Transalkylation of Methylamines: Kinetics and Industrial Simulation

Ind. Eng. Chem. Res. 2004, 43, 5123-5132

5123

Transalkylation of Methylamines: Kinetics and Industrial Simulation Nele Staelens, Marie-Franc¸ oise Reyniers,* and Guy B. Marin Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281 S5, B-9000 Gent, Belgium

A kinetic model for the transalkylation of methylamines over amorphous silica/alumina is presented. The experimental data obtained at temperatures ranging from 623 to 683 K and pressures ranging from 0.2 to 2 MPa were described adequately. Transalkylation reactions occur between ammonia/methylamine adsorbed on an acid site and ammonia/methylamine adsorbed on a neighboring base site. In all reaction paths, the surface reaction between adsorbed species was assumed to be rate determining. At all pressures, the fraction of free acid sites as calculated by the model is very low. The fraction of free base sites is low at high pressures only. Models derived from other mechanisms were rejected based on a statistical analysis, mechanistic considerations, and physicochemical interpretation of the parameters. An industrial transalkylation reactor was simulated. To enhance the rate of dimethylamine formation, a mixture with an excess of monomethylamine and a deficit of ammonia and trimethylamine is recommended as the inlet composition for a transalkylation reactor. Decreasing the inlet partial pressure of ammonia results in a reduced amount of catalyst required to obtain the equilibrium concentration of dimethylamine. Introduction The synthesis of methylamines is generally carried out by reaction of methanol and ammonia over solid acids in a tubular reactor. At industrial conditions, i.e., 623-723 K, 0.5-3 MPa, and a N/C ratio from 0.65 to 5 mol/mol, two stages, corresponding to different sections of the reactor, can be distinguished. In the first section of the reactor, the amination of methanol dominates, yielding monomethylamine, dimethylamine, and trimethylamine. In the second section of the reactor, generally at methanol conversions higher than 90%,1 the amination reactions become less important and reaction proceeds to the thermodynamic equilibrium by transalkylation among the methylamines (eqs 1-3).

2CH3NH2 a (CH3)2NH + NH3

(1)

2(CH3)2NH a CH3NH2 + (CH3)3N

(2)

NH3 + (CH3)3N a CH3NH2 + (CH3)2NH

(3)

Figure 1. Scheme of an industrial process consisting of an amination reactor in sequence with a transalkylation reactor. Table 1. Dependency of the Molar Equilibrium Distribution of the Methylamines on (a) Temperature for a Molar Nitrogen to Carbon Ratio N/C ) 1 and (b) on the N/C Ratio at 653 K (a) N/C ) 1 T (K) % MMA % DMA % TMA

573

623

653

673

723

773

25.3 26.0 48.7

29.3 28.2 42.5

31.4 29.3 39.3

32.6 29.9 37.5

35.6 31.1 33.3

38.2 32.1 29.8

(b) T ) 653 K

Because of the existence of these two sections, the industrial process can be represented as consisting of an amination reactor, in which complete methanol conversion occurs, in sequence with a transalkylation reactor, in which the reactions between methanol and the three methylamines occur (Figure 1). Although the equilibrium distribution of amines varies with the N/C ratio and temperature (see Table 1), the relative amount of dimethylamine is relatively independent of these process conditions and is the lowest of the three amines. However, dimethylamine is commercially the most attractive.2,3 The global market breakdown is estimated to be 24% monomethylamine, 57% dimethylamine, and 19% trimethylamine.3 Because * To whom correspondence should be addressed. Tel.: 0032/9/2644516. Fax: 0032/9/2644999. E-mail: [email protected].

N/C % MMA % DMA % TMA

0.5

0.65

0.83

1.33

2

2.1

13.6 24.1 62.3

20.5 27.3 52.2

26.6 28.8 44.6

38.1 29.3 32.6

47.2 28.4 24.5

48.3 28.0 23.6

of this mismatch between the market demand and the methylamine distribution, recycling of the excess of monomethylamine, trimethylamine, and ammonia is required in order to obtain a higher yield of dimethylamine. Hence, understanding the kinetics of the transalkylation reactions is a must to optimize the production of dimethylamine. Industrially, methylamine synthesis occurs over silica/ alumina catalysts. The active sites on silica/alumina are generally assumed to be either Brønsted or Lewis acid sites. In some cases, a combination of a Brønsted site with an adjoining Lewis site may be needed for catalytic activity. Evidently, the same types of sites catalyze not all reactions and many different types of acid sites exist

10.1021/ie049861x CCC: $27.50 © 2004 American Chemical Society Published on Web 06/29/2004

