Development of a Kinetic Model for the Hydrogenolysis of CCl2F2

Jan 18, 2007 - A kinetic model for the main products, CHClF2, CH2F2, and methane, in the selective hydrogenolysis of CCl2F2 over a 1 wt % palladium on...
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Ind. Eng. Chem. Res. 2007, 46, 4158-4165

Development of a Kinetic Model for the Hydrogenolysis of CCl2F2 Over 1 wt % Pd/C Andre´ Wiersma, Andreas ten Cate, Emile J. A. X. van de Sandt, and Michiel Makkee* Department of Chemical Engineering, Delft UniVersity of Technology, Julianalaan 136, NL 2628 BL Delft, The Netherlands

A kinetic model for the main products, CHClF2, CH2F2, and methane, in the selective hydrogenolysis of CCl2F2 over a 1 wt % palladium on the activated carbon catalyst has been developed. The rate expressions in this kinetic model are derived from the elementary steps, which are based on the reaction mechanism. The reaction proceeds via a combination of parallel and serial reaction pathways rather than the expected serial reaction. This complicated reaction scheme dramatically changes the way in which the rate equations should be derived from the elementary steps. However, the calculations themselves appear to be rather straightforward. It will be shown that, in spite of the large number of possible surface intermediates, a practical and usable kinetic model can be derived. When the performance of such a model is compared with the different types of more generally derived Langmuir-Hinshelwood-Hougen-Watson (LHHW) models, it appears that the performance of all models is similar. Hence, it is possible to derive a useful kinetic model directly from elementary steps for a complicated reaction scheme with a combination of serial and parallel reactions. The performance of such a model is not inferior to other types of kinetic models, which are often put forward on the basis of the general form of the LHHW models. 1. Introduction

r)

Nowadays, it is generally accepted that fully halogenated hydrocarbons (CFCs) contribute significantly to the depletion of the ozone layer,1 and therefore, the production and use of CFCs has been strictly regulated. The conversion of CFCs into useful products, and especially the conversion of CCl2F2 into CH2F2, is a promising possibility to speed up the recovery of the ozone layer.2 At Delft University of Technology, a 1 wt % palladium on a purified activated carbon support has been selected as a suitable catalyst for this conversion.2 The development of rate expressions for the main products in the hydrogenolysis reaction of CCl2F2 over this catalyst, i.e., CHClF2, CH2F2, and methane, is essential for the design of a reactor for this CCl2F2 conversion process. The majority of the reactions catalyzed by supported metals follow the Langmuir-Hinshelwood type of mechanism.3 In this mechanism, the reaction rate equations can be derived directly from a sequence of elementary steps, which can be derived from the reaction mechanism. A mechanism for this reaction has been proposed previously.4 Either one step or a few steps are selected to be rate determining. All other steps are assumed to be in quasi-equilibrium. A reaction rate equation can be mathematically derived by coupling of the reaction rates of elementary steps with quasi-equilibrium relationships and a site balance. If this mathematical process becomes too complicated to solve or the derived rate equations are too complicated for use in a process simulation program, a more general approach can be used, which leads to a so-called Langmuir-HinshelwoodHougen-Watson-type of the kinetic model (LHHW-type model). This LHHW-type model can be found by replacing each of the terms as presented in eq 1, a kinetic factor, a driving force of reactants, and an inhibition of the reaction rate by adsorbed species, in a logical way.5 * To whom correspondence should be addressed. Tel.: +31 15 278 1391. Fax: +31 15 278 5006. E-mail: [email protected].

(kinetic factor)‚(driving force) (1 + adsorbed species)n

(1)

There is no kinetic model for the reaction rates of CCl2F2 to the different hydrogenolysis products available. However, a number of authors have derived reaction rate equations for the overall CCl2F2 hydrogenolysis rate on different palladium catalysts. Coq et al.6 have used two different models of a general Langmuir-Hinshelwood type, one with adsorption of hydrogen and another with adsorption of CCl2F2. Ahn et al.7 derived rate equations from a sequence of elementary steps using adsorption measurements of pure components, including hydrochloric acid, to determine a number of parameters in the kinetic model. The value of these models is limited because (a) not enough data are available to describe a complete model, (b) no data are presented on the accuracy of the model predictions, (c) adsorption data measured at conditions different from reaction conditions are not necessarily relevant for kinetics, and (d) chlorine adsorption should be taken into account in the kinetic models. It has been demonstrated that hydrochloric acid has not only an inhibiting effect on the reaction rate but also an influence on the selectivity for CHClF2 and CH2F2.4 The strong influence of hydrochloric acid on the reaction rate has also been found for palladium catalysts in other hydrogenolysis reactions of the carbon-chlorine bond. Campbell and Kemball8,9 reported good results using a first-order Langmuir-Hinshelwood model with adsorption of HCl for ethyl chloride. Coq et al.10 reported for the catalytic hydrogenolysis of chlorobenzene that the adsorption of hydrochloric acid was 20-150 times stronger than the adsorption of chlorobenzene. The objective of this study is to develop a practical reactor model for a conceptual process design for a set of reaction rate equations for the main products in the catalytic hydrogenolysis of CCl2F2 over the selected catalyst, which is based on the reaction mechanism. The parameters in the equations are fitted with experimental data. In the approach used, the reaction mechanism will be simplified based on experimental results and thermodynamic data. Subsequently, the most important reaction

