Combined Hydrogenation and Isomerization Combined

chromatography and combined peak fitting. Diffusion limitations, even at low Thiele modulus, were found to have a significant impact on the product di...
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Ind. Eng. Chem. Res. 2005, 44, 9668-9675

Combined Hydrogenation and Isomerization Combined Hydrogenation and Isomerization under Diffusion Limiting Conditions Martijn M. P. Zieverink,* Michiel T. Kreutzer, Freek Kapteijn, and Jacob A. Moulijn Reactor and Catalysis Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands

Methyl oleate and methyl elaidate (two industrially relevant FAMEs, methyl esters of fatty acids) were hydrogenated in a batch slurry autoclave using a supported palladium catalyst. The mixture of reaction products formed as a result of the competitive reaction network of positional isomerization, geometrical isomerization, and hydrogenation were analyzed using gas chromatography and combined peak fitting. Diffusion limitations, even at low Thiele modulus, were found to have a significant impact on the product distribution. Depending on the starting material, either the cis or the trans double bonds apparently migrated faster along the carbon chain. Also, with increasing Thiele modulus, the conversion level at which cis-trans equilibrium was reached increased: if significant intraparticle gradients were present, the equilibrium was never reached. Several of these phenomena have previously been ascribed to different kinetics of the various isomers, which would stem from the differences in adsorption strength. For the experimental data of this work, mass transfer effects were found to satisfactorily account for the differences in product composition using a simple reaction-diffusion model for all the isomers involved, without needing to assume significant differences in adsorption strength. The result presented in this work gives fundamental insight into the product composition of fat hardening processes. Introduction Simultaneous processes occur during hydrogenation of unsaturated carbon-carbon bonds: double bonds can be saturated, migrate, or isomerize from cis to trans or vice versa. The age-old process of fat hydrogenation is a fine example of the importance of having control over these processes. The aims in fat hydrogenation are 2-fold: selective hydrogenation of poly-unsaturates toward mono-unsaturates, without formation of saturates while at the same time minimizing isomerization of cis to trans fats. Both saturated and trans fats are known to have an adverse influence on health,1 and there is increasing legislative pressure to control the levels of unwanted isomers in fat-based food products. Fats are triglycerides of fatty acids and glycerol. The fatty acids can be tri-, di-, or mono-unsaturated or completely saturated. The unsaturated fats can be in the cis or in the trans configuration. The large amount of possible combinations makes fats difficult to analyze. Moreover, fat molecules are large, making the reaction sensitive to the occurrence of diffusion limitations. Mechanistic research is better done using fatty acid methyl esters (FAMEs), which can be readily analyzed by gas chromatography. The aim of this contribution is to determine how kinetic aspects and diffusion limitations determine the detailed composition of partially hydrogenated FAMEs, without lumping groups of isomers. We choose two simple FAMEs, methyl 9 cis-octadecenoate (methyl oleate) and methyl 9 trans-octadecenoate (methyl elaidate) for our experiments. Our prime interest was to * Corresponding author e-mail: [email protected].

Figure 1. Simplified reaction scheme. Hydrogenation reactions have been omitted.

investigate if there are differences in the way trans and cis double bonds migrate and what influence mass transfer has on combined hydrogenation and isomerization reactions. Figure 1 schematically shows all 31 isomers of methyl octadecenoate and their isomerization reactions (each isomer can also be hydrogenated, but this is not shown in the figure). Experimental Section Catalyst. The catalyst was prepared by wet impregnation of a γ-alumina substrate using palladium acetate in toluene. The catalyst support was Puralox SBa-200 γ-alumina, with a mean pore size of 5-6 nm, BET surface area of 173 ( 3 m2 g-1, a porosity of 0.37 cm3 g-1 (0.57 cm3 cm-3), and an average particle size of 36 µm. After impregnation the catalyst was dried, followed by calcination and reduction in hydrogen at 453 K. The palladium surface area was determined with CO chemisorption using a Quantachrome Autosorb 1-C and was found to be 0.076 m2 g-1. From the theoretical palladium loading of 0.045 wt %, the palladium dispersion is estimated at 38%. Equipment. The hydrogenation experiments were carried out in a 500 mL batch slurry autoclave, equipped with baffles and a self-inducing stirrer. Temperature

