Kinetics of Limonene Hydrogenation in High-Pressure CO2 at

2084

Ind. Eng. Chem. Res. 2010, 49, 2084–2090

Kinetics of Limonene Hydrogenation in High-Pressure CO2 at Variation of Hydrogen Pressure V. I. Anikeev,*,† A. Yermakova,† Ewa Bogel-Lukasik,‡ and Manuel Nunes da Ponte‡ BoreskoV Institute of Catalysis SB RAS, NoVosibirsk, 630090 Russia, and REQUIMTE, Departamento de Quimica, Faculdade de Ciencias e Tecnologia, UniVersidade NoVa de Lisboa, 2829-516 Caparica, Portugal

A mechanism of limonene hydrogenation in high-pressure CO2 has been suggested using the experimental data. The experimental data on limonene hydrogenation in high-pressure CO2 were processed to elucidate the reaction mechanism and calculate the kinetic constants in rate equations for the proposed reaction scheme. The relationship between the total rate constant of limonene reduction and hydrogen pressure has been found. 1. Introduction This work continues a cycle of studies on limonene hydrogenation in high-pressure CO2.1-3 The Pd-catalyzed hydrogenation of limonene in the two-phase gas-liquid (hydrogen-limonene) system has been studied earlier and published in refs 4-6. The main products were p-menth-1-ene, trans-p-menthane, and cisp-menthane. The limonene isomerization products such as terpinolene and γ-terpinene were detected also. The presence of p-menth-3-ene in the product of the catalytic hydrogenation of limonene was reported in ref 7. Hydrogenation of terpenes in high-pressure CO2 exhibits some advantages in comparison with the reaction in the liquid phase in the absence of CO2.4 Experimental data processing is made to elucidate the reaction mechanism and calculate the kinetic constants in rate equations for the proposed reaction scheme. The cited work1 presents a thorough study of the hydrogen pressure effect on limonene reduction in the atmosphere of high-pressure CO2 over a heterogeneous palladium catalyst. In the experiments, temperature and pressure were chosen so as to provide a two-phase composition of the reaction mixture. The liquid, denser phase comprised CO2, limonene, and H2 dissolved in these substances. The gas, less dense phase comprised hydrogen, CO2, and limonene vapor in equilibrium with the liquid phase. Comparison of the hydrogenation reaction rate of such a biphasic system with the supercritical monophasic ones did not reveal any essential advantages of the latter. The calculation of phase equilibrium with the use of earlier developed programs8,9 showed the molar fraction of liquid phase for the considered system to vary from 6.6 to 11.3% depending on the partial pressure of hydrogen at a constant total pressure of 12.5 MPa; see Table 1. Since the liquid phase, which includes 99% of limonene present in the system, contains a large amount of diluted CO2 and hydrogen, such a mixture is called also the “CO2-expanded liquid”. This state of reaction mixture decreases its viscosity and increases the diffusion rate of reagents toward the surface of heterogeneous catalyst compared with, e.g., reactions conducted only in the liquid phase.4 According to preliminary processing of experimental data listed in Tables 2-6, which was made by the authors of ref 1, the total rate constant of limonene hydration increases linearly with a growth of hydrogen partial pressure in the system at * To whom correspondence should be addressed. E-mail: anik@ catalysis.nsk.su. † Boreskov Institute of Catalysis SB RAS. ‡ Universidade Nova de Lisboa.

