Preliminary Assessment of Membrane Reactors as a Means To

Preliminary Assessment of Membrane Reactors as a Means To. Improve the ...... notice in Figure 8 is that the selectivity of the membrane reactor is al...
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Ind. Eng. Chem. Res. 1999, 38, 4552-4562

Preliminary Assessment of Membrane Reactors as a Means To Improve the Selectivity of Methylamine Synthesis Chimin Sang, Chen-Chang Chang, and Carl R. F. Lund* Chemical Engineering Department, SUNYsBuffalo, Buffalo, New York 14260-4200

Methylamine synthesis from ammonia and methanol was studied using an amorphous silicaalumina catalyst. A combined thermodynamic and kinetic analysis shows that the selectivity ratio initially observed at high methanol conversion is a kinetic ratio, not a thermodynamic ratio. In some cases in the past this kinetic ratio has been taken to represent thermodynamic equilibrium. However, if the reaction is allowed to continue beyond the point where conversion of methanol and dimethyl ether is essentially complete, the product composition continues to change, albeit at a much lower rate. Eventually the thermodynamic selectivity ratio is obtained. A simple kinetic model was developed that captures this behavior, and this model was used to assess whether a membrane reactor might be used to alter the overall selectivity of methylamine synthesis. Four different membrane reactor configurations were considered. There were operational regimes where each configuration showed advantages, but these either occurred at low conversions or required extremely large reactors. These configurations are limited by currently available catalysts and membrane materials. The impact of membrane reactors could be increased with catalysts that retain high activity during methylamine disproportionation, i.e., after all methanol has been consumed. The development of membrane materials with better permselectivities would also increase the attractiveness of membrane reactor processes. The catalytic synthesis of methylamines (MAs) from a methanol (MeOH)-ammonia feed is a significant commercial process. The literature related to this process was reviewed recently by Corbin et al.10 It is widely held that thermodynamic equilibrium favors the production of trimethylamine (TMA), whereas market demand is stronger for monomethylamine (MMA) and dimethylamine (DMA). As a consequence there have been many studies (e.g., refs 1, 9, 11, 14, 16, 22-24, and 29) seeking methods to alter the selectivity of the reaction system to favor MMA and DMA over TMA. Almost uniformly it has been assumed that the MAs are produced via a consecutive pathway (eqs 1-3), and the general approach has been to seek means to reduce the rate of TMA production without affecting the rates of MMA and DMA generation.

NH3 + CH3OH / MMA + H2O

(1)

MMA + CH3OH / DMA + H2O

(2)

DMA + CH3OH / TMA + H2O

(3)

In this context the present investigation was originally undertaken to assess whether a membrane reactor might be useful in improving the yield of MMA and DMA relative to TMA. Improved selectivity might be expected for a few reasons. First, if the primary reaction pathway is indeed a consecutive one, then it might be possible to selectively remove the intermediate products, MMA and DMA, through the membrane.2,4,15,21 This would lead to lower DMA concentrations and, consequently, a lower rate of TMA production. Alternatively, * To whom correspondence should be addressed. Telephone: 716 645-2911 x2211. Fax: 716 645-3822. E-mail: [email protected].

if the reaction system approaches equilibrium, then selective removal of MMA and DMA through a membrane may lead to a higher yield of these products than that which would result via equilibration without selective product removal,3,20,25,28,30 the so-called equilibrium shifting effect. It may additionally be possible to improve selectivity in a third way, namely, by supplying the feed on opposite sides of the membrane.4,12,13 This would distribute the methanol feed along the length of the reactor instead of introducing it all at the inlet. Methanol would permeate through the membrane in order to reach the catalytic zone, and as a consequence the methanol concentration in the reaction zone would be low. A high ammonia-to-methanol ratio is known to disfavor TMA production.10 In the first two cases the key to improved yields of MMA and DMA would be the selective removal of these components.18,19 A variety of equilibrium molar selectivities (MMA/ DMA/TMA) have been reported in the literature. Often these are presented without a corresponding temperature and feed composition (or ratio of nitrogen to carbon in the feed, N/C). This limits their utility and makes it impossible to verify their calculation. A molar selectivity of 17/21/62 is frequently cited and in some of those cases is related to a temperature of 400 °C and N/C ) 1.0. In the course of our investigation, we found that for these conditions this ratio is not correct. In this paper we present our thermodynamic analysis along with supporting experimental evidence. Following this, kinetic pathways in MA synthesis are discussed and a simple, empirical kinetic model is developed for MA synthesis over a silica-alumina catalyst. Finally, an initial assessment is made of a few approaches to improve the selectivity of MA synthesis via membrane reactors. This assessment uses the thermodynamic selectivities and the kinetic model from the present study.

10.1021/ie990317b CCC: $18.00 © 1999 American Chemical Society Published on Web 10/29/1999

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4553

Figure 1. Schematic representation of the portion of the reactor system used to measure methylamine synthesis kinetics.