5124 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

on silica/alumina surfaces. The nature and strength of the acid sites is dependent on the preparation method and the global preparation process, which involves drying, exchange with NH4+, and calcination.4 Despite the importance of acid sites as the active sites in many catalyzed reactions, a catalytic role of base sites has been suggested in some reactions. Acid/base pairs are formed during dehydration of the surface by condensation of Al-OH groups and contain a reactive oxide ion (or ions) closely adjoining an exposed aluminum ion.5 Adsorption of alcohols on adjoining acid/base sites has been proposed by Jain and Pillai6 for the dehydration of alcohols on alumina with formation of ethers or olefins. Reaction mechanisms for the dehydration of alcohols involving acid/base sites have also been suggested by Pines and Pillai7 and Kno¨zinger et al.8 In methylamine synthesis, only a little information concerning the nature and strength of the active sites is reported in the literature. Some authors conclude that only Brønsted sites are important;9 others observed high activities over Lewis catalysts.10 Yamamoto et al.11 and Shannon et al.12,13 reported that both Lewis and Brønsted sites are active in methylamine synthesis. Mechanisms for the transalkylation reactions were proposed over zeolite catalysts only. An Eley-Rideal mechanism was reported by Gru¨ndling et al.14 for the transalkylation over H mordenites. They propose a methyl-scavenging mechanism whereby the attacking molecule scavenges a methyl group from the methylammonium ion on the surface. The attacked molecule remains on the surface. Corbin et al.15 suggest a SN2 attack of a (methyl)ammonium ion by weakly adsorbed ammonia or methylamine over hydrogen zeolites. The authors did not specify the reaction products. Chen et al.16 proposed that (methyl)ammonium ions adsorbed on weak acid sites react with (methyl)ammonium ions adsorbed on strong acid sites. The authors based their conclusions on microcalorimetric measurements and kinetic studies over silica/alumina and acidic zeolites. However, the proposed reaction mechanism is unlikely because ammonium ions have no nucleophilic character. Only a few reports deal with transalkylation kinetics over amorphous catalysts.10,17,18 The kinetic models proposed by these authors consist of pseudohomogeneous reaction rate equations and thus do not take the catalyst into account. A more fundamental LangmuirHinshelwood-Hougen-Watson (LHHW) model has been presented recently.19 Although this model allowed an adequate description of the experimental results, the corresponding reaction mechanism assumes a reaction between two molecules adsorbed on acid sites. However, because (methyl)ammonium ions do not possess nucleophilic character, it seems unlikely that a (methyl)ammonium ion will displace a methyl group from another (methyl)ammonium ion. The goal of the work presented here was to develop a kinetic model based on a fundamental reaction mechanism that describes the transalkylation reactions at industrially relevant conditions and to apply this model to the simulation of an industrial reactor. At industrial conditions, the transalkylation reactions occur in the presence of water. Weigert10 observed an influence of water on the transalkylation of monomethylamine (eq 1) over a Harshaw Al-0104 alumina catalyst. Selectivity toward dimethylamine and ammonia was significantly lower in the presence of water. However, no significant influence of water on the

Table 2. Range of Experimental Conditions catalyst temperature/K total pressure/MPa inlet partial pressures/MPa ammonia monomethylamine dimethylamine trimethylamine water space time/kgcat s mol-1

silica/alumina 623-683 0.2-2.1 0-1.7 0-1.9 0-1.8 0-0.6 0-0.3 2-125

transalkylation kinetics over the silica/alumina catalyst used in this work was found. Therefore, the presence of water was not taken into account for the kinetic modeling. Experimental Sectiom Kinetic Experiments. Kinetic experiments have been performed in an integral high-pressure reactor. The range of experimental conditions used is given in Table 2. Experimental temperatures and pressures are representative of typical industrial conditions. Experiments were performed at intrinsic kinetic conditions. A detailed description of the experimental setup and data evaluation has been given elsewhere.19 The online gas analysis section contains a HP 6890 gas chromatograph equipped with a thermal conductivity detector (TCD) and a flame ionization detector (FID). Separation of the components is achieved by two CP-sil 5B capillary columns. The composition, as analyzed by TCD detection, was used to calculate mole fractions and conversions. FID was used to observe the formation of byproducts. Negligible amounts of byproducts were observed only at the highest temperature (683 K) investigated. No deactivation of the catalyst has been observed. Nitrogen was also used as an internal standard in the gas chromatography (GC) analysis. Quantification of the product components was done by relating the peak surface areas to the flow rate of the internal standard. Mass flow rates were normalized by the total mass balance for each analysis. Conversions were calculated by the direct method

Xi )

Fi,0 - Fi Fi,0

where Xi is the conversion of product i, Fi the normalized molar flow rate of i, and Fi,0 the normalized initial flow rate. Mass, C, H, and N balance closed between 95 and 105%. Temperature-Programmed Desorption (TPD). Catalyst samples of 50-200 mg were used. To remove any adsorbed species on the catalyst surface, the catalyst sample was first heated to 973 K with a heating ramp of 10 K/min under a flow of helium (30 mL/min). The sample was kept for 180 min at this temperature. Then ammonia was adsorbed for 60 min at 393 K (30 mL/min). The sample was kept at 393 K for 90 min under a flow of helium (30 mL/min) to desorb physisorbed molecules. Subsequently, the sample was heated to 973 K with a heating ramp of 10 K/min and kept for 30 min at this final temperature. The amount of acid sites and the maximum peak temperature were found to be independent of the amount of catalyst used, indicating that readsorption can be neglected.

