Kinetic Modeling of Limonene Epoxidation over PW-Amberlite

Ind. Eng. Chem. Res. 2009, 48, 647–653

647

Kinetic Modeling of Limonene Epoxidation over PW-Amberlite Rolando Barrera Zapata,* Aı´da L. Villa, and Consuelo Montes de Correa Departamento de Ingenierıá Quı´mica, UniVersidad de Antioquia, Calle 67 No. 53 · 108, Medellıń, Colombia

The kinetics of limonene epoxidation catalyzed by PW-Amberlite under triphasic conditions is described. A mechanistic pathway was postulated, and a heterogeneous kinetic model was derived following pseudostationary-state theory. Using adsorption parameters that were estimated from independent binary adsorption experiments, the resulting kinetic model fitted the experimental data quite well. 1. Introduction Limonene epoxide has traditionally been used as a precursor for the synthesis of perfumes, drugs, and food additives. Currently, there is a growing interest in limonene epoxide because biodegradable polymers can be obtained by coupling of trans-limonene epoxide with CO2.1 Several alternative heterogeneous catalytic systems have been reported to diminish the negative effects of processes that use environmentally unacceptable stoichiometric amounts of peracids.2-5 For example, limonene conversions and selectivities higher than 80% and 90%, respectively, can be achieved under mild reaction conditions (24 h, 38 °C) with hydrogen peroxide as the oxidant (eq 16,7) over PW-Amberlite, a catalyst obtained by the immobilization of a phosphotungstate complex on a commercial macroreticular ion-exchange resin. acetonitrile/PW-amberlite

C10H16 + H2O2 98 C10H16O + H2O

(1)

Because of the low solubility of aqueous hydrogen peroxide in limonene, a solvent is required to obtain high epoxide yields. When more than 82 wt % acetonitrile is added to the reaction mixture, a homogeneous liquid phase is obtained. Thus, the biphasic system consists of a liquid phase and a solid catalyst. Following the Langmuir-Hinshelwood formalism, a kinetic model for the epoxidation of limonene over PW-Amberlite under biphasic conditions was previously reported.7 A kinetic expression with an apparent activation energy of 76 kJ/mol was obtained considering the adsorption of the reactants and the solvent on the catalytic surface. However, when the concentration of acetonitrile is lower than 82 wt %, a triphasic system, consisting of two liquid phases and a solid phase, is formed. Through an analysis of both the aqueous and organic phases, the effects of the temperature and the concentrations of limonene, hydrogen peroxide, catalyst, water, and acetonitrile on limonene epoxidation and hydrogen peroxide decomposition rate were determined for the triphasic system. Several pseudohomogeneous models based on the empirical power-law approach were proposed in terms of concentrations and activities.8 Under triphasic conditions, the apparent activation energies found for limonene epoxidation and hydrogen peroxide decomposition were 25 and 100 kJ/mol, respectively. Because PW-Amberlite deactivates as limonene epoxide is formed, the pseudohomogeneous model proposed for the triphasic system adequately describes the system only for short reaction times. Therefore, an empirical first-order deactivation factor that accounts for catalyst deactivation was considered in * To whom correspondence should be addressed. Tel.: (57) (4) 2196606. Fax (57) (4) 2196609. E-mail: [email protected].

