Al2O3 Catalyst in a

The kinetics of hydrogenation of 2,4-dinitrotoluene (2,4-DNT) using a 5% Pd/Al2O3 catalyst was studied in a semibatch slurry reactor in a temperature ...
0 downloads 0 Views 469KB Size
Download PDF
592

Ind. Eng. Chem. Res. 1997, 36, 592-604

Hydrogenation of 2,4-Dinitrotoluene Using a Pd/Al2O3 Catalyst in a Slurry Reactor: A Molecular Level Approach to Kinetic Modeling and Nonisothermal Effects Malyala V. Rajashekharam, Dattu D. Nikalje, Rengaswamy Jaganathan, and Raghunath V. Chaudhari* Chemical Engineering Division, National Chemical Laboratory, Pune 411 008, India

The kinetics of hydrogenation of 2,4-dinitrotoluene (2,4-DNT) using a 5% Pd/Al2O3 catalyst was studied in a semibatch slurry reactor in a temperature range of 323-363 K. Experimental data on the concentration-time and H2 consumption-time profiles were obtained, and the effects of 2,4-DNT concentration, H2 pressure, and catalyst loading were studied under both isothermal and nonisothermal conditions. A fundamental approach based on a molecular level description of the catalytic cycle has been used to derive the rate models. Several rate forms were derived considering different types of interactions, but the rate equations derived assuming that the reaction between the transient molecular species formed due to the interactions of H2 and liquid phase components on different sites of Pd catalyst were found to best represent experimental data. The overall hydrogenation rate was found to vary by approximately second order with respect to catalyst loading, and this trend is adequately explained by the kinetic model proposed. It was found that the intraparticle diffusional effects were important for particle sizes (dp) > 3 × 10-4 m, but the external mass-transfer (gas-liquid and liquid-solid) effects were unimportant. For a complex rate equation observed, an approximate expression for the overall effectiveness factor was derived and the experimental data for different particle sizes were found to agree with the predictions of the model incorporating intraparticle diffusion effects. Under certain conditions, a significant temperature rise was observed and the increase in temperature was found to vary with time and the initial set of conditions. A mathematical model to predict the temperature and concentration profiles in a semibatch reactor under nonisothermal conditions has been proposed. A comparison of the experimental data with model predictions showed an excellent agreement. Introduction Hydrogenation of nitro compounds is practiced in a variety of industrial processes for the manufacture of aromatic amines, which find applications as intermediates in fine chemicals and pharmaceuticals. An important example of this class of reactions is the hydrogenation of 2,4-dinitrotoluene (2,4-DNT) to 2,4-toluenediamine (2,4-TDA), which finds application as an intermediate in the manufacture of polyurethane foams. This is a well-known commercial route for 2,4-TDA, and the process is usually carried out in continuously operated stirred-tank slurry reactors (Kirk-Othmer, 1978; Kosak 1984). The processes vary depending on the catalyst type used and mode of separation of the catalyst from products. Hydrogenation of 2,4-DNT involves complex multistep reactions with significant exothermicity (-∆H ) 5.56 × 105 kJ/kmol of nitro group; McNab, 1981). The overall performance of such reactors would depend on intrinsic kinetics, interphase mass transfer, intraparticle diffusion, heat-transfer efficiency, and mixing of the fluid phases. A knowledge of intrinsic kinetics is most essential to investigate the modeling of such industrially important reaction systems. In this paper, kinetic modeling of hydrogenation of 2,4-DNT using 5% Pd/Al2O3 catalyst in a slurry reactor has been reported using a molecular level approach. Hydrogenation of 2,4-DNT to 2,4-TDA proceeds through several steps involving complex consecutive and parallel reactions. The conversion of 2,4-DNT with 5% * Author to whom correspondence should be addressed. S0888-5885(96)00365-X CCC: $14.00

Pd/C catalyst is known to proceed via intermediate products such as 4-(hydroxylamino)-2-nitrotoluene (4HA2NT), 2-amino-4-nitrotoluene (2A4NT), and 4-amino-2-nitrotoluene (4A2NT) (Janssen et al., 1990a,b; Neri et al., 1995). These authors have studied intrinsic kinetics of the reaction using 5% Pd/C catalyst and proposed rate equations based on the L-H mechanism considering Scheme 1. In both cases noncompetitive adsorption of liquid-phase components and hydrogen was found to represent the experimental data. However, the rate expressions reported by Janssen et al. (1990b) assume a dissociative adsorption of hydrogen, while the rate model reported by Neri et al. (1995) is based on adsorption of molecular hydrogen on the active catalyst. Further, Janssen et al. (1990b) have also suitably corrected the reaction rate constants by taking into account the rapid deactivation during the induction period (before catalyst attained a stable activity) in the kinetic model. The intrinsic kinetics and intraparticle diffusion effects for hydrogenation of 2,4-DNT are also reported by Molga and Westerterp (1992) for 5% Pd/ Al2O3 catalyst pellets, wherein Pd was supported only in the outer shell of 100 µm thickness. It was shown that intraparticle diffusion effects were significant for catalyst particles >60 µm. While the L-H approach for kinetic modeling of catalytic reactions has been extensively used in chemical reaction engineering, it is believed that these models are empirical in nature and do not reflect deeper understanding about the nature of the active sites and real catalytic species (Waugh, 1996). Also, some unusual kinetic trends are not adequately explained by these empirical models. It is more appropriate to © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 593 Scheme 1

Table 1. Range of Operating Conditions 4HA2NT

H2

4A2NT

2H2

3H2

2,4-DNT

2,4-TDA

3H2

2A4NT

3H2

consider reaction mechanisms which describe stoichiometric interactions between the reactants and catalysts to evolve mechanistic rate models. With recent developments of modern tools for characterization of catalytic species and advances in molecular modeling (Lerou and Ng, 1996), it is possible to develop rate equations which are mechanistically more meaningful. In this paper, a detailed description of the mechanism of hydrogenation of 2,4-DNT has been considered involving molecular level interactions of the different species, to analyze intrinsic kinetic data. For the purpose of kinetic modeling, using a 5% Pd/ Al2O3 catalyst, the effect of 2,4-DNT concentration, catalyst loading, agitation speed, H2 pressure, and catalyst particle size on concentration-time and H2 consumption-time profiles was studied in a temperature range of 323-363 K. Several rate equations were derived considering elementary steps which lay stress on the different types of interactions occurring between the reactant/products and the active catalyst particles. Also, the discrimination of various rate models, evaluation of kinetic parameters, and adequacy of different models have been discussed. It was also the goal of this work to understand the rate behavior on a particle level and hence study the intraparticle diffusion effects in a stirred basket reactor. For this purpose, the 5% Pd/ Al2O3 catalyst powders themselves were pelletized to achieve catalyst particles with uniform Pd distribution. Hydrogenation of 2,4-DNT is also an interesting example of a complex multistep reaction with large heat effects. Hence, experimental data were also obtained under nonisothermal conditions in which concentration and temperature profiles in a semibatch slurry reactor were observed. A mathematical model for a semibatch slurry reactor under nonisothermal conditions has been developed which allows prediction of concentration and temperature profiles. A comparison of the experimental data with model predictions has been discussed. Thus, this paper presents a detailed reaction engineering case study for a complex exothermic reaction of industrial significance including a molecular level approach to kinetic modeling. Experimental Section Materials. 2,4-DNT obtained from M/s Fluka, Buchs, Switzerland, was thoroughly dried to remove moisture before use. The solvent ethyl acetate was obtained from M/s S.D. Fine Chemicals, Bombay, India, and was freshly distilled prior to use. H2 and N2 gases were obtained from M/s Indian Oxygen Ltd., Bombay, India, and were used directly without further purification. The precursor for the catalyst PdCl2 was supplied by M/s Arora Matthey, Calcutta, India, and the support activated alumina (Puralox SCFA-240) from M/s Condea Chemie, Germany, was used. The catalyst was prepared by the method described by Mozingo (1956). The powdered catalyst was pelletized and sieved through standard test sieves to obtain the desired range of particle sizes (3 × 10-4, 6.3 × 10-4, 1 × 10-3, and 2 ×