constant temperature and total pressure. Study of the detailed reaction mechanism and calculation of the rate constants for each route will allow one to find objective dependences on hydrogen pressure, not only for sum constant but also for reaction constant of each reaction route. 2. Experimental Section The hydrogenation of limonene has been performed with an apparatus (50 mL total volume) consisting of one sapphirewindowed cell connected by a pump to a fixed bed tubular reactor. This experimental setup was described in detail previously.2 The reaction was carried out in the presence of 0.2 g of Pd catalyst and 1 mL of limonene at 323.15 K. A measured pressure of hydrogen was first loaded into the sapphire cell. Five different pressures of hydrogen were used in separate experiments. Carbon dioxide was then charged into the cell through a liquid pump up to the total pressure in the reactor of 12.5 MPa. The reaction mixture in the cell was vigorously stirred for 5 min, in order to attain phase equilibrium before starting the circulation through the catalytic bed and initiating the reaction. The reactants were withdrawn from the bottom of the view cell, circulated through the catalyst bed, and sent back to the upper entrance of the cell. Throughout the reaction time, stirring in the view cell continued, so that the feed would always be liquid in equilibrium with its vapor. The reaction mixture in all the used condition remained in two separate fluid phases, but taking into account that the concentration of limonene in the liquid, more dense phase is significantly higher than in the gas, less dense phase, the limonene hydrogenation reactions occur in the liquid phase. The rate flow in the tubular reactor was measured with accuracy better than 0.23% and was kept constant during all experiments at 3.3 mL/min. The product samples from the tubular reactor have been taken to the 100 µL sampling loop. Carbon dioxide in the loop was carefully vented to the atmosphere. A measured amount of hexane was used as a solvent. The liquid products were identified by GC-MS followed by quantitative analysis using HRGC-3000C gas chromatograph with a CP-Sil 8 CB column from Varian Inc. with a flame ionization detector. Nonane in hexane (1.5 mM) was used as external standard for GC analysis (response factor: R-(+)limonene, 1.42; (+)-p-menth-1-ene, 1.26; (+)-p-menth-3-ene, 1.26: terpinolene, 1.44; γ-terpinene, 3.76; cis-p-menthane, 1.44; and trans-p-menthane: 1.43 [precision of the method, better than 10%]).

10.1021/ie9010996  2010 American Chemical Society Published on Web 01/27/2010

Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010

2085

Table 1. Calculation of the Fraction of Liquid and Gas Phase Depending on the Hydrogen Concentration at a Constant Total Pressure of 12.5 MPa and Temperature of 323 K composition of phase, mol % liquid

a

gas a

pressure of H2, MPa

CO2

H2

limonene

W, %

CO2

H2

limonene

W,a %

2.5 3.45 3.8 4.16 4.40

79.68 72.31 70.23 67.63 66.32

4.09 4.40 4.61 4.71 4.88

16.22 23.30 25.16 27.66 28.80

11.27 8.02 7.47 6.84 6.59

77.79 70.23 67.39 64.48 62.55

22.02 29.62 32.48 35.4 37.34

0.19 0.14 0.13 0.12 0.11

88.73 91.98 92.53 93.16 93.41

W, molar part of liquid or gas.

Table 2. Experimental Data on Limonene Hydrogenation at Partial Hydrogen Pressure of 2.5 MPa time, min

trans-p-menthane

p-menth-3-ene

cis-p-menthane

p-menth-1-ene

limonene

γ-terpinene

terpinolene

0 1 2 6 10 16 20 23 24 25 30 40 45 50 60 80 100 120 140 160 180 200 220 240

0.00 2.93 3.10 5.81 6.79 9.71 11.50 12.98 12.80 12.28 13.92 15.36 15.94 16.42 19.30 27.13 36.02 48.52 57.06 58.93 62.47 62.79 65.29 65.02

0.00 1.84 3.03 5.78 11.51 16.08 17.57 20.17 19.99 18.09 19.37 19.22 19.79 19.40 20.79 20.80 19.06 14.05 7.53 4.76 4.05 2.71 0.27 0.00

0.00 1.24 1.74 2.98 3.89 6.58 7.56 9.26 9.31 9.31 10.00 11.48 11.91 13.79 15.28 16.51 21.51 25.90 32.29 34.78 33.48 34.51 34.43 34.98

0.00 4.08 7.90 15.94 38.59 45.37 47.21 47.58 47.22 47.57 48.55 46.82 46.25 45.19 40.23 32.91 23.41 11.54 3.13 1.53 0.00 0.00 0.00 0.00

100.00 88.35 82.13 65.72 35.09 19.41 16.17 10.02 10.67 10.44 8.16 6.56 5.63 4.84 4.40 2.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.07 0.71 0.56 0.95 0.88 0.00 0.00 0.00 0.80 0.00 0.56 0.47 0.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 1.49 1.38 3.21 3.17 1.96 0.00 0.00 0.00 1.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


trans-p-menthane

p-menth-3-ene

cis-p-menthane

p-menth-1-ene

limonene

terpinolene

0 1 2 5 10 15 20 23 24 25 30 35 40 45 50 60 80 100 120 121 140 160

0.00 2.35 3.05 3.12 5.11 5.42 10.05 13.94 15.24 16.06 17.47 23.92 37.39 48.26 54.96 65.55 66.40 66.84 66.87 67.10 66.27 67.25