the proposed model9 to fit the data for the reaction over time. The resulting design equation for limonene epoxidation on PWAmberlite under triphasic conditions in a batch reactor was9 W dX ) k[C10H16]0a+b(1 - X)a(2 - X)b [a* + (1 - a*) × dt NL0 exp(-kdt)] (2) where k is the specific reaction rate constant; [C10H16]0 is the initial limonene concentration; a and b are the reaction orders with respect to limonene and hydrogen peroxide, respectively; W is the mass of catalyst; NL0 is the initial number of moles of limonene; a* is the residual activity; kd is the deactivation constant; and t is the time.9 Although the proposed pseudohomogeneous model for the triphasic system8 adequately fits the experimental data, when it is modified with the empirical deactivation term,9 it does not describe the adsorption phenomena on the catalytic surface. Furthermore, to simulate the system using Aspen Plus software, it is necessary to employ additional Excel or Fortran subroutines, including the time-dependent terms of eq 2.10 Thus, it would be desirable to develop an adsorption-based model that adequately describes the heterogeneous epoxidation of limonene over PW-Amberlite under triphasic conditions. Song and co-workers studied the kinetics of methyl acetate over ion-exchange resins.11 They obtained adsorption equilibrium constants from independent binary nonreactive adsorption experiments and proposed five adjustable parameters.11 The parameters were the specific reaction rate constant and four adsorption equilibrium constants. Three of the adsorption equilibrium constants were expressed as a function of the fourth. The composite isotherms describing the adsorption phenomena on the catalytic system are represented by the equation n0∆X nS(K2,1a1X2 - a2 X1) ) m K2,1a1 + a2

(3)

where n0 corresponds to the total initial number of moles in the liquid phase; ∆X is the change in the mole fraction in the liquid phase; m is the mass of the catalyst; nS is the number of moles adsorbed per unit mass of solid, assumed to be constant for all the binary mixtures investigated;11 and ai and Xi are the liquidphase activity and the molar fraction of component i in the binary experiment, respectively. Ki,j is the equilibrium constant ratio of two independent adsorption tests. Although the model of Song and co-workers fits the experimental data quite well for the methyl acetate reaction, Po¨pken and co-workers12 suggested that it should be modified because the assumption of constant number of moles adsorbed is not appropriate. Through swelling tests, Po¨pken and co-workers

10.1021/ie800822n CCC: $40.75  2009 American Chemical Society Published on Web 12/17/2008

648 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 Table 1. Initial Compositions, Equilibrium Compositions, and Activity Coefficients of the Studied Binary Pairs Water + Limonene run

dry catalyst (g)

water (g)

limonene (g)

water mass fractiona

water activity coefficient, γ

limonene activity coefficient, γ

1 2 3 4 5 6 7 8

0.0557 0.0538 0.0598 0.0482 0.0611 0.0538 0.0509 0.0462

0.1089 0.1515 0.2055 0.2495 0.3001 0.3570 0.4042 0.4556

0.4049 0.3509 0.3015 0.2519 0.2013 0.1519 0.1049 0.0533

0.0299 0.0849 0.2236 0.3608 0.5412 0.6786 0.7592 0.9209

72.636 18.924 3.9262 1.9836 1.2963 1.0001 1.0001 1.0001

1.1398 2.0600 15.509 123.20 1602.1 385478 385478 385478

Water + Limonene Epoxide run

dry catalyst (g)

water (g)

limonene epoxide (g)



limonene epoxide activity coefficient, γ

9 10 11 12

0.0499 0.0533 0.064 0.0512

0.0510 0.2004 0.2548 0.3058

0.4604 0.3149 0.2529 0.2026

0.0953 0.3632 0.5510 0.6953

9.5979 1.7607 1.2276 1.0804

2.0992 81.278 976.84 5659.9

Water + Acetonitrile run

dry catalyst (g)

water (g)

acetonitrile (g)



acetonitrile activity coefficient, γ

13 14 15 16 17 18 19 20 21

0.0459 0.0485 0.0508 0.0548 0.0655 0.0609 0.0471 0.0677 0.0689

0.0534 0.0970 0.1519 0.2139 0.2611 0.3299 0.3482 0.4068 0.4596

0.4487 0.4025 0.3493 0.3034 0.2522 0.2002 0.1532 0.1012 0.0496

0.1421 0.1967 0.2885 0.3908 0.4956 0.6267 0.7013 0.8291 0.9684

3.1129 2.4843 1.8686 1.4979 1.2815 1.2841 1.0757 1.0221 1.0007

1.1570 1.2842 1.5777 2.0402 2.7025 3.9028 4.8383 7.0489 10.732

Water + Hydrogen Peroxide run

dry catalyst (g)

water (g)

hydrogen peroxide (g)