catalyst loading (kg/m3) agitation speed (Hz) hydrogen pressure (MPa) 2,4-DNT concentration (kmol/m3) temperature (K) particle size for kinetic study (m) particle size for studying intraparticle diffusion effects (m) volume of liquid phase (m3)

6.3-18.7 8-22 0.34-2.75 0.12-0.93 323-363 1 × 10-5 3 × 10-4-2 × 10-3 1.25 × 10-4

Specifications of the Catalyst Used Pd content [% (w/w)] 5 support Al2O3 particle size (m) 1 × 10-5 particle density (kg/m3) 1.8 × 103 porosity 0.5 surface area (m2/kg) 2.4 × 105

10-3 m). The detailed specifications of the catalyst are given in Table 1. Kinetic Study. All hydrogenation experiments were carried out in a 3 × 10-4 m3 capacity stirred pressure reactor with provisions for automatic temperature control, variable stirrer speeds, and sampling of gases and liquids. A schematic of the experimental setup is shown in Figure 1. In a typical hydrogenation experiment, known amounts of 2,4-DNT, catalyst, and solvent ethyl acetate were charged into the reactor. The reactor was first purged with N2 and then with H2 at room temperature. The contents were heated to a desired temperature, and then H2 gas was introduced to the required pressure level. The reaction was started by switching the stirrer on. The progress of the reaction was followed by recording the H2 pressure drop in the reservoir vessel. Liquid samples were also withdrawn at regular intervals of time and were analyzed by using a Sigma 2000 Perkin-Elmer gas chromatography (GC) containing a 2 m long SS column packed with 5% Dexil 300 on DMCS, Chromosorb W(AW) 80-100 mesh. The conditions of GC analysis are as follows: FID temperature, 573 K; injection temperature, 573 K; column temperature, 423-463 K (programmed at 5 K/min); N2 carrier gas, 3 × 10-5 m3/min. A few samples were also analyzed by GCMS to confirm the various products. Experiments To Study Intraparticle Diffusion Effects. In order to study the intraparticle diffusion effects in hydrogenation of 2,4-DNT, a basket type of reactor is used. A wire mesh basket was made to suspend the catalyst particles in the stirred reactor. The wire mesh basket was made of SS sieve of 120 mesh (BSS) and was stationary, attached to the dip tube of the reactor. Experiments under Nonisothermal Conditions. Experiments under nonisothermal conditions were carried out in a manner similar to that described in the Experimental Section to study the kinetics, except that the circulation of water through the cooling coil was disconnected and the reactor was brought to the desired temperature by circulating hot 10% aqueous ethylene glycol solution through the outer jacket of the reactor. Results and Discussion The experiments on hydrogenation of 2,4-DNT (Figure 2) were carried out with the aim of (a) first defining the reaction scheme and identifying the products, (b) understanding the kinetics of hydrogenation of 2,4-DNT based on a more fundamental approach of molecular level modeling, (c) understanding intraparticle diffusion

594 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

Figure 1. Schematic of the reactor setup: (1) reactor; (2) stirrer shaft; (3) impeller; (4) cooling water; (5) sampling valve; (6) magnetic stirrer; (7) furnace; TI, thermocouple; PI, pressure transducer; CPR, constant-pressure regulator; PR, pressure regulator; TR1, reactor temperature indicator; TRG, gas temperature indicator; PR1, reactor pressure indicator; PR2, reservoir pressure indicator; TR2, reservoir temperature indicator.

Scheme 2 3H2

4A2NT 2

2,4-DNT 1

2,4-TDA 4

3H2

2A4NT 3

Figure 2. Reaction mechanism for hydrogenation of 2,4-DNT.

effects, and (d) understanding the performance of a nonisothermal semibatch slurry reactor.

3H2

3H2

Experimental data were obtained for a wide range of operating conditions as shown in Table 1 to observe both the initial rate of hydrogenation and integral concentration-time profiles, under isothermal conditions. In order to study nonisothermal behavior, the conditions were chosen such that both the concentration and temperature varied as a function of time. The products formed during the hydrogenation of 2,4-DNT were found to be 4-(hydroxylamino)-2-nitrotoluene (4HA2NT), 2-amino-4-nitrotoluene (2A4NT), 4-amino-2-nitrotoluene (4A2NT), and 2,4-toluenediamine (2,4-TDA) as identified GC and GCMS analysis. Typical concentration profiles are shown in Figures 7 and 8 for 343 and 363 K for powdered catalyst 5% Pd/Al2O3. Since in the entire range of conditions studied in this work the amount of hydroxylamine intermediate (4HA2NT) formed was less than 2% of 2,4-DNT converted, the stoichiometric reaction pathway in Scheme 2 was considered. The initial experiments on the hydrogenation of 2,4DNT showed that the material balance of the reactants consumed (H2 and 2,4-DNT) and the products formed (2A4NT, 4A2NT, and 2,4-TDA) agreed to the extent of 95-97% as per the above stoichiometry. No hydrogenation took place without the catalyst, indicating the absence of homogeneous side reactions. Reproducibility of the rate measurements was found to be within 2-5% error as indicated by a few repeated experiments. Experiments to ensure constancy of the catalytic activity during a run were ensured by catalyst recycle studies (see Table 2). It was observed that the activity of the catalyst does not change significantly even after 10 recycles. Analysis of Initial Rate Data. The effects of various reaction parameters like 2,4-DNT concentration,

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 595 Table 2. Initial Rates and Catalyst Activity: Catalyst Recycle Studya catalyt (5% Pd/Al2O3)

initial rate RA × 104 kmol/m3/s

activity, kmol/kg of Pd/h

fresh recycle no. 1 4 10

6.25

13.16

6.2 6.22 6.19

13.04 12.99 12.01

a Concn of DNT: 0.46 kmol/m3. Catalyst: 12.5 kg/m3. Solvent: ethyl acetate. Temperature: 343 K. H2 pressure: 1.38 MPa. Reaction volume: 1.25 × 10-4 m3.