10.1021/ie050287e CCC: $30.25 © 2005 American Chemical Society Published on Web 09/01/2005

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9669 Table 1. Assignment of Cis and Trans Species to Peaks in the Chromatogram peak

trans

1 2 3

4 5 6, 7, 8

4 5 6 7 8

9 10 11 12 13, 14

9 10 11 12 13 14 15

15

16

cis

reference

Christie,4 Scholfield5 Ratnayaka and Pelletier,6 Harrod et al.11 Kramer et al.8

6, 7, 8 Kramer et al.,8 Ackmann9 AOCS official method Ce 1f-963 Chrompack Application note 899 - GC10 9 10 Kramer et al.8 11 3,12 Christie,4 Scholfield5 13 14 Kramer et al.,8 Ackmann9 15

was controlled within 1 K and the pressure within 8 kPa. Samples were taken through a sample line and stored for later analysis. A total reaction volume of 270 mL was used. The reactant mixture consisted of 13 mol m-3 methyl oleate or elaidate (99+% pure, Sigma-Aldrich) in n-decane. The catalyst loading (cat) was 1.25 × 10-4 m3cat m-3 reac. Prior to the experiment, the autoclave was flushed three times with nitrogen at high stirrer speeds to remove all air from the system. After reaching the reaction temperature, hydrogen pressure was applied to the autoclave to a total pressure of 2.0 MPa. The hydrogen concentration under these conditions was estimated at 93 mol m-3, using a correlation given by Chaudhari et al.2 Analysis. The analysis of the reaction products was carried out on a Chrompack 9001 equipped with a 50 m × 0.25 mm × 0.2 mm CP-Sil 88 fused silica column and a flame ionization detector. A split ratio of approximately 1:200 was used. Depending on the conversion, between 1 and 4 µL of sample was injected. Helium was used as a carrier gas. The column pressure was maintained at 150 kPa, and the flowrate was 0.45 mL min-1. The column was operated isothermally at 443 K, and both the injector and detector were kept at 523 K. AOCS Official Method Ce 1f-963 recommends an operating temperature of 448 K, but we obtained slightly better separation at a lower temperature. The methyl esters of 6,9 and 11 trans-c18:1 and 6,7, 9,11 and 12-cis-c18:1 were purchased from SigmaAldrich and Alltech. It was found that the order of elution was 6,9,11 trans-c18:1, followed by 7,6,9,11,12 cis-c18:1. The elution of 7 cis-c18:1 before 6 cis-c18:1 on a CP-Sil 88 or similar column has also been observed by Christie.4 The resulting peaks could be described by Gaussian curves with a peak width of 0.034 min. It is well-established that the retention time increases as the double bond position is increased from the eighth to the 16th position for both the cis species4-6 and the trans species.6,7,8 6,7 and 8 cis-c18:1 are reported to be inseparable as are 6,7 and 8 trans-c18:1.4,5,6,8,9 17-c18:1 and 16 cis-c18:1 elute at the same time.4 16 trans-c18:1 and 14 cis-c18:1 elute at the same time8,9 as do 3 cisc18:1 and 12 cis-c18:1.4,5 6,7,8 cis-c18:1 and 12,13 transc18:1 show almost complete overlap.3,8-10 On the basis of the available literature, we analyzed our chromatograms by fitting them to 15 Gaussian curves using a least-squares method, each curve with

Figure 2. Typical gas chromatograph of reaction product. The numbers refer to the peaks in Table 1.

