ARTICLE pubs.acs.org/IECR
Reaction Kinetic Study of Biodiesel Production from Fatty Acids Esterification with Ethanol L. D. T. C^amara*,† and D. A. G. Aranda‡ †
Departamento de Engenharia Mec^anica e Energia (DEMEC), Instituto Politecnico da Universidade do Estado do Rio de Janeiro (IPRJUERJ), Nova Friburgo-RJ, Brazil ‡ Departamento de Engenharia Química, Laboratorio de Tecnologias Verdes (GreenTec), Escola de Química da Universidade Federal do Rio de Janeiro (EQ-UFRJ), Rio de Janeiro-RJ, Brazil ABSTRACT: The kinetic of fatty acids esterification with ethanol utilizing niobium oxide catalyst (79.8% of NbO5 and 19.6% of water) for the production of biodiesel was analyzed through a reversible kinetic modeling for the determination of the kinetic and thermodynamic data of the reactions. The reactions were carried out with three kinds of fatty acids (stearic, palmitic, and lauric) with anhydrous and hydrated ethanol. From the kinetic study it was possible to calculate the theoretical equilibrium data which were compared to experimental data of each reaction. From the comparison between the experimental and calculated conversions it was possible to analyze the accuracy of the estimations, providing a good way to apply statistical treatments in the improvement of the kinetic and thermodynamic properties calculated.
1. INTRODUCTION The production of biodiesel from raw materials that can be used for food is not the best way to generate and develop renewable energy.1 Therefore, the alternative sources, such as the fatty acids (byproduct), are a good option as these materials lead to low cost biodiesel production without interfering in food production.2 In the literature there are many works related to research and development of technologies for the conversion of fatty acids into biodiesel.3-20 There are researches where the main objective is the conversion of pure fatty acids,3-11 and others in which the fatty acids are part of the oil phase medium.12-20 In the latter case sometimes it is necessary to convert the fatty acids to reduce the problems of saponification which reduce the yield of the reaction of transesterification by alkali. In the reactions of esterification for the production of biodiesel a great variety of catalyst are found, such as sulfuric acid,4,5,12,13 acid resins,3,7,9-11 acid polymers17,18 and others (tungstophosphoric acid,14,16 tungstosilicic acid,16 niobium oxide (Nb2O5),19 zinc hydroxide nitrate (Zn5(OH)8(NO3)2 3 2H2O)8 and Fe2(SO4)3/C).6 The most common is sulfuric acid and acid resins used in the catalysis of such reactions. The use of niobium oxide is a promising possibility observed in a previous work.19 In the work of Aranda et al.19 different catalysts were tested and compared in the esterification of a mixture of fatty acids residue. They observed a better performance of the polynaphthalene sulfonic acid and the niobium oxide (Nb2O5) if compared to that of a zeolite catalyst. The authors also observed higher conversion when utilizing the methanol if compared to using the ethanol. From the literature can be seen works related to the kinetic modeling studies of the esterification reactions of fatty acids for the production of biodiesel.4,6,10,11,19,20 In the work of Berrios et al.4 the authors applied a reversible reaction kinetic model that is first order in the forward direction and second order in the r 2010 American Chemical Society
