Ind. Eng. Chem. Res. 2010, 49, 4099–4106
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Reversible Autocatalytic Hydrolysis of Alkyl Formate: Kinetic and Reactor Modeling Olatunde Jogunola,*,† Tapio Salmi,† Kari Era¨nen,† Johan Wa¨rnå,† Matias Kangas,† and J.-P. Mikkola†,‡ Process Chemistry Centre, Laboratory of Industrial Chemistry and Reaction Engineering, Åbo Akademi, FI-20500 Åbo/Turku, Finland, and Technical Chemistry, Chemical-Biological Centre, Department of Chemistry, Umeå UniVersity, SE-90187 Umeå Sweden
The kinetics and thermodynamics of alkyl formate hydrolysis in liquid phase were studied in a laboratory-scale autoclave at temperatures between 333 and 383 K using different molar ratios of the reactants. The process was found to exhibit an autocatalytic effect due to the acid formed. More so, the rate of neutral hydrolysis of ethyl formate is faster compared to methyl formate in the uncatalyzed reaction. However, the autocatalytic effect is more pronounced in methyl formate hydrolysis. In addition, the effect of adding a small amount of formic acid as an initial charge upon the equilibrium conversion and kinetics was investigated, and it was found that the addition improved the reaction rate by reducing the induction period but it suppressed slightly the equilibrium conversion. A kinetic model was proposed to explain these experimental trends, and the model agreed well with the experimental results. Introduction Formic acid (FA) can be produced by the hydrolysis of lower alkyl (C1-C4) formates.1 The process involves a reversible endothermic reaction which is slow at neutral pH. However, the formic acid produced in the process is found to catalyze the reaction (autocatalysis). In practice, this implies that the hydrolysis is relatively slow at the beginning of the reaction because there is little or no catalyst present but accelerates progressively as more hydroxonium ions are produced and then slows down as the reactant concentration decreases. Few academic researchers have published works related to the autocatalytic effect of alkyl formate hydrolysis in the open literature.2-4 Begum et al.5 studied the kinetics of the hydrolysis of methyl formate in neutral medium using a temperature range 293-343 K and evaluated the rate constants. Gladii et al.6 investigated autocatalytic hydrolysis of methyl formate at 293-363 K in diluted aqueous solutions. They presented some empirical equations which relate the effective hydrolysis rate constant with the concentration of formic acid and methyl formate. The purpose of our work is to determine the detailed kinetics and thermodynamics of the autocatalytic process involved in alkyl (methyl and ethyl) formate hydrolysis and to develop a mechanistic model for the reaction system. Furthermore, the kinetic parameters of the model are determined to enable its use for the optimization of the hydrolysis process.
In the mathematical modeling, we assume that the system can be treated as a pure liquid-phase system and the role of the gas phase, including the volatilization of the components can be ignored since vaporization was prevented by carrying out the reaction under pressure and the gas volume was very small (99 wt %) and methyl formate (SigmaAldrich, 97 wt %) in case of methyl formate hydrolysis (MFH) or ethanol (Altia, 99.5%) and ethyl formate (Sigma-Aldrich, 97 wt %) in the case of ethyl formate hydrolysis (EFH) were discharged into the feeding vessel with the aid of a dropping funnel. The nitrogen line to the reactor and the vent lines were connected to the system. The stirred reaction vessel was heated until it was 283 K higher than the desired temperature. After the temperature has stabilized, the ester was discharged into the reaction vessel as quickly as possible using nitrogen pressure, and the reaction commenced. The initial total amount of the hydrolysis mixture was close to 0.3 kg. The schematic diagram of the laboratory reactor is shown in Figure 1. The experimental matrix is displayed in Table 5. 2.2. Gas Chromatographic Analysis. The samples were taken in defined sample intervals (5, 10, 15, or 20 min) using reactor system pressure and were analyzed off-line with a gas chromatograph: 6890N, injection port temperature 423 K, oven
