Influence of the Axial Dispersion on the Performance of Tubular

3000 Santa Fe, Argentina. ReceiVed April 27, 2006. ReVised Manuscript ReceiVed August 4, 2006. Transesterification of fats and oils by methanol is kno...
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Influence of the Axial Dispersion on the Performance of Tubular Reactors during the Noncatalytic Supercritical Transesterification of Triglycerides Mariana Busto, Silvana A. D’Ippolito, Juan C. Yori, Marisa E. Iturria, Carlos L. Pieck, Javier M. Grau, and Carlos R. Vera* Instituto de InVestigaciones en Cata´ lisis y Petroquı´mica (FIQ-UNL, CONICET), Santiago del Estero 2654, 3000 Santa Fe, Argentina ReceiVed April 27, 2006. ReVised Manuscript ReceiVed August 4, 2006

Transesterification of fats and oils by methanol is known to proceed by a three-step consecutive reaction mechanism in which the formation of the diglyceride is the rate-limiting step. At low conversion values ( 240 °C).9-15 Methanol in the supercritical state has the mobility of a gas and such an enhanced reactivity that the reaction proceeds without the aid of any catalyst. This noncatalytic system has some advantages over the reacting system catalyzed by alkalis or acids: (i) the reacting system is monophasic; (ii) catalyst addition, catalyst neutralization, and catalyst removal steps can be eliminated; (iii) the reaction tolerates fairly big concentrations of water and proceeds independently of the amount of free fatty acids in the feed. The latter is specially important because the cheaper feedstocks are usually those containing high concentrations of free fatty acids and they cannot be directly processed by the alkali catalyzed method. The usual implementation of the supercritical process uses only a one batch discontinuous reactor charged with a triglyceride and methanol, an R value of 42, pressures higher than 7 MPa, and temperatures in the 250-350 °C range. The addition of cosolvents has been attempted in order to alleviate (3) Dasari, M. A.; Goff, M. J.; Supes, G. J. Am. Oil Chem. Soc. 2003, 80, 189-192. (4) Noureddini, H.; Harkey, D.; Medikonduru, V. J. Am. Oil Chem. Soc. 1998, 75, 1775-1783. (5) Srivastava, A.; Prasad, R. Renewable Sustainable Energy ReV. 2000, 4, 111-133. (6) Ma, F.; Clements, L. D.; Hanna, M. A. Bioresour. Technol. 1999, 69, 289-293. (7) Boocock, D. G. B.; Konar, S. K.; Mao, V.; Lee, C.; Buligan, S. J. Am. Oil Chem. Soc. 1998, 75, 1167. (8) Boocock, D. G. US Patent 6,712,867, 2000. (9) Sasaki, T.; Suzuki, T.; Okada, F. US Patent 6,187,939, 2000. (10) Keiichi, T.; Guo-Tang, L. European Patent 1,061,120, 2000. (11) Warabi, Y.; Kusdiana, D.; Saka, S. Bioresour. Technol. 2004, 91, 283-287. (12) Kusdiana, D.; Saka, S. Fuel 2001, 80, 693-698. (13) Saka, S.; Kusdiana, D. Fuel, 2001, 80, 225-231. (14) Demirbas, A. Energy ConVers. Manage. 2003, 44, 2093-2109. (15) Kusdiana, D.; Saka, S. Bioresour. Technol. 2004, 91, 289-295.