0.00 1.18 2.64 6.16 9.19 11.58 17.15 17.68 18.32 19.13 18.49 17.65 13.59 11.23 8.68 1.90 0.00 0.00 0.00 0.00 0.00 0.00

0.00 1.59 1.77 1.92 3.20 4.24 5.53 8.90 9.03 9.32 12.33 16.94 22.03 24.60 30.76 32.55 33.60 33.16 33.13 32.90 33.73 32.75

0.00 8.24 8.80 33.07 46.24 49.99 49.80 49.76 50.61 49.80 46.75 37.67 24.20 13.90 4.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00

100.00 84.00 80.22 51.61 30.81 21.95 13.28 9.73 6.80 5.69 4.97 3.81 2.78 2.01 0.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 2.65 3.52 4.12 5.45 6.82 4.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

On a spherical granulated activated carbon, 1 wt % Pd was used as catalyst in the hydrogenation of limonene. A detailed procedure for catalyst preparation and investigation of its properties has been already presented.1 3. Results and Discussion 3.1. Possible Mechanism of the Limonene Hydrogenation Reaction. The mechanism of limonene hydrogenation in high-pressure CO2 is still poorly understood, being a subject

of further investigation and discussion. Kinetic and mechanistic studies on isomerization of monoterpene compounds in supercritical lower alcohols (ethanol, isopropyl alcohol)10 give ground to suppose that limonene, via reversible reactions of its catalytic isomerization, forms the isomers p-mentha-1,4(8)-diene (terpinolene), p-mentha-1,4-diene (γ-terpinene), and p-mentha-1,3diene (R-terpinene) (see the proposed scheme of limonene transformations in Scheme 1), which further, via irreversible

2086



trans-p-menthane

p-menth-3-ene

cis-p-menthane

p-menth-1-ene

limonene

0 1 2 3 5 10 15 20 25 30 35 40 45 50 60 80 100 120 140 160

0.00 0.00 3.39 2.32 4.61 10.20 12.76 13.55 17.68 23.48 32.22 41.16 50.86 60.76 66.45 67.59 67.26 67.55 67.49 67.41

0.00 0.39 1.54 2.36 3.75 9.10 12.47 14.36 14.22 13.70 13.70 11.58 9.31 5.32 0.64 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.97 0.98 2.31 6.93 7.95 9.67 12.20 16.39 19.05 23.17 25.86 29.10 32.41 32.41 32.74 32.45 32.51 32.59

0.00 0.00 11.60 27.88 42.99 50.88 52.54 52.75 49.78 42.87 32.67 22.32 12.54 4.43 0.50 0.00 0.00 0.00 0.00 0.00

100.00 99.61 82.50 66.47 46.34 22.90 14.28 9.67 6.12 3.56 2.36 1.77 1.43 0.39 0.00 0.00 0.00 0.00 0.00 0.00


trans-p-menthane

p-menth-3-ene

cis-p-menthane

p-menth-1-ene

limonene

0 1 2 3 5 10 15 20 25 30 35 40 45 50 60 80 100 120 140 160

0.00 0.00 3.30 2.36 4.55 10.64 13.41 14.72 19.64 26.40 35.51 44.08 53.54 61.66 66.78 67.59 67.26 67.55 67.49 67.41

0.00 0.39 1.05 1.58 2.33 3.41 4.96 5.50 6.32 6.14 5.48 4.33 3.70 2.83 0.64 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.94 1.00 2.27 7.23 8.36 10.51 13.55 18.43 20.99 24.81 27.22 29.53 32.58 32.41 32.74 32.45 32.51 32.59

0.00 0.00 14.38 30.47 51.16 60.04 61.23 59.46 54.35 45.43 35.88 25.34 14.65 5.97 0.00 0.00 0.00 0.00 0.00 0.00