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5125

Catalyst Characterization The catalyst used was a commercial amorphous silica/ alumina catalyst obtained from UCB Chemicals. The physical properties of the investigated catalyst were reported elsewhere.19 The packed apparent bulk density was measured to be 0.74 g cm-3. The surface area was found to be 3.52 × 105 m2 kg-1. The particle diameter used ranged from 0.3 × 10-3 to 0.7 × 10-3 m. TPD of ammonia determined a site number density of 1018 sites m-2. An estimation of the adsorption enthalpy of ammonia can be made from TPD measurements. Assuming first-order irreversible kinetics for desorption of ammonia, the preexponential factor Ad and desorption activation energy Ed can be estimated by regression of eq 4, where Tm is the temperature corresponding to the

Ed RTm

2

)

( )

Ad -Ed exp β RTm

(4)

maximum rate of desorption and β the heating rate.20 The maximum peak temperature was found to be 508 K for a heating rate equal to 10 K/min. Assuming a preexponential factor for desorption20 equal to 1013 s-1, a desorption activation energy for ammonia of approximately -145 kJ/mol was determined. Modeling and Regression Analysis Mass and heat transport limitations were evaluated using the appropriate correlations given in the literature.38-42 Because temperature and pressure gradients could be neglected and the reactor was operated in such a way that an ideal plug-flow model could be assumed, a one-dimensional, isothermal, isobar, pseudohomogeneous reactor model was applied for the simulation of the experimental reactor. The set of ordinary differential equations to calculate the gas-phase concentrations is given by eq 5, where yi is the mole fraction

dyi ) Ri W d Ftot,0

( )

(5)

of component i, W the total mass of the catalyst, Ftot,0 the total inlet molar flow rate, and Ri the net production rate of component i. The integration of the set of ordinary differential equations was performed with the LSODA subroutine21,22 available at Netlib.23 The net production rates Ri in eq 5 can be calculated from the rates of the reaction paths considered in the reaction mechanism (eq 6), where rj is the reaction rate of the

Ri )

∑j νi,jrj

lection of the 45 experiments was done in such a way that the three temperature levels were represented and that the whole experimental grid was taken into account. An isothermal parameter estimation based at 653 K was performed in order to obtain good initial parameter values for the nonisothermal parameter estimation. To avoid strong binary correlation between the Arrhenius parameters, the Arrhenius equations were reparametrized according to the procedure outlined by Kittrell.25 In this case, 653 K was taken as the reference temperature. The parameters were evaluated based on their physicochemical significance and tested on their statistical significance on the basis of their individual t values. The statistical significance of the global regression was expressed by means of the F test. The adequacy of the mathematical model used for the regression was tested by analysis of the residuals. Discrimination between two rival models A and B was done by calculating the ratio of the corresponding residual sum of squares, divided by their degrees of freedom. This ratio is distributed as the F distribution. If the calculated F value comparing the global regression of model A to that of model B is higher than the corresponding tabulated F value, then the global regression of model A is significantly better than the global regression of model B. In this paper, only the ultimately selected kinetic model is discussed in detail. Thermodynamics The method to calculate the equilibrium composition for a given temperature and feed composition is described earlier.19 The thermodynamic values required for calculation of the equilibrium coefficients of the transalkylation reactions (eqs 1-3) were obtained from Poling et al.26 The calculated distributions of methylamines at equilibrium conditions (see Table 1) are in agreement with those reported by Sang et al.27 Simulation of an Industrial Reactor Reactor Model. An adiabatic fixed-bed reactor for the transalkylation of methylamines was simulated using a one-dimensional pseudohomogeneous reactor model. Based on the appropriate correlations given in the literature,38-42 mass and heat transport limitations were found to be negligible. The transport mechanism in the axial direction was considered to be of the plugflow type. The axial reactor temperature and concentration gradients were calculated by solving the continuity equation (7) and the energy equation (8) along the reactor coordinate z, where T is the reaction tempera-

dyi FbΩRi ) dz Ftot,0

(6)

reaction path j (mol kgcat-1 s-1) and vi,j the stoichiometric coefficient of component i in reaction path j. Stoichiometrically, two reaction rates rj are required in order to calculate the outlet concentration. However, three reaction rates have been considered here based on mechanistic considerations. Estimation of the kinetic parameters was performed by minimization of the residual sum of squares of the response variables with a multiresponse LevenbergMarquardt algorithm.25 A selection of 45 experiments at three temperatures levels (623, 653, and 683 K) were used for the nonisothermal parameter estimation. Se-

(7)

nreact

dT dz

FbΩ )

rj∆H°r,j ∑ j)1

ncomp

(8)