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the high temperature and pressure conditions. These cosolvents, e.g., CO2 or propane,16,17 allow the onset of a one-phase system under milder conditions though the system still needs relatively high pressure and temperatures to react spontaneously. Other researchers have proposed performing the reaction in two steps in order to use lower R values and decrease the total pressure.18 It must be remarked that the continuous operation of supercritical transesterification reactors was initially considered of low feasibility due to the high excess of methanol needed.19 However, recent reports implement the continuous production of fatty acid methyl esters (FAME) with one-reactor20 and tworeactors setups.18 In ref 20, the authors recommended the use of a tubular reactor with perforated plates. In the examples provided by the authors, the reactions were also carried out at relatively high space velocities despite the resulting low residence times and low conversion values. These factors may indicate that the continuous operation of supercritical reactors is affected by backmixing phenomena. In fact, the molecular diffusivity of methanol in the subcritical range is about 0.000 05 cm2 seg-1, while in the supercritical state this value is 100 times higher.21 The effect of backmixing on the performance of tubular reactors performing the supercritical, noncatalytic transesterification of triglycerides, in one-reactor and two-reactor setups, is studied in this work. The problem of one- and two-phase formation in MeOH-TG systems is also revisited. A focus is put on the consequences for the production of fuel-grade biodiesel in noncatalytic reactors. Experimental Section Miscibility of the FAME-MeOH-TG System. The miscibility of the FAME-MeOH-TG system was studied at 40 °C and atmospheric pressure. A MeOH-TG solution with a given R value (R ) methanol/oil molar ratio ) 3, 6, 10, 15, and 20) was first prepared and put in a flask. The flask was immersed in a thermostatic oil bath with a 40 °C temperature setpoint. The solution was gently stirred while FAME (methyl soyate) was added dropwise from a buret. From time to time, the addition of FAME was stopped and the solution was left unstirred for 15 min. Then, the formation of one or two phases was detected by visual inspection. When one homogeneous phase was formed, the global composition of the FAME-MeOH-TG solution was taken down. Methanol (99.9+%) was supplied by Dorwill. The triglycerides mixture (TG) was a commercial grade refined soy oil provided by COTO SACIF. Fatty acid methyl esters (FAMEs) were prepared by alkaline transesterification of soy oil following a two-step reaction procedure described elsewhere.22 The fuel was thoroughly washed and centrifuged until no free glycerol was detected by the method of Plank and Lorbeer.23 Water and methanol traces were eliminated by stripping with nitrogen. This gas was bubbled in the FAME sample at 110 °C for 1 h, and then, the FAME sample was kept in a previously dried flask for further use. Pressure-Temperature Curves. Pressure-temperature equilibrium curves were determined in a microautoclave of low thermal (16) Cao, W.; Han, H.; Zhang, J. Fuel 2005, 84, 347-351. (17) Han, H.; Cao, W.; Zhang, J. Process Biochem. 2005, 40, 31483151. (18) Vera, C. R.; D’Ippolito, S. A.; Pieck, C. L.; Parera, J. M. Proceedings of the 2nd Mercosur Congress on Chemical Engineering, ENPROMER 2005, Rı´o de Janeiro, Brazil, 2005; p 245. (19) Minami, E.; Ehara, K.; Kusdiana, D.; Saka, S. Proceedings of the 5th International Biomass Conference of the Americas, Orlando, Florida, 2001. (20) Goto, V.; Sasaki, T.; Takagi, K. US Patent 6,812,359, 2004. (21) Asahi, N.; Nakamura, Y. J. Chem. Phys. 1998, 109, 9879-9887. (22) Jeong, G.-T.; Park, D.-H.; Kang, C.-H. Appl. Biochem. Biotechnol. 2004, 116, 113-116. (23) Plank, C.; Lorbeer, E. J. Chromatogr., A 1995, 697, 461-468.

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Busto et al.