100.00 99.61 80.34 64.59 39.69 18.67 12.05 9.81 6.15 3.59 2.14 1.43 0.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Table 6. Experimental Data on Limonene Hydrogenation at Partial Hydrogen Pressure of 4.4 MPa time, min trans-p-menthane cis-p-menthane p-menth-1-ene limonene 0 1 2 5 7 10 15 16 17 20 30 40 41 42 50 60 80 100 120

0 0.00 5.99 5.70 8.97 8.70 14.70 12.46 12.07 14.15 30.98 47.45 48.24 52.86 63.21 64.56 68.53 67.69 68.85

0 0.00 0.00 3.26 6.41 7.44 9.41 10.12 9.73 9.60 18.46 27.84 27.86 27.13 29.67 32.70 31.47 32.31 31.15

0 0.00 39.24 48.64 57.29 61.30 65.81 67.41 65.31 67.12 46.78 24.70 23.90 20.01 7.12 2.73 0.00 0.00 0.00

100 100.00 54.77 42.41 27.32 22.55 10.07 10.01 12.88 9.13 3.77 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

reactions of their hydrogenation, lead to the products listed in Tables 2-6. According to the proposed scheme, precursors of the limonene hydration reaction are represented by such compounds as

p-mentha-1,4(8)-diene, γ-terpinene, and R-terpinene, which are in equilibrium both with limonene and with each other. In the products of limonene hydration, see Tables 2 and 3, small amounts of p-mentha-1,4(8)-diene and γ-terpinene are identified only at “low” hydrogen pressures of 2.5 and 3.45 MPa and only in the initial period of conversion. As hydrogen content in the reaction mixture increases, so does the hydration rate of these compounds; as a result, p-mentha-1,4(8)-diene, γ-terpinene, and R-terpinene are not detected anymore in the reaction products. It means that at high hydrogen content the rate of hydration considerably exceeds the rate of isomerization. Since concentration of these compounds in the reaction products is insignificant, their amounts were added to limonene when processing the experimental data. This gave a group of initial substances (mainly limonene) having two double bonds. To process the experimental data of Tables 2-6, a scheme of limonene hydrogenation routes is suggested; it is similar to Scheme 1 but has some additions and simplifications: here, A, limonene + γ-terpinene + R-terpinene + terpinolene; B, p-menth-1-ene; C, p-menth-3-ene; D, cis-p-menthane; E, transp-menthane. The suggested Scheme 2 allows a reversible transition between substances p-menth-1-ene and p-menth-3-ene by


2087

Scheme 1. Scheme of Limonene Hydrogenation Reactions

Scheme 2. Scheme of Limonene Hydrogenation Routes

reaction 3. This may seem unobvious, but thermodynamic calculations confirm the possibility of such transition. 3.2. Kinetic Model Equations. The rate of each reaction 1-8 in Scheme 2 can be represented by the following kinetic equations:

refs 1 and 2) can be represented by a scheme of differential equations:

R1)k1yA

(1)

dyB ) R 1 - R3 - R4 - R5 dt

R2)k2yA

(2)

dyC ) R 2 + R3 - R6 - R7 dt

(3)

dyD ) R 4 + R6 - R8 dt

R4)k4yB

(4)

R5)k5yC

dyE ) R5 + R7 + R8 dt

(5)

R6)k6yC

(6)

R7)k7yC

(7)

(

R3)k3yB 1 -

(

R8)k8yD 1 -

yC /yB Keq 3

yE /yD Keq 8

)

)

K3eq

dyA ) -R1 - R2 dt

at t ) 0:

yA ) 1,

(9)

y B ) yC ) yD ) yE ) 0

Here, t is the reaction time, and yj is the mole fraction of the j-component. The desired kinetic parameters k1-k8 were found by minimization of the target function

(8) Nexpt NS

K8eq

The values of equilibrium constants and in eqs 3 and 8 were found by calculation; at T ) 323 K and P ) 12.5 MPa they are equal to K3eq ) 0.589 and K8eq ) 3.418. Taking into account Scheme 2 and eqs 1-8, a mathematical model of the experimental reaction unit (batch reactor, see

S)

∑ ∑ (y

exp ij

- ycalc ij ) f min

(10)

j)1 i)1

calc where yexp are the experimental and calculated values ij and yij of the jth component in the ith experiment at specified T and were obtained by numerical integration of PH2. Values of ycalc ij

