Kinetics of Transesterification of Soybean Oil

BIOCATALYSIS ARTICLES

H. Noureddini* and D. Zhu Department of Chemical Engineering, University oi Nebraska, Lincoln, Nebraska 68588-0126

ABSTRACT: Transesterification of soybean oil with methanol holysis, acidolysis, vinyl interchange, and ester-ester inrer- was investigated. Three stepwise and reversible reacttons are change contains many of the reported studies. believed to occur. The effect of variations in mixing intensity The transesterification kinetics for vegetable oils and fatty (Reynolds number = 3,100 to 12,400) and temperature (30 to esters has been reported in a few studies. Dufek and cowork- 70'CJ on the rate oireaction were studied while the molar ratio ers (10) studied the acid-catalyzed esterification and transes- of alcohol to triglycerol (6:l) and the concentration of catalyst terification of 9(1O)-carboxystearic acid and its mono- and di- (0.20 wt% based on soybean oil) were held constant. The variations in mixing intensity appear to effect the reaction parallel to methyl esters and reported unequal chemical reactivity for the variations in temperature. A reaction mechanism consisting different carboxyl and carboxymethyl groups. Freedman and of an initial mass transfer-controlled region followed by a kinet- conorkers (l) investigated both acid- and alkaline-catalyzed ically controlled region is proposed. The experimental data for transesterification of soybean oil with butanol and methanol. the latter region appear to be a good fit into a second-order ki- They determined the reaction rate constants as reaction param- netic mechanism. The reaction rate constants and the activa- eters such as temperature, molar ratio of alcohol to soybean tion energies were determined for all the forward and reverse oil, and catalyst type and concentration were varied. Gener- reactions. ally. a second-order reaction for all three reversible reactions lAOCS 74,1457-1463 (1997). provided a satisfactory mechanism. At a molar ratio of methanol to soybean oil of 61,a second-order mechanism KEY WORDS: Biodiesel, kinetics, methyl esters, mixing, re- with a fourth-order shunt mechanism best described the ki- newable fuels, soybean oil, transesterification. triglycerides. netics. Other kinetic studies include transesterification of CL8 unsaturated fatty acids contained in tall oil with methanol Over the last few years. fatty acid methyl esters have assumed (ll), acidolysis of castor oil with oleic acid (12). esterifica- importance as research has intensified on the utilization of tion of oleic acid with l-octanol using an immobilized en- vegetable oils and animal fats derivatives for liquid fuels, zyme on polymeric support (13), and the idealized kinetic known as biodiesel. Fatty acid methyl esters are products of model for the lipase-catalyzed interesterification of fats and the transesterification of fats and oils with alcohols in the oils (14). This model, which was based on an idealized sys- presence of an acid or an alkaline catalyst. Three consecutive tem of two fatty acids, provided a base to quantitatively study and reversible reactions are believed to occur (l). Mono- the role of minor components in these reactions. (MG) and diglycerides (DG) are the intermediates formed in A factor of particular importance in the transesterification these reactions. process is the degree of mixing between the alcohol and The variables affecting the transesterification process (also triglyceride (TG) phases. TG and alcohol phases are not mis- called alcoholysis) have been intensively investigated as cible and form two liquid layers upon their initial introduc- widening industrial uses were found for esters (2-6). Molar tion into the reactor. Mechanical mixing is normally applied ratio of alcohol to vegetable oil, type of catalyst, temperature, to increase the contact between the reactants, resulting in an and presence of impurities such as free fatty acids and mois- increase in mass transfer rate. Therefore, variations in mixing ture are among the variables that have been studied. intensity are expected to alter the kinetics of the transesterifi- There are a number of kinetic studies in the literature on cation reaction. the transesterification of esters with alcohol. However, only a .4lthough some type of mixing, mostly in the fonnof a me- few of these studies deal with vegetable oils and fatty esters. chanical stirrer. has been applied in all kinetic studies, the ef- The studies on the transesterification kinetics for nonfatty es- fect of mixing intensity on the kinetics of the reaction has not ters include: the determination of the reaction rate constants, been fully addressed. Better understanding of the mixing ef- the equilibrium constant, and the activation energy for the fects on the kinetics of the transesterification process will be acid-catalyzed reaction of butanol with ethyl acetate (7) and a valuable tool in process scale-up and design. ethanol with butyl acetate (8). .4 review by Sridharan and In this study, the effect of mixing on the kinetics of the Mathai (9) on the transesterification reactions involving alco- transesterification of soybean oil with methanol was investigated. The molar ratio of alcohol to TG and the concentration -To whom correspondence should be addressed. E-&. [email protected]. of catalyst (sodium hydroxide) were kept constant while tem-