inertia (32 mL internal volume, length/diameter ) 7.5). A low thermal inertia was needed for enabling a relatively fast and steady heating rate of 5-10 °C min-1, from room temperature to 300 °C. It was considered that at temperatures lower than the critical temperature of methanol (Tc ) 238 °C) no reaction occurred due to the low reactivity of subcritical methanol and the little time elapsed from the beginning of the heating. At temperatures higher than Tc, the noncatalytic tranesterification was started but the degree of conversion during the heating ramp was assumed to be negligible because of the fast heating. Therefore, the pressure of the system was assumed to be that of the MeOH-TG mixture only. P-T curves were obtained for mixtures of MeOH:TG ) 6, 10, and 15. The procedure was repeated for one-phase mixtures of FAMEMeOH-TG of R ) 6, 10, and 15 and of minimum FAME content. The pressure was measured with a precision Cimpa Bourdon in the 0.1-20 MPa range. Mathematical Modeling. The model described by eqs 5-7 was solved by an algorithm of finite differences with a mesh of variable density. The asymptotic models (plug flow, Pe f ∞; perfectly mixed, Pe f 0) at steady state correspond to systems described by total derivatives and initial conditions, and they were solved with an algorithm of variable step integration of the predictor-corrector type. All programs were written and run in the Matlab 6 for Windows environment. The whole reaction network described by eqs 1-3 was considered. Forward and inverse reactions for each reaction were modeled using a second-order model in which the reaction rate was proportional to the product of the concentration of each reactant or product. For example for the TG species, dCTG ) k1CTGCMeOH - k2CFAMECDG dt

Figure 1. Comparison of kinetic constants k1 of the second-order kinetic model dCTG/dt ) -k1CTGCMeOH: (b) noncatalytic, subcritical; (9) noncatalytic, supercritical;8,9 (2) catalytic, subcritical (NaOH 0.1 N 2).

(10)

It has been extensively reported that the first reaction proceeds at a slower rate than the second and the third, so it was considered for simplicity that the formation of the digliceryde was the limiting step of the three-reaction network and that the other reactions were in equilibrium. The equilibrium constants were taken from the work of Noureddini and Zhu.2 It has been shown that transesterification equilibrium constants show only a negligible dependence on temperature24 and that they are also nearly independent of solvent and salt effects.25 With these assumptions, the kinetic model was fully determined with the knowledge of the value of k1 as a function of the temperature. This value was fitted from data reported elsewhere, in the form of pseudo-first-order constants.13,14

Results and Discussion Figure 1 contains the Arrhenius plots of the k1 constant for one catalytic and another noncatalytic system. The noncatalytic data set corresponds to that reported by Saka et al.13 for R ) 42 that is the most detailed one available in the open literature. The kinetic data of the alkali catalyzed system corresponds to the report by Noureddini and Zhu.2 It can be seen that the reaction rate of a homogeneous alkali catalyzed system, which is one of the fastest TG-MeOH reacting systems, can be equalled by the reaction rate of a similar system working in supercritical conditions with no catalyst, provided that the temperature is high enough to activate the carboxyl bond and that the pressure is high enough to maintain the supercritical state (Pc ) 7.84 MPa). Two Arrhenius plots can be distinguished for the noncatalytic system, the subcritical one and the supercritical one. The limit between the two zones in the data of Saka et al.13 is not exactly the critical temperature of methanol, and the last points of the subcritical, slow kinetics regime have a temperature slightly superior to 240 °C. For this reason, the (24) Kimmel, T. Doctoral Thesis, Technischen Universita¨t Berlin, 2004. (25) Pereira, W.; Close, V.; Patton, W. J. Org. Chem. 1969, 34, 20322034.

Figure 2. Composition of homogeneous solutions MeOH-TG-FAME of minimum cosolvent (FAME) content as a function of the MeOH/ TG molar ratio (R).

region between 235 and 275 °C has been shaded to indicate that this can be considered as a “transition” zone. Figure 2 contains compositional data of one-phase mixtures of FAME-MeOH- TG of different R values. When no FAME is added to a MeOH-TG mixture, the system shows two immiscible phases. If energetically stirred, the two-layer mixture turns into an emulsion. The stability of this emulsion was found to depend on R. At higher R values, the emulsion was more stable. Under the conditions of the experiments, the emulsion was broken if stirring was stopped and the formation of two layers was always achieved though it took longer times at higher R values. When FAME was added to the MeOH-TG mixture, it was confirmed that FAME acts as a cosolvent. The cosolvent effect is weaker than that reported for other smaller molecules, e.g., tetrahydrofuran.7 The formation of a homogeneous solution occurs upon the addition of 36% (vol/vol) of FAME for an R value of 6. This percentage has another more important interpretation. The degree of conversion of a MeOH-TG mixture should also be of about 36% (R ) 6) in order to break the emulsion and form one phase. This is valid both for stirred tank reactors and for tubular reactors. The consequence for processes working with two or more consecutive stirred tank reactors26 is obvious; the first reactor must be operated at conversion values higher than 36% to eliminate mass transfer limitations. For continuous tubular reactors with no recycle, the consequence is that an emulsion regime of a low effective reaction rate is unavoidable at low conversion values. Similar (26) Hamilton, C. Biofuels made easy; Lurgi Life Science Technical Brochure, 2004.