Figure 4. Effect of partial pressure of hydrogen on the initial rates of hydrogenation. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

Figure 3. Effect of DNT concentration on the initial rates of hydrogenation. Reaction conditions: catalyst, 12.5 kg/m3; solvent, EtOAC; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

catalyst loading, H2 pressure, and agitation speed on the initial rate data of hydrogenation of 2,4-DNT were studied at 323, 343, and 363 K. For calculating the initial rate data, the hydrogen consumption-time profiles observed under different conditions were fitted to a second-degree polynomial by a linear regression procedure. The effect of 2,4-DNT concentration on the initial rate of hydrogenation at different temperatures is shown in Figure 3. These results indicate a zeroorder dependence with respect to 2,4-DNT concentration in most conditions. The data presented in Figure 3 mainly represent the conversion of 2,4-DNT to 2A4NT and 4A2NT, and hence the trend observed cannot be generalized for all the hydrogenation steps. The other product, water, also had no effect on the initial rate for the present conditions. This was checked with separate experiments in which water concentration was varied. The rate of reaction was found to be linearly dependent on H2 pressure in a low-pressure range (3.44 × 102-6.89 × 102 KPa) and then the rate became independent of pressure, indicating a zeroorder dependence at high pressures as shown in Figure 4. The effect of catalyst loading on the initial rate (see Figure 5) indicates approximately a secondorder dependence at both 323 and 363 K. This trend with catalyst loading has been reported earlier by Alcorn et al. (1984) for hydrogenation of tallow fatty acids. However, these authors have explained their results based on the assumption that there is a certain critical concentration of the catalyst required to

Figure 5. Effect of catalyst loading on the initial rates of hydrogenation. Reaction conditions: concn of DNT, 0.46 kmol/ m3; solvent, EtOAC; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

initiate the reaction and termed it as “a threshold effect”. The classical approach of L-H type rate mechanisms may not be able to explain such complex effects, and hence a more fundamental approach needs to be considered. The effect of agitation speed on the initial rate is shown in Figure 6. The rate was found to be independent of the agitation speed, indicating the absence of external mass-transfer resistances under these conditions. Analysis of Mass-Transfer Effects. For the purpose of kinetic study it is important to ensure that the rate data obtained are under the kinetic regime. The initial rate data were analyzed to check the significance of gas-liquid, liquid-solid, and intraparticle masstransfer effects under the conditions used to study the kinetics following the quantitative criteria proposed by Ramachandran and Chaudhari (1983). In these criteria

596 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

R1, R2, and φexp, which are defined as the ratios of the observed rate to the maximum rates of gas-liquid, liquid-solid, and intraparticle mass-transfer rates, respectively, were calculated (see Appendix I). It was found that the values of R1, R2, and φexp were less than 0.095, 0.0058, and 0.17 for the data presented here, indicating that the rates obtained with 5% Pd/Al2O3 catalyst (dp ) 1 × 10-5 m) are in the kinetic regime and can be reliably used to evaluate the intrinsic kinetic parameters. For dp > 3 × 10-4 m the values of R1 and R2 were found to be in the range of 0.005-0.04 and 0.007-0.015, indicating that the gas to liquid and liquid to solid mass-transfer resistances may not be important even for higher particle sizes. The value of φexp was found to be >2.31, clearly indicating that there is significant intraparticle diffusional resistance for dp > 3 × 10-4 m. Kinetic Modeling: A Molecular Level Approach. For the purpose of kinetic modeling of a multistep catalytic reaction as involved in hydrogenation of 2,4DNT, the initial rate approach is not very useful. Analysis of integral concentration-time profiles under different initial sets of conditions is necessary in this case. This requires definition of a reaction scheme describing a detailed reaction mechanism which, in previous work, was based on a L-H type approach (Janssen, et al., 1990a,b; Molga and Westerterp, 1992; Neri et al., 1995). In this paper, a molecular level description of the catalytic cycle has been considered. For this purpose, knowledge of the stoichiometric interactions between Pd metal sites and the reactants, namely, H2 and 2,4-DNT, is necessary. The activation of H2 by Pd metal sites was investigated earlier by Paal and Menon (1983), Geus (1988), Christmann (1988), Burch (1980), and Engel and Kuipers (1979), in which it is proposed that Pd can form hydrides of the form shown in eq 1. Although the H Pd + H2 2Pd + H2

Pd

H

(1)

2Pd H

formation of these hydrides (R and β hydrides differing in hydrogen content are known to form with Pd surfaces) involves a L-H type mechanism, it is well understood that dissolved H2 on Pd metal surface can have a dramatic influence on the reaction rate since Pd can act as an H2 reservoir for reactive species (Benedetti et al., 1995). This effect, however, is normally overlooked due to the poor solubility of hydrogen in most metals, but for Pd, it becomes significant as it is known to form hydrides even at room temperature (Christmann, 1988, Engel and Kuipers, 1979). The activation of 2,4-DNT itself was not studied earlier; however, stoichiometric reactions between Pd complexes of the type [PdCl2(PPh3)]2 and PhNO2 allowed isolation of activated species such as [PdCl2(PPh3)PhNO2] with well-defined molecular structure (Banerjee and Sen, 1981). On the basis of this information, we propose a catalytic cycle to describe the mechanism of hydrogenation of 2,4-DNT as shown in Figure 2. It is also well-known that the reduction of the nitro group proceeds through nitroso and hydroxylamine intermediates. In most cases of Pd-catalyzed hydrogenation of nitro compounds, the nitroso derivative is not observed; however, hydroxylamine derivatives as intermediates are formed depending on the type of catalyst used and the reaction conditions. Considering the observed prod-

Figure 6. Effect of agitation speed on the initial rates of hydrogenation. Reaction conditions: concn of DNT, 0.46 kmol/ m3; catalyst, 12.5 kg/m3; solvent, EtOAC; PH2, 1.38 MPa; reaction volume, 1.25 × 10-4 m3.

uct distribution in the present work, the steps involving reduction of nitroso and hydroxylamine were considered to be very fast compared to the first step of formation of the nitroso derivative. Thus, several rate expressions were derived, assuming different types of interactions between Pd surface and reactants. In the derivation of the rate models some general assumptions made are as follows: (a) Hydrogen and reactant/product interact differently with the catalyst. (b) Depending on the position of the nitro group undergoing the reduction, the interactions may differ with the catalyst; however, in the final rate expression these steps are lumped. (c) The interactions are characterized by equilibrium constants which are analogous to the adsorption equilibrium constants used in the L-H type models. (d) Organic compounds compete with one another while interacting with Pd surfaces. (e) The unknown transient species are suitably expressed in terms of known parameters by taking into account the overall catalyst balance. Case 1. This model is derived assuming the reaction between palladium dihydride (Pd-H2) species with the transient molecular species formed due to the interactions of Pd and 2,4-DNT as the rate-limiting step as shown in eq 2. In order to arrive at a suitable rate CH3 Pd

H

N O2

+

Pd H

NH2 CH3 2

Pd + N O

+ H2O

(2)

NO2

equation, it is necessary to account for the overall Pd balance. From the scheme given in Figure 2, the overall Pd balance can be given by taking into account the different transient species formed with Pd and reactants/ intermediates as shown in eq 3.