10.1021/ie0611195 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/18/2007

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Figure 2. Simplified mechanism of CCl2F2 hydrogenolysis.

Figure 1. Reaction scheme for C1-CFCs. The bold arrows represent the reactions aimed for. The numbers represent the Gibbs free energies at 500 K corresponding with the reactions as formulated in the text (e.g., eqs 7-10).

Table 1. Complete List of Surface Species Within C1 System *CClF2 *CCl2F *CHF2 *CH2F *CHCl2 *CH2Cl *CHClF *CH3 *CF2 *CCl2 *CH2 *CHF *CHCl *F *Cl *H *

intermediates and reactions involved will be drawn up. The kinetic model is derived from these reactions and fitted with experimental data. Finally, the results are compared with the results that would have been obtained if a more general approach had been used. 2. Theory Initially it was anticipated that CCl2F2 would be converted according to a serial reaction scheme, in which CCl2F2 is converted via CHClF2 into CH2F2. This is illustrated in Figure 1, in which all C1 derivatives containing H, Cl, and F are shown. The hydrogenolysis reactions starting from CCl2F2 are exothermic irreversible reactions. Thermodynamically, the formation of methane is favored, but a selective conversion to CH2F2 can be expected because the carbon-fluorine bond is much stronger than the carbon-chlorine bond. The main product in the hydrogenolysis of CCl2F2 over the selected catalyst is CH2F2, whereas the most important other products are CHClF2 and methane. Table 1 shows all surface intermediates in the reaction mechanism. The large amount of surface intermediates would lead to complicated reaction rate equations. More practical reaction rate equations can be obtained by selection of the most abundant reaction (or surface) intermediates (mari) according to Boudart and Djega-Mariadassou.11 The mari can be selected by a combination of thermodynamical data and behavior of the catalyst. A detailed description of the thermodynamical data involved and the reaction mechanism is given by Makkee/Moulijn and coworkers;4 only the most important aspects are mentioned here. Obviously, the first step in the reaction is dissociative adsorption of CCl2F2 into *CClF2. This intermediate might

Figure 3. Elementary steps for the formation of CHClF2 and CH2F2.

desorb to form CHClF2 or react further to a stable carbene intermediate *CF2. This carbene intermediate can react with adsorbed hydrogen or chlorine to give *CHF2 or *CClF2, respectively. *CHF2 can desorb to form CH2F2. These intermediates are important for the reactions mechanism, since CHClF2 and CH2F2 are the main products in the reaction. This mechanism can explain the observed selectivities for CHClF2 and CH2F2: addition of hydrogen leads to an increases in selectivity for CH2F2, whereas addition of hydrochloric acid leads to an increase in selectivity for CHClF2. However, the selectivity for methane appeared to be rather constant and independent of additions of HCl or H2. Therefore, methane cannot be formed via a sequential reaction from *CF2. Moreover, the formation of the reaction intermediate involved, *CHF, would be thermodynamically difficult. Hence, methane is formed via a different parallel route on the catalyst surface. The most logical route is the adsorption of CCl2F2 into *CCl2F. This leads to very reactive intermediates, which react immediately to methane. Coq et al.6 already proposed this direct route to methane from CCl2F2. Measurements of the amount of chlorine and fluorine present on palladium black catalysts showed that substantial amounts of both chlorine and fluorine are present on these catalysts after use.12 However, the fluorine presence on the catalyst surface proved to be catalytically not significant, as demonstrated by the fact that no CHF3 formation was found over palladium black catalysts, and therefore, the possible presence of fluorine is not incorporated in the kinetic models.12 Hence, for the development of a kinetic model, *CClF2, *CHF2, *CF2, *H, and *Cl can be identified as mari. the basis of these observations, a simplified reaction mechanism has been drawn up, depicted in Figure 2, which consists of a combination of a serial and a parallel reaction mechanism. The reaction rate equations can be derived directly from the individual steps in the mechanism. Hence, a complicated reaction scheme (Figure 1) with a large number of possible surface intermediates (Table 1) has been simplified to a reaction scheme with five surface intermediates and six reactions. At first sight, the reaction scheme seems to be too complicated to derive the reaction rate equations from it. Especially the fact that more than one reaction should be considered to be rate determining would make the derivation of the reaction rate equations more complex. However, it will

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Figure 4. Elementary steps for the formation of methane.