a peakwidth of 0.034 min. The specific retention time for each peak was determined either from the available model compounds or deduced from literature. A list of the peaks is given in Table 1 together with the relevant literature data. The numbers in boldface refer to internal standards used by us. Peaks for 2-3 trans-c18:1 were never observed as they probably disappear under the peak for methyl stearate. Peaks for 2,4 and 5 cisc18:1 should be somewhere below the lower trans peaks, but there is no indication as to where precisely. An example of a chromatogram and the results of the peak-fit are shown in Figure 2. Using the areas of the various peaks it becomes possible to calculate the distribution of the double bonds among the cis and trans species. Reactant Diffusivity. The effective diffusivities of methyl oleate and methyl elaidate were unknown and had to be estimated. Shieh and Lyons12 measured the diffusivity of hexadecane in n-octane and n-dodecane at 298 K and found D ) 5.7 × 10-10 and D ) 6.8 × 10-10 m2 s-1, respectively. Assuming a Stokes-Einstein dependency on temperature (D ∼ T/η) and a square root dependency on molecular mass (D ∼ M) we find that the diffusivity of c18:1 in n-decane at 373 K should lie between 1.7 × 10-9 and 1.9 × 10-9 m2 s-1. According to Yaws,13 the diffusivities of several cis and trans alkenes in water have the same value within 1%. Therefore, we assumed the diffusivity of both methyl oleate and methyl elaidate in n-decane at 373 K to be 1.8 × 10-9 m2 s-1. Results The results of the hydrogenation of methyl oleate and elaidate are shown in Figures 3 and 4. The conversion is defined as the total fraction of unsaturates that have been hydrogenated toward methyl stearate or

conversion )

t)0 C unsat - Csat t)0 Cunsat

(1)

The distribution of double bonds at three different conversion levels is given in Figure 3. For sake of clarity, the distributions have been normalized to 100%. As the conversion increases, the double bonds spread out over the carbon chain showing a slight preference for the end of the chain away from the ester group. When starting from oleate (cis), the trans double bonds spread out faster over the carbon chain. Conversely, starting from elaidate (trans), the cis double

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µ1,iso )

iCi,iso ∑ i)2 16

(2)

Ci,iso ∑ i)2 16

2 µ2,iso )

(i - µ1,iso)2Ci,iso ∑ i)2 16

(3)

Ci,iso ∑ i)2

Figure 3. Double bond distribution at different conversion levels, starting from methyl oleate (a) and methyl elaidate (b) (T ) 373 K and p ) 2.0 MPa).

Figure 4. Trans-cis ratio of ∆9 (×), ∆10 (4), ∆11 (0), and ∆12 (]), starting from methyl oleate (a) and methyl elaidate (b) (T ) 373 K and p ) 2.0 MPa). Dashed line for thermodynamic equilibrium.

bonds spread out faster. The mean and the width of the distributions evaluated using the first and second moment of the distribution, as calculated by

in which iso is either cis or trans. Several of the GC peaks overlap. For those peaks, we have assumed for simplicity that all contributing isomers contribute to the peak with equal weight. This introduces some error, and the moments have to be interpreted with some care. In Figure 5, the second central moment (standard deviation) of the distributions of the cis and trans isomers is plotted as a function of conversion. When the cis isomer was the starting material, the trans distribution was much wider than the cis distribution. In an experiment with a trans isomer as starting material, the width of the distributions were comparable. In Figure 4, the trans-cis ratios of various positions of the double bond are plotted versus conversion. The rate at which equilibrium is reached is dependent on the location of the double bond: in Figure 4a, the ∆10 double bond approaches trans-cis equilibrium faster than the ∆9 double bond. At high conversions the trans-cis ratio of ∆9 and ∆10 appear to be moving away from equilibrium. One explanation could be that the equilibrium ratio at 373 is lower than 3.8. but this is clearly contradicted by the available literature. Van der Plank14 suggested that a change in the reaction orders of hydrogenation and isomerization at high conversions could be responsible for this behavior. Since our reaction system was very diluted the surface coverage of the unsaturates could not significantly have changed during the experiments. Most likely it is an artifact due to unresolved peaks resulting in skewed values of the trans-cis ratio. 10 cis and 15 trans overlap in the chromatogram so at high conversions the ratio (10 trans)/(10 cis) becomes (10 trans)/(10 cis + 15 trans), lowering its actual value. Moreover, starting with methyl elaidate this phenomenon is absent. The high trans-cis value of ∆12 (>3.8) could be due to contribution of underlying 4 and 5 cis peaks to 12 trans peaks. Diffusion Limitations. The measured initial rate (rv,obs) for the experiments shown in Figures 3 and 4 was approximately 39 mol m3cat s-1. Using eq 4 we calculated the Weisz-Prater number (Φ) to determine whether internal diffusion limitations of the reactant were present during reaction:

Φ)

()

dp 6 DeffC

rv,obs

2

(4)

Correcting for catalyst porosity and tortuosity, the effective diffusivity of the reactants in n-decane is approximately 1.8 × 10-10 m2 s-1. Using this value we calculate Φ ∼ 0.58, which indicates that diffusion interferes with the reaction. Given the high hydrogen

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the cis-trans ratio from a parameter fit of kinetic rate expressions. Both found the equilibrium constant to be independent of pressure and decrease slightly with temperature (∆Hiso ≈ -2.5 kJ mol-1). Other authors used thiyl radicals prepared by γ-radiolysis to reversibly attack the double bonds of methyl oleate and dioleoyl phosphatidyl choline (DOPC).18-20 The available literature data are summarized in Figure 8. The combined experimental datapoints were correlated using the following expression:

ln Ktc )

Figure 5. Standard deviation of the distribution of positional isomers on the C18-chain: (a) starting from the ∆9 cis isomer; (b) starting from the ∆9 trans isomer.

Figure 6. Influence of catalyst activity on trans-cis equilibrium during methyl oleate hydrogenation (T ) 373 K and p ) 2.0 MPa): Φ e 1 (4), Φ ) 7 (O), and Φ ) 50 (]). Dashed line for thermodynamic equilibrium.

concentration (93 mol m-3) and given that hydrogen will have a higher effective diffusivity due to its small size, we can assume that hydrogen concentration profiles were absent. The influence of internal diffusion limitations on the overall trans-cis ratio was investigated by using identical catalysts with varying palladium loading to hydrogenate methyl oleate. Figure 6 shows that the transcis ratio at a given conversion is dependent on the Weisz-Prater number (Φ) (eq 4), which is a measure for the severity of diffusion limitations. Discussion Cis-Trans Equilibrium. Literature on the transcis equilibrium is surprisingly scarce. Litchfield et al.15 used catalysts over which the isomerization is fast as compared to the hydrogenation. Using both selenium and HNO2 as catalyst, they determined that an equilibrium mixture contains 75-80% elaidic acid and 2025% oleic acid. Gut et al.16 and Grau et al.17 determined

-∆Hiso ∆S + RT R

(5)

with ∆S ) 4.42 J mol-1 K-1 and ∆Hiso ) -2.46 kJ mol-1 and is represented by the solid line in Figure 8. The difference in the formation enthalpy was also measured by calorimetry for both the acids and the methyl esters by Rogers and Siddiqui21 and Rogers et al.22 and found to be around -4 kJ mol-1, which is slightly higher than our fit of the available literature data. Using eq 5, we calculate that the trans-cis equilibrium of 9-c18:1 at 373 K is approximately 3.8. According to Gunstone et al.,23 this value is independent of the position of the double bond save the ∆2 position. In our own experiments, we have found that the overall cis-trans ratio approaches 3.8, as indicated in Figure 4 and Figure 6 at 373 K. It is difficult to determine whether equilibrium has really been established in an experiment. Note that the equilibrium constant could only be determined directly by the experiment that was least affected by diffusion limitations, where the measured value reaches a stable value at high conversion. The obtained value of 3.8 is in good agreement with the available literature data. Positional Equilibrium. There is even less experimental data for the positional equilibria along the carbon chain than for the overall cis-trans equilibria. Isbell et al.24 used an acidic clay to produce estolides from oleic acid and as a side-reaction protonated double bonds migrated over the carbon chain. They reported a cis-trans equilibrium value of 1.3, which is substantially lower than the value we would obtain by extrapolating Figure 8. Therefore, it is doubtful if trans-cis equilibrium was obtained by Isbell et al.24 This holds even more so for positional equilibrium, which takes longer to establish because it involves a much longer chain of reactions. The data presented by Isbell et al.24 are nevertheless useful: a more or less equal distribution of double bonds around the original ∆9 position was observed, with a slight preference toward the end of the carbon chain away from the acid group. Brown and Swidler25 reported an almost even distribution of double bonds around the ∆9 position on octadecenoic acid after prolonged exposure to an acidic catalyst at high temperature. In this work, the hydrogenation was too fast to allow an equilibrium for the double-bond shift reactions to establish; the “width” of the distribution of the cis and trans isomers was still increasing as the hydrogenation neared completion. The middle ∆9 position appears to be the most favorable with a more or less symmetrical distribution of the other double bond positions with a slight preference toward the end of the carbon chain. In this respect, an experiment starting from the ∆12 position was especially useful. Figure 7 shows that at high conversion the mean of the distribution over the