"- Copyrigh! O 1997 by *ClCS Press .8 -27 JAOCS,Vol. 74, no. 11 (1 9971 1458 H hOLREDDINI AW0 ZHU perature and mixing intensity were varied. Kinetic data were propeller provided the mixing requirements. During the collected at three mixing intensities and five temperature lev- course of the experiment, samples were withdrawn with a 2- els. The temperature dependency of the reaction rate con- mL disposable pipette through an opening on top of the reac- stants and the activation energies were determined for all the tor. forward and reverse reactions. The dependency of the reac- Procediires. The reactor was initially charged with 200 g tion rate constants on mixing intensity was also investigated. of soybean oil.The reactor assembly was then placed in the circulating constant-temperature bath and heated to the desired temperature. Measured amount of the methanollsodium EXPERIMENTAL PROCEDURES hydroxide stock solution 144.3 g), which was heated sepa- Marerials. Refined and bleached soybean oils were obtained rately to the reaction temperature, was added to the reactor from Archer Daniels .Midland Company (Lincoln, NE). Free and the mechanical stirrer was started.The reaction was timed acid content of the oil was determined according to AOCS as soon as the mechanical stirrer was turned on. method #Ca 5a-40 (15) to be 0.09%. Certified methyl alcohol Sa~nplir~gn11d a~~nlysis.Samples were drawn at pre-speci- of 99.9% purity was purchased from Baxter Diagnostics Inc. fied time intervals. Approximately 15 samples were collected (McGrau Park, [L). Sodium hydroxide pellets of 98.2% pu- during the course of each reaction (90 min).The frequency of rity were purchased from Fisher Scientific Company (Pitts- sample collection varied and was dictated by the reaction con- burgh, PA). The high-performance liquid chromatograph ditions. Reactions at higher temperatures and mixing intensi- (HPLC) standards for methyl esters were obtained from ties required more frequent sampling at the beginning of the Sigma Chemical Company (St. Louis, MO). reaction. As the reaction temperature and mixing intensity A 0.907 wt9 stock solution of sodium hydroxide in were decreased, an initial delay in the reaction was experi- methanol was prepared and used in all of the reactions. A 6:l enced, and sample collection was delayed accordingly. This molar ratio of this stock solution with soybean oil amounted phenomenon is explained in later sections. Samples were to about 0.20 wt9 sodium hydroxide in soybean oil. taken at I- and 2-min intervals, early in the reaction, and at Reaction conditions. Experiments were designed to deter- 10- to 15-min intervals, later in the reaction. mine the reaction rate constants. A 6:1 molar ratio of alcohol Samples were collected in 10-mL test tubes filled with 4 to soybean oil, which is a typical ratio for transesterification mL of distilled water. The test tubes were kept in an ice bath of vegetable oils, was used in all experiments. To examine the at about 5°C prior to use. Samples (2 mL) were quenched in temperature dependency of the reaction rate constants, reac- the