Experimental Methods An amorphous silica-alumina catalyst was used in this investigation as the catalyst for methylamine synthesis. This catalyst was prepared by first dissolving 41.15 g of Na2SiO3‚9H2O (99.9%, Fisher certified) in 500 mL of distilled water with continuous stirring. After 15 min, 200 mL of 6.0 M HCl was added to acidify the solution, after which a solution of 9.566 g of Al(NO3)3‚ 9H2O (98.6%, Fisher) in 250 mL of distilled water was added. After the solution was stirred for 10 min, an amount of aqueous NH4OH just sufficient to neutralize the solution was added. A cogel formed and was allowed to age overnight. The gel was then filtered and washed with an amount of distilled water equal to 3 times the volume of the gel. The filtered gel was held under vacuum at 100 °C for 12 h. The resultant catalyst was ground, and the 60/80-mesh fraction was kept for experimental use. A conventional tubular reactor was used for initial reaction studies. The experiments reported here were conducted in a batch recirculation reactor that can operate either as an isolated reactor or as a membrane reactor.5,6 The experiments reported here did not use the membrane reactor configuration, and Figure 1 schematically represents the part of the system used in the present kinetic studies. In a typical kinetic experiment 0.035 g of catalyst was loaded into the reactor. With the isolation valve positioned to include the reactor in the recirculation loop, the loop was filled with gaseous ammonia (Praxair, anhydrous, liquified) at 1 atm. The reactor, filled with ammonia, was then isolated from the rest of the recirculation loop. Methanol (99.8%, Aldrich, ACS reagent grade) was mixed with fresh ammonia using a Sage model 361 syringe pump and a vaporizer. This mixture was used to recharge the recirculation loop (not including the reactor). The loop was then closed and a Flurocarbon pump was used to recirculate the mixture around the loop, usually for ca. 3 min. At this point the isolation loop was switched so that the reactor was included in the recirculation loop, and the reaction was started. The rate of recirculation within the loop was sufficiently high that the conversion per pass was differential. The tubing comprising the recirculation loop was wrapped with heating tape to prevent condensation. The volume of the recirculation loop was 110.6 mL when the reactor was isolated and 121.3 mL when the reactor was included. A gas sampling valve (not shown) was used to periodically inject samples from the recirculation loop into a Perkin-Elmer model Sigma 300 HWD gas chromatograph. The carrier gas was helium (CS Gases Inc.,

high purity) which was additionally purified by passage through a Supelco carrier gas drying tube, a Supelco carrier gas purifier, and a Supelco OMI-2 indicating purifier. A 12 ft long, 1/8 in. o.d. stainless steel column packed with 4%Carbowax 20M + 0.8% KOH on Carbograph 60/80 mesh was used to separate the reaction mixture. The signal from the thermal conductivity detector was collected and stored on a computer disk. PeakSimple II (SRI) was used to analyze the areas of the response peaks. Typically the molar concentrations of all species except water were calculated from the GC response using corresponding calibration factors. The amount of water was calculated from the reaction stoichiometry. For both the estimation of rate constants via leastsquares fitting and the simulation of different membrane reactor configurations, Maple was used as the primary computational tool. The method used to solve ordinary differential equations was a Fehlberg fourthfifth-order Runge-Kutta method in Maple’s dsolve package. The Gauss-Newton method was programmed in Maple to find the best estimates for the reaction rate constants.

Thermodynamic Analysis The reaction system can be represented in a variety of ways. Equations 1-3 suggest a series pathway, but eqs 1, 4, and 5 achieve the same result in a parallel fashion. Additionally, disproportionations are possible, as in eqs 6-8. Experimentally, it is known that dimethyl ether (DME) is formed, e.g., via eq 9, and this opens the additional possibility of direct reaction between DME and NH3 (or MMA or DMA). Such DME amination reactions could similarly be written either as a series pathway or as a parallel pathway. Of course, not all of these reactions are stoichiometrically independent. For thermodynamic analysis there is a number of sets of four mathematically independent reactions; one such set consists of reactions (1)-(3) and (9).

NH3 + 2CH3OH / DMA + 2H2O

(4)

NH3 + 3CH3OH / TMA + 3H2O

(5)

2MMA / DMA + NH3

(6)

MMA + DMA / TMA + NH3

(7)

2DMA / MMA + TMA

(8)

2CH3OH / DME + H2O

(9)

Having identified a set of stoichiometrically independent reactions, one may calculate the equilibrium constant at temperature T, KT-j, for each independent reaction j using eq 10. It is important to note that the

(

KT-j ) exp

)

-∆GT-j RT

(10)

free-energy change, ∆GT-j, in eq 10 must be evaluated at the temperature of interest, not at 298 K. Stull et al.26 provide free energies of formation, ∆GfT-i, as a function of temperature for all species, i, of interest. These values can be used to calculate the free-energy

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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 Table 1. Comparison of Calculated Equilibrium Constants to Molar Compositions selectivity ratio nMMA/nDMA/nTMA

corresponding nTMAnMMA/nDMA2

17/21/62 32/33/34

2.4 1.0

a

equilibrium constant K673K-8

incorrect equilibrium constant,a K8

1.0

2.4

Calculated via eq 10 using T ) 673 K, but with ∆G298K-8.