Figure 6. Reaction rate equations of the basic LHHW-type model.

Figure 7. Reaction rate equations of the H2 LHHW-type model (the expression for ADS is similar to that for the basic LHHW-type model (Figure 6)).

Figure 5. Reaction rate equations derived for the mechanistic model.

be shown that, with a number of justifiable assumptions, a practical and usable kinetic model can be derived from these equations, which would make the use of the more general approach superfluous. The following basic assumptions were made for the derivation of the rate equations: (1) The total number of active sites is constant. (2) All surface species occupy not more than one catalyst site. (3) All reactions take place on the catalyst surface: no gasphase reactions occur. (4) CHClF2 is formed via a reaction of *CClF2 with *H. The possible reaction of *CHF2 with *Cl is neglected. (5) The sequential reaction of *CHF2 to methane is neglected. Methane is formed via route 2. (6) There is no fluorine presence on the catalyst surface. *F is neglected. (7) There is no adsorption of CHClF2, CH2F2, and CH4 on the catalyst surface. 2.1. Elementary Steps. The elementary steps in route 1 for the formation of CHClF2 and CH2F2, divided into adsorption reactions, surface reactions, and desorption reactions, are shown in Figure 3. The elementary steps for the formation of methane, formed via route 2 ,are shown in Figure 4. The most important difference with route 1 is that, during adsorption of CCl2F2, a carbon-fluorine bond is broken. This leads to reactive surface intermediates, which react to the thermodynamically most stable

product, i.e., methane. The detailed route to methane on the catalyst surface is not fully elucidated. However, because of the reactivity of the intermediates, only the dissociative adsorption reaction is kinetically significant; all the other reaction steps (11-14) can be neglected. Therefore, the exact routes to methane or intermediates involved are insignificant for the kinetic equations. The most logical elementary steps leading to the formation of methane are shown in Figure 3. Reactions 8 and 15 are similar to the elementary steps of the formation of CHClF2 and CH2F2. Regardless of the exact route, reactions 9 and 14 should be incorporated in the reaction mechanism. 2.2. Rate Equations for the Formation of CHClF2, CH2F2, and CH4. Using only the mari, it can be concluded that reactions 2-9 are kinetically significant. Reactions 2, 5-7, and 9 are assumed to be rate determining. Reactions 3, 4, and 8 are assumed to be in quasi-equilibrium. The rate equation can be found using quasi-equilibrium relationships, the site balance as shown in eq 17, and coupling of the reaction rates of reactions 2, 5-7, and 9.

Site balance: Nt ) * + *Cl + *H + *CClF2 + *CF2 + *CHF2 (17) The rate equations derived are shown in Figure 5. ADS2 is the combined adsorption of all carbon containing surface intermediates. This expression can be divided into three contributions, which are shown in eq 23 for *CHF2, *CF2, and *CClF2, respectively. The mechanistic model shows that all reactions are first order in CCl2F2. Furthermore, a rather simple expression for the selectivity for CHClF2 and CH2F2 is obtained.

selectivity for CH2F2 )

(

1

1+S

CHCl

xCH

)

(18)

2

Equation 18 shows that this selectivity depends on the amount of chlorine and hydrogen adsorbed on the catalyst surface.

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Figure 8. Changes applied in the adsorption term of the basic LHHWtype model. Table 2. Summary of LHHW-type Models Applied name of model

driving force change

adsorption group change

basic HCl 29 f 33 CCl2F2 29 f 34 HF 29 f 35 H2 26-28 f 30-32

dissociative adsorption of H2 adsorption of HCl dissociative adsorption of HCl adsorption of CCl2F2 added adsorption of HF added reaction order hydrogen increased by 0.5 in all reactions

Figure 9. Results reference measurements (conditions: T ) 490 K, P ) 0.2 MPa, WHSV ) 0.67 g/(g‚h), H2/CCl2F2 ) 7 mol/mol (1...7 ) sequence in which reference measurements were performed)).