test tubes by placing them in the ice bath immediately tions at 30,40,50,60, and 70°C were studied. All reactions after removal from the reactor. The test tubes were then were carried out at atmospheric pressure. shaken to stop the reaction. Upon washing,glycerol (CL) and Three different mixing intensities were used to investigate sodium hydroxide are transferred to the water phase, and es- the effect of mixing on the kinetic behavior. The rotational ters and unreacted GL form a separate liquid layer. The lay- speed of the impeller was set at 150,300, and 600 rpm. The ers were then centrifuged at 1600 rpm for about 15 min to en- mixing intensity may also be presented by Reynolds number sure a thorough separation. (NRe). The irnpeller rotational speed and the NRe are related An HPLC (ISCO, Lincoln, NE), equipped with a model in Equation 1. 2350 pump and a refractive index detector, Refracto .Monitor IV (Thermal Separation Products. Riviera Beach, FL), was used for the analysis. Teniperature for the column was controlled with a circulating constant-temperature bath. Data col- where n is the rotational speed of the impeller, D" is the im- lection and analysis were performed with Hewlett-Packard peller diameter, and p and p are the fluid density and viscos- (Wilmington. DE) Chemstation Software. A Spherisorb OSD ity, respectively. The numerical values for NRe at the begin- 2 column (Phase Separation Inc., Norwalk, CT) (250 X 1.6 ning of the reactions were determined to be 3100.6200, and mm with 80 A pore size and 5 pm particle size) was used for 12,400 for rotational speed of 150,300, and 600. respectively. the separation. The HPLC mobile phase consisted of a 5050 There is a significant increase in NRe values as the reaction volumetric mixture of acetone and acetonitrile. The mobile progresses, which is primarily due to lower viscosity of the system was degassed for 15 min in an ultrasonic bath before products. ln the following sections when the mixing intensity use in the HPLC system. The HPLC pump operated at 0.70 is presented by NRe, it is referring to the start of the reaction. mLImin, and the column temperature was set at 35°C. Stan- Apparatus. A 1500-mL glass cylindrical reactor equipped dards for methyl esters, MG, DC, and TG were used to estab- with a mechanical stirrer, thermometer, built-in condensing lish the calibration charts. Csing these calibration charts. all coil, and sample port was used in all kinetic experiments. The the integration results were corrected for the weight percent- reactor was immersed in a constant-temperature circulating age of the individual components. bath, Mode! 1157 VWR Scientific (Philadelphia, TA) which Kinrric modeling. An hiLAB computer program (Civi- was capable of controlling the temperature to within 5 0.01"C lized Software Inc.. Washington, DC), which is a general, in- of the set point. A mechanical stirrer ;Model SL 1200, Fisher teractive system for mathematical and statistical modeling. Scientific (Fairlawn, NI) fitted with a stainless steel folding was used. MLAB can simultaneously fit multiple nonlinear