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Table 1. Selected Values of the Molecular Diffusivity of Methanol in the Subcritical and Supercritical States as Reported by Asahi and Nakamura21 from NMR Measurements diffusivity, ×10-5 cm2 seg-1

temperature, °C

reduced density

408 438 423 192 229 70 89 1.9 4.5

236 253 298 233 298 240 307 15 67

0.183 0.183 0.183 0.372 0.372 1.0 1.0 1.0 1.0

conclusions are obtained for other R values. A practical remark is that when performing a transesterification reaction at subcritical conditions in the absence of cosolvents or FAME recycle, it is convenient to work with a first stage composed of a stirred tank reactor working with a conversion high enough to produce total miscibility of the FAME-MeOH-TG mixture. Under supercritical conditions as it was explained in the Introduction, a homogeneous system is formed. The molecular diffusivity of the reacting species is altered by the enhanced mobility of methanol. There is no available data of the diffusivity of TG, FAME, Gly, and glycerides in supercritical methanol, but it can be deduced that the diffusivity is enhanced significantly. In this work in order to estimate the effect of the supercritical condition on the backmixing in tubular reactors, the diffusivity of the species will conservatively be approximated to that of supercritical methanol in order to calculate this effect under the worst conditions. Diffusivity values of supercritical methanol do not abound. The most accurate values are those based on NMR measurements. The values reported by Asahi and Nakamura21 that correspond to the pressure and temperature ranges of noncatalytic supercritical reactors for biodiesel production are included in Table 1. The authors reported both NMR and molecular dynamics (MD) results for MeOH from the subcritical range up to the supercritical region. They made a chemical shift study of MeOH from 289 to 580 K and at reduced densities Fr (Fr ) F/Fc, Fc ) 272 kg m-3) between 0.183 and 1.008. They concluded that the experimental self-diffusion coefficients observed in the supercritical region were in good agreement with those calculated from MD simulations and via the Chapman-Enskog (CE) kinetic theory. Their MD simulations have also shown that hydrogen-bonded clusters of MeOH are chainlike and that the number of molecules in the clusters decreases with increasing temperature and decreasing density. In the case of supercritical reactors with the autogenous pressure (closed system) of this work, the pressure and temperature varied between 250 and 300 °C and 7-15 MPa (Figure 3). In these ranges, the diffusivity of methanol varies between 0.002 and 0.005 cm2 seg-1. Conservatively, the upper value was taken for all calculations. The autogenous pressure of supercritical reactors is a function of the temperature, R, and the concentration of cosolvents, if any. Values of this autogenous pressure measured in the microautoclave are plotted in Figure 3. In the case of an open system, continuous reactors, the pressure can be reduced by regulating the backpressure downstream of the reactor. The autogenous pressure increases at higher R values and higher temperatures. In the absence of FAME (cosolvent) at low temperatures, two phases coexist and the vapor pressure of the MeOH-TG mixture is the sum of the vapor pressure of methanol and that of the triglyceride (negligible). For this reason, it can be seen that in the subcritical range the pressure of the MeOH-TG system for R ) 10 coincides with the vapor

Figure 3. Pressure-temperature traces of MeOH-TG-FAME and MeOH-TG closed systems of different R values.