FicpG,i ∑ i)1

ture, Fb,k the catalyst bulk density, Ω the cross-sectional surface area of the reactor, ∆H°r,j the reaction enthalpy, Fi the molar flow rate of component i, and cpG,i the ideal gas heat capacity of component i in the gas phase at constant pressure. The axial effective diffusion of mass

5126 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Figure 2. Observed (symbols) and calculated (lines) mole fractions of ammonia (9), monomethylamine ([), dimethylamine (b), and trimethylamine (2) as a function of W/FMMA,0 for a monomethylamine/water feed at 653 K. pMMA,0 ) 1 MPa. Empty symbols: pH2O,0 ) 0 MPa. Filled symbols: pH2O,0 ) 0.19 MPa. The calculated mole fractions have been obtained using eqs 5 and 1113 with the kinetic parameters of Table 4. For the range of experimental conditions, see Table 2.

is neglected. External mass and heat transport limitations as well as intraparticle mass and heat gradients were found to be negligible. Industrial applied pressures are generally between 1.5 and 2.0 MPa, and the total pressure drop is approximately 0.1 MPa. For the simulations, it was assumed that the pressure drop in the industrial reactor is negligible. An inlet pressure of 1.8 MPa was taken for the simulations. Integration Procedure. Integration of the set of ordinary differential equations (7) and (8) is performed with the integration routine LSODA21,22 available at Netlib.23 For each integration step, reaction equilibrium coefficients, reaction enthalpies, and heat capacities are calculated.

Figure 3. Observed (symbols) and calculated (lines) conversions of dimethylamine (A) and monomethylamine (B) at different total pressures [0.2 MPa (0), 1 MPa (]), 1.5 MPa (×), and 1.8 MPa (4)] as a function of space time at 653 K. The calculated conversions have been obtained using eqs 5 and 11-13 with the kinetic parameters of Table 4. For the range of experimental conditions, see Table 2.

Figure 4. Hougen-Watson reaction mechanism for the transalkylation. Reaction between monomethylamine adsorbed on an acid site and monomethylamine adsorbed on a neighboring base site are shown.

can be reached at higher pressure and to facilitate the separation of the methylamines. The influence of the total pressure has been further investigated here. In all cases, it could be concluded that conversions increase with increasing pressure, but only until about 1.0 MPa. From then on, conversions were independent of the total pressure. This is illustrated in Figure 3 for pure dimethylamine and monomethylamine feeds.

Effect of Reaction Conditions Water Pressure. The influence of water has been investigated for a pure monomethylamine and a trimethylamine/ammonia feed at 653 K. The partial pressure of water was varied between 0 and 0.31 MPa, while the partial pressures of the other reactants are kept constant. Industrially, a typical product stream contains about 20-25 mol % water at complete methanol conversion, while the total pressure is commonly 1.8 MPa. In all experiments, methanol and dimethyl ether were not detected and no conversion of water was observed. This indicates that the reverse reactions of the amination reactions are negligible at these conditions. It was observed that the kinetics of the transalkylation in the absence of water are not significantly different from the kinetics observed in the presence of water. This is illustrated for a monomethylamine feed in Figure 2. Hence, the transalkylation kinetics can be investigated in the absence of water. In contrast to our findings, Weigert10 observed a decrease in the dimethylamine selectivity in the disproportionation of methylamine on Al2O3. Total Pressure. As reported earlier,19 it was observed that conversion is dependent on the pressure at low pressures only. However, industrially manufacturing methylamines at pressures higher than 1 MPa can be advantageous because of the higher capacities that

Reaction Mechanism The reaction mechanism proposed here involves adsorption on acid/base sites. Whereas ammonia and the methylamines strongly adsorb on the acid sites of silica/ alumina, it is not excluded that weak interaction with the base sites of the catalyst occurs. Chemisorption on the acid site polarizes the N-C bond and favors attack of a nucleophile on the carbon atom of the methyl group of the adsorbed amine. Chemisorption on a base site, which is here represented as a hydrogen bonding to an oxide ion on the surface, increases the nucleophilicity of the nitrogen atom of the adsorbed molecule.6 Reaction occurs then as a nucleophilic attack of the nitrogen of a molecule adsorbed on the base site, on the methyl group of a molecule adsorbed on the acid (Figure 4). The adsorption of trimethylamine on base sites is not considered because trimethylamine does not have free hydrogens to form hydrogen bonds with the oxygen atom of the base site. The above reaction mechanism is similar to an Eley-Rideal mechanism. In the latter case, however, the nucleophilic attack occurs by a gasphase molecule and not by a weakly adsorbed molecule. Kinetic models based on an Eley-Rideal mechanism were also considered. However, these were all rejected because their F values were considered to be too low for a significant global regression and the model predic-

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5127 Table 3. Elementary Steps and Reaction Pathsa

a

* ) acid sites. s ) base sites.

tions did not describe the experimental data adequately over the entire range of experimental conditions. Therefore, these models are not discussed further.