IAOCS, Vol. 74, no. 11 (1 9973 KINETICS OF TRANSESTERIFICATION 1459 functions, some or all of which may be implicit functions, or studies, MLAB was used for simultaneously fitting the sys- may even be defincd by a systcnl of differential equations. tem of differential equations, Equation 3, into the experimen- One of the central components of this system is a curve-fit- tal data. ring program which will adjust the parameters of a model One of the difficulties in the curve fitting of nonlinear ful~ctionto minimize the weighted sum of the emon raised to problems is that the solution may be nonunique and sepa- a specific power. rated. The surface which reflects the sum of squares may not Transesterification of TG with methanol, in the presence look like a bowl, a ir does in linear systems, but more like a of an alkaline catalyst, yields esters of fatty acids and CL. series of craters and gullies. Moreover, finding the bottom of MG and DC are the intermediates. The reaction steps are in one depression is no guarantee that it is the deepest depres- Equation 2 where k,-, are rate constants. sion. In nonlinear curvc fitting, the sum of squares value is usually a local minimum rather than a global minimum. Kow- ever, it is still a good measure of the goodness-of-fit, provided reciprocals of variances have been entered as weights. The choice of the initial estimates for the parameters also plays an important role in the curve-fitting path to alocal minimum. Therefore, in our fitting procedures many different combinations for the first estimates were chosen, and the final Overall reaction: results for the reaction rate constants are presented in terms of ranges rather than a single number. For some of the rate constants, this dependency is not significant and the range is fairly narrow, whereas for some, the dependency is signifi- The general form of the governing set of differential equa- cant.The final outputs from the curve-fit uhich determine the tions characterizing the stepwise reactions involved in the goodness-of-fit, such as the final sum of squares, the root- transesterification TG is in Equation 3. mean-square, and the determination coefficient (R'), were 5 practically identical for the given ranges. In other words, all ill TC I the values in the reported ranges are squally applicable to the -- --k,ITClIAl +~,IDCII&-I,ITCIIAIJ +I,IA]ICLIJ d1 rcaction kinetics. Acrivnriun ergerg?. Acdvation energies were estimated by an expression similar to the Arrhenius equation (Equation 4).