hydrogen peroxide activity coefficient, γ

22 23 24 25 26

0.0422 0.0488 0.0598 0.0495 0.0466

0.4788 0.4403 0.4220 0.3913 0.3539

0.0320 0.0607 0.0926 0.1225 0.1517

0.9606 0.9118 0.8570 0.8018 0.7476

1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000

Limonene + Acetonitrile run

dry catalyst (g)

limonene (g)

acetonitrile (g)

limonene mass fractiona



27 28 29 30 31 32 33

0.0465 0.0470 0.0443 0.0520 0.0468 0.0462 0.0597

0.0482 0.1010 0.1519 0.1989 0.2473 0.3009 0.3495

0.4488 0.3984 0.3507 0.2992 0.2492 0.2014 0.1520

0.0603 0.1801 0.2767 0.3999 0.5255 0.6675 0.7174

7.5559 6.5240 5.6796 4.6153 3.5838 2.8163 2.2118

1.0006 1.0069 1.0195 1.0532 1.1259 1.2446 1.4481

Limonene + Limonene Epoxide run

dry catalyst (g)

limonene (g)


limonene mass fractiona



34 35 36 37 38 39

0.0557 0.0508 0.0796 0.0523 0.0486 0.0532

0.0465 0.1037 0.1500 0.2018 0.2515 0.3010

0.4504 0.3999 0.3537 0.3008 0.2512 0.2020

0.0893 0.2005 0.2923 0.3969 0.4962 0.5972

1.0464 1.0357 1.0280 1.0204 1.0143 1.0091

1.0005 1.0024 1.0051 1.0096 1.0151 1.0220

Acetonitrile + Limonene Epoxide run

dry catalyst (g)

acetonitrile (g)


acetonitrile mass fractiona



40 41 42 43 44

0.0423 0.0425 0.0453 0.0532 0.0546

0.0496 0.1457 0.2493 0.3505 0.4519

0.4461 0.3497 0.3551 0.1495 0.0507

0.0766 0.3017 0.4408 0.7136 0.8823

2.2139 1.1638 1.0606 1.0063 1.0001

1.1223 1.7622 2.1448 2.7244 2.9461

a

Equilibrium value.

demonstrated that the numbers of moles of water and methyl acetate adsorbed at 25 °C on Amberlyst 15 differ by up to 1

order of magnitude. Therefore, they suggested assuming a constant adsorbed mass per gram of catalyst instead of a constant

Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 649

Figure 1. Possible structures of the anions (a) [PW4O16]3-and (b) [PW4O20]3-, S (adapted from ref 16), and (c) the polyoxoperoxophosphotungstate complex [PO4[WO(O2)2]4]3-, S1.15,17,18

Figure 2. Mechanistic pathway for limonene epoxidation over PWAmberlite, adapted from ref 7. Table 2. Results of Swelling Experiments with Pure Components8

component water limonene acetonitrile limonene epoxide

swellinga (%)

adsorbed volumeb (mL g-1)

adsorbed massc (g g-1)

adsorbed mmol (mmol g-1)

45.5 9.1 6.8 1.5

0.0204 0.0041 0.0030 0.0007

0.0204 0.0034 0.0024 0.0006

1.1335 0.0252 0.0578 0.0037

a Swelling experiments were carried out with 0.1 g of catalyst at 25 °C. b Adsorbed volumes were calculated assuming that each microsphere of the resin adsorbs the same volume. c Catalyst density ) 2.23 g mL-1.

number of adsorbed moles. The composite isotherms proposed by Po¨pken and co-workers are given by12 m0(W 01 - W L1 ) mS K1a1W L2 - K2a2W L1 ) mcat mcat 1 + K1a1 + K2a2

(4)

where the subscripts 1 and 2 are arbitrarily assigned to the components of the binary pair, m0 is the total liquid weight, mS is the total adsorbed mass, mcat is the weight of catalyst, W0i is the overall weight fraction, and WLi is the equilibrium liquidphase weight fraction. K is the equilibrium adsorption constant. Consequently, the adsorption equilibrium constants can be obtained from eq 4 rather than being obtained as adjustable parameters in the kinetic data fit. Nevertheless, eq 4 has three adjustable parameters (mS/mcat, K1, and K2) in contrast to the two adjustable parameters in eq 3 (nS and K2,1). Po¨pken and co-workers found that the parameter mS/mcat obtained with eq 4 is between 2 and 4 times higher than the values obtained from swelling experiments. This difference was ascribed to the increase in the resin swelling when a liquid mixture is used