(

)

pMMApTMA / Keq,2 {(1 + Ka,NH3pNH3 + Ka,MMApMMA + Ka,DMApDMA +

r2 ) k2Ka,DMAKs pDMA2 -

Ka,TMApTMA)[1 + Ks(pNH3 + pMMA + pDMA)]} (12)

Kinetic Model The reaction paths considered for the transalkylation reactions (eqs 1-3) and the corresponding elementary steps are listed in Table 3. The concentrations of the surface species were calculated assuming the pseudo steady state of the latter, and in each reaction path, the surface reaction was considered to be rate determining. In combination with the total site balances (eqs 9 and 10), the reaction rate equations can then simply be

Acid site balance: Ltot,* ) L* + LNH3* + LMMA* + LDMA* + LTMA* (9) Base site balance: Ltot,s ) Ls + LNH3s + LMMAs + LDMAs

(10)

written as explicit functions of the partial pressures of the gas-phase components, the reaction rate coefficient of the rate determining step, the equilibrium coefficients of the reactions (1)-(3), and the adsorption equilibrium coefficients. The total concentration of active sites is taken into account implicitly in the kinetic coefficients. To restrict the number of parameters, the adsorption coefficients for adsorption of ammonia, monomethylamine, and dimethylamine on the base sites were assumed to be the same. Although reaction can only occur between two molecules adsorbed on neighboring sites, this is not explicitly taken into account in the kinetic model. In this manner, the following rate equations were obtained (eqs 11-13).

(

r1 ) k1Ka,MMAKs pMMA2 -

)

pDMApNH3

/ Keq,1 {(1 + Ka,NH3pNH3 + Ka,MMApMMA + Ka,DMApDMA + Ka,TMApTMA)[1 + Ks(pNH3 + pMMA + pDMA)]} (11)

(

)

pMMApDMA / Keq,3 {(1 + Ka,NH3pNH3 + Ka,MMApMMA + Ka,DMApDMA +

r3 ) k3Ka,TMAKs pNH3pTMA -

Ka,TMApTMA)[1 + Ks(pNH3 + pMMA + pDMA)]} (13) Regression of the set of 45 experiments using eqs 5 and 11-13 resulted for all parameters in statistically significant estimates. An F value equal to 1919 was found. The highest absolute value of the binary correlation coefficient was obtained between the standard adsorption enthalpy of ammonia on acid sites and the standard adsorption enthalpy on base sites (-0.877). The parity diagrams obtained for the complete data set (111 experiments from which 45 were used for the regression analysis) are presented in Figure 5. A good agreement was found between simulated and experimental data. Increasing the total pressure leads to increased conversions calculated by the model up to about 1 MPa. This is illustrated for a pure dimethylamine feed at 653 K in Figure 6 and corresponds with the experimental observations (Figure 3). The corresponding fractional surface coverages of the acid and base sites at 0.2 and 1.8 MPa, calculated from eqs 14 and 15, for respectively the acid and base sites, using the parameter estimates θi* )

Li* ) Ka,ipiL* ) Ltot,*

Ka,ipi 1 + Ka,NH3pNH3 + Ka,MMApMMA + Ka,DMApDMA + Ka,TMApTMA

(14) θis )

Lis Kspi ) KspiLs ) Ltot,s 1 + Ks(pNH3 + pMMA + pDMA) (15)

5128 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Figure 5. Parity diagrams for the mole fractions of the transalkylation components for the complete set of 111 experiments. The calculated mole fractions have been obtained using eqs 5 and 11-13 with the kinetic parameters of 43. For the range of experimental conditions, see Table 2.

Figure 6. Calculated conversions of dimethylamine as a function of space time at 653 K for different inlet partial pressures of dimethylamine (0.2-1.8 MPa). The calculated conversions have been obtained using eqs 5 and 11-13 with the kinetic parameters of Table 4. For the range of experimental conditions, see Table 2.

are shown in Figure 7. At 0.2 MPa, the fraction of free acid sites is approximately 0.2, while at 1.8 MPa, the fraction of free acid sites is almost zero. Gru¨ndling et al.14 reported that free Brønsted acid sites were not detected during FTIR experiments on H mordenite at 633 K and 0.01 MPa. The fraction of free base sites is higher than the fraction of free acid sites at all pressures (Figure 7). At 1.8 MPa, the fraction of free base sites is approximately 0.3, while at 0.2 MPa, the fraction of free base sites is about 0.8. The parameter estimates and their 95% confidence interval are listed Table 4. The value of the reaction rate coefficient k2 at the mean temperature of 653 K, which equals the reparametrized preexponential factor of k2, is clearly higher than k1 and k3, while k3 is significantly lower than k1. The higher reactivity for