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Figure 7. Mean of the distribution of positional cis isomers in an experiment starting with ∆12-cis.

Figure 8. Trans-cis equilibrium constant of ∆9-c18:1 as a function of temperature. (1) Litchfield et al.;15 (2) Chatgilialoglu et al.;18 (3) Adhikari et al.;20 (4) Chatgilialoglu et al.;19 (5) Gut et al.;16 (6) Grau et al.;17 (7) Gunstone et al.23 Dotted line as calculated by Mu¨nzing.26

chain tended to the ∆9 position, away from the starting ∆12. Although reactive experiments such as those performed in this work and by Isbell et al.24 never reach full positional equilibrium, the ∆12 experiment shows that the favorable position is close to ∆9 or ∆10. Observed Different Bond-Shift Rates for Cis and Trans Species. From a mechanistic point of view, several simultaneous processes take place during hydrogenation of FAMEs: double bonds can saturate, migrate, or isomerize from cis to trans or vice versa. We assume that hydrogen dissociates upon absorption the active sites, and we consider the elementary reactions of adsorbed FAME species with the hydrogen atoms on neighboring sites. Chemisorption of an unsaturated carbon bond can be accompanied by either abstraction of a hydrogen atom or by the insertion of a hydrogen atom. The former leads to the formation of the so-called allylic π-complex, the latter to the half-hydrogenated state or σ-complex. Since allylic π-complexation requires a hydrogen atom to be abstracted, one expects that this mechanism is feasible at low hydrogen coverage of the active site (i.e., at low hydrogen pressure). At high hydrogen pressure, hydrogen atoms are abundant at the catalytic surface, and the formation of σ-complexes is more likely. In the σ-complex, free rotation of the double bond becomes possible, and subsequent removal of an hydrogen atom results overall in a cis-trans isomerization Analogously, subsequent removal of hydrogen from an adjacent carbon atom results overall in a positional isomerization The insertion of a second hydrogen is assumed to be the rate-limiting step for hydrogenation. In the half-hydrogenated state, there is no longer a