reverse direction. They studied the esterification of free fatty acids in sunflower oil with methanol and sulfuric acid. They determined the activation energies by the Arrhenius equation, observing a decrease in the activation energy with an increase in the catalyst concentration. Tesser et al.10 applied a detailed kinetic/equilibrium model that takes into account different aspects of the esterification of oleic acid with soybean oil with methanol and acid exchange resins. The developed kinetic model was able to correctly represent the experimental data both as a function of temperature and of catalyst concentration. In the work of Aranda et al.19 the authors applied two different kinetic models to study the esterification of fatty acids with polynaphthalene sulfonic acid, niobium oxide, and zeolite catalyst utilizing ethanol and methanol. They studied an empiric heterogeneous model and a homogeneous model. The parameters for both models were obtained utilizing the Statistical software and applying nonlinear regression. The authors observed that the homogeneous model is more adequate to represent the esterification with methanol, whereas the heterogeneous model better represents the esterification with ethanol. This work presents the study of the kinetics of fatty acid esterification with ethanol and niobium oxide catalyst (NbO5) for the production of biodiesel. A reversible kinetic model was assumed in the determination of the kinetic parameters of three different kinds of pure fatty acids (stearic, palmitic, and lauric) with anhydrous and hydrated ethanol. From the experimental equilibrium data, it was possible to analyze the accuracy of the
Special Issue: IMCCRE 2010 Received: March 10, 2010 Accepted: June 24, 2010 Revised: June 23, 2010 Published: July 12, 2010 2544
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Table 1. Experimental and Calculated Data for Esterification of Stearic Acid temp (oC) stearic HE
stearic AE
k1 (L/(mols 3 min))
k2 (L/(mols 3 min))
keq = k1/k2
expt convn (%)
calcd convn (%)
ΔH (kJ/mol), ΔS (J/(mol 3 K)) 193.2, 428.6
150
0.0021
0.0999
0.021
22
21
200
0.0116
0.0016
7.25
77
94
150
0.0063
0.2958
0.021
21
22
200
0.0171
0.0108
1.58
78
81
145.5, 311.3
Table 2. Experimental and Calculated Data for Esterification of Palmític Acid
palmitic HE
palmitic AE
temp (oC)
k1 (L/(mols 3 min))
k2 (L/(mols 3 min))
keq = k1/k2
expt convn (%)
calcd convn (%)
ΔH (kJ/mol), ΔS (J/(mol 3 K))
150
0.0106
1.1673
0.01
17
15
151.3, 319.3
200
0.0104
0.0111
0.94
73
74
150
0.0108
0.0587
0.18
52
49
200
0.0174
0.0034
5.11
84
92
expt convn (%)
calcd convn (%)
ΔH (kJ/mol), ΔS (J/(mol 3 K)) 55.9, 117.2
111.7, 249.8
Table 3. Experimental and Calculated Data for Esterification of Lauric Acid temp (oC) lauric HE
lauric AE
k1 (L/(mols 3 min))
k2 (L/(mols 3 min))
keq = k1/k2
150
0.0081
0.0485
0.17
50
47
200
0.0100
0.0110
0.91
75
74
0.04
31
28
84
96
150
0.0029
0.0708
200
0.0155
0.0013
11.9
189.2, 420.4
estimations and determine the thermodynamic properties of the reactions studied.
2. EXPERIMENTAL SECTION Three types of fatty acids (acid stearic, palmitic, and lauric) were studied in terms of esterification with ethanol (anhydrous ethanol AE and hydrated ethanol HE) for the production of biodiesel.21 The HE utilized comprised 4% w/w water. The reactions were carried out in autoclave batch reactor with temperature control (Parr Instruments 4560). The solid catalyst utilized was the niobium oxide (79.8% NbO5 and 19.6% water; superficial area of 180 m2/g) at 20% w/w in relation to the quantity of fatty acid. The excess molar ratio of alcohol was set to 3 to provide a more favorable reaction kinetic for the formation of products. The reaction products were analyzed through gas chromatography with samples taken periodically from the reactor. The analytical method was based on the EN 14103 method using a capillary column (Carbowax 20M) 30 m 0.32 mm 0.25 μm and methyl heptadecanoate and heptadecanoic acid as internal standards. 3. KINETIC AND THERMODYNAMICAL MODELING The reaction of esterification was modeled through a reversible kinetic model (eq 1) with the kinetic constants k1 and k2 related, respectively, to the direct and inverse reaction. The correlation with the experimental data, to calculate the kinetic constants k1 and k2, was done utilizing the stochastic routine R2W (Random Restricted Window).22 dCbio ¼ k1 Cf at acid Cethanol - k2 Cbiodiesel Cwater dt
ð1Þ
Figure 1. Correlation between the kinetic model and the experimental data for the palmitic acid esterification at 200 °C (HE, hydrated ethanol; AE, anhydrous ethanol).