Figure 3. Comparison between experimental and predicted (eq 3) data for relative liquid adsorption over PW-Amberlite at 25 °C for the binary mixtures (a) water + limonene (R2 ) 0.84), (b) water + limonene epoxide (R2 ) 0.99), (c) water + acetonitrile (R2 ) 0.96), and (d) water + hydrogen peroxide (R2 ) 1.0).

instead of a pure solvent, but it is not a general rule.8,13 The data for the esterification of acetic acid with methanol over ion-

650 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 Table 3. Relative Adsorption Equilibrium Constants with Respect to the Adsorption Equilibrium Constant of Water Ki,5 i

Ki,5

nS adsorbed (mol/g of catalyst)

limonene hydrogen peroxide acetonitrile limonene epoxide

9.50 1.39 0.09 0.067

0.10 0.02 0.01 0.07

Table 4. Model Discrimination and Parameter Estimation of Several Kinetic Expressions for Limonene Epoxidation under Triphasic Conditions parameter KL KP KSolv KE KW k3 k4 R2 SSR F probe a

model A 34.09 0.427 9.360 0.006 0.139 3.988 6.921 0.412 0.055 0.595

model B a

1.805 0.265a 0.017a 0.013a 0.190 220.0 0.220 0.998 0.024 0.804

model C 19.00a 12.50a 1.097a 3.09 × 10-5 a 0.212a 197.0 0.210 0.998 0.008 0.850

Obtained from experimental adsorption equilibrium probes.

exchange resins were well reproduced with eq 4, with all of the adsorption constants obtained independently of the kinetic fit.12 The aim of this article is to propose a mechanistic pathway for limonene epoxidation under triphasic conditions and derive a kinetic expression describing the adsorption phenomena from pseudo-stationary-state theory. The mechanistic pathway is similar to that proposed for the biphasic system.7 Other steps included in the mechanism are hydrogen peroxide decomposition on the catalytic surface, desorption of the products from the catalytic surface, and water adsorption on the catalyst. Nonlinear regression and independent binary adsorption experiments were used for parameter estimation. The models were discriminated by statistical approaches and Aspen modeling. For comparison purposes, we adopted both the Song et al.11 and Po¨pken et al.12 models for limonene epoxidation over PW-Amberlite. 2. Experimental Section All commercial products were used without further purification. They included (R)-(+)-limonene (97 wt %, Aldrich), aqueous hydrogen peroxide (30 wt %, J. T. Baker), acetonitrile (99.5 wt %, Merck), Amberlite IRA-900 ionic form chloride (Sigma), tungstic acid (99 wt %, Aldrich), tetrabutylammonium hydrogen sulfate (97 wt %, Aldrich), phosphoric acid (85 wt %, Merck), and sodium nitrate (95 wt %, Merck). PW-Amberlite was synthesized as reported elsewhere.6,7 The desired particle size was obtained by grinding the Amberlite IRA-900 resin before converting it to its nitrated form. The reactions were carried out in 8-mL magnetically stirred glass flasks immersed in a temperature-controlled oil bath (33.0 ( 0.5 °C). A stirring speed of >1000 rpm and a catalyst particle diameter of acetonitrile > limonene > limonene epoxide. The nonreactive binary pairs used in the adsorption experiments were (1) water + limonene, (2) water + limonene epoxide, (3) water + acetonitrile, (4) water + hydrogen peroxide, (5) limonene + acetonitrile, (6) limonene + limonene epoxide, and (7) acetonitrile + limonene epoxide. Binary adsorption experiments were not performed with hydrogen peroxide + limonene and limonene epoxide + acetonitrile because of their reactive nature, leading to the spontaneous decomposition of hydrogen peroxide into water and oxygen. 2.1. Activity Coefficients. The activity coefficients, γi, required for the determination of the activity, ai at different mole fractions, Xi ai ) γi Xi