disproportionation of dimethylamine (k2) as compared to monomethylamine (k1) agrees well with the experimental observations (Figure 3) and with the reported literature. The rate coefficient for disproportionation of dimethylamine (k2) estimated by Weigert10 over D-970 silica/alumina was twice as high as that for disproportionation of monomethylamine (k1), while Mitchell et al.18 found an approximately 3 times higher value at 653 K. The previously mentioned authors also estimated the lowest rate coefficient for reaction between ammonia with trimethylamine (k3). The order of magnitude of the preexponential factor for Hougen-Watson surface reactions given by Dumesic et al.20 ranges from 108 to 1013 mol kgcat-1 s-1, taking into account a site number density of 1018 sites m-2 as determined by NH3-TPD and a surface area of 3.52 × 105 m2 kg-1 of the catalyst used. The estimated preexponential factors range from 1010 to 1013 mol kgcat-1 s-1, assuming that the total amount of acid sites equals the total amount of base sites, which corresponds with the range given by Dumesic et al.20 The standard adsorption enthalpies on the acid sites increase with increasing proton affinity of the sorptive molecule (NH3 < MMA < DMA < TMA). In the reported literature, no agreement is found for the sequence of the standard adsorption enthalpies. Parrillo et al.28 and Lee et al.29 report an order of adsorption of NH3 < MMA < DMA = TMA over H-ZSM-5 and H mordenite, respectively. Chen et al.,30 however, report the sequence NH3 < TMA < MMA < DMA for the adsorption strength on both strong and weak acid sites over H-ZSM535 and H mordenite. The estimated value of the standard adsorption enthalpy of ammonia (-145 kJ/mol) is in line with the value calculated from TPD data and also with values reported in the literature. Cardona-Martinez and Dumesic31 proposed an adsorption enthalpy of ammonia over silica/alumina of approximately -180 kJ/mol. Adsorption enthalpies of ammonia between -162 and -120 kJ/mol have been reported by several authors for high-strength acid sites on H mordenite and H-ZSM5.29,30,32-35 Parrillo et al.28 proposed adsorption enthalpies of -185, -205, and -205 kJ/mol for monomethylamine, dimethylamine, and trimethylamine over H-ZSM-5, repsectively. Lee et al.29 determined adsorption enthalpies for methylamines over H mordenite via microcalorimetric measurements and found values of -200, -225, and -220 kJ/mol for monomethylamine, dimethylamine, and trimethylamine, respectively. Chen et al.30 reported similar values for adsorption of monomethylamine and dimethylamine on strong acid sites over H-ZSM-5 and H mordenite. The adsorption enthalpy of trimethylamine determined by Chen et al.,30 however, was significantly lower (-155 ( 7 and -140 ( 12 kJ/mol, respectively) than those reported by Parrillo et al.28 and Lee et al.29 In comparison with the estimated values here over silica/alumina, it can be concluded that the estimated adsorption enthalpy of monomethylamine over the amorphous catalyst used here is lower than those reported in the literature for zeolites, while those for dimethylamine and trimethylamine are higher. The estimated adsorption enthalpy of trimethylamine (-263 ( 9 kJ/mol) is in very good agreement with the value proposed by Cardona-Martinez and Dumesic31 over silica/alumina (-267 kJ/mol). Values for monomethyl-

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5129

Figure 7. Calculated fractional surface coverages on acid sites (*) and on base sites (s) at 0.2 and 1.8 MPa for a pure dimethylamine feed at 653 K. The calculated fractional surface coverages have been obtained using eqs 5, 14, and 15 with the kinetic parameters of Table 4. For the range of experimental conditions, see Table 2. Table 4. Parameter Estimates with Their 95% Confidence Interval, Obtained by Regression of 45 Experimental Data Points Using Equations 5 and 10-13 reparametrized preexponential activation preexponential factor energy or factor [mol kgcat-1 s-1] or adsorption -1 -1 -1 [10 mol kgcat s adsorption entropy enthalpy [J mol-1 K-1] [103 J mol-1] or 10 MPa-1] k1 k2 k3 Ka,NH3 Ka,MMA Ka,DMA Ka,TMA Ks

0.83 ( 0.01 5.75 ( 0.02 0.35 ( 0.01 1.75 ( 0.01 2.24 ( 0.03 2.16 ( 0.01 2.61 ( 0.03 0.138 ( 0.001

3 × 1012 6 × 1013 4 × 1010 -194.8 -215.4 -370.6 -395.0 -31.9

169 ( 8 176 ( 7 151 ( 2 -130 ( 4 -145 ( 3 -246 ( 6 -263 ( 9 -10 ( 1

amine and dimethylamine were not reported by Cardona-Martinez and Dumesic.31 The estimated enthalpy for adsorption on base sites is very low compared to those for adsorption on acid sites (10 times lower), as is to be expected. The same sequence of increasing adsorption entropy was obtained as that for the estimated adsorption enthalpies. Rules and guidelines to determine whether the values of entropy of adsorption obtained for a LHHW

model have any physical meaning and thereby support the proposed reaction model were formulated by Boudart et al.36 for dissociative, dual-site adsorption.37 Two rules were offered as guidelines (eq 16):

10 e -∆S°a e 12.2 - 0.0014∆H°a

(16)