4.91 6.58

4.28 6.76 0.66 1.75 5.06 3.63 6.36 1.92 1.99 5.19

3.43 4.95

mean error, % mean error, % mean error, %

7.59 × 10-2 ( 3.43 × 10-2 4.55

2.20 × 10-2 ( 4.40 × 10-3 1.66 × 10-2 ( 3.42 × 10-3

1.72 × 10-1 ( 3.81 × 10-3

10 10-4 10-3 10-3 10-3 10-3 10-2 10-4

× × × × × × × × 3.69 6.86 9.42 3.47 6.91 6.71 6.29 3.21 ( ( ( ( ( ( ( ( 10 10-7 10-2 10-2 10-2 10-6 10-1 10-6

× × × × × × × × 4.23 8.76 1.38 3.91 1.34 3.41 2.77 3.27 ( ( ( ( ( ( ( ( 10 10-7 10-2 10-2 10-3 10-7 10-1 10-6

2.41 7.21 3.53 3.13 7.08

mean error, %

2.79 × 10 2.51 × 10-3 1.06 × 10-3 2.23 × 10-3 2.56 × 10-3 1.22-03 7.77 × 10-3 9.64 × 10-3 ( ( ( ( ( ( ( ( 10 10-2 10-7 10-2 10-2 10-6 10-2 10-6

mean error, %

3.25 4.35 2.84 2.99 4.61

component

limonene p-menth-1-ene p-menth-3-ene cis-p-menthane trans-p-menthane

10 10-4 10-3 10-3 10-3 10-3 10-2 10-2

× × × × × × × × 1.16 9.90 4.13 3.29 3.34 2.01 1.01 1.46 ( ( ( ( ( ( ( ( 10 10-2 10-4 10-3 10-3 10-7 10-3 10-2

k1 k2 k3 k4 k5 k6 k7 k8 root-mean-square error, %

constant, 1/min

5.85 2.18 4.63 8.86 5.99 4.69 9.26 1.37 3.68

× × × × × × × ×

-2

PH2 ) 2.5 MPa

-3

8.17 2.07 1.51 1.41 2.05 1.51 2.02 2.25 5.12

× × × × × × × ×

-2

PH2 ) 3.45 MPa

-3

1.25 4.60 4.93 1.45 2.44 6.39 1.07 1.67 4.2

× × × × × × × ×

-1

PH2 ) 3.8 MPa

10 10-4 10-2 10-3 10-3 10-3 10-2 10-4

Figure 1. Matching of the experimental and calculated data. PH2 ) 2.5 MPa. Points, experiment; lines, model calculation: (1) limonene; (2) p-menth-1-ene; (3) trans-p-menthane; (4) cis-p-menthane; (5) p-menth-3ene.

-3

1.41 1.72 2.10 1.36 1.08 1.39 1.42 1.33 4.32

× × × × × × × ×

-1

PH2 ) 4.16 MPa

-3

PH2 ) 2.5 MPa


Table 7. Constants and Confidence Intervals and Accuracy of Experimental Data Representation

2088


the set of eqs 9. Initial experimental data yexp ij are listed in Tables 2-6. The mathematical basis, minimization procedure, and statistical analysis of the data obtained are reported in our earlier works.11,12 Composition of the reaction mixture normalized to the initial concentration of limonene, %. 3.3. Kinetic Model Identification. Processing of a Series of Experimental Data at T ) 323 K and PH2 ) 2.5 MPa, Table 7. Table 7 shows the results of identification for a series of experiments obtained at T ) 323 K and PH2 ) 2.5 MPa. These results demonstrate that the model for reaction Scheme 2 is degenerate with respect to the k6 constant for the appropriate reaction. As a result, confidence intervals for other constants are also extended. The root-mean-square absolute error in matching the experimental and calculated data, which is equal to 3.69%, also increases, but can be considered allowable. The second part of Table 2 shows the error distribution for the reaction mixture components. Figure 1 displays the plots that illustrate matching of experimental and calculated data. One can see that mismatch is most pronounced for cis-p-menthane and trans-p-menthane, their time dependence obtained in the experiment being s-shaped at all values of hydrogen pressure, especially for trans-pmenthane. Such behavior of trans-p-menthane may have different reasons. Of them, most probable is the preferential