Furthermore, when the formation of CHClF2 and that of CH2F2 are added, the selectivity term disappears and a first-order reaction in CCl2F2 is found for the adsorption reaction of CCl2F2 as shown in eq 25:

r9 )

k2sNtC12 (ADS)2

(25)

Hence, a constant ratio in the formation of CHClF2 and CH2F2 compared with the formation of methane is predicted by these rate equations. At first sight, the mechanistic model appears to be rather complicated. However, upon closer inspection, neglecting ADS2 results in a practically useful model. The term ADS2 describes the adsorption of all carbon containing species in the model (*CClF2, *CF2, and *CHF2). It can be expected that the surface coverages of carbon containing species are low because of the following: (i) hydrochloric acid has a large influence on the reaction f strong chlorine adsorption; (ii) methane and CH2F2 main products f high surface coverage of hydrogen; (iii) only a small amount of coupled products such as ethane and propane; and (iv) no readsorption of CHClF2 and CH2F2 on the catalyst surface. Thus, the catalyst surface would be mainly occupied by hydrogen, chlorine, and fluorine. The adsorption of carbon containing species can be neglected. 2.3. General LHHW-Type Models. A more general approach leads to so-called Langmuir-Hinshelwood-HougenWatson-type models (LHHW-type models), as represented, for example, by eqs 26-29 in Figure 6. The following basic assumptions were made in deriving these models: (i) adsorption of CCl2F2 is the rate-determining process; (ii) the number of sites involved in the rate-determining process is two; and (iii) dissociative adsorption of hydrogen. In practice, LHHW models are often just postulated based on the general form of the LHHW rate equation (eq 1). This more general approach will be used here. First a basic LHHWtype of model will be postulated. Subsequently, a number of improvements to this basic model will be discussed. The discrimination between the various LHHW-type models is done on the basis of the evaluation of the fits of the model to experimental data. 2.3.1. Basic LHHW-Type Model. The reaction rate equations for the basic LHHW-type of model have been derived using the following assumptions: (i) the active sites are not occupied

Figure 10. Comparison of prediction by mechanistic and basic LHHWtype model (conditions: T ) 490, P ) 0.28 MPa, H2/CCl2F2 ) 10 mol/ mol)(measured values: (2) ) conv., (b) ) sel. CH2F2, (0) ) sel. CHClF2, (O) ) sel. CH4) (solid lines ) mechanistic model, dotted lines ) basic LHHW-type model).

by carbon containing species or HF; (ii) methane formation independent of hydrogen concentration f zero order in hydrogen; (iii) CH2F2 formed via reaction with adsorbed hydrogen f 0.5 order in hydrogen; and (iv) CHClF2 formed via reaction with adsorbed HCl f first order in HCl. This leads to the reaction rate equations shown in Figure 7. Clearly, the equations in this model are less complicated than in the mechanistic model. The main difference between the mechanistic and the LHHW-type model is that the adsorbed species are directly coupled to the concentration of one of the reactants or products for the LHHW-type model. Moreover, the catalytic routes on the catalyst surface are not taken into account. Therefore, the fact that a number of adsorbed species can be formed from more than one substance (*H can be formed from HCl or H2 and *Cl can be formed from CCl2F2 or HCl) is not taken into account. A number of adaptations can be made to compensate for these shortcomings of the LHHW model, such as the following: (1) Variation in the reaction order in hydrogen. Generally, this option would be a logical way to improve the model performance. It should be noted, however, that this improvement might compensate for shortcomings in the adsorption term. For example, the reaction order of hydrogen might be increased by a factor of 0.5 in all reactions. (2) Variations in the adsorption term. Examples of possible adaptations in the adsorption term are shown in Figure 8. A number of variations will be used for comparison with the mechanistic model. A summary of these models, included in the evaluation, is shown in Table 2. 3. Experimental 3.1. Materials. Sodium hydroxide pellets (>98.5% purity) and 36-38% hydrochloric acid (Baker grade) were supplied