species including OH groups and water in their structures, such as {PO4[WO(O2)2]2[WO(O2)2(H2O)]}3- and {PO3(OH)[WO(O2)2]2}3-.18 Therefore, the mechanism we propose here for limonene epoxidation includes the following elementary steps: (i) The peroxo PW anion, [PW4O16]3- or [PW4O20]3-, S, interacts with hydrogen peroxide and forms the polyperoxophosphotungstate complex [PO4[WO(O2)2]4]3-, S1 (Figure 2, eq 6). (ii) Limonene diffuses into PW-Amberlite and adsorbs on the complex (eq 7). (iii) The reaction takes place through transfer of an oxygen atom (eq 8). (iv) The products are desorbed, and the active site S is regenerated (eq 9). Under triphasic conditions, the decomposition of hydrogen peroxide into water and molecular oxygen at 33 °C and short reaction times is mainly due to catalytic effects (eq 10).8 Also, the resin swells in the presence of water and acetonitrile.8 Additionally, even though water and acetonitrile can adsorb on the catalyst, it appears that there is no interaction of water or acetonitrile with the catalytic active sites, as the rates of neither epoxidation nor hydrogen peroxide decomposition decrease with water or acetonitrile concentration.8 Moreover, the difference between the molecular sizes and chemical characteristics of limonene and water or acetonitrile make competition for the catalytic active sites less probable. Therefore, we assume that acetonitrile (eq 11) and water (eq 12) are adsorbed on sites S but not on the S1 catalytic active sites. k1

H2O2 + S a S1 k-1

(5)

were estimated with Aspen Plus (2004.1) software and the modified UNIFAC-DMD group contribution method, which does not require additional adjustable parameters. For the binary mixture water + hydrogen peroxide, ideal behavior was assumed because of the similar physicochemical properties of the two compounds. The activity coefficients were calculated for each component over the entire range of compositions used in the adsorption experiments. 3. Results and Discussion 3.1. Development of a Kinetic Model. Several polyoxometalate and polyperoxometalate species with general structure [PmWnOo(O2)p]x-, such as [PW4O16]3- 15,16 and [PW4O20]3- 17 (Figure 1), have been detected for the catalytic system PW/H2O2;15 moreover, it is also possible to find

(6)

k2

S1 + C10H16 a S1•C10H16 k-2

k3

S1•C10H16 98 S1•products

(7) (8)

k4

S1•products a C10H16O + H2O + S k-4

k5 1 S1 98 S + H2O + O2(g) 2

(9) (10)

k6

CH3CN + S a CH3CN•S k-6

(11)

k7

H2O + S a H2O•S k-7

(12)

652 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009

Following pseudo-stationary-state theory19 and assuming that the surface reactions are the controlling steps, the limonene reaction rate, -rL, can be expressed by the equation

(

-rL ) k3KPKLCT[H2O2][C10H16] ⁄ 1 + KP[H2O2] + KPKL[H2O2][C10H16] +

k3KPKL [H2O2][C10H16] + k4

)

1 [H O][C10H16O] + Ksolv[CH3CN] + KW[H2O] (13) KE 2 where the adsorption equilibrium constants are defined as KP ) k1/k-1, KL ) k2/k-2, Ksolv ) k6/k-6, and KW ) k7/k-7 for hydrogen peroxide, limonene, solvent and water, respectively. KE ) k4/k-4 is the desorption equilibrium constant for limonene epoxide (1/KE is the limonene epoxide adsorption constant), and CT is the total concentration of sites on the catalytic surface. Equation 13 contains seven adjustable parameters: the forward reaction constant of limonene epoxidation (k3), the forward desorption constant of the products (k4), and the five adsorption equilibrium constants. These kinetic parameters were determined by minimization of the objective function, FO, shown in eq 14 with the optimization toolbox “slqnonlin” of Matlab 6.0. The experimental kinetic data, -rL,experimental, corresponds to the initial reaction rate data previously reported.8 Convergence difficulties can be solved when reaction data are used to obtain the parameters of models as in eq 13.11 FO )