This expression, derived from the transition state theory. shows the temperature dependency of the reaction rate constant. For 71 = 0, this relationsl~ipreduces to the Arrhenius equation. Equation 4 results in different activation energies when the value of n is varied. Experimental values of the reaction rate constants and temperature were curve-fitted into Equation 4 for !I = 0 and I where A and E denote the alcohol and ester concentrations, at NRe= 6200 and 12,400.Table l shows that activation ener- respectively. In Equat~on3, for the case uirhout the shunt- re^ gies at both mixing intensities were consistent for a given action scheme, k7 and ks are set equal to zero. In our kinetic value of n. This was expected owing to the kinetically con-

TABLE l Enerev of Activation lcal/rnol) at Different Mi NRr = 6200 NR, = 12400 Reaction Arrheniurd Modified Arrheniurb ,Arrheniur Modiiied Arrheniur TC-DC 13,145 11,707 13,600 12.130 DC-rTC 9,932 8,482 9,783 8.313 DG-rMC 19,860 18,439 18,769 16,767 MG-rDC 14,639 13,433 11,177 9.710 MC-rCL 6,421 7,937 5,182 8,036 -CL-MC 9.588 10,992 9,873 11.365 "rrheniur equalion, k= Ae-"'". ?L

JAOCS, Vol. 73, no. 11 (19971 1460 H. NOUREDDlNl AND D. ZHU trolled mechanism. The activation energies ranged from about actants initially form a two-phase liquid system. The reaction 6400 to 20,000 callmol for the Arrhenius model. This range is diffusion-controlled and poor diffusion between the phases was narrowed to about 8000 to 18.500 callmol when the mod- results in a slow rate. As methyl esters are formed, they act as ified model with n = 1 was used. a mutual solvent for the reactants and a single phase system The results obtained in this study are consistent with the is formed. This was substantiated experimentally by taking experimental values of the acti~ationenergies reported in the samples in the slow rate region and subjecting them to grav- literature for other transesterification reactions (7-10). Freed- ity settling. Results revealed that samples taken very early man and coworkers (l) reported activation energies for the into the reaction separated into two phases. However, as sam- reactions involved in the transesterification of soybean oil to pling was continued, a single phase was observed at a time be in the range of 8M)O to 20,000 callmol based on the Arrhe- corresponding to the beginning of the sudden surge in the nius equation. timelconcentration diagram. Figure 2 summarizes this delay or slow rate region as a function of mixing intensity at a constant reaction temperature of 50°C. As expected, this lag time RESULTS AND DISCUSSION decreased as the mixing intensity was increased and reached Alkaline-catalyzed transesterification of soybean oil at three a constant value of about 1 to 2 min for NRc greater than mixing intensities and five temperatures were studied. The 10,000. This result supports the mass transfer controlled the- molar ratio of methanol to soybean oil was constant at 6: 1, ory during the initial stage of the reaction. and sodium hydroxide amounted to 0.2 wt% based on the Figure 2 also reveals that the mixing effect is most signifi- mass of the soybean oil. cant during the slow rate region of the reaction. As the single Transester~ficationreaction analysis. A typical concentra- phase is established, mixing becomes insignificant and the re- tion curve for the transesterification of soybean oil at 50°C is action rate is primarily intluenced by the reaction tempera- presented in Figure l. This figure shows the rate of consump- ture. This is clearly evident from the slope of the curves in tion of TG and formation of methyl esters and GL as well as Figure 2. One could easily overlap the kinetically controlled the intermediate compounds. regions of all three curves. Depletion of the reactants and for- Examination of Figure I reveals a sigmoidal curve for the mation of the products result in a more dominant reverse re- productional methyl esters and GL. This indicates a slow reaction later in the reaction. The final slou. region is formed action rate or delay at the beginning which is followed by a and eventually equilibrium is reached. Figure 2 reveals that sudden surge and finally a lower rate as the reaction ap- this region may also be overlapped at various mixing intensi- proaches completion. This is a typical behavior for autocat- ties and therefore is believed to be controlled by chemical re- alytic reactions or reactions with changing mechanisms. action. This also suggests that inhibition is not a factor, since Since the transesterification reaction of TG is not known to GL will have a tendency to phase-separate at low NR,. be an autocatalytic reaction, the second possibility was hy- Effect of te~f~perorfrre.Temperature dependency of the over- pothesized as a mass transfer controlled region (slow) fol- all reaction rate is presented in Figures 3 and 4 at two different lowed by a kinetically controlled region (fast) and a final slow mixing intensities. This dependency is similar to the effect of region as equilibrium is approached. This hypothesis will be mixing intensity and will ix analyzed separately for the previ- discussed in more detail and will be supported with experi- ously hypothesized mass transfer and kinetically controlled re- mental data in the following sections. gions. The time for the mass transfer region is shortened as Effect of mixing. In the transesterification reaction, the re- temperature is increased (Figs. 3 and 4) which may be due to

l - 1 -

S l l -5 40 U, ! (- l W - I ' ,. ,. 8 - S 20 L*' . 5 1.I l , ' . ! 0 20 40 60 80 100 0 mme (rnin) 0 10 40 60 80 100 T~rne(mm) FIG. 1. The composition of the reaction mixture during the transesteriii- cation oi soybean oil at 50°C and Reynoldr number IN& = 6200. (A, FIG. 2. The eiiect oi mixing intensity and time on the orjerall conver- trigiycerider; 1.1 methyi esters; (Xi digiycerider; (0)monoglycerider; sion to methyl esters at 50°C. 4;sRe = 3100; [A)NRe = 6200; l01 Nse (a)glyceroi. = 12400; (AI Ns, = 18600. See F~gure1 for abbreviation. KINETICS OF TRANSESTERIFiCATION 1461

