased with increasing ethanol-to-acid molar ratio at the same reaction temperature. Moreover, as indicated, reaction temperature exhibited less of an effect on the conversion ratio at different ethanol-to-acid molar ratios. This could be due to the fact that reaction temperature was not a significant factor (Table S3, Supporting Information). Optimization of Reaction Conditions. The optimum values of selected variables were obtained by solving the regression equation (eq 4) using MATLAB6.5 software, and the optimal conditions for ethyl ester production of esterification of oleic acid with ethanol estimated by the model equation were X1 = 11%, X2 = 11.6:1, and X3 = 89.3 °C. The theoretical conversion ratio predicted under these conditions was Y = 91.47%. To confirm the prediction by the model, three independent experiments were conducted at the established optimal conditions. The average conversion ratio reached (91.33 ± 0.56)% and was close to the predicted value. Thus, response surface methodology with appropriate experimental design can be effectively applied to optimize the process in this esterification synthesis of ethyl stearate with D418 catalyst. Evaluation of the Catalyst D418. Figure S1 (Supporting Information) displays the XRD spectra of D418 catalyst before and after reaction, which shows that the mechanical stability of D418 catalyst was still good after the esterification reaction, because its diffraction peak at about 23° did not change. Moreover, the thermogravimetric curves reflect the thermal stability of the materials. Figure S2 (Supporting Information) shows the thermogravimetric curves of D418 catalyst before and after reaction at the range of 25−800 °C, and the results were shown in Figure 6 below. As can be seen, for D418 in the interval between room temperature (25 °C) and 170 °C, the first mass loss of 5.0% can be attributed to the release of physisorbed water molecules, and the other further mass loss at higher temperature can be attributed to the organic ligands anchored on the surface and the decomposition of the resin. Moreover, the two curves are very similar. Therefore, these data indicate that D418 before and after reaction has good thermal stability and that it should be applied at temperatures below 170 °C. At the same time, biodiesel production from the esterification of the free fatty acid stearic acid catalyzed by concentrated sulfuric acid under the same experimental conditions was also investigated, and the conversion ratio was found to be 94.5%. Marchetti reported studies on the esterification reaction of free
Figure 4. Interaction and response surface of the three process variables on the conversion of stearic acid. 5405
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fatty acids catalyzed by sulfuric acid, and the final conversion ratio could reach 96%.18 Although the conversion ratios were higher, concentrated sulfuric acid is more difficult to separate from reaction mixtures. However, D418 catalyst was separated from the system completely without any loss. The catalyst recovered after reaction was repeatedly used, and the catalytic ability was still very good. Moreover, the activity (turnover frequency or TOF) of the catalyst was calculated from the conversion data obtained, and the relevant equation was obtained as19 TOF = kn0,SA /n H+
The values of K (equilibrium constant) and Y were calculated according to eqs 8 and 9 using MATLAB6.5 software, and then Y was plotted as a linear function of t at different temperatures, as shown in Figure 5. This shows that the forward and reverse
(5)
where k is the rate constant of a pseudo-first-order rate equation, n0, SA is the initial quantity of stearic acid, and nH+ is the number of strong acid sites on the catalyst. The highest TOF observed was 129.7 h−1, which was higher than that of carbon-based solid acid catalysts (78 and 109 h−1).19 Furthermore, to test its reusability, the D418 catalyst was repeatedly used for ethyl stearate synthesis. The catalyst was filtered, leached, and reused in a new reaction cycle. The reusability of the catalyst under the optimal experimental conditions was investigated, and the results are presented in Figure S3 (Supporting Information). It is clear that the stearic acid conversion ratio still reached 88.30% after four reaction cycles. However, the catalytic activity of other heterogeneous catalysts such as Amberlyst 1520 gradually decrease with recycling. Therefore, the D418 catalyst is favorable and useful for the synthesis of ethyl stearate. It appears to be a promising alternative for producing biodiesel, and it can probably be used industrially in perspective. Kinetic Model. In this work, the pseudohomogeneous (PH) model was used to simulate the experimental data. The esterification reaction of boidiesel production was carried out under the optimal conditions, and the stearic acid conversion at different temperatures for different times was measured, as reported in Table S4 (Supporting Information). It was assumed that the forward and reverse reactions for this esterification were second-order reactions, so that, for the esterification reaction of the free fatty acid stearic acid and ethanol, the apparent reaction rate can be described by −
dCA = k+CAC B − k −CCC D dt
Figure 5. Plots of Y−t at different temperatures (B, 75; D, 85; and F, 95 °C).