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by Baker. CCl2F2 was supplied by Uniechemie (Arcton 12, ∼98% purity). Palladium chloride was supplied by Alfa (99% purity). Hydrogen was supplied by Air Products (99.95% purity) and was used as received. The activated carbon extrudates (RB1, d ) 1 mm, l ) 3-5 mm, and BET ) 1060 m2) were a gift from Norit N.V. Palladium (1 wt %) on purified RB1 activated carbon was a gift from Johnson Matthey Plc. 3.2. Catalyst Preparation. A 1 wt % palladium on activated carbon catalyst has been prepared by incipient wetness impregnation using palladium chloride dissolved in hydrochloric acid. Optionally, the activated carbon support was crushed and sieved before introduction of the palladium. The acid concentration was chosen to give a chlorine-to-palladium ratio of 10 mol/ mol. Prior to introduction of the palladium, 50 g of the activated carbon has been sequentially treated with 0.5 M aqueous sodium hydroxide, water, 0.5 M aqueous hydrochloric acid, and water with a flow of 1 L/h for 5 h and dried overnight at 373 K. The prepared catalyst was treated in nitrogen, while the temperature was raised to 623 K with a heating rate of 1 K/min and kept at that temperature for 1 h. The catalyst was reduced in situ under hydrogen flow from ambient temperature up to 540 K with a heating rate of 1 K/min. Optionally, the exact amounts of catalyst to be used were crushed using a pepper mill before introduction into the microreactor, which resulted in particles of 1 mm and smaller. This procedure was used in order to prevent differences in activity and selectivity between the crushed catalysts. It has been shown that the used catalyst is of the eggshell type.2 Because the palladium is not homogeneously distributed throughout the activated carbon extrudates, it is not possible to obtain a reproducible catalyst sample after the catalyst is crushed and sieved. Furthermore, on a commercial production scale, 1 wt % palladium on RB1 activated carbon was prepared by Johnson Matthey Plc. according to the same recipe. 3.3. Catalytic Experiments. The catalytic experiments have been carried out using a multi-microflow-reactor setup, including GC product analysis. Before the actual kinetic experiment, catalysts with different particles sizes were used in order to check for occurrence of internal mass transfer limitations in the kinetic experiment according to Kapteijn et al.13 In the second (kinetic) experiment, pepper-milled catalyst samples of the commercially produced catalyst by Johnson Matthey Plc were used. Six samples of catalyst (1.03, 1.54, 2.01, 2.56, 2.94, and 4.05 g) were crushed using a pepper mill, then quantitatively mixed with SiC, and placed in a reactor with additional SiC. The catalysts were heated with hydrogen from room temperature up to the reaction temperature under flowing hydrogen. Subsequently, the CCl2F2 was introduced and a sequence of measurements was carried out at different process conditions. The concentrations of CCl2F2 and hydrogen were varied during the kinetic experiment between 25-65 kPa and 7-13 kPa, respectively. The experimental sequences were measured at 470, 480, 490, 500, 510, and 520 K. The CCl2F2 feed was 2 g/h at temperatures of 470, 480, and 490 and 3 g/h at 500, 510, and 520 K. A reference measurement at 490 K, a CCl2F2 feed of 2 g/h, a H2/CCl2F2 ratio of 10 mol/mol, and a total pressure of 0.5 MPa was carried out before and after the measurements at one temperature to check for changes in catalyst performance. For practical reasons, the experimental sequence has not been randomized. The temperature was measured in the following order:

490 - 470 - 480 - 520 - 500 - 510 - 490 K The kinetic parameters in the different models have been estimated by fitting the rate expressions to the experimental data

Figure 11. Comparison of the fit of different LHHW-type models (conditions: T ) 490 K, P ) 0.7 MPa, and H2/CCl2F2 ) 10 mol/mol) (for details, see Figure 10).

Figure 12. Comparison of prediction by mechanistic and basic LHHWtype model (conditions: P ) 0.5 MPa, H2/CCl2F2 ) 10 mol/mol, WHSV ) 1 g/(g‚h))(for details, see Figure 10). Table 3. Parameter Values for the Mechanistic Model parameter

value

sNtk2,0 sNtk9,0 S0 K3,0 K8,0 Ea,2 Ea,9 Ea,s ∆Hads,3 ∆Hdes,8

1.62 × 1013 5.32 × 1013 1.17 × 10-4 4.29 8.4 × 10-4 102 kJ/mol 119 kJ/mol -29.2 kJ/mol -27 kJ/mol 0.3 kJ/mol

95% confidence 7.61 × 1012 2.50 × 1013 8.19 × 10-6 2.15 2.1 × 10-4 11.8 10.4 6.2 17.2 0.26

95% confidence (%) 47 47 6.9 50 25 12 9 21 64 86

by means of a nonlinear least-squares minimization of the relative error in the prediction of the concentration of products, using a homemade FORTRAN program NLS,14 with a simplex algorithm followed by a Levenberg-Marquardt minimization routine. The residuals were calculated relative to the measured concentrations. The differential equations have been integrated using the Bulirsch-Stoer method, assuming plug flow. The Arrhenius equation was used for the temperature dependency of the reaction rate equations, as shown in eq 36: -Ea

k ) k0 e RT

(36)

Before starting the optimization procedure, the pre-exponential factors (k0) and the activation energy (Ea) were reparameterized according to Mezaki and Kittrell15 in order to reduce the crosscorrelated dependency of these parameters. External mass transfer was assumed to be not limiting, whereas external heat transport limitations were checked for by calculating the criterion of Kapteijn et al.,13 shown in eq 37.

dp|∆Hr|r RT < 0.3 RT Ea

(37)