adsorption of dienes on the catalyst surface followed by their isomerization, which leads to retardation of catalytic hydration and formation of cis-p-menthane and trans-p-menthane. Further acceleration of cis-p-menthane and trans-p-menthane formation is likely to relate with clearing the catalyst surface for hydration of monoenes. To develop the kinetic model of limonene hydration taking into account processes on the catalyst surface and calculated reaction rate constants, we should know at least the adsorption constants for dienes, the fraction of blocked catalyst surface, and its properties, etc. In the absence of such data, we have chosen the kinetic model represented by eqs 1-8 according to Scheme 1. Processing of a Series of Experimental Data at T ) 323 K and PH2 ) 3.45 MPa, Table 7. This series of experimental data was processed using the above model based on eq 9 and Scheme 2 of limonene hydrogenation reactions. The results of model identification and the constants obtained are listed in Table 7; matching of calculation and experiment is demonstrated in Figure 2. Analysis of the reaction rate constants and the value of root-mean-square error indicate that, within the suggested Scheme 3

2089


model, agreement between experimental and calculated data for this series of experiments is somewhat worse than for the preceding series. Disagreement is most pronounced in the initial period, up to 40-50 min, for changes in the concentration of p-menth-1-ene and trans-p-menthane, respectively. And certainly, such a discrepancy between experimental and calculated data can hardly be attributed to the choice of first-order kinetic equations of reaction. The discrepancy may be caused, first, by inaccuracy of quantitative analysis of the reaction products. Second, the initial mathematical model of experimental batch reactor (set of eqs 9) might appear quite approximate for some conditions of the experiment. The results of identification of a series of experimental data at T ) 323 K, PH2 ) 3.8 MPa and PH2 ) 4.16 MPa are presented in Table 7 and Figure 3 and Figure 4. Processing of a Series of Experimental Data at T ) 323 K and PH2 ) 4.4 MPa, Table 7. In contrast to the experimental data of Tables 2 and 3, here component p-menth-3-ene was not found in the reaction products. As a result, this series of experiments cannot be interpreted within the above model based in Scheme 2. Thus, we propose a simplified scheme of chemical transformations for the limonene hydrogenation reaction. The proposed Scheme 3 was used for processing of experimental data at PH2 ) 4.4 MPa. Note that the decreased number of equations and components allowed us to include the equilibrium constant of reaction 8 in the desired model parameters. The results of identification are presented in Table 7 and Figure 5. Analysis of the model identification shows that, similar to the previous cases, a certain disagreement is observed between experimental and calculated values for p-menth-1-ene. However, the 4.55% root-mean-square deviation of experimental and calculated data is allowable taking into account possible sources of error in experimental data and in representation of the mathematical model of the reactor. Results of the study aimed at processing the kinetic data of limonene hydrogenation reaction using the model of the experimental reactor allowed us (1) to confirm the validity of the proposed scheme of limonene transformations in hydrogenation reaction and (2) to determine the reaction rate constants and their confidence intervals for each route of the scheme.

2090


4. Conclusions A detailed mechanism of limonene hydrogenation in highpressure CO2 has been suggested. The experimental data on limonene hydrogenation in high-pressure CO2 were processed to elucidate the reaction mechanism and calculate the kinetic constants in rate equations for the proposed reaction scheme. The earlier devised methods of experimental data processing and kinetic model development were used to calculate rate constants for each reaction route in the proposed scheme. The relationship between the total rate constant of limonene reduction and hydrogen pressure has been found. Literature Cited Figure 6. Sum of constants k1 + k2 versus hydrogen pressure in the reaction mixture.