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Table 6. Effect of Temperature on Equilibrium Composition and Constant (A ) MeFo or EtFo) equilibrium concentration (mol/kg)
activity coefficient
temp (K)
C0A (mol/kg)
MeFo
H2O
FA
MeOH
KC
MeFo
H2O
FA
MeOH
Ka
Kaa
353 363 373 383
10.488 10.488 10.488 10.488
6.983 6.850 6.760 6.677
15.367 15.237 15.147 15.060
3.507 3.637 3.727 3.813
4.447 4.580 4.670 4.753
0.145 0.160 0.170 0.180
2.369 2.340 2.311 2.283
1.384 1.378 1.373 1.368
0.752 0.766 0.777 0.788
1.224 1.224 1.224 1.224
0.041 0.047 0.051 0.056
0.093 0.098 0.103 0.107
353 363 373 383 a
9.043 9.043 9.043 9.043
EtFo
H2O
FA
EtOH
5.671 5.653 5.613 5.583
12.910 12.892 12.853 12.822
3.372 3.391 3.430 3.460
3.808 3.828 3.865 3.895
0.175 0.178 0.184 0.188
EtFo
H2O
FA
EtOH
2.504 2.473 2.443 2.415
1.592 1.584 1.577 1.570
0.766 0.775 0.785 0.794
1.373 1.374 1.374 1.373
0.046 0.048 0.052 0.054
0.039 0.043 0.046 0.049
According to eq 14.
temperature 423 K, HP-PLOT U column, 250 m × 530 µm × 20 µm, carrier gas helium (15 mL/min at 1 min), flame ionization detector (FID; 523 K, H2 flow 40 mL/min, air flow 450 mL/min). The calibration was performed by using acetonitrile (Labscan, >99%) as an internal standard. The calibration of the internal standard solution was always done before the analysis of any sample. The analysis time for the sample was between 5 and 11 min. The experimental results were based on alcohol analysis (methanol in case of MeFo, and ethanol in case of EtFo) due to the volatility of the ester and the difficulty in getting a reliable analysis method for the formic acid. 3. Results and Discussion The values of the activity coefficients were determined for each experimental temperature using the composition of the reactants and products after the equilibrium had been attained in order to deduce the value of the standard heat of reaction. The initial concentrations of the reactants for all temperatures were the same (see Table 5). A typical plot which shows a
Figure 2. Comparison between the experimental temperatures and the originfitted Boltzmann equation for temperatures.
Figure 3. Temperature dependence of the equilibrium constant.
Table 7. ∆H°r Values Obtained from Different Sources source
∆H°r (kJ/mol) MFH
∆H°r (kJ/mol) EFH
HSC chemistry 7.0 database KC (Figure 3) Ka (Figure 3) CRC handbook(see Table 3)
+5.44 +8.0 +11.6 +7.7
+7.91 +2.74 +5.97 +13.7
comparison of the experimental temperatures with the origin fitted Boltzmann equation for temperature is given in Figure 2. 3.1. Temperature Dependence of the Equilibrium Constant. The effect of temperature on the chemical equilibrium was investigated at 353, 363, 373, and 383 K. KC was computed from experimental data by using eq 7. The corresponding activity coefficients were obtained with the UNIFAC method. Then, Ka was calculated from eq 9. Their values were compared to the one obtained by the thermodynamic calculation (eq 14) using data obtained from HSC chemistry data bank (see Table 3). However, calculating Ka using the values of ∆G°r and ∆H°r obtained from HSC chemistry database or any other source might introduce some degree of error into the results because of the uncertainty involved in the determination of ∆H°f especially for MeFo and EtFo (see Tables 3 and 4). Furthermore, the uncertainty might increase because ∆G°f for MeFo and EtFo in the liquid phase are calculated from ∆G°f in the vapor phase and partial vapor pressure due to the unavailability of the data in the literature. The results are illustrated in Table 6. A plot of the natural logarithm of the equilibrium constants KC and Ka against the reciprocal of the absolute temperature is shown in Figure 3. The slope based on the linear regression of the data points is equal to -∆H°r /R (see eq 14). For a relatively narrow temperature interval, which is true