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 597 CH3 Pd +

(Pd)total =

+

Pd

Pd

N O2

H

CH3

H

H

Pd

+

N O2

+

Pd H

NO2

NO2

CH3

CH3 Pd

N O2

CH3 +

Pd

Pd + N O

2

N O2

+ H2O

(10)

+ NO2

NO2 NH2 Pd

N O2

CH3

(3)

NH2

RA )

Equation 3 can be rewritten as (Pd)total =

∑kiCi-1 (1 + (KH C*H )0.5 + ∑KjCj)2 W2C* H2 2

Pd (1 + KH 2CH * + KjCj)

(4)

2

The following generalized rate expression is obtained for different hydrogenation steps shown in Scheme 2.

ki1KH2Ki(Pdtotal)2C* H2Ci-1

ri )

The overall rate of hydrogenation can be given as

(5)

∑KjCj)2

(11)

2

In order to verify the applicability of the above rate models under integral conditions and to evaluate the kinetic parameters for the models, experimental data on the liquid-phase concentrations of 2,4-DNT, 2A4NT, 4A2NT, and 2,4 TDA as a function of time were used. For constant hydrogen pressure and isothermal conditions, the following set of material balance equations (for case 1) were solved: 2 dC1 1 W C* H2(k1C1 + k2C1) ) dt 3 (1 + K C* + K C )2

(12)

2 dC2 1 W C* H2(k1C1 - k3C2) ) dt 3 (1 + K C* + K C )2

(13)

When i ) 1, Ci-1 ) Ci, and where ki ) ki1KH2Ki, Pdtotal is related to W as Pdtotal ) W(0.05/mol wt of Pd), considering the actual Pd content in the catalyst. The overall rate of hydrogenation is given as

2 dC3 1 W C* H2(k2C1 - k4C3) ) dt 3 (1 + K C* + K C )2

(14)

∑kiCi-1 RA ) 2 (1 + KH C* H + ∑KjCj)

2 dC4 1 W C* H2(k3C2 + k4C3) ) dt 3 (1 + K C* + K C )2

(15)

(1 + KH2C* H2 +

H2

This rate equation can be simplified as

ri )

W2kiC* H2Ci-1 (1 + KH2C* H2 +

(6)

∑

KjCj)2

H2

W2C* H2 2

(7)

H2

2

Case 2. If the reaction between Pd hydride species (Pd-H2) and liquid-phase components is assumed to be rate limiting as shown in eq 8, following the approach CH3

CH3

H

+ N

Pd H

Pd + N O

O2 NO2

+ H2O

(8)

NO2

shown in case 1, the overall rate of hydrogenation can be derived as

RA )

H2

∑kiCi-1 1 + KH + ∑KjCj WC* H2

(9)

2

Case 3. In this case it is assumed that both H2 and 2,4-DNT competitively react with the active Pd species to form the transient species (1). The reaction between a Pd monohydride species (Pd-H) and species 1 was assumed to be rate limiting.

H2

H2

H2

H2

∑

∑ ∑ ∑

j

j

j

j

j

j

j

j

with the initial conditions at t ) 0, C1 ) C10, and C2 ) C3 ) C4 ) 0, where C1, C2, C3, and C4 are the liquidphase concentrations of 2,4-DNT, 4A2NT, 2A4NT, and 2,4-TDA in kmol/m3. The above equations were solved using an optimization routine based on Marquardt’s algorithm combined with a Runge-Kutta method. For this purpose, the approximate values of the parameters were estimated from the typical concentration profiles as described earlier (Chaudhari et al., 1985). The experimental data were simulated for each temperature separately for different initial conditions, and the best common set of rate and equilibrium parameters were determined for different models and are listed in Table 3. For the purpose of model discrimination, the following object function was chosen as an optimization criterion and the optimization method involves the minimization of this criterion.

φmin )

∑(Yi

exp

- Yimod)2

(16)

The mean average of the relative residuals (% RR) was calculated as,

2.15 × 10-12 1.17 × 10-12 1.98 × 10-12 (21 (28 (33 19.56 7.89 -2.54 21.26 -3.62 2.54 28.21 79.54 106.4 20.01 26.16 23.42 2.02 24.03 -12.39 22.92 -13.57 54.51

n ) 1 for model 2 and n ) 2 for models 1 and 3. a

2 j

j

∑K C )] [1 + (KH2C*H2)0.5 + (

ri )

W2kIC*H2Ci-1

(1 + KH2C*H2 +

ri )

WkiC*H2Ci-1

j

j

∑K C )

2 j

j

∑K C ) (1 + KH2C*H2 +

ri )

% RR )

8.68 13.39 -5.25 100.12 -32.48 168.21 323 343 363

8.1 × 10-17 5.5 × 10-17 5.5 × 10-17 (10 (9 (13 4.53 4.23 6.8 1.31 1.81 3.27 8.01 15.06 23.26 0.52 0.94 2.71 3.93 × 10-2 9.11 × 10-2 1.8 × 10-1 9.31 × 10-3 2.45 × 10-2 8.19 × 10-2 2.36 × 10-2 6.79 × 10-2 1.70 × 10-1 3.32 × 10-2 1.08 × 10-1 3.44 × 10-1 323 343 363

φmin % RR

(8 (6 (7 2.38 1.62 1.44

K3 K2

2.35 1.44 0.83 10.12 5.25 3.11

K1 KH2

0.53 0.31 0.12 18.21 42.13 96.44

k4 k3

8.42 22.81 63.23 13.41 35.90 83.82

k2 k1

36.12 75.11 178.02 323 343 363

T, K rate equation

W2kiC* H2Ci-1

adsorption constants × 103 m3/kmol rate constants, (m3/kg)n(m3/kmol) s-1 a Table 3. Best-Fit Parameters for Different Models

1.28 × 10-18 5.37 × 10-17 3.90 × 10-18

598 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

(Yiexp - Yimod) Yiexp

× 100

(17)

The rate parameters for each model were evaluated by appropriately substituting in eqs 12-15 and solving the resulting equations by the procedure described above. The rate models were discriminated based on the values obtained for the optimization criterion and the meanaverage relative residuals. These values are also given in Table 3. The other methods to discriminate rate models, suggested by Froment and Bischoff (1979), were also considered. Thus, it was found that the first model in Table 3 based on the mechanism shown in Figure 2 fits best the experimental data. Furthermore, it was observed that, for constant catalyst loading, the second model also could explain the rate behavior reasonably well for a few sets of initial conditions. However, rate model 1 could explain the integral concentration-time profiles and H2 consumption time profiles for different sets of initial conditions at different temperatures. Also, this model explained reasonably well, unlike model 2, the effect of catalyst loading in which we observed an approximate second-order dependence. The rate equation of model 3 gave negative values as parameters and hence was rejected. Thus, based on the criteria of φmin and % RR values, model 1 representing the reaction mechanism described in case 1 was found to be the best to represent the kinetics of hydrogenation of 2,4-DNT. This model also represents several concentration-time profiles obtained under different initial sets of conditions unlike the other models. The experimental and predicted concentration-time data were found to agree within 6-8% error as shown in Figures 7 and 8 for 343 and 363 K, respectively. The kinetic parameters are presented in Table 3. Based on the temperature dependence of rate parameters, the activation energies were also evaluated as shown in Table 4. The activation energies for the four steps of hydrogenation were found to be in the range of 40-50 kJ/mol. These values are typically in the range reported by Bird and Thompson (1980) and Neri et al. (1995) for Pd catalysts. The heat of adsorption of H2 was found to be 38.24 kJ/mol, which is in the range (30.18 kJ/mol) reported in the literature for a Pd/C catalyst (Janssen et al., 1990b). The heats of adsorption of liquid-phase components were found to be in the range of 20-30 kJ/mol (see Table 4). These results indicate the strong interactions of these compounds with the Pd surface. Also, the ratios of equilibrium constants K1/K2 and K1/K3 being >1 indicate a stronger interaction of 2,4-DNT than 4A2NT and 2A4NT, as a result of which the depletion of 4A2NT and 2A4NT begins after almost all 2,4-DNT is consumed (see concentration-time profiles shown in Figures 7 and 8). The analysis of % RR as a function of H2 pressure and 2,4-DNT concentration also showed no particular trend, indicating the suitability of the model. These results indicate that the model derived based on the molecular level approach explains best the observed trends and is applicable for a wide range of conditions. Thus, the rate model reported in this work is different from the model reported by Molga and Westerterp (1992) for Pd/ Al2O3 catalyst. In their case, the 5% Pd/Al2O3 catalyst pellets wherein Pd was coated only on the outer shell of 100 µm thickness were crushed to study the intrinsic kinetics of the reaction. In this work, the catalyst has been prepared as a fine powder (dp ) 1 × 10-5 m) and hence a uniform distribution of Pd on the support was achieved. Also, the overall rates of hydrogenation in