Ind. Eng. Chem. Res., Vol. 46, No. 12, 2007 4163 Table 4. Parameter Values for the LHHW-type Modelsa basic k0,22 k0,32 k0,50 Ea,22 Ea,32 Ea,50 KH2 KHCl K12 KHF ∆HH2 ∆HHCl ∆H12 ∆HHF a

e

HCl

e

CCl2F2

e

HF

e

H2

e

6.3 × 3.2 × 1016 7.2‚1016 87.2 124 130 3.4 × 104 3.7 × 10-11

40 40 40 8 7 7 40 62

3.6‚ × 1.4 × 1014 2.5 × 1014 78.5 114 119 1.7 × 103 7.2 × 102

30 30 30 12 11 9 34 18

1.2 × 104 -8.7 -103

24 68 70

-18 0

95 83

-2.4

70

6.3 × 3.6 × 1010 6.5 × 1010 43.2 80.0 85.1 1.1 × 10-3 4.6 × 10-3

36 36 35 30 22 18 38 23

1.4 × 7.9 × 1015 1.6 × 1016 90.6 128 133 2.7 × 104 2.9 × 10-6

25 24 24 7 7 6 27 24

1.1 × 7.5 × 1013 1.3 × 1014 68.1 106 111 8.4 × 104 2.7 × 10-3 47

28 28 28 9 9 7 33 19 54

-68 -1.4 × 10-3

38 76

-2.5 × 10-2 -1.9

74 91

-3.5 × 10-2 -0.12 -3.5 × 10-2

89 89 89

105

1011

109

1011

e ) Relative error of parameter (%); Ea and ∆H in kJ/mol.

Table 5. Overall Relative Error in the Fit of the Selectivity to the Different Components and Overall Conversion

sel. CH2F2 sel. CHClF2 sel. CH4 conversion

mechanistic (%)

LHHW basic (%)

LHHW HCl (%)

LHHW CCl2F2 (%)

LHHW HF (%)

LHHW H2 (%)

1.1 14 12 18

1.9 10 17 17

1.3 15 10 15

1.9 14 17 18

1.3 11 17 15

1.3 11 17 16

4. Results No differences in performance between the catalysts of different particle sizes were observed under the conditions tested in the explorative experiment. However, it appeared that a significant difference was observed between the different reference measurements during the kinetic experiment. 4.1. Reference Measurements. Figure 9 shows the results of the reference measurements. This figure shows that, depending on the history of the catalyst, significant fluctuations in the catalyst performance occur. The main differences are found in the catalyst activity, whereas only minor differences in selectivity are observed. In previous experiments,4 it was concluded that modifications of the active catalyst surface occur, which depend on the reaction conditions applied. Obviously, these modifications cannot be compensated for in the kinetic experiment and are, therefore, an intrinsic effect of the catalyst. Figure 10 shows that the relative error introduced by the catalyst modifications during the kinetic experiment is in the order of 10%. In general, the selectivities to the desired products CH2F2, CHClF2, and CH4 are on average 80 ( 2%, 12 ( 2%, and 8 ( 2%, respectively, almost independent of conversion level of CCl2F2 and the applied reaction conditions. Only when a relatively high concentration of HCl is in the gas phase does the selectivity toward CHFCl2 slightly increase at the expense of CH2F2. This once more illustrated that, for the conversion of CCl2F2, a serial mechanism for the production of CHClF2 and CH2F2 is applicable and, for the formation of methane, a parallel mechanism is in force. 4.2. Kinetic Model Prediction. Figure 11 shows a typical result of the prediction of the conversion and the selectivities for the main products CHClF2, CH2F2, and methane as a function of the amount of catalyst. This figure shows that the catalyst activity is not linearly dependent on the amount applied. For example, the conversion observed with 1.5 g of catalyst is higher than or equal to the conversion observed with 2 g. The kinetic experiment has been carried out with a 1 wt % palladium on activated carbon catalyst produced at a commercial produc-