difference between trans and cis (i.e., the adsorbed molecule no longer contains information concerning its previous state). As a consequence, both the hydrogenation and the double bond migration rates should be equal for both species. When a π-complex is formed, geometrical isomerization will always coincide with positional isomerization. Two cis and two trans π-complexes can be formed (see Figure 9). Dutton et al.27 first reported apparent faster migration of trans double bonds when hydrogenating methyl oleate over palladium- and platinum-supported catalysts. Similar observations were made by Van der Plank14,28 and Van der Plank and Van Oosten29 for silica-supported nickel catalysts. They all found that starting from both oleate and elaidate trans double bonds migrated faster than cis double bonds. The experiments by Van der Plank were carried out at atmospheric pressure where one would expect more formation of allylic π-complexes as compared to our experiments at 2.0 MPa. However, at higher pressure we essentially observed a similar result: the trans species spead out faster over the carbon-chain, provided we start with a cis isomer. On the basis of the spatial arrangement of these intermediate complexes, Van der Plank and Van Oosten29 argued that the steric stability of these π-complexes decreases in the order of IV > III g II > I. Consequently, the rate of positional isomerization of trans double bonds will be larger than of cis double bonds. In other words, the observed faster spreading of the double bonds over the chain was interpreted purely kinetically. The results that were obtained in this work cannot fully be explained with the kinetic arguments used by Van der Plank and Van Oosten.29 We observed that starting from a cis isomer the positional isomerization of trans components appeared faster, while starting from a trans isomer we did not observe a wider distribution for the trans components. If the kinetic argument would hold, then we would have observed the faster migration of the trans components, irrespective of the starting isomer. The results presented in Figure 6 indicate that the observed cis-trans reaction rates are strongly related to diffusional limitations, and we discuss below the effect of diffusion limitations on the observed rate of positional isomerization. Effects of Diffusion Limitations. To investigate the effect of diffusion limitations on a system that combines hydrogenation, positional, and geometrical isomerization, a model was developed that combined reaction and diffusion. The reaction scheme is given in Figure 1 and shows the positional and geometrical hydrogenation reactions. The hydrogenation reactions have been omitted from this figure for sake of clarity. For this model a number of simplifying assumptions were made: • The trans-cis equilibrium is equal for all positions of the double bond (∆2 through ∆16) (Ktc ) 3.8). • At equilibrium the double bonds are distributed equally across the carbon chain (Kp ) 1). The ∆12 experiment showed that this is not exactly true, but assuming an equal distribution simplifies the modeling and still allows the model to demonstrate the effect of diffusion. • Hydrogen is not limiting (i.e., there are no hydrogen gradients inside the catalyst).

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Figure 9. Adsorbed allylic π-complexes; top half from cis, bottom half from trans monoenes.29

• All reactions are first order in the concentration of double bonds. • The double bond hydrogenation rate constant (kH), the geometrical isomerization rate constant (ktc), and the positional isomerization rate constant (kp) are equal. (This implies that the trans and cis double bond migration rates are equal.) For the cis and trans species, the following rate equations were defined:

ri,cis ) (-2kp - ktcKtc - kh)Ci cis + kp(Ci-1 cis + Ci+1 cis) + ktcCi trans (6) ri,trans ) (-2kp - ktc - kh)Ci trans + kp(Ci-1 trans + Ci+1 trans) + ktcKtcCi cis (7) where i ) 2-16. For 2 trans and 2 cis, the equations are reduced since there is neither 1 cis nor 1 trans. Likewise for the 17-c18:1 where the double bond is at the end of the carbon chain. This results in a total of 31 rate equations. For modeling of a batch slurry reactor, the following reaction/diffusion equation inside a spherical particle was solved for each component:

Deff

(

)

∂2C 2 ∂C + -r)0 z ∂z ∂z2

(8)

with boundary conditions z ) 0, ∂C/∂z ) 0, and z ) dp/2, C ) Cbulk. The change in bulk concentration of each component in the reactor is given by

∂Cbulk ∂C 6 ) - catDeff |z)dp/2 ∂t dp ∂z

(9)

We assumed the concentration of hydrogen throughout the particle to be equal to the bulk concentration. The extent of diffusion limitations of the reactants can be expressed with the Thiele modulus defined by

φ)

x

dp 6

k Deff

(10)

Results of the modeling are shown in Figures 10 and 11, starting respectively from oleate and elaidate. When diffusion limitations are absent, equilibrium is reached at the same rate for all positions of the double bond. This is the line marked “kinetic” in the graphs. However

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Figure 10. Modeling results starting from methyl oleate. Dashed lines give trans-cis ratio of ∆9, ∆10, ∆11, and ∆12 under diffusion limiting conditions. Solid lines give overall trans-cis ratio for kinetic and diffusion limiting conditions (a, φ ) 0.19; b, φ ) 0.60).