The R2W is a simple method of search by random estimations in the domain of the parameters. In this inverse routine initially there is a random estimation of the parameters, and after the determination of the best solution there is a new restricted search near the best solution encountered in the previous step. The best solution is obtained by the square residue function (Q) which is obtained through the comparison between the experimental (Cexpt) and calculated (Ccalcd) concentrations (eq 2). Q ¼
n X i¼1
ðCexpti - Ccalcdi Þ2
ð2Þ
From the calculations of the equilibrium constant utilizing the kinetic constants k1 and k2 (eqs 2) it was possible to determine 2545
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Table 4. Statistical Treatment for the Esterification of Stearic Acid at 200 °C
stearic HE
case
k1 (L/(mols 3 min))
k2 (L/(mols 3 min))
keq = k1/k2
expt convn (%)
calcd convn (%)
residue Q (mol/L)
1
0.0116
0.0016
7.25
77
94
101.7
2
0.0133
0.0034
3.97
77
90
7.0
Figure 2. Statistical analysis in the correlation between the kinetic model and the experimental data for the stearic acid esterification at 200 °C.
the free Gibbs energy and the enthalpy and entropy variation (eqs 4 and 5). keq ¼
k1
=k 2
ð3Þ
ΔG ¼ - RT lnðkeq Þ
ð4Þ
ΔG ¼ ΔH - TΔS
ð5Þ
From the equilibrium constant calculated before, the theoretical conversion of the reaction utilizing the following expression (eq 6) can be determined. In eq 6 the equilibrium constant is related to the concentration of the species considering the stoichiometry of the reaction. The concentration of the compounds in eq 6 can be converted in a conversion that is determined with the value of the equilibrium constant (calculated conversion can be found in Tables 1, 2, and 3). In the case of alcohol excess, eq 6 must take into account such an effect in the calculation of the equilibrium constant. keq ¼
Cbiodiesel Cwater Cf at acid Cethanol
ð6Þ
4. RESULTS AND DISCUSSION The first step in this work was the calculation of the kinetic constants (eq 1) utilizing the experimental data of fatty acid esterification with ethanol. Figure 1 shows the good fit between the kinetic model and the experiments of palmitic fatty acid utilizing hydrated ethanol (HE) and anhydrous ethanol (AE). Figure 1 shows the more favorable reaction (in general) for the use of anhydrous ethanol (AE). In general it can be observed that there is a higher conversion when utilizing the anhydrous ethanol (HE), but higher results of conversion also can be obtained with hydrated ethanol. Experimentally it was observed that depending
on the reaction condition any fatty acid can achieve a higher conversion with hydrated ethanol. Probably the molecular size has a significant effect as the higher molecular fatty acid led to a higher number of conversions with hydrated ethanol (stearic fatty acid). The Table 1 presents the kinetic constants (k1 and k2), the equilibrium constant, the experimental conversion at the equilibrium (considered 60 min of reaction), the calculated conversion at the equilibrium (from eq 5) and the enthalpy and entropy (from eq 4), respectively, for the esterification reaction of stearic acid with HE and AE. In a comparison of the experimental and theoretical values of conversion, it can be observed that the results are very close to each other, which validates the kinetic model applied to the reaction of esterification and the values of kinetic constants estimated for each condition of temperature. Some discrepancies can be attributed to the error associated to the experimental measurement; therefore, a statistical analysis can be used to improve the correlation leading to an estimation of the parameters with higher accuracy. The same properties were obtained for the esterification of palmitic acid (Table 2) and lauric acid (Table 3) also showing the results of experimental and theoretical conversion being very close to each other. The results of enthalpy and entropy variation for the esterification of the three types of fatty acids showed reactions with endothermic behavior and positive increase in the entropy. Marchetti et al.7 also observed endothermic behavior studying the esterification of fatty acids with acid resins and anhydrous ethanol. For the stearic and palmitic acid the enthalpy and entropy variation was lower for the esterification with anhydrous ethanol (AE) if compared