reactions of this esterification reaction are second-order reaction. The positive and reverse reaction rate constants (k+, k−) at different temperatures are listed in Table 1. The Table 1. Rate Constants at Different Temperatures temperature (K) 348 358 368
k+ [L·(mol·min)−1] −4
3.35 × 10 3.39 × 10−4 4.19 × 10−4
k− [L·(mol·min)−1]
K
6.62 × 10−4 5.41 × 10−4 5.81 × 10−4
0.5049 0.6266 0.7208
influence of temperature on the reaction rate was determined by fitting k+ and k− to the Arrhenius equation. Both the frequency factor (A) and the activation energy (Ea) were attained through nonlinear regression by employing plots of ln k as a function of T−1 (Figure 6). The results are listed in Table
(6)
where CA, CB, CC, and CD are the concentrations of stearic acid, alcohol, ethyl stearate, water, respectively, and k+ and k− are the kinetic constants for the forward and reverse reactions, respectively.21 The initial concentrations of stearic acid and ethanol are denoted as a and b, respectively. Meanwhile, the initial concentrations of ethyl stearate and water are 0, but the concentrations of these two products are x at time t. Therefore, eq 5 can be integrated to give
∫0
x
dx (a − x)(b − x) −
1 2 x K
=
∫0
t
Figure 6. Effects of temperature on the reaction rate.
k+ dt (7)
2. The activation energies of the forward and reverse reactions are Ea+ = 34.22 kJ/mol and Ea− = 11.09 kJ/mol, respectively, and the kinetic equation of this esterification reaction is as follows
where K = k+/k− and t is the reaction time. Meanwhile K=
c2 (a − c)(b − c)
(8)
r = 41.78exp( −34.22/RT )CAC B − 3.05 × 10−2exp(
where c is the concentration of the product. Then Y = k+t
−11.09/RT )CCC D
(9) 5406
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(4) Shu, Q.; Gao, J.; Nawaz, Z.; Liao, Y.; Wang, D.; Wang, J. Synthesis of biodiesel from waste vegetable oil with large amounts of free fatty acids using a carbon-based solid acid catalyst. Appl. Energy 2010, 87, 2589. (5) Lou, W. Y.; Zong, M. H.; Duan, Z. Q. Efficient production of biodiesel from high free fatty acid-containing waste oils using various carbohydrate-derived solid acid catalysts. Bioresour. Technol. 2008, 99, 8752. (6) Zhang, D.; Bai, S.; Ren, M.; Sun, Y. Optimization of lipasecatalyzed enantioselective esterification of (±)-menthol in ionic liquid. Food Chem. 2008, 109, 72. (7) Silva, G. F.; Camargo, F.; Ferreira, A. L. O. Application of response surface methodology for optimization of biodiesel production by transesterification of soybean oil with ethanol. Fuel Process. Technol. 2011, 92, 407. (8) Zabeti, M.; Daud, W. M. A. W.; Aroua, M. K. Biodiesel production using alumina-supported calcium oxide: An optimization study. Fuel Process. Technol. 2010, 91, 243. (9) Hameed, B. H.; Lai, L. F.; Chin, L. H. Production of biodiesel from palm oil (Elaeis guineensis) using heterogeneous catalyst: An optimized process. Fuel Process. Technol. 2009, 90, 606. (10) Abdullah, A. Z.; Razali, N.; Lee, K. T. Optimization of mesoporous K/SBA-15 catalyzed transesterification of palm oil using response surface methodology. Fuel Process. Technol. 2009, 90, 958. (11) Oliveira, A. C.; Rosa, M. F.; Aires-Barros, M. R.; Cabral, J. M. S. Enzymatic esterification of ethanol and oleic acidA kinetic study. J. Mol. Catal. B: Enzym. 2001, 11, 999. (12) Umar, M.; Patel, D.; Saha, B. Kinetic studies of liquid phase ethyl-tert-butyl ether (ETBE) synthesis using macroporous and gelular ion exchange resin catalysts. Chem. Eng. Sci. 2009, 64, 4424. (13) Zhang, Y.; Ma, L.; Yang, J. Kinetics of esterification of lactic acid with ethanol catalyzed by cation-exchange resins. React. Funct. Polym. 