Figure 2, where the same conditions lead to a molar ratio of 32/33/34 (16/33/51 on a carbon basis). To lessen confusion, only the molar basis will be used henceforth; the point is that while a 17/21/62 ratio is very commonly cited, our calculations and Figure 2 lead to a 32/33/34 ratio. It is instructive to consider reaction (8) at this juncture because that reaction involves only the three MAs. This is convenient for the purpose of checking the validity of the two ratios. At equilibrium, eq 13 should Figure 2. Equilibrium fractions of the three methylamines on a carbon basis as a function of the N/C ratio at three different temperatures.

change for each of the mathematically independent reactions using eq 11 where νij is the stoichiometric

∆GT-j )

∑i νij∆GfT-i

(11)

coefficient of species i in reaction j (reactants are negative and products positive). Assuming ideal gas behavior, the equilibrium constants are related to the equilibrium partial pressures of the species, Peq-i, through the thermodynamic activities, ai, fugacities in the standard state (1 atm for ideal gases), ˆfss-i, fugacities in the mixture, ˆfi, and fugacity coefficients (unity for ideal gases), φi, according to eq 12. Thus, for a given

KT-j )

∏i

aiνij )

( ) ∏( ) ∏( )

∏i ˆf

ˆfi

ss-i

Peq-iφi

νij

)

i

νij

)

1 atm

Peq-i

i

1 atm

νij

(12)

temperature, T, the values of ∆GT-j and KT-j are found from equations 11 and 10, respectively. If only NH3 and CH3OH are present in the feed, then specifying the N/C ratio and the total pressure allows calculation of the equilibrium partial pressures, Peq-i, using eq 12. The latter can be converted to moles, neq-i, using the ideal gas law and any convenient volume as a basis. In MA synthesis the equilibrium yield has been presented in two common ways. The first is on a molar basis where the MMA/DMA/TMA ratio is expressed as neq-MMA/neq-DMA/neq-TMA. The second is on a carbon basis where the MMA/DMA/TMA ratio is expressed as neq-MMA/ 2neq-DMA/3neq-TMA. Figure 2 presents our calculated equilibrium yields (carbon basis) versus the N/C ratio for three different temperatures. The data are presented on a carbon basis only because it is then possible to see that this figure is identical to Figure 1 in Corbin et al.’s review.10 Though the temperature of 400 °C and N/C ) 1 are not always mentioned, it is commonly noted in the literature (e.g., 1, 9, 10, 11, and 14) that the equilibrium molar MMA/DMA/TMA ratio is 17/21/62. This corresponds to a ratio of 7/17/76 on a carbon basis. This is not consistent with the results presented in

K673K-8 )

Peq-TMAPeq-MMA (Peq-DMA)

2

)

neq-TMAneq-MMA (neq-DMA)2

(13)

be satisfied. To check the two ratios, we calculated K673K-8 according to eq 10 above. We additionally calculated K8 but incorrectly used the free-energy change at 298 K, ∆G298K-8, instead of that at 400 °C (673 K), ∆G673K-8. Finally, for each of the two ratios we calculated the right-hand side of eq 13. The results are presented in Table 1. Comparing the second column of Table 1 to the final two columns shows that the commonly cited 17/21/62 ratio is consistent with the incorrect K8 calculated using ∆G298-8. The 32/33/34 ratio agrees with K673K-8, suggesting that 32/33/34 is the correct molar equilibrium ratio. It is curious, however, that the apparently incorrect 17/21/62 ratio has continued to be cited in light of all of the experimental research that has been conducted on this system. This might be explained briefly as follows: the reaction rates are high until the CH3OH plus DME conversion becomes nearly complete. At this point the molar ratio of the products is on the order of 17/21/62, in apparent agreement with the incorrect equilibrium ratio. Thus, if the contact time is varied only to the point where the CH3OH and DME reactants run out, the final yield ratio appears consistent with the incorrect equilibrium ratio. Indeed, the initial experiments in this study were run in a plug-flow reactor, and the contact time was varied to span methanol conversions from ca. 40% to 97%. These experiments consistently lead to a yield ratio closer to the incorrect one than to the one calculated thermodynamically, and initially an error in the thermodynamic calculations was suspected. The key to understanding these results lies in recognizing that, at the point where essentially all of CH3OH and DME have been consumed, the experimental ratio is a kinetic ratio, not an equilibrium ratio. That is, after essentially all of CH3OH and DME have been consumed, the reaction rate becomes much lower, but the system does continue to slowly react. This can be seen in the results from a batch-mode reactor experiment, presented as discrete data points in Figure 3. The run shown in Figure 3 was conducted at 375 °C, 1 atm, and N/C ) 1.56, but it illustrates the point. Almost all of CH3OH and DME are consumed after about 200 min. At this point the experimental yield ratio is 29/24/47, but a proper equilibrium calculation indicates an equi-

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4555

two kinetic regimes exist. In the first regime, amination reactions dominate, methanol and DME are consumed, and MAs are produced. In a classical series reaction scheme one might expect the MMA concentration to first pass through a maximum followed in time by a maximum in the DMA concentration before the TMA concentration finally becomes large. The data do not display this behavior. If intermediate products are strongly adsorbed on the catalyst’s surface, the reactions can appear to occur in parallel from the gas phase even though the surface catalytic processes are serial. Consequently, both series and parallel schemes were tested. In the second reaction regime, transformations among the MAs predominate because essentially all of methanol and DME have been consumed. These transformations can be captured in the model either by explicitly adding the disproportionation reactions or more simply by treating the direct aminations as reversible processes. Therefore, two parallel schemes, one including disproportionation reactions and one not including them, and similarly two series schemes were kinetically evaluated. In short, the kinetic schemes using a parallel pathway gave a poorer fit to the experimental data than those using a series pathway did. Furthermore, explicitly adding additional kinetic terms for the rates of the disproportionation reactions did not lead to a significantly better fit despite the addition of more adjustable parameters. Hence, a simple four-reaction kinetic model was used in the studies described here. The reactions consisted of eqs 1-3 and 9, and the rate expressions were assumed to be of the form given in Table 2. It should be noted that these rate expressions account for the reversibility of the reactions, because this is critical if the model is to capture the full kinetic behavior (both kinetic regimes). The rate expressions given in Table 2 should be considered as empirical, and the associated preexponential factors and activation energies should be taken as apparent values. The corresponding reactions are not elementary steps. Two different rate expressions were tested for reaction (9). A second-order expression has been used in previous kinetic models for silica-alumina catalysts for this reaction system.1,29 In Table 3 the rate coefficients measured in the present study [using the second-order expression of reaction (9)] are compared