to the hydrated ethanol (HE). The inverse behavior was observed for the esterification of lauric acid. The influence of hydrated ethanol in the thermodynamic properties can be probably attributed to different dissociation constants of the carboxylic acids associated with stabilization of the carboxylic anion by water. The dissociation constants of carboxylic acids (pka) increase with the decrease in the molecular chain size (pka of stearic acid > palmitic > myristic > lauric).23 The presence of water in the reaction medium stabilizes the conjugate base (A:(-)) of the fatty acid which shifts the equilibrium to the right. The fatty acid with the lower dissociation constant is the stearic acid, so the aqueous medium can probably influence the reaction more significantly. In this case the water probably has a more significant effect in the dissociation of the stearic acid, which manifests into a higher number of conversions with HE. Table 4 presents a statistical treatment for the condition of high deviation between the experimental and calculated conversion for the esterification of stearic acid (T = 200 °C and HE). The residue Q represents the deviation between the experimental data and the simulation results. A higher residue Q represents a higher deviation. The original correlation, with all experimental points (black and white points), can be seen in Figure 2 in which the black line corresponds to simulations from the kinetic model. The statistical treatment of the experimental data was performed omitting the experimental points with more deviation from the 2546
dx.doi.org/10.1021/ie1005806 |Ind. Eng. Chem. Res. 2011, 50, 2544–2547
Industrial & Engineering Chemistry Research curve (points 2 and 4). This procedure leads to simulation results with better agreement between the experimental data and the kinetic model (gray line in Figure 2). From Table 4 it can be seen that the optimized condition (case 2) leads to a closer conversion calculated (90%) with a lower residue Q, indicating a lower deviation between the experiments and the simulations.
5. CONCLUSIONS From the reaction kinetic model it was possible to represent the experimental data of fatty acids esterification for the production of biodiesel. The inverse routine applied (R2W) led to a good fit between the experimental data and the simulation results which validates the utilization of such a kinetic model in such reactions. The veracity of the kinetic constants is verified through the comparison between the experimental and calculated conversion values at the equilibrium obtained from the equilibrium constants. The equilibrium constants also were used in the determination of the thermodynamic properties, enthalpy and entropy. In all cases the increase in the temperature increased both the enthalpy and entropy. The increase in the enthalpy is related to endothermic behavior. The influence of hydrated ethanol in the thermodynamic properties can probably be attributed to different dissociation constants of the carboxylic acids associated with stabilization of the carboxylic anion by water. Statistical treatment of the experimental data can be used to improve the accuracy in the estimation of the kinetic constants and consequently the calculation of the enthalpy and entropy. ’ NOMENCLATURE HE = hydrated ethanol AE = anhydrous ethanol C = concentrations k1 and k2 = kinetic constants, L/(mols 3 min) keq = equilibrium constant ΔG = variation in free Gibbs energy ΔH = variation in the enthalpy, kJ/mol ΔS = variation in the entropy, J/(mol 3 K) T and R = temperature and universal constant (8.314 j/mol 3 K), respectively Q = square residue
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors acknowledge the financial support provided by CNPq, FAPERJ, CAPES, UFRJ, UERJ (Instituto PolitecnicoIPRJ) and CBMM. ’ REFERENCES (1) Gazzoni, D. R. Conflict between food and energy. Biodiesel Braz., http://www.biodieselbr.com/colunistas/gazzoni/conflito-alimentosenergia-24-09-07.htm, 24 September, 2007. (2) Aranda, D. A. G.; Rosa, L. P.; Oliveira, L. B.; Costa, A. O.; Pimenteira, C. A. P.; Mattos, L. B. R.; Henriques, R. M. Energy generation from waste and vegetable oils. In Renewable sources of energy in Brazil; Tolmasquim, M. T., Ed.; Interci^encia/Cenergia: Rio de Janeiro, 2003; Vol. 1, Chapter 2, p. 93-161.
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