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 599

different particle sizes. Analysis of initial rate data for different particle sizes indicated that the values of R1, R2, and φexp values were in the range of 0.005-0.04, 0.007-0.015, and 2.31-11.32. These results indicate that the external mass-transfer resistances (gas-liquid and liquid-solid) may not be important, while intraparticle mass-transfer resistance needs to be incorporated. Effectiveness factor equations applicable to the kinetics of hydrogenation of 2,4-DNT have been developed following the well-known approaches (Ramachandran and Chaudhari, 1983, Bischoff, 1965). The overall rate of hydrogenation can then be given as

RA )

∑kiCi-1 2 (1 + KH C* H + ∑KjCj) ηW2C* H2 2

Figure 7. Concentration-time profile at 343 K. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; temp, 343 K; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

(18)

2

Here η is the overall effectiveness factor incorporating both external and internal mass-transfer resistances. For this analysis it is assumed that the intraparticle diffusional gradients exist for dissolved H2 and the concentration of liquid reactant is uniform throughout the particle. This assumption is justified since, in most conditions, the criteria De,iCi/νDe,CH2C*H2 . 10 was satisfied. The expression for the overall effectiveness factor, η, is

(

ηc(1 + K* H2C* H2) 1 η)

[

(

1 + K* H2C* H2 1 -

η σA

η σA

)]

)

(19)

2

where

ηc )

1 1 coth 3φ φ 3φ

(

)

(20)

Here, φ is the Thile parameter and is given by the following approximate solution (Ramachandran and Chaudhari, 1983) φ)

[ ] Fpk1 De

Figure 8. Concentration-time profile at 363 K. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; temp, 363 K; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

our case were found to vary as first order with respect to H2 pressure and an approximately second order with respect to catalyst loading, unlike the case reported by Molga and Westerterp (1992), wherein they observe a square root dependence on H2 pressure and a linear dependence on catalyst loading. Intraparticle Diffusion Effects. For three phase catalytic reactions, intraparticle diffusion with reaction has been earlier studied for many cases and important work has been reviewed by Satterfield (1970) and Ramachandran and Chaudhari (1979, 1980, 1983). For hydrogenation of 2,4-DNT intraparticle diffusional effects have already been analyzed by Molga and Westerterp (1992) based on the analysis of the effectiveness factor and it was concluded that pore diffusional resistances are significant for particle sizes >60 µm. It was thought important to study intraparticle diffusion effects for the present case in order to understand the applicability of the kinetic model derived on a molecular level approach to explain the trends of rate behavior at

x[

(

0.5

K*H2C*H2 1 -

(

)/(

η σA

[

2 ln 1 + K* H2C* H2 1 -

[

1 + K* H2C* H2 1 -

]) (

η σA

(

K* H2C* H2 1 -

-

[

])

η σA

2

)

η σA

1 + K* H2C* H2 1 -

]

])

η σA

(21) where k1, K* H2, and σA are defined as

k1 )

∑WkiCi 1 + ∑KjCj

K* H2 )

σA )

(

K H2 1+

1 1 + kLaB ksap

)

∑KjCj

-1

(22)

(23)

2 (1 + K* H2C* H 2)

W2k1

(24)

Incorporating the contribution of intraparticle diffusion

600 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Table 4. Activation Energy Parameters (kJ/kmol) activation energy for hydrogenation step 1, E1 activation energy for hydrogenation step 2, E2 activation energy for hydrogenation step 3, E3 activation energy for hydrogenation step 4, E4 heat of adsorption of hydrogen, -∆HH2 heat of adsorption of DNT, -∆HDNT heat of adsorption of 4A2NT, -∆H4A2NT heat of adsorption of 2A4NT, -∆H2A4NT

39.05 45.10 49.44 40.85 38.24 29.92 25.80 20.39

Table 5. Estimated Values of the Tortuosity Factor from Best-Fit Values of Effective Diffusivity and Porosity temp, K

particle size dp × 103 m

simulated values of De × 1010 m2/s

tortuosity factor, τ

323 343 343 343 343 343 363

1.0 0.29 0.6 0.6 1.0 2.0 1.0

8.46 6.92 6.91 8.72 6.89 6.91 6.51

3.55 5.50 5.51 4.36 5.52 5.5 8.03

effects as described in eqs 18-24 in the mass balance equations (12)-(15), it is possible to predict the concentration-time and H2 consumption-time profiles in a semibatch slurry reactor. For predicting η the additional parameters required are dp and effective diffusivity, De, alongwith klaB and ks. The correlations used for calculating klaB and ks are discussed in Appendix I. The effective diffusivity values were evaluated by simulating the concentration-time profiles. The simulated values of De at different temperatures for different particle sizes are shown in Table 5. We have used the Wilke and Chang (1955) equation to evaluate the molecular diffusivity at different temperatures. The porosity of the catalyst was determined experimentally by a water absorption method. An average value of 0.22 was found to be the porosity of the catalyst. Thus, the calculated tortuosity factor τ is included in Table 5 and is shown to increase with temperature. A similar observation was made by Yucelen (1984) for the liquidphase hydrogenation of 2,6-DNT using Pd/Al2O3 catalyst. Also, the magnitude of the tortuosity factor obtained from this work compares well with the values reported in the literature by Satterfield (1970). Based on this model, the concentration-time profiles were predicted, and a comparison is shown for a typical case in Figure 9 for dp ) 6.3 × 10-4 m at 343 K. Also, the predictions of total hydrogen consumption vs time data for different particle sizes at 363 K match well with the experimental data as shown in Figure 10. Thus, a good agreement is found in within (8% experimental error, indicating that the above model explains the intraparticle diffusion effects satisfactorily. Nonisothermal Modeling. In this section the experimental results on the performance of a semibatch slurry reactor reactor under nonisothermal conditions are presented and compared with model predictions. Hydrogenation of 2,4-DNT is an excellent example of a highly exothermic reaction (-∆H ) 5.56 × 105 kJ/mol of a nitro group or 1.88 × 105 kJ/mol of hydrogen (McNab, 1981)), and the design and scaleup of the reactors for such processes must consider the nonisothermal effects. In this case, the kinetics, solubility, and mass-transfer parameters will also change in addition to changes in concentration of liquid-phase components with time due to temperature variation. This would affect the relative rates of mass transfer and chemical reaction at different times, and hence this factor needs to be considered in the analysis of nonisothermal slurry reactors. A detailed analysis of the nonisothermal batch