Figure 3. Composition over the course of a batch kinetic experiment at 375 °C and N/C ) 1.56 showing that reaction continues beyond the point (at ca. 200 min) where most of the methanol and dimethyl ether are consumed. The discrete points represent the experimental data; the curves show the kinetic model that was fit to the data.

librium ratio of 42/32/26. When the reaction is allowed to continue for an additional 800 min, the MAs continue to react, and as the figure shows, the yield ratio continues to approach the calculated equilibrium ratio. Even after 800 min, however, the system has not attained thermodynamic equilibrium. The extended period without sampling (between 200 and 800 min) should not affect the results. The objective in these experiments was to determine whether equilibrium was attained at the same time methanol and DME were consumed or if it took substantially longer. The reactor system could operate for longer than this interval without leaking. Kinetic Analysis For the purpose of assessing the effect of different membrane reactor configurations upon product selectivity, a kinetic model is essential. Batch reactor data like those shown in Figure 3 were used to find an empirical kinetic model that was quantitatively accurate. The experimental trends displayed in Figure 3 suggest that

Table 2. Empirical Kinetic Model and Parameters for Methylamine Synthesis reaction number (1)

r1 ) k01 exp

(2)

r2 ) k02 exp

(3)

r3 ) k03 exp

(9) first order

r9 ) k09 exp

(9) second order

r9 ) k09 exp

( ( ( ( (

rate expressiona

)[ )[ )[ )[ )[

] ] ]

preexponentialb

activation energyb (kJ mol-1)

PMMAPH2O -E1 PNH3PMeOH RT KT-1

k01 ) 4.8 × 106 L2/(gmol s g)

E1 ) 71.9

PDMAPH2O -E2 PMMAPMeOH RT KT-2

k02 ) 2.1 × 106 L2/(gmol s g)

E2 ) 53.9

PTMAPH2O -E3 PDMAPMeOH RT KT-3

k03 ) 7.6 × 104 L2/(gmol s g)

E3 ) 32.1

PDMEPH2O -E9 PMeOH RT KT-9PMeOH

k09 ) 0.0019 L/(s g)

E9 ) -3.59

] ]

PDMEPH2O -E9 PMeOH2 RT KT-9

a The equilibrium constants, K b T-j, and their temperature dependence are known and are calculated as described in the text. The fit to the experimental data was much better when the first-order expression for reaction (9) was used; consequently, only values for that fit are presented.

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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999

Table 3. Comparison of Literature Kinetic Parameters and the Ones Calculated from Batch Run Data with a Second-Order Dimethyl Ether Production Assumed equation

Weigert

Abrams

this work

NH3 + MeOH / MMA + H2O MMA + MeOH / DMA + H2O DMA + MeOH / TMA + H2O 2MMA / DMA + NH3 2DMA / TMA + MMA MMA + DMA / TMA + NH3 2MeOH / DME + H2O

≡1a 20 120 4 7.2 20.4 ∼1

≡1a 22.8 42.1

≡1a 12.4 23.3

1.35

0.41

a

The rates of all other reactions are normalized to this rate.

to the values reported previously. In the table all rate coefficients are normalized to that of reaction (1). Unfortunately, neither of the previous models explicitly state the temperature, so only a qualitative comparison can be made. Weigert’s model explicitly includes the MA disproportionation reactions, and therefore it is probably only valid to compare the rate of reaction (9) in that study to the present results. Abram’s model includes the same reactions and can be compared more directly. The table shows that in the present study reactions (2), (3), and (9) were observed to occur at about half the rate that was observed in the other studies [or alternatively reaction (1) occurred about twice as fast as that in the other studies]. In light of differences in catalyst properties and the unknown temperatures for the other models, this difference is not unreasonable. Nonetheless, a much better fit to the experimental data was obtained in the present study when a firstorder rate expression was used for reaction (9). This has been observed experimentally and explained theoretically in other studies.7,8 Reaction (9) may appear to be first order if the concentration of intermediate surface methoxy groups is limited by the availability of adsorption sites on the surface. When a first-order expression is used to describe reaction (9), the predicted and measured DME levels agree reasonably well, as can be seen in Figure 3. The best fit using a second-order rate expression for reaction (9) results in a severe overprediction of the amount of DME. The fit of the model to the experimental data for the other species is also shown as continuous curves in Figure 3, and the values of the associated kinetic parameters are presented in Table 2. If one compares Figures 3 and 4, it at first appears that the model predicts the growth of significant local maxima and minima in the methylamine amounts following relatively small changes in the reactor conditions. However, overall mole fractions are plotted in Figure 3 whereas the percentage within the amine fraction is plotted in Figure 4, and consequently the two figures should not be directly compared. In fact, the small shoulders that can be seen in the simulations in Figure 3 correspond to similar local minima and maxima for those conditions if the data are replotted on the basis of mole percentage within the amine fraction. It is not clear from Figure 3 whether the shoulders are real or simply an artifact of the very simple kinetic model used. A more thorough kinetic study would be required to answer this question. The selectivity ratio of 17/21/62 that is often cited in the literature (but appears from the previous section to be incorrect) is for a temperature of 400 °C and N/C ) 1. When runs were attempted at these conditions in the present study, additional undesired reactions apparently started to occur as evidenced by the appearance