Figure 4. Conversion at 275 °C and R ) 6 as a function of the residence time and the axial Pe´clet number.

pressure of pure methanol as predicted by the Antoine equation. The curves for R ) 6 and 15 coincided with the curve for R ) 6. For R ) 42 (data taken from scientific literature and patent reports), a small positive deviation can be seen in the subcritical range but this is clearly an experimental error. In the case of the pressure of the FAME-MeOH-TG one-phase system, the curve for R ) 10 was plotted for comparison. The curve is below Antoine’s curve in the subcritical range because now the pressure of the system is that of a homogeneous solution and the net effect of FAME addition is to depress the total pressure because of the lower pressure of FAME with respect to MeOH. It can be confirmed from the P-T traces of Figure 3 that the pressure varies in the 7-15 MPa range at supercritical temperatures for R ) 6-20. For the analysis of the effect of backmixing, some numerical solutions to the system of differential equations with axial diffusion terms are first presented in Figures 4 and 5 as a function of the residence time of the reacting mixture inside the supercritical reactor at two different reaction temperatures. The kinetic rate constant used is that fitted in Figure 1, and the reacting mixture of the simulation is MeOH-TG with no intermediate or final products (zero conversion feedstock). To discuss these results, values should be first established for the desired conversion and the residence time. In biodiesel production processes, it is important to achieve an almost complete conversion because the quality standard for this fuel establishes a maximum content of total glycerol (free and bound, Gly + TG + DG + MG) of 0.24%.27 If it is supposed that all the bound glycerol is in the form of TG and that the concentration (27) ASTM D6751 Norm.

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Figure 5. Conversion at 300 °C and R ) 6 as a function of the residence time and the axial Pe´clet number.

of DG and MG is negligible, then the minimum conversion should be approximately 99.8%. With respect to the residence time, it can be seen from scientific reports and industrial patents that values close to 1 h are typical of alkali catalyzed systems.2 Much higher residence times are needed in acid catalyzed transesterification due to slow kinetics.28 In supercritical reactors, the residence time can amount to a few minutes, but if longer residence times are needed, they should not be greater than 1-1.5 h due to the inconvenience of high reactor volumes at the high pressure and temperature of the reaction. The results of Figures 4 and 5 indicate in the first place that at relatively small molar ratios of R ) 6-10 conversion is not close to being complete and therefore the reaction must be performed in two steps. Nearly complete conversion in one reaction step has been reported to be feasible if R is equal to or greater than 40.13 Raising the temperature reduces the residence time needed to achieve a certain value of conversion. However, high reaction temperatures are not desirable because they produce high pressures in the reactor and increase the operative costs related to pumping and the fixed costs related to manufacturing of the vessels. Axial dispersion increases the residence time values needed for a given conversion. At 300 °C, a Pe value of 50 is enough to ensure that these effects are negligible. At 275 °C, the lower reactivity demands longer reaction times and Pe values equal or higher than 100 are needed to achieve near plug-flow behavior. In case a one-reactor setup is used, the conversion of the reactor must be higher than 99%. Figure 6 contains isoconversion plots linking residence time values, and the R molar ratio, for a conversion of 99% and different values of axial Pe and reaction temperature. The needed residence time to achieve 99% shows a strong dependence on the reaction temperature (Tr) and a weaker dependence on the Pe number. High temperatures and high Pe numbers improve the performance of the reactor. Pe values lower than 100 can increase the residence times by a factor of 2-4. At Tr ) 250 °C, R must be higher than 30 and Pe equal or higher than 100 to enable minimun residence times lower than 2 h. From another point of view, if a low Pe value is unavoidable because of process conditions, the R value and the temperature must be increased to permit suitable residence times. Figure 6 shows that, in one-reactor setups, when the reaction is performed with low Pe values, a large residence time is needed to achieve a high conversion grade. If the residence time (28) Lotero, E.; Liu, Y.; Lopez, D. E.; Suwannakarn, K.; Bruce, D. A.; Goodwin, J. G., Jr. Ind. Eng. Chem. Res. 2005, 44, 5353-5363.

Busto et al.

Figure 6. Isoconversion (99%) curves linking the residence time and R, at different temperatures and values of the axial Pe´clet number.