tion scale. Differences in amount of palladium on the extrudates of the relatively small catalyst samples might be the cause of the inhomogeneous distribution of palladium. The fit of the selectivities is rather accurate, whereas the largest error is observed in the fit of the conversion. Generally, at lower amounts of catalyst, a too-high conversion is predicted, whereas at higher amounts, a too-low conversion is predicted. A comparison of the model fit as a function of temperature, as depicted in Figure 12, shows a too-high predicted conversion at lower temperatures, whereas at higher temperature, the prediction is too low. The parameter values are summarized in Tables 3 and 4. This table shows that the accuracy of the estimated parameters is higher for the activation energies and lower for the pre-exponential factors. Furthermore, the error in the selectivity determining term S is relatively small. The overall error in fitting the conversion level is 18%. 4.3. Comparison of Kinetic Model with LHHW-Type Models. Figures 11 and 12 show a comparison of the kinetic model with the basic LHHW model. It shows that the prediction of both models is similar; the error in the prediction of the conversion is 17%. The main conclusion of the comparison of the different models was that the behavior and fit of all LHHWtype models appears to be rather similar. Table 5 summarizes the error of all kinetic models. From this table, it is clear that the overall relative error in the fit of the conversion is between 15 and 18%, depending on the model used. The mechanistic model has the largest error. The LHHW-type models can be divided into two groups, based on their error in the conversion: the basic and the CCl2F2 LHHW-type models with a similar error of 17% and the HCl-, HF-, and H2 LHHW-type of models with reduction of the error to ∼15%. 5. Discussion 5.1. Mass or Heat Transfer Limitation. Mass transfer is not limiting during the kinetic experiment. The crushed catalysts in the explorative experiment showed a slightly lower conversion, whereas the conversion should be inversely proportional to the diameter of the catalyst pellet in the case of mass transfer limitation. Moreover, the activation energies, as found by fitting the kinetic models to the experimental data, also strongly support a chemically controlled reaction rate. Heat transfer limitations have not occurred during the kinetic experiment, as is demonstrated when the criterion for external heat transfer is calculated. For example, in a worst-case scenario (i.e., methane is produced at the initial rate of CH2F2), eq 37 can be solved with the following assumptions: dp ) 0.0015 m, ∆Hr ) -300 kJ/mol, r ) 0.01 mol/s, T ) 500 K, R ) 10 J/(m2‚

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K‚s), and Ea ) 120 kJ/mol. It follows that

dp|∆Hr|r RT ) 0.009; 0.3 ) 0.01 RT Ea

(38)

Thus, the criterion is satisfied within the experimental window applied, and no mass or heat transfer limitations have occurred during the kinetic measurement. Hence, the measured conversion and selectivities can be used for kinetic modeling. 5.2. Comparison of the Kinetic Models. The kinetic modeling is complicated because of the modification of the catalyst with process conditions and the history of the catalyst. This modification has also been found in other experiments2 and can be considered to be an intrinsic effect of the catalyst. Because the exact influence of the process conditions on the catalyst modification is not clear, it cannot be compensated for in the kinetic experiment. Thus, the error introduced by the modification of the catalyst, estimated at 10-15%, is also introduced in all kinetic models. Another error is introduced by the fact that the measured conversion is not a linear function of the amount of catalyst. A logical explanation for this observed phenomenon would be that the palladium is not homogeneously distributed over the activated carbon extrudates. Differences in the amount of palladium on the extrudates of the relatively small catalyst samples are then unavoidable, because a representative catalyst sample is difficult to obtain. Only 1-4 grams of the commercial catalysts were taken. The inhomogeneous distribution of palladium is not surprising, because the kinetic experiment has been carried out with a 1 wt % palladium on activated carbon catalyst produced at a commercial production scale. It can be concluded that the performance of all models is satisfactory. Considering the error introduced into the measured values by the catalyst modification and the inhomogeneous distribution of palladium, a discrimination between the different models on the basis of the experimental dataset is not possible. Hence, discrimination between the LHHW-type models on the basis of the fitting results cannot be justified. On the other hand, the performance of the mechanistic model is, in spite of the assumptions and neglections, surprisingly accurate and similar to the more general LHHW model. Adding more adsorbed components or more parameters in the model can make only minor improvements to the performance of this LHHW model. Although such minor improvements to the mechanistic model might also be possible, such as addition of the reaction of *CHF2 with *C or *CHF2 to methane, the effect of these improvements can be expected to be small considering the large experimental error. It can be concluded that, on the basis of the fitting results, no discrimination between the models can be made. However, all the aspects of the reaction mechanism as described in ref 4 are intrinsically incorporated in the mechanistic model, whereas in postulation of the LHHW type of models, a large concession to these aspects had to be made. This strongly favors the mechanistic model. Hence, for the development of kinetic models in cases where the experimental error is large and a discrimination between different kinetic models is difficult, the use of mechanistic models is preferable. The reaction of CCl2F2 to CH2F2 can be used as an example of the derivation of a reaction mechanism for a reaction with a combination of parallel and serial reactions on the catalyst surface. 6. Conclusions A kinetic model based on the reaction mechanism was derived with an overall relative error of 18% in the prediction of the