Figure 4. PFR simulation of methylamine synthesis at N/C ) 1 and temperatures of 400 °C using the kinetic model developed in this study.

of additional peaks eluted from the GC. This is why data at 375 °C and N/C ) 1.56 were used in the preceding discussion. However, the kinetic model that was developed here can be used to predict the behavior at 400 °C and N/C ) 1, and this is shown in Figure 4. The most striking feature of the figure is that the predicted selectivity at the point where methanol is 97% converted is 15/23/62. This is very close to the incorrect equilibrium ratio of 17/21/62 and probably explains why the latter has been accepted as correct in many studies. While methanol and DME are consumed in approximately 150 min, it requires almost an order of magnitude more time for the system to reach the correct equilibrium selectivity ratio of 32/33/34. Clearly the transformations among the MAs are much slower than their synthesis from ammonia and methanol. It is also interesting to note that this simulation predicts local extrema in MMA and DMA at low conversions. These predictions were not tested experimentally because of the experimental complications already mentioned. Approaches for Improving Yields As noted in the Introduction, a major focus of research in methylamine synthesis has been on altering the selectivity to favor MMA and DMA over TMA. In most cases a kinetic approach has been followed, e.g., the use of shape-selective catalysts. The results of the previous sections suggest that significant gains might be realized as well by seeking catalysts or reactor designs that would accelerate the disproportionation reactions so that true equilibrium could be attained in a reasonable contact time. This could lower the percentage of TMA from 62% to 34% and would seem to be a fruitful avenue for additional research. However, Corbin et al.10 report that market demand is in the range of 8-15% TMA. The remainder of this paper uses the thermodynamic and kinetic results just presented to briefly assess a few membrane reactor configurations and see whether they might offer any further reduction in TMA selectivity. The objective here is not to present a comprehensive study of each membrane reactor configuration and to

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4557 Table 4. Relative Permeation Coefficients of the Different Species species

relative permeation coefficient

SNH3 SMeOH SMMA SDMA STMA SDME SH2O

1 0.73 0.74 0.61 0.54 0.61 0.97

model for membrane reactors of this kind has been presented previously2,4,5,18,19 and is used here. Briefly, this model has been shown to provide good agreement with experimental results. It assumes plug flow on both sides of the membrane with no boundary layer effects at the membrane surfaces. The governing equations for MMA, in dimensionless form, for the reaction side of the reactor are given in eq 14 and those for the annular side in eq 15. In these equations Fi denotes the dimeni

i

i

i

i

1 dFMMA FMeOHFNH3 FMMAFH2O ) Da dZ Fi 2 K Fi 2

(

total

FiMeOHFiMMA κ2 i 2 Ftotal

1 total

-

)

i FiDMAFH 2O i 2 K2Ftotal

(

-

)

FoMMA SMMA FiMMA -φ o (14) DaPe Fi Ftotal total

(

)

FoMMA dFoMMA DaSMMA FiMMA φ ) o dZ DaPe Fi Ftotal total

Figure 5. Schematic representations of membrane reactor configurations considered for methylamine synthesis.

optimize each design. The goal here is to get a preliminary indication of the magnitude of the improvement in selectivity that that configuration might offer and to identify most important factors limiting performance in each configuration. Before the results are presented, it is very important to point out that in a membrane reactor the operating conditions can be very different from a conventional reactor.17 The predictions made here for these kinds of situations (e.g., very high N/C) are only as good as the extrapolation of the present, simple kinetic model to such conditions. Much more rigorous predictions could be made if the kinetics were studied in detail at conditions found in the membrane reactor and a model were developed to accurately describe those kinetics. The first membrane reactor considered was a standard concentric tube configuration where the inner tube is a permeable membrane and the catalyst is packed inside this inner tube. The reactants are fed to this inner tube, and the idea is to have selective removal of MMA and DMA through the membrane, thereby increasing their yield relative to TMA. This configuration is shown schematically in Figure 5a. The simulation here assumes a reactor temperature of 400 °C, a reaction side pressure of 20 atm, an outer shell pressure of 1 atm, a feed ratio of N/C ) 1, and relative rates of permeation based upon Knudsen diffusion. A relatively simple

(15)

sionless flow rate of species i (with superscript i denoting the tube side and o the annular side), Kj denotes the equilibrium constant for reaction j, φ is the ratio of annular to tube pressure, and Z represents the dimensionless axial position within the reactor. The full model includes 12 similar equations for each of the other species. Apart from the relative reaction rate coefficients, κj (here dictated by the kinetic model) and the relative permeation coefficients, Si (here assumed to be Knudsen diffusion ratios; Table 4), there are two other important reactor parameters, the Damkohler number, Da, and a Damkohler-Peclet product, DaPe. Because this reaction takes place at elevated temperatures, it is reasonable to assume that a porous ceramic type of membrane would be used, and hence the assumption of Knudsen diffusion ratios is reasonable. The value of DaPe used here (1000) is reasonable for a normal reactor geometry using ceramic-type membranes.4 It is assumed that products are recovered from both streams leaving the process. Figure 6 shows that the membrane reactor does provide very good selectivities at low conversions of methanol. However, even before the methanol conversion has passed 50%, TMA has become the majority product, and it remains so at all higher conversions studied. This is not particularly surprising. Previous work has shown that a major problem with this kind of membrane reactor is the loss of reactant through the membrane.2,4 In the present case methanol and ammonia will both permeate through the membrane faster than the products. As a consequence, there is a point in the reactor beyond which the reactants actually must