∑ [(-r

L,experimental) - (-rL,calculated) i

]2

(14)

i

In the present work, the subscripts 1-5 correspond to limonene, hydrogen peroxide, acetonitrile, limonene epoxide, and water, respectively. The adsorption equilibrium constants, Ki, in eq 13 were determined considering water as the reference component, KL ) (K1,5KW); KP ) (K2,5KW); Ksolv ) (K3,5KW), and KE ) (K4,5KW). The Ki,5 parameters were obtained from regression of the data from Table 1 in eq 3. KW, k3, and k4 (eq 13) were derived from nonlinear regression of previously reported kinetic data.8 3.2. Multicomponent Sorption Equilibria. Table 1 lists the compositions of the binary mixtures used in the adsorption experiments, the equilibrium compositions, and the respective estimated activity coefficients. From the activity coefficients in Table 1, it can be concluded that the binary mixtures water + hydrogen peroxide (entries 22-26) and limonene + limonene epoxide (entries 34-39) behave as ideal mixtures. The rest of the mixtures show a positive deviation from ideality, which is smaller for limonene + acetonitrile (entries 27-33) and acetonitrile + limonene epoxide (entries 40-44). Previous swelling experiments8 showed that neither the number of adsorbed moles nor the adsorbed mass per gram of catalyst are constant (see Table 2). Indeed, the best adsorption data fit was obtained when different adsorbed amounts in terms of masses or numbers of moles of the components were considered for each independent adsorption experiment. Thus, the amount of the liquid mixture adsorbed on the catalyst more likely depends on the nature of the mixture. An estimation of the maximum mass of liquid mixture that was adsorbed was obtained from the weight difference between the wet and dry catalyst samples after being separated from the liquid mixture. The minimum amount of liquid mixture that was adsorbed was estimated from the weight difference between the used catalyst (dried at room temperature for 48 h) and the fresh one. These

intervals were used as limiting boundaries for the corresponding parameter estimation, nS (eq 3) and mS (eq 4) in each of the independent adsorption experiments. Water was selected as the reference component to apply the adsorption model of Song and co-workers. The relative numbers of moles of water adsorbed by mixtures of limonene, limonene epoxide, acetonitrile, and hydrogen peroxide obtained experimentally were compared with the values predicted by eq 3 (Figure 3a-d). The equation adequately represents the experimental data. The adjustable parameters of eq 3 (Kij and nS) were determined with the “Solver” tool of Excel, by minimizing the squared sum of the differences between the experimental and calculated data. The estimation was carried out with progressive derivatives using the Newton method. The precision and convergence value was 1 × 10-6, with a tolerance of 2% (Table 3). The estimated adsorption equilibrium constants and the remaining parameters of eq 13 are reported in Table 4. Three sets of binary data from Table 1 are necessary for the estimation of the five equilibrium adsorption constants following the adsorption model of Po¨pken and co-workers (eq 4). The liquid adsorption characteristics over PW-Amberlite of the binary mixtures limonene + limonene epoxide, limonene + acetonitrile, acetonitrile + limonene epoxide, and water + hydrogen peroxide were determined with eq 4 (Figure 4a-d). The data are adequately represented by the model. The parameters in Table 4 were estimated from the data of Figure 4a-d. The consistency of the models was checked with the rest of the experimental data in Table 1. Table 4 lists the values of the parameters of the kinetic expression (eq 13) when correlations were performed using kinetic data alone (model A) and when kinetic data were coupled with adsorption probes described by either eq 3 (model B) or eq 4 (model C). The resulting numbers of kinetic adjustable parameters were seven, three, and two for models A-C, respectively. The correlation coefficient (R2), the squared sum of residuals (SSR), and the Fisher statistics distribution (F probe) were used as statistics for the comparison of experimental data taken under conditions free from mass-transfer limitations and different model predictions for limonene conversion under triphasic conditions (Figure 5). The equilibrium desorption constant of limonene epoxide, KE, obtained using the three models has low values (Table 4). As the inverse value of KE, corresponding to the equilibrium adsorption constant of limonene epoxide is large, the limonene reaction rate predicted by eq 13 will strongly decrease with formation of limonene epoxide. Table 4 shows that the highest relative adsorption constant was not for water, as was expected from swelling experiments (Table 2). In contrast to the swelling phenomena, adsorption depends not only on the number of moles adsorbed but also on the nature of the adsorbed substance. Hence, the highest swelling does not necessary lead to the highest adsorption. Table 4 lists the values of parameters together with a statistical comparison between the three models. The low values of SSR indicate that the three models are appropriate and that the data used for the correlations are sufficient. Models B and C have correlation coefficients (R2) close to 1, indicating that they give good data predictions; in contrast, the low correlation coefficient of model A indicates poor model predictions. The lowest squared sum of residuals (SSR) and the highest F probe (statistics of Fischer distribution) values suggest that model C, obtained from the adsorption model proposed by Po¨pken and co-workers, is the best model for the kinetic representation of limonene epoxidation on PW-Amberlite under tiphasic conditions.

Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 653

3.3. Kinetic Modeling. Equation 13 was modeled using Aspen Plus (2004.1) with the parameters obtained in models A-C (see Table 4). The pure-substance properties for hydrogen peroxide, limonene, acetonitrile, and water were obtained from the “Pure 13” database of Aspen, whereas those of limonene epoxide were estimated with the UNIFAC-DMD prediction method available in the software. A batch reactor from Aspen Plus libraries with one inlet stream (reaction mixture) and one outlet stream (reaction products) was used. Thermodynamic properties were estimated with the UNIFAC-DMD group contribution method. For comparison purposes, the reactor feed and the operating conditions were typical of those used in laboratory tests. A comparison of experimental data with the software predictions for models A-C is shown in Figure 5. Excellent predictions of the experimental data were obtained with models B and C, which include parameters determined from adsorption experiments and kinetic regression (Figure 5). Model A, including parameters obtained only by regression of the kinetic data, gives poor predictions, as expected from its low correlation coefficient (Table 4). 4. Conclusions A model for the kinetics of limonene epoxidation over PWAmberlite catalyst under triphasic conditions was developed. The mechanistic pathway includes the interaction of H2O2 with peroxophosphotungstate species of the catalyst to form polyperoxophosphotungstate active sites, where limonene can be adsorbed to produce limonene epoxide or hydrogen peroxide can be decomposed. The proposed mechanism adequately represents the experimental data when the adsorption equilibrium constants are obtained from independent adsorption experiments and the remaining parameters are obtained from nonlinear regression of the kinetic data. The proposed kinetic expression describes the adsorption phenomena of all species over the catalytic surface, including limonene epoxide. Acknowledgment The authors acknowledge the financial support of Colciencias and UdeA through CENIVAM Contract RC No. 432. R.B. is grateful to Colciencias for his doctoral fellowship. Literature Cited (1) Byrne, C. M.; Allen, S. D.; Lobkovsky, E. B.; Coates, G. W. Alternating Copolymerization of Limonene Oxide and Carbon Dioxide. J. Am. Chem. Soc. 2004, 126, 11404. (2) Oliveira, P.; Rojas-Cervantes, M. L.; Ramos, A. M.; Fonseca, I. M.; Botelho do Rego, A. M.; Vital, J. Limonene Oxidation over V2O5/TiO2 Catalysts. Catal. Today 2006, 118, 307.