in our case, a constant reaction enthalpy is assumed. This enables us to compare the experimental results to the ones estimated by using thermodynamic data from the literature. The values of ∆H°r obtained from four different approaches are given in Table 7. For MFH, It can be deduced that the value of ∆H°r obtained from KC (computed from experimental data) is in good agreement with that estimated from CRC handbook and in relatively good agreement with the value calculated from HSC chemistry databank. Furthermore, the ∆H°r value obtained from Ka (using the concept of activity coefficient) is in relatively good agreement with that obtained from CRC handbook. However, for EFH, the ∆H°r value obtained from Ka is in relative good agreement with that calculated from HSC chemistry data bank, but it differs quite significantly from that estimated from CRC handbook. This might be due to the fact
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Table 8. Summary of the Estimated Parameters and Statistical Data jk jk′ parameters KC Ea Ea′ (kJ/mol) (kJ/mol) SI units (kg/mol · min) (kg2/mol2 · min) methyl formate hydrolysis value error (%)
0.026 20.4
value error (%)
0.1 10.6
0.12 9.3
0.17 2.9
88.2 18.6
66.4 10.2
89.2 5.1
48.2 7.4
ethyl formate hydrolysis
Figure 4. Dependence of the initial FA charge on hydrolysis rate and equilibrium conversion.
Figure 5. Temperature dependence of reaction rate and induction period for MeFo hydrolysis.
0.12 12.3
0.19 2.3
conversion were affected by the amount of FA present at the beginning of the reaction as shown in Figure 4. The addition of a small amount of FA as an initial charge increases the rate of reaction. This is due to the catalytic effect of the acid. However, it reduces the equilibrium conversion slightly due to the more accumulation of product (FA), which encourages the backward reaction. Therefore, the hydrolysis reaction should not contain any substantial amount of FA as an initial charge at the beginning of the reaction. 3.3. Effect of Temperature on Hydrolysis Rate and Induction Period. Experiments were performed at 353, 363, 373, and 383 K without any initial formic acid charge. The rate of the hydrolysis reaction increases with increasing temperature, but the temperature has no pronounced influence on the equilibrium conversion. This can be explained by the weak temperature dependence of the equilibrium constant, i.e. the low value of the reaction enthalpy (∆H ) +5.44 kJ/mol) for MFH. This is visible in Figure 5. At lower temperatures, (353 and 363 K), the autocatalytic graphical feature is more pronounced compared to higher temperatures (373 and 383 K), i.e. the kinetic curve tends to be sigmoidal (S-shaped) at lower temperatures. Also, there is an induction period (i.e., time interval between the commencement of the reaction and the first sign of an appreciable conversion) at lower temperatures. As temperature increases, the induction period decreases. However, for the ethyl formate hydrolysis, the induction period ceases to exist at lower temperatures as depicted by Figure 6. Furthermore, the
Figure 6. Temperature dependence of reaction rate and induction period for EtFo hydrolysis.
Figure 7. Extent of autocatalysis at 363 K during the course of the reaction.
that ethyl formate has a much more weak temperature dependence on equilibrium constant. Thus, one can notice the difference in the values of ∆H°r obtained from HSC chemistry database and CRC handbook. Finally, it can be concluded that the concept of activity coefficient using UNIFAC method did give a significant improvement to the description of the experimental data especially in the case of ethyl formate hydrolysis. 3.2. Effect of the Initial Formic Acid Concentration on the Rate and Equilibrium Composition. The effect of the initial FA concentration charge was monitored by varying the FA/MeFo molar ratio from 0.0 to 0.1, while keeping other parameters constant. Thus, the hydrolysis rate and equilibrium
Figure 8. Model prediction of non- and autocatalytic reaction rates at 363 K.