Violation of either of these two rules indicates inconsistencies in the proposed kinetic model, and the coefficients appearing to represent values of Ka,i have no physical meaning in the Langmuirian sense.37 The estimated values for -∆S°a correspond with the guidelines of Boudart et al.36 The upper limit is exceeded slightly for adsorption of dimethylamine and trimethylamine on acid sites and for adsorption on base sites only (Table 5). Cardona-Martinez and Dumesic31 reported that the loss of entropy upon sorption on silica/alumina increases with the base strength for the adsorbed molecule (i.e., ammonia, pyridine, and trimethylamine), which was also found here. The model presented here is preferred over the LHHW model presented earlier19 because of mechanistic considerations. Reaction between a nucleophilic methylamine/ammonia and (methyl)ammonium ion is much more likely than reaction between two (methyl)ammo-

5130 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 Table 5. Estimated Standard Adsorption Entropies and Corresponding Upper Limits Calculated via Equation 1636 Ka,NH3 Ka,MMA Ka,DMA Ka,TMA Ks

-∆S°a

12.2 - 0.0014∆H°a

194.8 215.4 370.6 395.0 31.9

194.5 215.2 356.9 380.6 26.3

nium ions as in the latter case. Moreover, an analysis of the physicochemical meaning of the estimated parameters was in favor of the model presented here. The estimated preexponential factors and adsorption enthalpies of the model presented here are in good agreement with values reported in the literature, which was not the case for all parameters of the LHHW model presented earlier.19 No discrimination, however, could be made based on a statistical F test. The F value, comparing the global regression of the model presented here to that of the previous model, was calculated to be 0.90, which is lower than the corresponding tabulated F value (1.49). Effect of the Inlet Composition on the Performance of the Transalkylation Section of an Industrial Reactor Industrially, methanol is completely converted before the reaction mixture enters the transalkylation section of the reactor. Therefore, simulations were performed in the absence of methanol. The transalkylation section of the reactor was simulated as a tubular reactor with a length of 4 m. The inlet temperature was taken to be equal to 677 K and the inlet pressure 1.8 MPa corresponding to typical conditions in the transalkylation section of the industrial reactor. Dimethylamine, commercially the most interesting product, is considered to be formed by transalkylation reactions between ammonia and the three methylamines. Over amorphous catalysts, the maximum concentration of dimethylamine obtained along the reactor coordinate is the equilibrium concentration. Hence, the performance of the transalkylation reactor can be evaluated based on the minimum amount of catalyst required to obtain the thermodynamic equilibrium concentration for dimethylamine. As a criterion for equilibrium, a relative deviation of 5% on the percentage of dimethylamine as compared to the equilibrium percentage is taken (molar distributions). To investigate the influence of the inlet partial pressure of ammonia, the partial pressure of ammonia was varied between 0.09 and 1.31 MPa. The partial pressures of the methylamines were taken to be constant for each data set. Because the outlet concentration of an amination reactor shows a deficit of dimethylamine compared to equilibrium, the molar distribution was taken equal to 45/10/45 mol % MMA/DMA/TMA. As the partial pressure of ammonia is varied while keeping the partial pressures of the methylamines constant, the N/C ratio is changed for each data set. For the range of ammonia pressure considered here, an N/C ratio from 0.6 to 1.9 was covered. The data sets considered in this paragraph are summarized in Table 6. For the inlet conditions considered here, the transalkylation occurs almost isothermally. Outlet temperatures varied between 668 and 682 K. The influence of the different outlet temperatures on the equilibrium product distribution is not significant. However, for the

Table 6. Data Sets Considered To Investigate the Influence of the Inlet Partial Pressure of Ammonia on the Performance of the Transalkylation Reactor N/C ratio pNH3,0/MPa

0.60 0.09

1.00 0.47

1.25 0.70

1.50 0.94

1.75 1.17

1.90 1.31

Table 7. Equilibrium Conversion and Distributions for the Inlet Conditions of 65 at the Calculated Outlet Temperature Tcalc distribution/% N/C

Tcalc/K

conversion NH3/%

MMA

DMA

TMA

0.60 1.00 1.25 1.50 1.75 1.90

682 674 671 670 669 668

-86.0 -3.5 1.5 3.5 4.5 4.7

21 33 38 42 46 47

28 30 30 30 29 29

51 37 32 28 25 24

Table 8. Calculated Reactor Length l and Relative Amount of Catalyst Wrel of the Transalkylation Section Required To Obtain the Equilibrium Concentration of Dimethylamine (For Inlet Conditions, See Table 6) N/C ratio l/m Wrel/%