(3) Grigoropoulou, G.; Clark, J. A Catalytic, Environmentally Benign Method for the Epoxidation of Unsaturated Terpenes with Hydrogen Peroxide. Tetrahedron Lett. 2006, 47, 4461. (4) Llamas, R.; Jimeńez-Sanchidriań, C.; Ruiz, J. Environmentally Friendly Baeyer-Villiger Oxidation with H2O2/Nitrile over Mg(OH) 2 and MgO. Appl. Catal. B 2007, 72, 18. (5) Sepulveda, J.; Teixeira, S.; Schuchardt, U. Alumina-Catalyzed Epoxidation of Unsaturated Fatty Esters with Hydrogen Peroxide. Appl. Catal. A 2007, 318, 213. (6) Sels, B. F.; Villa, A. L.; Hoegaerts, D.; De Vos, D. E.; Jacobs, P. A. Application of Heterogenized Oxidation Catalysts to Reactions of Terpenic and Other Olefins with H2O2. Top. Catal. 2000, 13, 223. (7) Villa de P, A. L.; Taborda, F.; Montes de Correa, C. Kinetics of Limonene Epoxidation by Hydrogen Peroxide on PW-Amberlite. J. Mol. Catal. A 2002, 185, 269. (8) Barrera Zapata, R.; Villa, A. L.; Montes de Correa, C. Limonene Epoxidation: Diffusion and Reaction over PW-Amberlite in a Triphasic System. Ind. Eng. Chem. Res. 2006, 45, 4589. (9) Barrera, R.; Villa, A. L.; Montes de Correa, C. Modelado de la Epoxidacioń de Limoneno con PW-Amberlita. Sci. Tech. 2007, 33, 451. (10) Aspen Tutorial, Getting Started Customizing Unit Operation Models, Creating an Excel Unit Operation Model; Aspen Technologies, May 2007; see http://www.aspentech.com (accessed May 2007). (11) Song, W.; Venimadhavan, G.; Manning, J. M.; Malone, M. F.; Doherty, M. F. Measurement of Residue Curve Maps and Heterogeneous Kinetics in Methyl Acetate Synthesis. Ind. Eng. Chem. Res. 1998, 37, 1917. (12) Popken, T.; Gotze, L.; Gmehling, J. Reaction Kinetics and Chemical Equilibrium of Homogeneously and Heterogeneously Catalyzed Acetic Acid Esterification with Methanol and Methyl Acetate Hydrolysis. Ind. Eng. Chem. Res. 2000, 39, 2601. (13) Paä¨kko¨nen, P. K.; Krause, A. O. Diffusion and Chemical Reaction in Isoamylene Etherification within a Cation-Exchange Resin. Appl. Catal. A 2003, 245, 289. (14) Chirico, R. D.; Frenkel, M.; Diky, V. V.; Marsh, K. N.; Wilhoit, R. C. ThermoMLsAn XML-Based Approach for Storage and Exchange of Experimental and Critically Evaluated Thermophysical and Thermochemical Property Data. 2. Uncertainties. J. Chem. Eng. Data 2003, 48, 1344. (15) Mizuno, N.; Yamaguchi, K.; Kamata, K. Epoxidation of Olefins with Hydrogen Peroxide Catalyzed by Polyoxometalates. Coord. Chem. ReV. 2005, 249, 1944. (16) Bre´geault, M. J.; Vennat, M.; Salles, L.; Piquemal, J. Y.; Mahha, Y.; Briot, E.; Bakala, P. C.; Atlamsani, A.; Thouvenot, R. From Polyoxometalates to Polyoxoperoxometalates and Back Again: Potential Applications. J. Mol. Catal. A 2006, 250, 177. (17) Duncan, D. C.; Chambers, R. C.; Hecht, E.; Hill, C. L. Mechanism and Dynamics in the H3[PW12O40]- Catalyzed Selective Epoxidation of Terminal Olefins by H2O2. Formation, Reactivity, and Stability of {PO4[WO(O2) 2]4}3-. J. Am. Chem. Soc. 1995, 117, 681. (18) Yangying, C.; Xiuwen, H. Progress in Catalytic Epoxidation of Olefins with Hydrogen Peroxide. Prog. Chem. 2006, 18, 399. (19) Fogler, H. S. Elements of Chemical Reactions Engineering, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 2001.

ReceiVed for reView May 22, 2008 ReVised manuscript receiVed September 24, 2008 Accepted October 26, 2008 IE800822N

Kinetic Modeling of Limonene Epoxidation over PW-Amberlite

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