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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 i i PiMMAPH ) K1PNH Pi 2O 3 MeOH

(16)

i ) K2PiMMAPiMeOH PiDMAPH 2O

(17)

i PiTMAPH ) K3PiDMAPiMeOH 2O

(18)

i ) K9PiMeOHPiMeOH PiDMEPH 2O

(19)

i o PNH - PNH 3 3

SMMA(PiMMA - PoMMA) i o PNH - PNH 3 3

SDMA(PiDMA - PoDMA) i o - PNH PNH 3 3

permeate back into the reaction zone to react. In the absence of a truly permselective membrane material (i.e., one that allows only MMA and DMA to permeate), this kind of membrane reactor is obviously of little utility if high conversions are desired. A second membrane reactor configuration was examined to see whether the problem of reactant loss might be overcome. As shown in Figure 5b, this configuration assumes that the reactor is fully backmixed and also that the contents are essentially at equilibrium. Actually achieving true equilibrium in a reasonable reactor volume would require improved catalysts that are active in the second kinetic regime discussed above. The only outlet from the reactor is through the membrane. Because methanol and DME conversions are near 100% at equilibrium, the driving force for their permeation will be small, and little of these species should be lost through the membrane. There will be ammonia loss because its conversion is less than 100%, and this becomes the central question for this kind of reactor: how much ammonia will pass through unreacted? Again it was assumed that the membrane would be a ceramic material and that permselectivities would be in the same ratio as Knudsen diffusivities. This configuration is interesting from a reactor design viewpoint. The governing equations consist of the equilibrium conditions (eqs 16-19), the relative permeation relations (eqs 20-25), the requirement that the outlet N/C ) 1 (eq 26), and one additional stoichiometric constraint (eq 27). In these equations Pn represents the pressure of species n, with superscript i denoting the reaction side and superscript o denoting the outlet side. Clearly, at steady state the effluent N/C ratio must equal the feed N/C ratio. At the same time, the effluent permeation rates are constrained to obey the Knudsen diffusion equations for the membranes. There are two factors which determine the permeation rates: the diffusion coefficients (which are fixed here at the Knudsen values) and the concentration gradients across the membrane. Thus, to meet the steady-state requirement that the inlet and outlet N/C ratios be equal, the reactor composition must simultaneously correspond to ther-

)

i o PNH - PNH 3 3

SDME(PiDME - PoDME)

SMeOH(PiMeOH - PoMeOH) i o - PNH PNH 3 3 i o SH2O(PH - PH ) 2O 2O

o PNH 3

(22)

o PNH 3

(23)

PoDME

)

)

(21)

PoDMA

PoTMA

)

i o PNH - PNH 3 3

(20)

PoMMA

o PNH 3

)

STMA(PiTMA - PoTMA) Figure 6. Performance of a concentric tube membrane reactor where permeation rates follow Knudsen diffusivity. The reactor temperature is 400 °C, the reaction side pressure is 20 atm, and the permeation side pressure is 1 atm.

)

o PNH 3

o PNH 3

PoMeOH

o PNH 3

(24)

(25)

o PH 2O

o ) PoMeOH + PoMMA + 2PoDMA + 3PoTMA + PNH 3

2PoDME (26) o ) PoMMA + 2PoDMA + 3PoTMA + PoDME PH 2O

(27)

modynamic equilibrium and additionally to a set of compositions that give permeation fluxes in the proper ratio. In other words, the steady-state N/C ratio within the reactor will of necessity be different from the inlet and outlet N/C ratios (which are equal). Figure 7 shows the conversion and selectivity as a function of temperature for this membrane reactor configuration and compares it to the equilibrium conversion in the absence of a membrane reactor. As before the reaction side is arbitrarily assumed to operate at 20 atm with the effluent side at 1 atm. The selectivity here is plotted as a selectivity factor Y ) (MMA + DMA)/ TMA. The results are initially surprising as can be seen, for example, at 400 °C. As already noted, the selectivity ratio at 400 °C is 32/33/34 corresponding to Y ) 1.91. Initial impressions would lead one to suspect a much better selectivity with the membrane reactor. Because the equilibrium concentrations are nearly equal, the driving forces for membrane permeation should all be equal, and therefore one might expect the permeation rates to be directly proportional to the Knudsen diffusivities. If this were true, the selectivity factor would indeed be better, Y ) 2.41. The flaw in this reasoning is that once the membrane is added to the system and it is allowed to attain equilibrium and steady state, the N/C ratio in the reactor is no longer 1 as just discussed. In fact, at 400 °C for feed and effluent N/C ratios equal to 1.0, the N/C ratio within the reactor at steady state will be only 0.77. At an N/C ratio of 0.77 the equilibrium selectivity is not 32/33/34 but instead is much, much

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Figure 7. Conversion and selectivity factor as functions of the reaction temperature for a feed N/C ratio of 1.0 in a membrane reactor where the effluent must permeate from the equilibrated reaction mixture via Knudsen diffusion (Figure 5b) compared to the equilibrium conversion and selectivity of a nonmembrane reactor.