esterification reactions is more favorable at higher tempera. tures (Figs. 3 and 4). This effect becomes minimal as temper. ature is increased and the overall conversion reaches an as- ymptotic value at about the boiling temperature of the alcohol (Fig. 4). Mechanism of transesterijication reaction. Freedman and coworkers (I)studied the kinetics of the acid- and alkaline- catalyzed transesterification of soybean oil with l-butanol and methanol at 30: 1 and 6: 1 molar ratios of alcohol to soybean oil. They proposed pseudo first-order kinetics at large molar excess uf alcohol and second-order kinetics combined with a shunt-reaction seheme at the lower alcohol excess level. In this study, a second-order reaction mechanism with and with- FIG. 3. The etiect of temperature and time on the overall conversion to out the shunt reaction was evaluated by mathematical model- methyl ester; at Nee =3100. (m)30°C: Ill 40"; (Ai50°C; 1.i 60°C; ing. In our kinetic modeling, the initial stage of the reaction (D':70°C. See Figure 1 ior abbreviation. was not included since it is short and is minimized at realistic temperatures and mixing intensities. For example, at 70°C and a high mixing speed of 600 rpm, time for the mass transfer-controlled region was practically nil. A total of l5 sets of experimental data were evaluated with both kinetic schemes. Figure 5 shows a typical fitting of the experimental results excluding the shunt mechanism. Reaction rate constants resultingfrom this curve fitting are tabulated in Table 2 together with the rare constants including the shunt mechanism. Bnarnination of the curve-fitting results showed good Kt of the lines to the experimental points in all cases. In- clusion of the shunt reaction did not improve the fit and the in- dicators which determine the goodness of the fit such as the final sum of squares, the root-mean-square, and R' were un- changed or less favorable. Furthermore, the values for the rate Time (min) constants, k, to k6, did not change significantly when the shunt FIG. 4. The effect oi temperature and time on the overall conversion :o mechanism was included, and the values fork, and k8 were methyl esters at NRe = 6200. (41 30°C; (A:40°C; (A)50°C; i.1 60°C; several orders of magnitude smaller than P, to k6.This was also (C,70°C. See Figure 1 for abbreviation. true when their significance in the rate equations was weighted against other terns rrsulting from k, to k6.Therefore, inclusion the higher energy state ofthe molecules resulting in more fruit- of a shunt mechanism to describe the transcstcrification kinet- ful collisions. Higher solubility of the reactants at elevated tem- ics is not necessary. peratures may also be partially responsible for this behavior. Mass transfer region is reduced from 55 to about 20 min as temperature is increased from 30 to 60°C at NRc = 3100 (Fig. 3). At higher mixing intensities. the mass transfer region is short and this effect is not significant (Fig. 4). In general, with multiple reactions, a high temperature favors the reaction of higher activation energy,and a low tem- pcrature favors the reaction of loweractivation energy. Table l lists the calculated activation energies for the three reversible reactions involved in the transesterification reactions. In the first two reactions (TG-DG and DG-MG) the energy of activation is higher for the forward reactions. Thus, higher temperatures should favor these reactions, and higher concentrations of MGare expected. However,for the third reaction !MG&+GL!. the foiwaid reaciion has a iower activa- Time fminl. . tion energy than the reverse reaction. Theoretically, this im~ FIG. 5. Kinetic modeling curves and experimental points ior the composi- plies a more favorable reaction at higher temperatures tion the mixture during the tranrejreriiication mybean oil at hi;:, appaxot!y, higher ioiiieniiations ofivic oifser this ei- 50'~and gRe= 6200. (+l Triglycerol; (0-1 mehyl esters; iE) diglycerids; iect and the Linetic-contmiied region for the combined trans- (01monaglycerider; (A)glycerol. See Figure 1 for abbreviation. 1462 H. hOLlREDDNI AND D. ZIiL;

TABLE 2 1.5 p--.-.-.- Averacc Constants at 511°C and N. 6200" " Reaction Rate S.? = Rate ronitarl LVithout shunt reaction With shunt reac!ion

~ -_ 0.5 .~'. kl 0.050 0.049 ':