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Table 9. Correlation Matrix of the Parameters in the Kinetic Model methyl formate hydrolysis jk jk′ KC Ea Ea′
jk
ethyl formate hydrolysis jk′ KC Ea Ea′
jk 1.00 1.00 KC 0.14 1.00 0.24 1.00 Ea 0.74 0.01 1.00 0.50 -0.04 1.00 jk′ -0.89 -0.24 -0.62 1.00 -0.93 -0.33 -0.43 1.00 Ea′ -0.74 -0.03 -0.88 0.79 1.00 -0.77 -0.14 -0.84 0.81 1.00
S-shaped becomes less pronounced at lower temperatures when compared with methyl formate hydrolysis. Generally, the rate is slow at the initial stage of the reaction but as the reaction proceeds and more H+ are formed, the
reaction becomes faster as the H+ formed catalyzes the reaction. Finally, the rate of the reaction gets slower again toward the end of the reaction as the chemical equilibrium is reached due to depletion of the concentration of the reactants. Furthermore, at higher temperatures (e.g., 383 K), there is an earlier accumulation of H+ which catalyzed the reaction and reduced the time for the reaction to reach the equilibrium and the curve tends to be hyperbolic as shown in Figures 5 and 6. 3.4. Kinetic Modeling Results. The fit of the kinetic model to the experimental results was achieved with MODEST software.14 The differential equations were solved by the backward difference method15 during the course of the estima-
Figure 9. (a) Comparison of the experimental results with the kinetic model for methyl formate hydrolysis. (b) Comparison of the experimental results with the kinetic model for ethyl formate hydrolysis.
Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010 Table A1. UNIFAC Group Interaction Parameters amn for Methyl Formate Hydrolysis8 n m 6 20 12 1 7
group interaction for methyl formate
6 0 339 227.8 697.2 289.6
20 -202 0 -268.1 663.5 -14.09
12 179.7 193.9 0 507 233.8716
1 16.51 315.3 329.3 0 300
7 -181 -66.17 124.6316 1318 0
Table A2. UNIFAC Group Interaction Parameters amn for Ethyl Formate Hydrolysis8 n m 5 20 12 1 7
group interaction for ethyl formate
5 0 -151 139.4 986.5 -229.1
20 199 0 -268.1 663.5 -14.09
12 267.8 193.9 0 507 233.8716
1 156.4 315.3 329.3 0 300
7 353.5 -66.17 124.6316 1318 0
Table A3. Vapour Pressures of the Pure Components of MeFo and EtFo A
B
C
D
E -6
methyl formate 77.184 -5.61 × 10 -8.39 × 10 7.85 × 10 2.0 ethyl formate 73.833 -5.82 × 103 -7.81 × 100 6.32 × 10-6 2.0 3
0
Table A4. Regressed Boltzmann Parameters (Equation 19) temperature (K)
T1 (K)
T2 (K)
dt (min)
353.5 363.7 374.6 384.4
4.0 4.2 5.4 5.5
354.0 363.9 373.9 383.9
4.8 4.5 4.2 3.8
MFH 353 363 373 383
344.5 344.3 349.1 362.0 336.9 344.3 350.2 361.7
tion of the kinetic and equilibrium parameters. The parameters were estimated from the experimental data by using the objective function n
Q(f) )
∑ (y
i
- yˆi)2
(20)
i)1
where yi is the experimental value of component i in the mixture and yˆi is the corresponding model prediction. In the present work, yi and yˆi represent the concentrations of the species. The parameter estimation was carried out with a combined simplex-Levenberg-Marquardt algorithm by minimizing the weighted sum of residual squares. The degree of explanation R2 of the kinetic model is defined as follows: R2 ) 1 -
∑ (y ∑ (y
i
- yˆi)2
i
- jyi)2