Figure 9. Concentration-time profile at 343 K for dp ) 6.3 × 10-4 m. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; temp, 363 K; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

Figure 10. H2 consumption vs time: effect of different particle sizes. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; temp, 363 K; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3.

slurry reactor for hydrogenation of m-nitrochlorobenzene has been addressed by Rode and Chaudhari (1994); such an analysis for a complex multistep reaction like hydrogenation of 2,4-DNT has not been reported. Considering the reaction mechanism given in Figure 2 and incorporating the changes in parameters that depend on temperature like saturation solubility, effective diffusivity, reaction rate constants, and mass-transfer parameters, a nonisothermal semibatch slurry reactor model has been derived applicable to hydrogenation of 2,4-DNT. The model takes into account the various complexities that arise due to exothermicity of the reaction. These complexities are (a) influence of temperature on the overall reaction rate and selectivity changes, (b) vaporization of the solvent, (c) parameters, He, CH2, rate constants, equilibrium constants, gasliquid mass transfer, which vary with temperature and hence with time. In deriving the nonisothermal batch slurry reactor model, the following assumptions have

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 601

respect to temperature, the variation of liquid-phase components under nonisothermal conditions can be expressed as follows:

Table 6. Thermicity Criteria for Intraparticle Heat Effects liquid saturation phase solubility C*H2 × 102 De × 1010 λeff × 103 bulk temp, K kmol/m3 m2/s kJ/s‚m‚°C β × 105

R

Rβ

323 323 433 433

6.77 6.77 11.53 11.53

8.46 8.46 5.5 5.5

41.8 4.18 41.8 4.18

15.5 155 5.35 53.5

27.08 27.08 20.21 20.21

0.004 0.042 0.001 0.01

been made: (a) Gas-liquid and liquid-solid mass transfer for H2 is considered, whereas liquid-solid mass-transfer resistance for liquid-phase components is assumed to be negligible. (b) Intraparticle and liquid-particle heat-transfer resistance is negligible, indicating that the bulk temperature is representative throughout the system. In order to justify the assumption of intraparticle heat transfer to be negligible, the criteria proposed by Mears (1971) were used. It is required to show the product of γβ is less than 0.05 (Mears, 1971), where γ and β are defined as

γ)

β)

E RgTs

(1 + (KH2)T(C*H2)T +

[

(1 + (KH2)T(C*H2)T +

[

(1 + (KH2)T(C*H2)T +

(-∆H)DeCH2,s λeffTs

(26)

(C*H2)T ) [P - (Pv)T](He)T

(27)

where

[

(1 + (KH2)T(C*H2)T +

(He)T ) 1.275 × 10-5 + 5.58 × 10-8T

( ( )) ( ( ))

(ki)T ) (ki)T0 exp (Kj)T ) (Kj)T0 exp

-Ei 1 1 R T T0

(30)

-∆Hj 1 1 R T T0

(31)

and the dependence of gas-liquid mass transfer on temperature is represented by the following equation:

KlaB ) KlaB

( ) T T0

0.5

(32)

On the basis of the above assumptions and taking into account the variation of different parameters with

(35)

]

(36)

dT ) dt (-∆HA)RAVR - UwAw(T - Tw) - QgFg(T - Tgt) (37)

(gVRFgCpg + VR(1 - g - w/Fp)FlCpl + WVRCps)

RA ) (C* H2)T

The above equation is applicable when ethyl acetate is used as a solvent (Weast and Astle, 1976). The dependences of kinetic rate constants and equilibrium constants on temperature are given as

]

The variation of temperature T is given by the following equation for a batch slurry reactor operated under nonisothermal conditions (Ramachandran and Chaudhari, 1983)

(28) (29)

(34)

∑(Kj)TCj)2 -1

W2[(k3)TC2 + (k4)TC3]

where

-0.2185 × 8365.2 + 8.00117 T

]

∑(Kj)TCj)2 -1

W2[(k2)TC1 - (k4)TC3]

dC4 1 1 1 ) (C* ) + + dt 3 H2 T (klaB)T (ksap)T 0

(33)

∑(Kj)TCj)2 -1

W2[(k1)TC1 - (k3)TC2]

dC3 1 1 1 ) (C* ) + + dt 3 H2 T (klaB)T (ksap)T 0

]

∑(Kj)TCj)2 -1

W2[(k1)TC1 + (k2)TC1]

dC2 1 1 1 ) (C* ) + + dt 3 H2 T (klaB)T (ksap)T 0

(25)

For the present study, as a first approximation the criteria given above were evaluated by assuming the surface concentration CH2,s and temperature Ts as C* H2 and Tb. The effective thermal conductivity, λeff, is normally in the range of 4.18 × 10-2-4.18 × 10-3 kJ/ s‚m‚°C as reported by Baldi (1981). Table 6 shows the product of γβ is less than 0.05 for all the temperatures studied. The change in partial pressure of H2 due to vaporization of solvent is accounted as

log(Pv)T )

[

dC1 1 1 1 ) (C*H2)T + + dt 3 (klaB)T (ksap)T0

[

1 1 + + (klaB)T (ksap)T0 (1 + (KH2)T(C*H2)T +

∑(ki)TCi-1]

W2[(

]

∑(Kj)TCj)2 -1

(38)

In order to predict the temperature and H2 consumption-time profiles, the above equations were solved using a Runge-Kutta method with the initial conditions at t ) 0, C1 ) C1 ) C10, C2 ) C3 ) C4 ) 0, and T ) T0. Here Tgi is the gas inlet temperature, Qg is the gas flow rate, g is the gas holdup, Tw is the temperature of the circulating liquid in the outer jacket of the reactor, Uw is the overall heat-transfer coefficient, and -∆HA is the heat of reaction. The values of different parameters used in deriving the nonisothermal model are listed in Table 7. The experimental data on H2 consumption and temperature rise-time profiles at different sets of initial conditions were compared with the model predictions. In all experiments, changes in temperature as well as H2 consumption (in the reservoir vessel) were observed as a function of time. Once eqs 33-36 along with eq 37 were solved to obtain the concentration of the liquidphase components and temperature at any given time

602 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

Figure 11. H2 consumption and ∆Tmax vs time at different temperatures. Reaction conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, EtOAC; PH2, 1.38 MPa; agitation, 18 Hz; reaction volume, 1.25 × 10-4 m3. Table 7. Values of Some Parameters Used for Nonisothermal Modeling heat capacity of gas, Cpg (J/kg/K) heat capacity of liquid, Cpl (J/kg/K) heat capacity of liquid, Cps (J/kg/K) heat of reaction, -∆H (kJ/kmol of H2) density of gas, Fg (kg/m3) density of liquid, F (kg/m3) reaction volume (m3)

13.83 × 10-3 2.01 × 103 7.106 × 10-4 1.88 × 105 9.0 × 102 0.8675 × 103 1.28 × 10-4