and increasingly higher for ∆10, ∆11, and ∆12. In Figure 11 the reversed is seen and the cis double bonds appear to move faster! The effect of φ ) 0.19 on the observed hydrogenation rate is negligible: the catalyst effectiveness is still higher than 98%. The modeling results indicate that even weak diffusion limitations will mask any intrinsic difference between trans and cis double bonds. Globally the modeling results confirm our experimental results: the apparent faster double bond shift of either trans or cis double bonds, depending on the starting material, is caused by diffusion limitations. On the basis of our experimental results, we can therefore not conclude that an intrinsic differense between trans and cis double bonds exists. The overall effect of diffusion limitations is that the trans-cis equilibrium is approached slower than under kinetically controlled conditions (Figures 10 and 11), which confirms our observations in Figure 6. Note that it is still possible that a kinetic contribution as proposed by Van Der Plank exists for FAME, but its presence is significantly masked by even minute diffusion limitations. The only way to determine if the kinetic effect exists would be to carry out experiments under fully kinetically controlled conditions (i.e., by using very minute catalyst particles or decreasing the amount of active material inside the catalyst). Decreasing the operating pressure to decrease the rate would be another option. However, this would run the risk of hydrogen becoming the limiting reactant with could have unforseen consequenses. Intraparticle gradients caused by diffusion limitations can account for all the observations made in this work, in addition to a kinetic effect. Conclusions

Figure 11. Modeling results starting from methyl elaidate. Dashed lines give trans-cis ratio of ∆9, ∆10, ∆11, and ∆12 under diffusion limiting conditions. Solid lines give overall trans-cis ratio for kinetic and diffusion limiting conditions (a, φ ) 0.19; b, φ ) 0.60).

even at a low value for φ a significant effect can be seen: in Figure 10 the trans double bonds appear to move faster resulting in lower trans-cis ratio for ∆9

The interplay of diffusion and reaction in a complex network of 31 isomers has been studied experimentally. Mixtures of fatty acid methyl esters were analyzed with a method that allowed the determination of the concentration of positional and geometrical isomers formed during the hydrogenation of methyl oleate or methyl elaidate. The results indicate that even mild diffusion limitations, with Thiele moduli of the order of 1, significantly altered the product distribution in comparison to kinetic limitations. First, a trend was observed between the Thiele modulus and the rate at which the cis-trans equilibrium establishes. Second, under diffusion-limiting conditions either trans or cis double bonds were found to migrate faster over the carbon chain depending on the reactant used. Modeling showed large effects on the apparent rate of double shift even under mildly limiting conditions. Modeling of the reaction network under diffusion-limited conditions indicated that mass tranfer limitations are a more likely explanation for the detailed product composition in fat hardening than previously reported kinetic arguments. Although the kinetic effect, based on different adsorption strengths of different isomers, may still be present, an experiment that used a trans isomer as starting material showed that mass transfer effects obscure such kinetic effects. Nomenclature FAME ) fatty acid methyl ester methyl oleate ) methyl 9 cis-octadecenoate methyl elaidate ) methyl 9 trans-octadecenoate

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9675 methyl stearate ) methyl octadecanoate c18:1 ) methyl octadecenoate ∆9 ) double bond on position 9 C ) concentration, mol m3 D ) diffusivity, m2 s-1 Deff ) effective diffusivity, m2 s-1 dp ) catalyst particle diameter, m ∆Hiso ) enthalpy of isomerization, J mol-1 kH ) hydrogenation rate constant, s-1 ktc ) trans-cis isomerization rate constant, s-1 kp ) positional isomerization rate constant, s-1 Kp ) positional equilibium constant, dimensionless Ktc ) trans-cis equilibrium constant, dimensionless M ) molecular weight, g mol-1 p ) pressure, MPa -1 r ) rate, mol m-3 cat s R ) gas constant, 8.314 J mol-1 K-1 -1 rv,obs ) observed rate, mol m-3 cat s ∆S ) entropy of isomerization, J mol-1 K-1 T ) temperature, K -3 cat ) catalyst loading, m3cat mreactor Φ ) Weisz-Prater number, dimensionless φ ) Thiele modulus, dimensionless η ) viscosity, Pa s µ1 ) first moment, dimensionless µ22 ) second moment, dimensionless

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Received for review March 1, 2005 Revised manuscript received June 3, 2005 Accepted June 9, 2005 IE050287E