2004, 61, 101. (14) Song, C.; Qi, Y.; Deng, T.; Hou, X.; Qin, Z. Kinetic model for the esterification of oleic acid catalyzed by zinc acetate in subcritical methanol. Renewable Energy 2010, 35, 625. (15) Kang, L. Modification and Research on Properties of Silica Gel/ Polystyrene Composite. Master’s Thesis, Ludong University, Yantai, China, 2009; p 47. (16) Dash, S. S.; Parida, K. M. Esterification of acetic acid with nbutanol over manganese nodule leached residue. J. Mol. Catal. A: Chem. 2007, 266, 88. (17) Kim, B. H.; Akoh, C. C. Modeling and optimization of lipasecatalyzed synthesis of phytosteryl esters of oleic acid by response surface methodology. Food Chem. 2007, 102, 336. (18) Marchetti, J. M.; Errazu, A. F. Esterification of free fatty acids using sulfuric acid as catalyst in the presence of triglycerides. Biomass Bioenergy 2009, 32, 892. (19) Geng, L.; Wang, Y.; Yu, G.; Zhu, Y. Efficient carbon-based solid acid catalysts for the esterification of oleic acid. Catal. Commun. 2011, 13, 26. (20) Park, J. Y.; Kim, D. K.; Lee, J. S. Esterification of free fatty acids using water-tolerable Amberlyst as a heterogeneous catalyst. Bioresour. Technol. 2010, 101, 562. (21) Li, Z.; Huang, B.; Zhang, W.; Zhang, K.; Fang, Y.; Zhou, B. Kinetic studies on synthesis of n-butyl acetate catalyzed by ionic liquid [Hnmp]HSO4. Ind. Catal. 2008, 16, 45.
Table 2. Activation Energies and Arrhenius Coefficients for This Esterification Reaction parameter
value
parameter
Ea+ (kJ·mol−1)
34.22
A+ [L·(mol·min)−1]
41.78
value
Ea− (kJ·mol−1)
11.09
A− [L·(mol·min)−1]
3.05 × 10−2
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CONCLUSIONS Biodiesel production from the esterification of the free fatty acid stearic acid catalyzed by D418 was investigated. The research results suggest that D418 is catalytically active for the esterification of stearic acid, and the optimum values for maximum esterification percentage can be obtained by using a Box−Behnken center-united design with a minimum of experimental work. At the optimal conditions (catalyst amount of 11%, 11.6:1 molar ratio of ethanol to stearic acid, and 89.3 °C reaction temperature), the predicted value of the conversion ratio was 91.47%. Validation experiments were also carried out to verify the availability and accuracy of the model, and the results showed that the predicted value was in good agreement with the experimental value [(91.33 ± 0.56)%]. Furthermore, the kinetics for the esterification catalyzed by D418 catalyst was studied, and the pseudohomogeneous model for this esterification reaction was established to simulate the experimental data. The kinetic equation for this esterification was found to be r = 41.78exp( −34.22/RT )CAC B − 3.05 × 10−2exp(
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−11.09/RT )CCC D
ASSOCIATED CONTENT
S Supporting Information *
Tables S1−S4 and Figure S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: + 86-535-6696162. Fax: + 86-535-6697667. E-mail:
[email protected] (P.Y.),
[email protected]. (H.C.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The support provided by the National Natural Science Foundation of China (Grants 51102127 and 51073075), the Nature Science Foundation of Shandong Province (2009ZRB01463), and the Foundation of Innovation Team Building of Ludong University (08-CXB001) is greatly appreciated.
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REFERENCES
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