richer in TMA. As the figure shows, this increase in TMA because of the lowering of the N/C more than offsets the lower diffusion coefficient of TMA relative to MMA and DMA. One might then reason that a feed ratio higher than 1.0 should be used in order to raise the steady-state N/C within the reactor. The problem with raising the feed N/C is that almost all of the added NH3 simply permeates out of the system unreacted and the conversion is little affected. Ultimately one reaches the same conclusion as for the first system considered, a porous ceramic membrane (where relative permeation rates correspond to Knudsen diffusion rates) simply is not sufficiently permselective to impact the overall selectivity. One significant difference between these two cases is that the latter case does not suffer as much from reactant loss. Indeed, if one could densify the membrane in such a way that the diffusion coefficient for TMA was reduced much, much more than that of DMA and MMA, then this membrane configuration could provide selectivities better than equilibrium. As already noted, the improved selectivity would likely come at the expense of a significantly larger reactor. The first membrane reactor configuration considered suffered from loss of both reactants through the membrane. The second membrane reactor configuration considered suffered from loss of ammonia through the membrane. A third configuration, shown in Figure 5c, was evaluated wherein the membrane side of the system is closed, and consequently there can be no loss through the membrane. In this configuration the reactants are fed on the tube side of the membrane. The catalyst is in the closed annular side of the reactor so the reactants must permeate to that side in order to react. The products then must permeate back to the tube side in order to leave the reactor. It is again assumed that the reaction occurs rapidly on the annular side of the reactor so that the reaction is at equilibrium there. It is also again assumed that relative permeation rates are those that would arise under Knudsen diffusion. The govern-

Figure 8. Conversion and selectivity factors at N/C ) 1 and a temperature of 400 °C as functions of the permeability of the membrane in a closed annular membrane reactor (Figure 5c) compared to the equilibrium conversion and selectivity in a nonmembrane reactor.

ing equation for the flow side in this configuration is given in eq 28. In this equation Si and Z have the same

dxoi ) SiPI(xii - xoi ) dZ

(28)

meaning as previously, PI is the permeation index defined in eq 29, and xi is the mole fraction of species i (superscript i denoting the equilibrated and closed side of the membrane and superscript o denoting the flow side). In eq 29 A is the membrane area, J the molar

PI )

DNH3 A P d J RT

(29)

flow rate, R the gas constant, T the temperature, d the membrane thickness, DNH3 the effective diffusivity of NH3, and P the pressure. It may be noted that the permeation index is the inverse of Pe used in the concentric tube configuration. In addition to eq 28, the model for the configuration of Figure 5c includes equilibrium relationships for the closed side of the membrane. These are equivalent to eqs 16-19 except that xii replaces Pii. The final component of the model is the requirement that at steady state the net flux of each element through the membrane must be zero. This requirement is given in eq 30 for nitrogen as an example; similar equations are necessary for carbon and oxygen. i o - xNH ) + SMMA(xiMMA - xoMMA) + (xNH 3 3

SDMA(xiDMA - xoDMA) + STMA(xiTMA - xoTMA) ) 0 (30) As in the previous cases this simulation uses a reaction temperature of 400 °C and a feed with N/C ) 1.0. The reactor pressure is 1 atm. The performance of this system, in terms of selectivity, is the most promising of the three configurations considered so far. Figure 8 shows the conversion and selectivity as a function of the permeation index, PI. The most significant thing to

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notice in Figure 8 is that the selectivity of the membrane reactor is always greater than or equal to equilibrium selectivity. Notably, even at 96% conversion of methanol the membrane reactor selectivity is 2.5% above the equilibrium value. Still, the gains offered by the membrane reactor are modest compared to the 8-15% TMA market demand mentioned previously which translates to a selectivity parameter Y of 5.67-11.5. As expected, as the permeation index increases, the advantages of the membrane reactor disappear because the two sides become equilibrated and the membrane reactor asymptotically approaches the equilibrated reactor performance. Also, the reactor volume for this configuration would undoubtedly be large because the residence time in the reaction zone has to be sufficient for the reaction to equilibrate. As with the previous design, this configuration would benefit tremendously from a membrane that was densified in such a way that TMA permeation was selectively attenuated with little or no effect on the permeation of DMA or MMA. Another intriguing possibility would be to recycle excess TMA from the final process separation and feed it back directly into the equilibrated reaction zone of the reactor. The final membrane reactor configuration examined involved a split reactant feed4,12,13 as mentioned in the Introduction. Ammonia is fed to the catalyst-loaded inner tube while methanol is fed to the outer shell as Figure 5d illustrates. The governing equations are essentially the same as the first configuration, only the boundary conditions differ. The simulation assumes that the pressure is 1 atm on both sides of the membrane, the reaction temperature is 400 °C, and the feed ratio is N/C ) 1. No reaction occurs until methanol permeates through the membrane that separates the two reactants. In this way the most favorable N/C ratio always exists on the reaction side of the membrane in this configuration. Similar to the first membrane reactor system considered, this configuration suffers from the loss of ammonia through the membrane when operated at equal pressures. This can be eliminated if a pressure drop is maintained across the reactor as has been shown in partial oxidation studies where zero reactant slip must be attained to prevent explosive conditions.12,27 Figure 9 shows the Damkohler number required to achieve 95% methanol conversion along with the selectivity factor as a function of the DaPe product for this feed distribution configuration. The figure also indicates the corresponding values for a conventional plug-flow reactor (PFR) and the equilibrium selectivity. At the lowest values of DaPe there is virtually instantaneous permeation through the membrane. As a consequence, the two sides of the reactor always have the same composition and the membrane reactor looks just like a PFR in terms of size and selectivity. As DaPe increases, the rate of reaction becomes faster than the permeation rate. This is the desired range of operation, because as the methanol arrives on the reaction side it is quickly consumed. This results in a high N/C ratio in the reaction zone, and this favors MMA and DMA production. The figure shows that in this regime the selectivity factor at 95% conversion is better than a PFR at the same conversion and in some cases better than the equilibrium selectivity. Of course the reason this works is that the slow step in the process is permeation. As Figure 9 shows, the size of the reactor increases tremendously at this point, meaning that this gain in