Table 8. Maximum Temperature Rise, ∆Tmax, Predicted at Different Initial Conditions for 323, 343, and 363 K temp rise, ∆Tmax, K initial conditions catalyst loading, kg/m3 9.4 12.5a 18.7 DNT concentration, kmol/m3 0.2 0.46a 0.8 H2 presure, MPa 0.8 1.38a 2.4

Ti ) 323 K

Ti ) 343 K

Ti ) 363 K

3 8 20

10 42 59

22 46 65

4 8 10

12 42 61

16 46 58

4 8 22

8 42 80

20 46 98

a Experimentally observed ∆T max also match within 5% error. General conditions: concn of DNT, 0.46 kmol/m3; catalyst, 12.5 kg/m3; solvent, ethyl acetate; H2 pressure, 1.38 MPa; reaction volume, 1.25 × 10-4 m3.

t for a set of initial conditions, the amount of hydrogen consumed was calculated as

H2 ) VR(3C2 + 3C3 + 6C4)

(39)

The kinetic parameters presented in Table 3 were used. The overall heat-transfer parameter, Uw, was evaluated by simulation of the H2 consumption-time and temperature profiles at 343 K. The value of Uw was 110.8 J/m2/s/K. This value was used for other temperatures as reliable correlations are not available and hence uncertainty in its value exists. Figure 11 shows the comparison between experimental and predicted temperature profiles and H2 consumption at different initial temperatures. Experimental results on the effect of different operating conditions, like the initial concentration of 2,4-DNT, catalyst loading, and H2 pressure on the maximum temperature rise (∆Tmax), were compared

with the model predictions, and these results are summarized in Table 8. An increase in catalyst loading increases the maximum temperature rise; however, it has been found that for catalyst loading greater than 12.5 kg/m3 the increase in ∆Tmax was found to be less significant. An increase in the initial concentration of 2,4-DNT increased ∆Tmax for all temperatures; however, the increase was negligible at lower temperatures, while it was significant for higher temperatures. Similarly, with an increase in the hydrogen pressure, ∆Tmax increased very significantly for all the temperatures under investigation. Thus, the theoretical model described here can be useful for an a priori prediction of the maximum temperature rise for a given set of parameters. The present study also confirms the applicability of the kinetic model derived based on a molecular level approach for integral conditions under nonisothermal conditions. Conclusions The kinetics of hydrogenation of 2,4-DNT was studied using a 5% Pd/Al2O3 catalyst in the temperature range of 323-363 K. The effect of 2,4-DNT concentration, H2 pressure, catalyst loading, agitation speed, and particle size on the concentration-time and H2 consumptiontime profiles was studied. The overall rate of hydrogenation was found to be zero-order-dependent with 2,4DNT concentration, first-order tending to zero-orderdependent on H2 pressure, and approximately secondorder-dependent on catalyst concentration. To explain the rate behavior, a more fundamental approach of the molecular level description of the catalytic cycle was used. A semibatch reactor model was developed to predict the concentration-time profiles and H2 consumption vs time data. The accuracy of the rate models and discrimination of different rate models has been discussed. On the basis of these data and the rate equations proposed, the kinetic and equilibrium parameters were evaluated. The activation energies for the four hydrogenation steps were found to be 39.05, 45.10, 49.44, and 40.85 kJ/mol, respectively. For dp > 0.3 × 10-3 m, intraparticle diffusional resistances were found to be significant, while the external mass-transfer resistances were found to be negligible. A model to describe the concentration-time profiles in a semibatch slurry reactor was developed, incorporating intraparticle diffusional effects. A nonisothermal reactor model was developed to predict the H2 consumption-time and temperature profiles in a semibatch slurry reactor and was compared with experimental data. The agreement was found to be excellent, indicating the applicability of the kinetics from a molecular level approach and the reactor model over a wide range of conditions. Acknowledgment M.V.R. thanks the Council of Scientific and Industrial Research (CSIR), India, for providing him with a Research Fellowship. Nomenclature ap ) external surface area of the catalyst per unit volume, m2/m3 CH2 ) concentration of hydrogen in the liquid phase, kmol/ m3 C*H2 ) concentration of hydrogen in equilibrium with the liquid phase, kmol/m3

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 603 Cs ) dimensionless surface concentration CH2,s ) concentration of hydrogen at the catalyst surface, kmol/m3 C10 ) initial concentration of DNT, kmol/m3 Ci ) concentration of species i, kmol/m3 Cpg ) heat capacity of gas, J/kg/K Cpl ) heat capacity of liquid, J/kg/K Cps ) heat capacity of solid catalyst, J/kg/K dp ) particle diameter, m D ) molecular diffusivity, m2/s De ) effective diffusivity, m2/s Ei ) activation energy, kJ/mol He ) Henry’s constant, m3/kmol/atm Qg ) gas flowrate, m/s ki-k4 ) kinetic parameters, (m3/kg)2(m3/kmol) s-1 K1-K3 ) adsorption equilibrium constants, m3/kmol klaB ) gas to liquid mass-transfer coefficient, s-1 ks ) liquid to solid mass-transfer coefficient, s-1 r1-r4 ) individual rates of hydrogenation for the four steps, kmol/m3/s r ) radius of the catalyst pellet, m RA ) overall rate of hydrogenation, kmol/m3/s Rg ) universal gas constant, kJ/kmol/K T0 ) initial temperature, K Tb ) bulk temperature, K Ts ) temperature on the catalyst surface, K Tw ) wall temperature, K Tgi ) gas inlet temperature, K ug ) gas velocity, m/s Uw ) heat-transfer coefficient, kJ/m2/s/K VL ) liquid volume, m3 VR ) reactor volume, m3 W ) catalyst weight, kg/m3 Greek Letters R1 ) parameter defined by eq AI.1 R2 ) parameter defined by eq AI.2 β ) thermicity parameter γ ) parameter defined by eq 21 to evaluate the importance of intraparticle heat effects -∆H ) heat of reaction, kJ/kmol  ) porosity of the catalyst particle g ) gas holdup φexp ) parameter defined by eq AI.3 φ ) Thile modulus ηc ) catalytic effectiveness factor η ) overall effectiveness factor λeff ) effective thermal conductivity, kJ/s‚m‚°C µl ) viscosity of the liquid, P Fg ) density of gas, kg/m3 Fl ) density of liquid, kg/m3 Fp ) particle density, kg/m3 ν ) stoichiometry of the reaction (1/3) τ ) tortuosity factor

Appendix I The following criteria described by Ramachandran and Chaudhari (1983) were used to check the significance of various mass-transfer effects. (a) The gas-liquid mass transfer can be considered unimportant if

R1 )

RA < 0.1 klaBC* H2

(AI.1)

(b) The liquid-solid mass transfer can be considered unimportant if

R2 )

RA < 0.1 ksapC*H2

where aP )

6w (AI.2) Fpdp

(c) Pore diffusion is considered to be negligible if

φexp )

(

dp FpRA 6 wDeC* H2

)

0.5

< 0.2

(AI.3)

For the above calculations the solubility data for H2ethyl acetate systems reported by Stephen and Stephen (1963) were used. The effective diffusivity De was given by

De ) D/τ

(AI.4)

where DM is the molecular diffusivity as defined by Wilke and Chang (1955). The gas-liquid mass transfer, klaB, was evaluated from the correlation proposed by Bern et al. (1976) for a stirred reactor.

klaB ) 1.099 × 10-2N1.16dI1.797ug0.32VL-0.521

(AI.5)

For calculation of ks, the correlation proposed by Sano et al. (1974) was used.