1.58 X 1 0.' 'See Table 1 ior aDoreviation.

Rrnciion rnre consi~inrs.Reaction rates almost always increase with temperature for elementary irreversible reactions. FIG. 7. The !en;perature dependency of Lhe reaction rate constants a! NRz= 6200. (M) k,!Cl k?; (01k3; !A)kz: (A! k,; !Xi ti;. 4lultiple and reversible reactions do occasionally exhibit an optimal temperature with respect to the yield of a desired product. The optimal terrlperature is observed by a maximum creased. This was discussed earlier in terms of the energy of on a rate constant vs. temperature plot, or it may simply be activation. In terns of the reaction rate constants, the forward the highest temperature under investigation. Our objective reaction rare constant in the third reaction is reduced by only was to explore the temperature dependency of the reaction a factor of 2, whereas the reverse reaction is reduced by a fac- rate constant for the transrsterification reactions. tor of 10 as temperature is increased. This means a more fa- The kinetic modeling procedures using MLAB programs vorable forward reaction than [he reverse reaction in the third were presented earlier. The representative modeling results reaction at high temperatures. The overall formalion rate of for the rate constants at NRc= 12,400 are presented in Figure the desired product (methll esters) is also more favorable :I[ 6 as a function of temperature where the rate constants are higher reaction temperatures (Fig. 4). No optimal tempera- presented as a range indicated by venical lines and the legend ture \v35 de~ectedfor the reaction, and rhe highest ternpera- marks denote the average values. Rate constants for the first ture,7O0C, was the most favorable in the temperature range two reactions in Equation 2 increase with temperature for under investigation. both the forward and reverse reactions (Fig. 6). The rate of Variations in rate constants with terrlperalure at SRC= 6200 increase xas much faster for the forward reaction than the re- were practically ideritical (Fig. 7). This finding further con- verse reaction. For example, for the reaction of TGtlDG, for- firms the hypotheses of kinetically controlled mechanism for ward reaction rate was increased by a factor of about 14 while the transesterification reactions after the formation of the sin- the reverse reaction was increased only by a factor of about 7 gle phase. fa hen the temperature xas raised from 30 to 70°C. For the re- In conclusion, the concentration curve for the product action of DG-IMG, there was a 37-fold increase in the for- methyl esters and GL was sigmoidal. Based on a stepwise arid ward reaction with only an 11-fold increase in the reverse re- reversible reaction mechanism, the experimer~tal results action. Therefore, in reactions one and two, both forward re- clearly demonstrated an initial mass transfer-controlled reactions are favored at higher temperatures. In the third gion Xvhich was followed by a kinetic-controlled region. The reaction, MG-GL, Figure 6 shows an apparent decrease in inclusion of the shunt reaction mechanism did not appear to the reaction rate constants as the reaction temperature is in- be necessary. The results also suggest that the inhibition effect of CL is not a factor even in the later stages of the reaction. Results on the activation enerzies sugsest that. over the range investigated. Arrhenius kinetics for the forward reactions dorninntes.

ACKNOWLEDGMENTS The authors express their gratitude to U.S. Deparrment of Agricul- ture Cooperative Stare Research Services and the Ncbraska Soybean Board for their suppor. of rhis brork.

REFERENCES 2.9 3.0 3.1 . 3.2 3.3 (1~).103 1. Frrdmnn. B., R.O. Butterfield. 2nd E.H. Pryde.Transesteritica- tion Kinetics of Soybsan Oil. I. Am. Oil Chm~.Soc. FIG. 6. The temperature dependency oithe reaction rate cons tan!^ at 63:1375-1380 (1986). X3= = 12400. (Mi k;;(U! k:: (0;kj: (A) k4; (&! kj; !X kb. 2. Frtedm?:. B., E.E. Pryds. and T.L. ?.locnt:. Va~izb!.: Affzct-

IAOCS. Yal. 74, no. l l (1 997) KINETICS OF TRAi.rSESTiKIFICATlON 1463

in. the Yield of Fatty Esters from Transesterified Vegetable and Trnnsestcrificarion of 9(1O)-Carboxystearic Acid and [ls Oils, Ibid.61:1638-L643 (1984). Merhyl Esrers. Kinstic Studies. J. A,n. Oil Che,,,. sot. 3. Ahn. E., E. Koncar, M. Mittelbach, and R. Marr.A LowWaste 49302-306 (1972). Process for the Production of Biodiesel. Sen. Sci. Tech. 11. Solor'cb, V.V., B.N. Bychkov, G.N. Koshcl, and L.A. Ro~ 30:20?1-2033 (1995) divilova. Kinetics of Esterifieation of CIJ Unsaturated Fat[? 4. Kusv. P.F.. Transesterlfication of Vegetable 011s for Fuels. Pro- Acids by Methrl Alcohol. Zh~3:178-187(1974). 10. Dufek, E.J., R.O. Butterfield, and E.N. Frankel. Esterification [Received Dscemberj, 1996; accepted June 7, 1997)