results; thus, the degrees of explanation for ethyl formate and methyl formate hydrolyses were 99% and 96.2%, respectively. The values of the estimated parameters are given in Table 8. From Table 8, the jk values for methyl formate and ethyl formate hydrolysis are 0.026 and 0.1 kg/mol · min, respectively, which indicates that the rate of neutral aqueous solution hydrolysis for ethyl formate is faster than methyl formate for the uncatalyzed reaction under the same reaction conditions. This is due to the fact that it takes a much longer time for methyl formate in contrast to ethyl formate to form the less stable tetrahedral intermediate which breaks down to release the alcohol. However, autocatalytic effect is more pronounced in methyl formate hydrolysis in contrast to ethyl formate hydrolysis as indicated in the ratio of their jk′CC/kj values (see Tables 6 and 8). For example, at 363 K, jk′CC/kj was plotted against time to see the extent of autocatalysis for the hydrolysis of methyl formate and ethyl formate during the course of the reaction. This is shown in Figure 7. The slope of MFH is greater than that of EFH. When formic acid is formed, it catalyzed methyl formate faster than ethyl formate because of the steric hindrance present in ethyl formate and the low solubility of ethyl formate in water (10.5 g per 100 mL H2O at 293 K) in contrast to methyl formate (30 g per 100 mL H2O at 293 K). The standard error for jk, jk′, KC, and Ea are quite low. An illustration of noncatalytic reaction rate (rnc) and autocatalytic reaction rate (rac) for MFH and EFH at 363K is given in Figure 8. The correlation matrix of the estimated parameters is shown in Table 9, and the correlations between the parameters are reasonable as revealed by the table. The fits of the kinetic data for MFH and EFH are given in Figures 9a and b. Conclusions
EFH 353 363 373 383
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The standard enthalpies of the ethyl and methyl formate hydrolysis reactions using the concept of activity coefficient (UNIFAC group contribution method) and thermodynamic data were determined and compared with the literature values. There was a good agreement among the values for methyl formate hydrolysis. However, for ethyl formate hydrolysis, the discrepancies were clearly noticeable. However, the concept of activity coefficient using the UNIFAC method did improve the calculations. The kinetics of the hydrolysis of the esters was accomplished with a model which includes the autocatalytic effect of the acid product in the rate equation. The kinetic model applied is based on the analytical data of one of the components, the methanol formed for methyl formate hydrolysis, or ethanol formed for ethyl formate hydrolysis. The fit of the model to the experimental data was satisfactory. The effect of the initial formic acid concentration charge was also investigated, and it was found that it increased the reaction rate but reduced slightly the equilibrium conversion as expected. Acknowledgment
(21)
where jyi is the mean value of the observations. In our model, the kinetic parameters (kj, jk′, Ea, and E′a) and equilibrium parameter KC were determined, while keeping the value of ∆H°r constant at +7.91 and +5.44 kJ/mol for ethyl formate hydrolysis and methyl formate hydrolysis, respectively (see Table 7) by using eq 6. The model was able to predict well the experimental
This work is part of the activities of the Åbo Akademi Process Chemistry Centre (PCC) within the Finnish Centre of Excellence Programme (2006-2011) by the Academy of Finland. Financial support from the Åbo Akademi Foundation is gratefully acknowledged. Appendix The following tables (Table A1-A4) show experimental data.