0.60 0.9 28

1.00 1.6 54

1.25 2.0 65

1.50 2.2 74

1.75 2.3 77

1.90 2.4 81

range of N/C ratios considered here, the equilibrium product distribution is strongly different (Table 7). Whereas the relative amount of dimethylamine at equilibrium is rather independent of the inlet product distribution, the minimum amount of catalyst required to obtain equilibrium for dimethylamine increases with increasing partial pressure of ammonia. This can be explained as follows. When the partial pressure of ammonia is varied, the N/C ratio and, consequently, the equilibrium distribution is changed. Hence, the driving force to obtain equilibrium is different for each data set. For low N/C ratios (i.e., low partial pressure of ammonia), ammonia has to be formed by conversion of monomethylamine in order to obtain equilibrium. For high N/C ratios, trimethylamine and ammonia have to be converted into monomethylamine and dimethylamine to obtain equilibrium. Because the rate coefficient of this reaction (eq 13) is lower than that of the conversion of monomethylamine into ammonia and dimethylamine (eq 11), the rate of dimethylamine formation will be higher for an excess of monomethylamine and a deficit of ammonia. Consequently, to enhance the rate of dimethylamine formation, a mixture with an excess of monomethylamine and a deficit of ammonia and trimethylamine is recommended as the inlet composition for a transalkylation reactor. Thus, decreasing the inlet partial pressure of ammonia results in a reduced amount of catalyst required to obtain the equilibrium concentration of dimethylamine (see Table 8). Conclusions The transalkylation of methylamines was investigated over a commercial amorphous silica/alumina catalyst. In the range of investigated experimental conditions, increased reaction rates were observed up to about 1 MPa. No significant effect of the total pressure on the conversions was observed between 1 and 1.8 MPa. It was found that water does not influence significantly the kinetics of the transalkylation. Kinetic modeling of the transalkylation of the methylamines was based on elementary steps. The proposed reaction mechanism involves Langmuir adsorption on

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5131

acid and base sites and Hougen-Watson surface reactions between species adsorbed on an acid site and a neighboring base site. Reaction rate equations have been derived based on the assumption of the surface reactions to be rate determining. A good agreement was found between simulated and experimental data. The transalkylation of dimethylamine to monomethylamine and dimethylamine was found to be much faster than the other transalkylation reactions. The estimated standard adsorption enthalpies of the amines on acid sites are in good agreement with reported values. The standard adsorption enthalpies and entropies of ammonia and the methylamines increase with increasing proton affinity. The adsorption enthalpy on the base sites was estimated to be 10 times lower than that on the acid sites. Reaction rates calculated by the model are independent of the total pressure from about 1 MPa on, which is in agreement with the experimental observations. At all pressures, the fraction of free acid sites as calculated by the model is very low. The fraction of free base sites decreases with increasing pressure from approximately 0.8 at 0.2 MPa to aprroximately 0.3 at 1.8 MPa. In the absence of methanol, inlet distributions with an excess of monomethylamine and a deficit of ammonia as compared to the equilibrium distribution enhance the rate of dimethylamine formation from monomethylamine, while the conversion of trimethylamine and ammonia into dimethylamine occurs very slowly. Consequently, to enhance the rate of dimethylamine formation, a mixture with an excess of monomethylamine and a deficit of ammonia and trimethylamine is recommended as the inlet composition for a transalkylation reactor. Thus, decreasing the inlet partial pressure of ammonia results in a reduced amount of catalyst required to obtain the equilibrium concentration of dimethylamine. Acknowledgment The authors are grateful to UCB Chemicals Belgium for their financial support. List of Symbols Roman Symbols Ad ) preexponential factor, s-1 cp,i ) heat capacity at constant pressure for component i, J mol-1 K-1 ∆H°a ) adsorption enthalpy, J mol-1 ∆Hr ) reaction enthalpy, J mol-1 Ea ) activation energy, J mol-1 Ed ) desorption energy, J mol-1 F ) molar flow rate, mol s-1 Ka,i ) adsorption equilibrium coefficient of component i, MPa-1 Keq,j ) equilibrium coefficient of reaction j kj ) kinetic coefficient of reaction j, mol kgcat-1 s-1 l ) reactor length or bed height, m Li ) surface concentration of component i, mol m-2 p ) total pressure, MPa R ) universal gas constant, 8.314 J mol-1 K-1 Ri ) net production rate of component i, mol kgcat-1 s-1 rj ) reaction rate of reaction j, mol kgcat-1 s-1 ∆S°a ) standard adsorption entropy, J mol-1 K-1 T ) temperature, K W ) mass of catalyst, kgcat yi ) mole fraction of component i z ) reactor coordinate, m

Greek Symbols β ) heating rate, K min-1 θ ) fractional surface coverage Fb ) catalyst bulk density, kg m-3 ν ) stoichiometric coefficient Ω ) cross section of the reactor, m2 Subscripts 0 ) initial or inlet condition b ) bulk i ) component i j ) reaction j G ) gas phase m ) maximum r ) reactor/reaction s ) base site * ) acid site tot ) total Abbreviations DMA ) dimethylamine MMA ) monomethylamine MM ) molecular mass, 10-3 kg mol-1 nreact ) number of reactions TMA ) trimethylamine TPD ) temperature-programmed desorption

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Received for review February 19, 2004 Revised manuscript received May 3, 2004 Accepted May 4, 2004 IE049861X