(

)( )

e(dp)4(Fl)3 ksdp ) 2 + 0.4 DFc (µl)3

0.25

µ FlD

0.33

(AI.6)

where Fc is the shape factor assumed to be unity for spherical particles and e, the energy supplied to the liquid, was calculated by the procedure described by Calderbank (1958). Literature Cited Alcorn, W. K. Catalysis of Organic Reactions; Kosak, J. R., Ed.; Chemical Industries Series; Dekker: New York, 1984. Baldi, G. In Multiphase Reactors, Volume II Design Methods: Proceedings of the NATO Advanced Study Institute on Multiphase Chemical Reactors; Rodrigues, A. E., Cole, J. M., Sweed, N. M., Eds.; Sijthoff and Noordhoff International Publishers B.V.: Alphen aan den Rijn, The Netherlands, 1981. Banerjee, T. Kr.; Sen, D. Homogeneous reduction of aromatic nitrocompounds by a Triphenylphosphine complex of Palladium. J. Chem. Technol. Biotechnol. 1981, 31, 676. Benedetti, A.; Fagherazzi, G.; Pinna, F.; Rampazzo, G.; Selva, M.; Strukul, G. The influence of a second metal component (Cu, Sn, Fe) on Pd/SiO2 activity in hydrogenation of 2,4-Dinitrotoluene. Catal. Lett. 1991, 10, 215. Bern, L.; Hell, M.; Schoon, N. H. Kinetics of the hydrogenation of rapeseed oil. Rate equations of Chemical reactions. J. Am. Oil Chem. Soc. 1975, 52, 391. Bird, A. J.; Thompson, D. T. Noble Metal Catalysis in Industrial Hydrogenations, Part I: palladium solubility and hydrogen availability. In Catalysis in Organic Synthesis; seventh conference; Jones, W. H., Ed.; Academic Press: New York, 1980; p 61. Bischoff, K. B. Effectiveness factors for general reaction rate forms. AIChE J. 1965, 11, 351. Burch, R. Chemical physics of solids and their surfaces; Royal Society of Chemistry: London, 1980; p 1. Calderbank, P. H. Physical rate processes in industrial fermentation. Part I. The interfacial area in gas-liquid contacting with mechanical agitation. Trans. Inst. Chem. Eng. 1958, 36, 443. Chaudhari, R. V.; Parande, M. G.; Ramachandran, P. A.; Bramhe, P. H.; Vadgaonkar, H. G.; Jaganathan, R. Hydrogenation of Butynediol to cis-Butenediol catalysed by Pd-Zn-CaCO3: Reaction kinetics and modelling of a batch slurry reactor. AIChE J. 1985, 31, 1891. Christmann, K. R. Hydrogen sorption on pure metal surfaces. Chem. Ind. (Dekker) 1988, 3. Engel, T.; Kuipers, H. Stud. Surf. Sci. 1979, 90, 162.

604 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979; p 264. Geus, J. Energetics of hydrogen adsorption on porous and supported metals. Chem. Ind. (Dekker) 1988, 85. Janssen, H. F.; Kruithof, A. J.; Steghuis, G. J.; Westerterp, K. R. Kinetics of the catalytic hydrogenation of 2,4 Dinitrotoluene (I): Experiments, reaction scheme and catalyst activity. Ind. Eng. Chem. Res. 1990a, 29, 754. Janssen, H. F.; Kruithof, A. J.; Steghuis, G. J.; Westerterp, K. R. Kinetics of catalytic hydrogenation of 2,4 Dinitrotoluene (II): Modelling of reaction rates and catalyst activity. Ind. Eng. Chem. Res. 1990b, 29, 1822. Kirk-Othmer. Encyclopedia of Chemical Technology, (Dekker) 3rd ed.; John Wiley and Sons: New York, 1978; Vol. 2, p 321. Kosak, J. R. Chem. Ind. (Dekker) 1984, 346. Lerou, J. J.; Ng, K. M. Chemical Reaction Engineering: a multiscale approach to a multiobjective task. Chem. Eng. Sci. 1996, 51, 1595. McNab, J. I. Inst. Chem. Eng. Symp. Ser. 1981, 68, 3/S:15. Mears, D. E. Tests for transport limitations in experimental catalytic reactors. Ind. Eng. Chem. Process. Des. Dev. 1971, 10, 541. Molga, E. J.; Westerterp, K. R. Kinetics of hydrogenation of 2,4Dinitrotolune using 5% Pd on alumina catalyst. Chem. Eng. Sci. 1992, 47, 1733. Mozingo, R. In Organic Syntheses, Hornning, E. C., Ed.; John Wiley: London, 1956; Collect. Vol. III, p 685. Neri, G.; Musolino, M. G.; Milone, C.; Galvagno, S. Kinetic modelling of 2,4-Dinitrotoluene hydrogenation over Pd/C. Ind. Eng. Chem. Res. 1995, 34, 2226. Paal, Z.; Menon, P. G. Hydrogen effects in metal catalysts. Catal. Rev. Sci. Eng. 1983, 25, 299. Ramachandran, P. A.; Chaudhari, R. V. Theoretical analysis of reaction of two gases in a catalytic slurry reactor. Ind. Eng. Chem. Procd. Res. Dev. 1979, 18, 703. Ramachandran, P. A.; Chaudhari, R. V. Overall effectiveness factor of a slurry reactor for non-linear kinetics. Can. J. Chem. Eng. 1980, 58, 412.

Ramachandran, P. A.; Chaudhari, R. V. Three Phase Catalytic Reactors; Gordon and Breach Publishers: New York, 1983. Rode, C. V.; Chaudhari, R. V. Hydrogenation of m-nitrochlorobenzene to m-chloroaniline: Reaction kinetics and modelling of a non-isothermal slurry reactor. Ind. Eng. Chem. Res. 1994, 33, 1645. Sano, Y.; Yamaguchi, N.; Adachi, T. Mass transfer coefficients for suspended particles in agitated vessels and bubble columns. J. Chem. Eng. Jpn. 1974, 7, 255. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds; Pergamon Press: London, 1963; Part I, Vol. 1, Table No. 1717, p 543. Sylvester, N. D.; Kulkarni, A. A.; Carberry, J. J. Slurry and trickle bed reactor effectiveness factor. Can. J. Chem. Eng. 1975, 53, 313. Waugh, K. C. Kinetic modeling of industrial catalytic processes based upon fundamental elementary kinetics under ultra high vacuum. Chem. Eng. Sci. 1996, 51, 1533. Weast, R. C.; Astle, M. J. CRC Handbook of Chemistry and Physics; Chemical Rubber Co.: Boca Raton, FL, 1976. Wilke, C. R.; Chang, P. Correlations of diffusion co-efficients in dilute solutions. AIChE J. 1955, 1, 264. Yucelen, F. Effects of Mass transfer in Liquid Phase Consecutive Hydrogenation of 2,6-Dinitrotoluene. Ph.D Thesis, ETH, Zurich, Switzerland, 1984.

Received for review June 27, 1996 Revised manuscript received October 30, 1996 Accepted November 8, 1996X IE960365L

X Abstract published in Advance ACS Abstracts, January 15, 1997.