conversion. A large part of this error is caused by an unavoidable catalyst modification during the catalytic experiments. The mechanistic model can describe the CCl2F2 hydrogenolysis reaction almost as accurately as the more commonly used Langmuir-Hinshelwood-Hougen-Watson (LHHW) type of kinetic models. The prediction and behavior of all models, both mechanistic and LHHW-types, were similar, and no clear discrimination could be made on the basis of the available data. The main difference between the models was observed in the prediction of the conversion, whereas all models predicted similar selectivities. The relative error in the predicted conversion is in the range of 15-18% for all models. The development of kinetic equations derived directly from a sequence of elementary steps leads to a practical and applicable model, in which the adsorption of carbon containing species can be neglected. Moreover, in spite of a complex reaction mechanism, the reaction rate equations found are not too complicated for practical use for the reactor design for a conceptual process design. Its theoretical background strongly favors the use of the LHHW model, based on the elemental steps. Nomenclature ADS ) adsorption term mechanistic model ADS2 ) adsorption term of carbon containing species ADS* ) adsorption term LHHW-type models C ) concentration (mol/m3) C12 ) CCl2F2 concentration (mol/m3) C22 ) CHClF2 concentration (mol/m3) C32 ) CH2F2 concentration (mol/m3) C50 ) methane concentration (mol/m3) CH2 ) hydrogen concentration (mol/m3) CHCl ) hydrochloric acid concentration (mol/m3) CHF ) hydrofluoric acid concentration (mol/m3) dp ) volume equivalent diameter of particles (m) Ea ) activation energy (kJ/mol) Ea,22 ) activation energy of CHClF2 formation (kJ/mol) Ea,32 ) activation energy of CH2F2 formation (kJ/mol) Ea,50 ) activation energy of methane formation (kJ/mol) Ea,i ) activation energy of reaction i (kJ/mol) Ea,s ) activation energy for selectivity term (kJ/mol) F0 ) flow (m3/s) Nt ) total number of active sites ki ) reaction rate constant of reaction i (varying) k22 ) reaction rate constant of CHClF2 formation (varying) k32 ) reaction rate constant of CH2F2 formation (varying) k50 ) reaction rate constant of methane formation (varying) k0,i ) pre-exponential factor of reaction (varying) k0,22 ) pre-exponential factor for CHClF2 formation (varying) k0,32 ) pre-exponential factor for CH2F2 formation (varying) k0,50 ) pre-exponential factor for methane formation (varying) k0,s ) pre-exponential factor for selectivity term (varying) Ki ) equilibrium constant of reaction i K12 ) equilibrium constant of CCl2F2 adsorption KH2 ) equilibrium constant of hydrogen adsorption KHCl ) equilibrium constant of HCl adsorption KHF ) equilibrium constant of HF adsorption r ) reaction rate (mol/s) ri ) reaction rate of reaction i (mol/s) r22 ) reaction rate for production of CHClF2 (mol/s) r32 ) reaction rate for production of CH2F2 (mol/s) r50 ) reaction rate for production of methane (mol/s) R ) gas constant (8.314) (J/(mol‚K))

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s ) number of neighboring sites S ) selectivity-determining term T ) temperature (K) n ) number of sites involved in the rate-determining step Nt ) total number of catalyst sites W ) amount of catalyst in reactor (kg) R ) heat transfer coefficient (kJ/(m2‚K‚s)) ∆Hr ) reaction enthalpy (kJ/mol) ∆HH2 ) adsorption enthalpy of hydrogen adsorption (kJ/mol) ∆HHCl ) adsorption enthalpy of HCl adsorption (kJ/mol) ∆H12 ) adsorption enthalpy of CCl2F2 adsorption (kJ/mol) ∆HHF ) adsorption enthalpy of HF adsorption (kJ/mol) ∆Hads,i ) adsorption enthalpy of reaction i (kJ/mol) ∆Hdes,i ) desorption enthalpy of reaction i (kJ/mol) Literature Cited (1) Kanta Rao, P.; Rama Rao, K. S.; Hari Padmasri, A. Transformation of chlorofluorocarbons through catalytic hydrodehalogenation. CATTECH 2002, 7, 218. (2) Wiersma, A.; Van de Sandt, E. J. A. X.; Makkee, M.; Van Bekkum, H.; Moulijn, J. A. Comparison of the performance of activated carbon supported noble metal catalysts in the hydrogenolysis of CCl2F2. J. Catal. 1998, 177, 29. (3) Averill, B. A.; Rietjens, I. M. C. M.; van Leeuwen, P. W. N. M.; van Santen, R. A. Bonding and elementary steps in catalysis in catalysis: An integrated approach. van Santen, R. A., van Leeuwen, P. W. N. M., Moulijn, J. A., Averill, B. A., Eds. Stud. Surf. Sci. Catal. 1999, 123, 109. (4) Van de Sandt, E. J. A. X.; Wiersma, A.; Makkee, M.; Van Bekkum, H.; Moulijn, J. A. Mechanistic study of the selective hydrogenolysis of CCl2F2 (CFC-12) into CH2F2 (HFC-32) over palladium on activated carbon. Recl. TraV. Chim. Pays-Bas 1996, 115, 505.

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ReceiVed for reView August 24, 2006 ReVised manuscript receiVed November 23, 2006 Accepted November 27, 2006 IE0611195