As noted above, the disagreement between experimental and calculated dependences is related most likely with the necessary choice of the “batch reactor” mathematical model for data processing instead of a more suitable “semi-batch reactor” model. This choice is caused by the lack of experimental data that could allow us to use the semi-batch reactor model for solving the inverse problem. Using the reaction rate constants obtained by model identification, we may plot the sum of two constants, k1 + k2, responsible for total consumption of limonene as the initial reactant, against hydrogen pressure in the reaction mixture, Figure 6. Second-order polynomial approximation of the sum reaction rate constant as a function of hydrogen pressure demonstrates that the observable order with respect to hydrogen is a variable quantity. Such behavior can be explained by the reaction conditions of Pd-catalyzed limonene hydrogenation in highpressure CO2.1 In the experiments, the reaction mixture remains always in two phases, gas and liquid; thus, variation of hydrogen pressure in the gas phase changes its concentration in the liquid phase. Since reaction rates in the accepted scheme of limonene transformations are presented by the first-order kinetic equations only with respect to the concentration of consumable reactant, the effect of hydrogen pressure, i.e., its concentration in expanded liquid containing mainly limonene, reveals itself in the reaction rate constants. In the “ideal” case, for experimental data processing and kinetic parameters determination it would be reasonable to calculate with the use of thermodynamic models the hydrogen concentration in expanded liquid (limonene, CO2, and H2) in dependence on its pressure in the gas phase. At that, the rate kinetic equations of corresponding reactions in Scheme 2 will include the hydrogen concentration in expanded liquid.

(1) Bogel-Lukasik, E.; Bogel-Lukasik, R.; Kriaa, K.; Fonseca, I.; Nunes da Ponte, M. Limonene hydrogenation in high-pressure CO2: Effect of hydrogen pressure. J. Supercrit. Fluids 2008, 45, 225–230. (2) Bogel-Lukasik, E.; Fonseca, I.; Bogel-Lukasik, R.; Tarasenko, Y. A.; Nunes da Ponte, M.; Paiva, A.; Brunner, G. Phase equilibrium-driven selective hydrogenation of limonene in high-pressure carbon dioxide. Green Chem. 2007, 9, 427–430. (3) Bogel-Lukasik, E.; Bogel-Lukasik, R.; Nunes da Ponte, M. Effect of flow rate of biphasic reaction mixture on limonene hydrogenation in high pressure CO2. Ind. Eng. Chem. Res., in press. (4) Grau, R. J.; Zgolicz, P. D.; Gutierrez, C.; Taher, H. A. Liquid phase hydrogenation, isomerization and dehydrogenation of limonene and derivatives with supported palladium catalysts. J. Mol. Catal. A: Chem. 1999, 148, 203–214. (5) Lesage, P.; Candy, J. P.; Hirigoyen, C.; Humblot, F.; Basset, J. M. Selective dehydrogenation of dipentene (R-(+)-limonene) into paracymene on silica supported palladium assisted by R-olefins as hydrogen acceptor. J. Mol. Catal. A: Chem. 1996, 112, 431–435. (6) Shimazu, S.; Baba, N.; Ichikuni, N.; Uematsu, T. Regioselective hydrogenation of dienes catalyzed by palladium-aminosilane complexes grafted on MCM-41. J. Mol. Catal. A: Chem. 2002, 182/183, 343–350. (7) Schneider, R. C. S.; Baldissarelli, V. Z.; Martinelli, M.; von Holleben, M. L. A.; Caramao, E. B. Determination of the disproportion products of limonene used for the catalytic hydrogenation of castor oil. J. Chromatogr., A 2003, 985, 313–319. (8) Yermakova, A.; Anikeev, V. I. Chemical and phase equilibrium taking into account reaction mixture nonideality. Russ. J. Phys. Chem. 2001, 75 (Suppl.1), 1394–1402. (9) Yermakova, A.; Anikeev, V. I. Phase diagram of compound mixtures in supercritical conditions. Russ. J. Phys. Chem. 1999, 73 (1), 140–142. (10) Anikeev, V. I. Transformations of organic compounds in supercritical solvents: From experiments to kinetics, thermodynamics, simulation, and practical applications. Kinet. Catal. 2009, 50 (2), 284–296. (11) Yermakova, A.; Gudkov, A. V.; Anikeev, V. I. Identification of kinetic models. Kinet. Catal. 1997, 38 (2), 309–318. (12) Yermakova, A.; Anikeev, V. I.; Gudkov, A. V.; Bobrin, A. S. Experimental setup - IBM” to investigation of kinetics and creation of kinetic models for compound reactions. Theor. Found. Chem. Techn. 1995, 29 (1), 61–70.

ReceiVed for reView July 8, 2009 ReVised manuscript receiVed November 13, 2009 Accepted December 29, 2009 IE9010996

Kinetics of Limonene Hydrogenation in High-Pressure CO2 at

Recommend Documents