Figure 9. Selectivity factor and required Damkohler number for a distributed feed membrane reactor for methylamine synthesis operating at 95% methanol conversion.

selectivity comes at a very substantial cost. Ultimately, at any DaPe if the Damkohler number is increased sufficiently, the reactor system will reach an equilibrium selectivity factor of 1.91, corresponding to thermodynamic equilibrium. The most important conclusion that can be drawn from the figure is that while a selectivity slightly better than equilibrium can be reached, the size of the reactor required to do so would be prohibitively large. The brief assessment just presented suggests two areas where breakthroughs might significantly improve the viability of membrane reactors for methylamine synthesis. The first would be a membrane system that was stable at reaction temperatures and that also was truly permselective for MMA and DMA over all other species, including ammonia and methanol. This is perhaps an unrealistic goal at present. The two equilibrated reactor configurations (Figure 5b,c) might be improved substantially with less of a membrane breakthrough. In these cases performance should increase if a membrane is used that reduces the TMA permeation rate relative to all other species. Because TMA is the largest of the molecules involved, this goal is perhaps more realistic and might be attained through membrane densification or with a zeolite membrane. However, in these cases a second breakthrough would be required, namely, a catalyst material that is active in both kinetic regimes and thereby is capable of rapidly bringing the reaction all the way to equilibrium. It appears that most current catalysts are not nearly as active once all of the methanol and DME are converted; i.e., they are only active in the first kinetic regime. Indeed, even without considering the use of a membrane reactor, it appears the selectivity of conventional reactor processes might be improved through the development of catalysts of this type. Conclusions The synthesis of methylamines from ammonia and methanol has been found to involve two kinetic regimes. In the first regime methanol and DME are consumed in the direct formation of methylamines. At the point where essentially all of methanol and DME are con-

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sumed, the methylamines are not equilibrated. This marks the beginning of the second kinetic regime wherein the methylamines are interconverted to eventually yield an equilibrium mixture. It appears that in the past the nonequilibrium selectivity that exists at the end of the first regime has sometimes mistakenly been taken to represent the equilibrium selectivity. The reason for this is probably related in part to the low catalytic activity of most current catalysts in the second kinetic regime. It also is probably related to the fortuitous coincidence that the kinetic selectivity at the end of the first regime is nearly equal to the selectivity that would be calculated if one ignores the change in free energy between standard conditions and reaction conditions. A reversible, serial reaction scheme that also includes conversion of methanol to DME has been shown to capture the kinetic behavior in both kinetic regimes. This kinetic model along with a proper thermodynamic equilibrium model has been used in a preliminary assessment of the benefits and limitations of membrane reactors as a means of altering selectivity. The goal is to match selectivity to market demand, and this requires reducing the selectivity for TMA relative to MMA and DMA. The membrane reactor configurations that were evaluated here certainly were not optimized. Nonetheless, the analysis highlights two significant limitations of current systems. The first limitation is that high temperature ceramic-type membranes are simply not sufficiently permselective. The smaller reactant molecules permeate much faster than the products, and this loss of reactant severely limits membrane reactor performance. The second limitation is catalytic; current catalysts are quite active as long as methanol and DME are present, but their activity for disproportionation reactions is an order of magnitude lower. If this catalytic limitation could be eliminated, some of the membrane reactor configurations might become attractive, even with existing membrane materials. Additionally, the further improvement of these same configurations would involve much less demanding changes in membrane performance. For example, with current catalysts a membrane is needed that permeates MMA and DMA faster than all other species (including reactants). If catalysts were available that could rapidly bring all reactions to equilibrium, it would only be necessary to develop membranes that slow the permeation of TMA relative to all other species. Acknowledgment This material is based upon work supported by the National Science Foundation under Award No. CTS9406620. Notation A ) membrane area ai ) activity of species i d ) membrane thickness Da ) Damko¨hler number Di ) effective diffusivity of species i Fi ) dimensionless flow rate of species i ˆfi ) fugacity of species i in the mixture ˆfss-i ) fugacity of species i in the standard state ∆GT-j ) Gibbs free energy change of reaction j at temperature T ∆GfT-i ) Gibbs free energy of formation of species i at temperature T

J ) molar flow rate Kj ) equilibrium constant for reaction j KT-j ) equilibrium constant for reaction j at temperature T Peq-i ) equilibrium partial pressure of species i Pi ) partial pressure of species i Pe ) Peclet number PI ) permeation index (inverse of the Peclet number) R ) gas constant Si ) ratio of the permeation coefficient of species i to that of ammonia P ) total pressure T ) temperature x ) mole fraction of species i Z ) axial position within the reactor Greek Symbols νij ) stoichiometric coefficient of species i in reaction j φi ) fugacity coefficient of species i φ ) ratio of annular side to tube side pressure κi ) relative reaction rate coefficient Superscripts i ) tube side o ) annular side

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Received for review May 3, 1999 Revised manuscript received September 13, 1999 Accepted September 17, 1999 IE990317B