Figure 7. Conversion at 300 °C and R ) 6 as a function of the residence time and the axial Pe´clet number: (feedstock) oil phase with a conversion of 85%, glycerol free; CTG ) 97 mol m-3.

needs to be decreased, the R value must be increased. For Pe ) 100, a value for which backmixing is less important, an almost total conversion can be obtained if the reactor is operated at Tr ) 300 °C with a moderate residence time. If the reaction is performed at Tr ) 250 °C, very high R values and residence times are needed to achieve nearly complete conversion. At this temperature, it seems unavoidable to adopt a solution like that suggested in ref 20, i.e., eliminating first glycerol and excess methanol, then separating FAME from glycerides, and finally recycling this fraction to the transesterification reactor. This solution is expensive from a process viewpoint because it requires the operation of a vacuum distillation column (pressure < 10 mmHg) with a very high recycle to the reactor. In any case, a residence time of 0.2-1 h should be adopted in order to limit the reactor volume and a value of Pe > 100 to perform the reaction efficiently. Lower Pe values would demand the use of more severe process conditions, i.e., higher temperatures and R values. With regards to the results presented in ref 20, it seems evident that though the Pe number adopted is adequate, the low residence time has been compensated with a very high R value () 50). As it has been previously pointed out,18 high R values increase the costs related to the evaporation of the excess methanol remaining after the reaction. In Figures 7-9, conversion values are plotted related to the reaction performed in two tubular reactor working in series with intermediate glycerol removal. It is supposed that an 85% conversion is achieved in the first reactor. It can be seen that conversion values equal to or higher than that needed to satisfy the quality standard can now be obtained with R > 10 and with residence times of 1 h, provided that the value of the axial Pe number is higher than 100. Particularly, the results of Figure 7

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If now we analyze the practical consequence of imposing minimum Pe values and minimum residence time values to achieve 99+% conversion values, these are related to relatively high minimum reactor lengths. Pe values much greater than 100, e.g., Pe ) 100-1000 are desirable. For example, for Pe ) 1000 and τ ) 2 h, applying the definition of residence time and axial Pe number, the minimum reactor length obtained is 2 m. This is not limiting for industrial reactors, but it may prove inconvenient for laboratory reactors used for the study of transesterification reactors carried out in the supercritical range.

Figure 8. Conversion at 250 °C as a function of R and the axial Pe´clet number: (residence time) 1 h; (feedstock) oil phase with a conversion of 85%, glycerol free.

Figure 9. Conversion at 250 °C and R ) 10 as a function of the residence time and the axial Pe´clet number: (feedstock) oil phase with a conversion of 85%, glycerol free.

show that for transesterification reactors working with Pe < 5 it is impossible to reach the value indicated by the norm unless R values higher than 30 are used. If the results of Figure 3 are recalled, increasing R increases the total pressure very rapidly and so also the costs related to pumping and to the construction of pipes and vessels.

τ ) L/u ) 2 h

(11)

Pe ) uL/DM ) L2/(DMτ) g 1000

(12)

Lg2m

(13)

Conclusions The molecular diffusivity of supercritical methanol can be as high as 0.005 cm2 seg-1. To dimminish the adverse effects of backmixing on the conversion of tubular transesterification reactors using supercritical methanol, the Pe number should be in the range 100-1000. Residence time values should also be equal or lower than 1 h, and therefore, axial lengths cannot be lower than 2 m if high conversion values are needed. This is not limiting for industrial reactors but may prove cumbersome for pilot studies of supercritical transesterification in laboratory reactors. Backmixing at low values of the Pe´clet number decreases the global conversion. In the case of the production of biodiesel, which demands conversion values higher than 99%, such low Pe conditions might need one of the following solutions: (i) an increase of the temperature and the methanol:oil ratio; (ii) the use of 1 reactor coupled to a step of separation of unreacted glycerides which are then recycled to the reactor; (iii) the use of two or more reactors in series, with intermediate separation of glycerol. Acknowledgment. This work was performed with the financial support of Universidad Nacional del Litoral through a CAI+D 2002 grant (Project 20-146). EF060184O