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Appendix Notation A ) pre-exponential factor a ) activity amn ) UNIFAC group interaction parameters between two groups C ) concentration, mol/kg Ea ) activation energy of the uncatalyzed reaction, kJ/mol Ea′ ) activation energy for the autocatalyzed reaction, kJ/mol f ) rate function G ) Gibb’s free energy, kJ/mol H ) enthalpy, kJ/mol KC ) concentration-based equilibrium constant Ka ) thermodynamic equilibrium constant Kγ ) activity coefficient-based equilibrium constant k ) rate constant of the uncatalyzed reaction, kg/mol · min k′ ) rate constant for the autocatalyzed reaction, kg2/mol2 · min m ) mass, kg n ) number of moles, mol P ) partial vapor pressure, Pa P° ) reference pressure, Pa pH ) power of hydrogen q ) relative van der Waals surface area Q ) objective function R ) gas constant, J/mol K R2 ) degree of explanation, % r ) relative van der Waals volume r ) reaction rate, mol/kg · min T ) temperature; set point temperature, K T(t) ) Boltzmann origin fitted temperature, K t ) time, min z ) transformed temperature, K-1 γ ) activity coefficient ∆ ) change ∑ ) summation - ) average Subscripts and Superscripts C ) combinatorial f ) formation i ) component index liq ) liquid L ) liquid mixture ° ) standard state r ) reaction, reactants p ) products R ) residual 0 ) initial value - ) backward reaction + ) forward reaction
AbbreViation ACN ) acetonitrile EtFo (A) ) ethyl formate EtOH (D) ) ethanol FA (C) ) formic acid FID ) flame ionization detector GC ) gas chromatograph H2O (B) ) water MeFo (A) ) methyl formate MeOH (D) ) methanol rac ) rate of the autocatalyzed reaction rnc ) rate of the noncatalyzed reaction rpm ) revolution per minute UNIFAC ) Universal Functional Activity Coefficient
Literature Cited (1) Lynn, J. B.; Homberg, O. A.; Singleton, A. H. Formic acid synthesis by lower alkyl formate hydrolysis. U.S. Patent 3907884 to Bethlehem Steel Corp., Sept. 23, 1975. (2) Begum, S. Kinetics of the Autocatalytic Hydrolysis of Esters in Neutral Medium. Sci. Int. (Lahore) 1992, 4 (3), 225. (3) He, J.; Chen, Y.-D.; Pang, X.-X.; Huang, Z.-T. Study on Direct Hydrolysis of Methyl Formate to Formic Acid. J. Nat. Gas Chem. 1992, 1, 38. (4) Mata-Segreda, J. F. Spontaneous Hydrolysis of Ethyl formate: Isobaric Activation Parameters. Int. J. Chem. Kinet. 2000, 32, 67. (5) Begum, S.; Zeb, M. A.; Pirzada, N. Hydrolysis of Methyl Formate in Aqueous Solution and the Evaluation of Rate Constants. J. Chem. Soc. Pak. 2000, 22 (4), 250. (6) Gladii, S. L.; Starchevskii, M. K.; Pazderskii Yu, A.; Moiseev, I. I. Autocatalytic Hydrolysis of methyl Formate. Russ. J. Appl. Chem. 1994, 67 (8), 1395 (translated from Russian to English). (7) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapour-Liquid Equilibrium using UNIFAC; Elsevier: Amsterdam, 1977. (8) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquid, 4th ed.; McGraw-Hill: New York, 1988. (9) Lide, D. R. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press inc.: Boca Raton, FL, 2004. (10) Roine, A. HSC chemistry 7.0; Outokumpu Research Oy: Pori, 2009. (11) Hine, J.; Klueppel, A. W. Structural effects on rates and equilibriums. J. Am. Chem. Soc. 1974, 96 (9), 2924. (12) Perry, R. H.; Green, D. W. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill: New York, 1998. (13) Dolfing, J.; Harrison, B. K. Gibbs free energy of formation of halogenated aromatic compound and their potential role as electron acceptors in anaerobic environments. EnViron. Sci. Technol. 1992, 26, 2213. (14) Haario, H. ModEst 6- A User’s Guide; ProfMath: Helsinki, 2007. (15) Hindmarsh, A. C. A Systematic Collection of ODE-Solver. In Scientific Computation; Stepleman, R., Eds.; IMACS: Amsterdam, 1983. (16) Wittig, R.; Lohmann, J.; Gmehling, J. Vapour-Liquid Equilibria by UNIFAC Group Contribution 6. Revision and Extension. Ind. Eng. Chem. Res. 2003, 42 (1), 183.
ReceiVed for reView December 22, 2009 ReVised manuscript receiVed March 15, 2010 Accepted March 21, 2010 IE902031D
