Ind. Eng. Chem. Res. 1999, 38, 4913-4918
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Decline in Hydrogen Permeation Due to Concentration Polarization and CO Hindrance in a Palladium Membrane Reactor S. Hara,* K. Sakaki, and N. Itoh National Institute of Materials and Chemical Research, Tsukuba 305-8565, Japan
Hydrogen separation from binary gas mixtures, Ar-H2 and CO-H2, using a double-tube type of palladium membrane reactor (PMR) was carried out and analyzed by solving mathematical models taking into account mixing diffusion of hydrogen in the radial direction of the catalystpacked bed. The experiment showed that carbon monoxide prevented hydrogen permeation through the membrane at temperatures less than 280 °C. The decline in hydrogen permeation could be estimated by solving a model describing the concentration polarization and the hindrance by cabon monoxide. Furthermore, the mathematical models were applied to analyze methanol decomposition in the same PMR, showing that a drop in hydrogen permeation due to both the factors had a significant influence on the performance of the PMR. 1. Introduction Palladium membrane reactors (PMR), containing a catalyst and a hydrogen permeable membrane in one reactor, have been successfully examined for various dehydrogenation reactions.1-8 However, in some reaction systems one of the reactants and products, such as carbon monoxide and carbon dioxide, can affect the hydrogen permeation of the palladium membrane,9 which can depress the reaction performance of membrane reactors lower than expected. Actually, we carried out methanol decomposition into carbon monoxide and hydrogen in a PMR and compared the results with that obtained by solving a simple model called an ideal model in the latter section.8 However, the conversions obtained by the experiment were much smaller than the calculated ones. This also seems to be partially due to the hindrance by resultant carbon monoxide. It is, therefore, interesting to find out whether carbon monoxide prevented hydrogen permeation, indeed, and how much the decrease in permeation performance affected the methanol decomposition in the PMR. In this study, to estimate the hindrance by carbon monoxide to hydrogen separation without making another membrane, hydrogen separation from gas mixtures containing carbon monoxide was carried out using the PMR employed in the previous study and the results were analyzed by solving mathematical models, taking account of the radial mixing diffusion of hydrogen in the packed-bed side. Furthermore, the models were applied to methanol decomposition in the PMR to investigate the influence of the hindrance on the performance of the PMR. 2. Experimental Section The double-tube membrane reactor employed is illustrated in Figure 1, which is the same one used in the previous study.8 This reactor consisted of a stainless steel shell tube and a 0.2-mm-thick membrane tube made of Pd91Ru6In3 alloy. A 1/16-in. pipe was inserted inside the membrane tube to exhaust sweep gas con* To whom correspondence should be addressed. Tel.: +81298-54-4663. Fax: +81-298-54-4674. E-mail:
[email protected].
Figure 1. Schematic of a double-tube type of palladium membrane reactor employed in this study.
taining hydrogen that permeated through the membrane. In the annular space around the membrane, catalyst pellets (1 wt % Pd/SiO2; 1.1-1.6 mm) were packed. Apparent density of the catalyst was estimated by the Archimedes method using 0.1-mm alumina particles instead of water. From the apparent density, the superficial volume and the weight of the catalyst, porosity of the catalyst bed, Eps, was determined, which was employed to obtain interstitial velocity, ui, appearing in the diffusion model. Hydrogen permeation properties of the membrane were tested for pure hydrogen and various concentrations of Ar-H2 and CO-H2 mixtures. These gases were introduced to the packed-bed side at a rate of 30 cm3 (STP)/min. Gas flow rates in the inlet and outlet of the feed side and the outlet of the permeate side were measured by a soap-film flowmeter to determine the hydrogen permeation rate. No argon permeation was detected by this method, indicating that the membrane was pinhole-free. The hydrogen separation was performed for three different modes: (i) opening only one end of the permeate side to the atmosphere to let the permeate side fill with permeated hydrogen (open mode); (ii) feeding argon gas at a rate of 10 cm3/min into the permeate side cocurrently to sweep the permeated hydrogen (sweep mode); (iii) evacuating the permeate side by a rotary vacuum pump (vacuum mode). Pressures in the inlets and outlets of both sides were monitored. The pressure drop along the reactor length in each side was found to be usually negligible, but in the vacuum mode the pressure in the inlet of the permeate side was always 2 orders of magnitude higher
10.1021/ie990200n CCC: $18.00 © 1999 American Chemical Society Published on Web 11/05/1999
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Table 1. Values Employed in the Mathematical Models dp Ep Eps k KC K l0
0.00135 m 6.4 × 103 J/mol 0.615 7.6 × 10-9 mol/m3‚s‚Pa 5.7 × 10-8 1/Pa 1.06 × 1012 Pa2 (220 °C) 0.208 m
P h0 r1 r2 r3 ∆R ∆L
3.0 × 10-8 mol/m‚s‚Pa1/2 0.00355 m 0.011 m 0.00335 m 1/16 1/100000
than that in the outlet. Therefore, the simple calculation in the previous study, assuming the permeate pressure to be zero for the vacuum mode, was insufficient. Because the pressure drop is probably attributed to the low conductance of the extremely narrow exhaust pipe, in the present study the pressure in the inlet is adopted as a permeate pressure, PTs. Moreover, the gaseous components in the effluent from the feed side were analyzed by a gas chromatograph (Shimadzu GC-14A), which were roughly consistent with the values expected from the flow rates. It was also made sure that no reactions occurred in the reactor, even in the case of separation from CO-containing gases.
the reaction side was adopted as Pstd for hydrogen separation from gas mixtures without reaction and the methanol partial pressure in the inlet for methanol decomposition. A. Ideal Model. Additionally, this model assumes complete mixing in the radial direction, or a flat concentration distribution in the reaction and separation side. The set of differential equations of UφXr’s to be solved for this ideal model is given as follows:
d(UφHr) ) -R˜ (xφHr - xφHs) + 2rM dL
(4)
d(UφMr) ) -rM dL
(5)
where
R˜ )
3. Model Development The models employed in this study are based on Itoh’s work,10 which assume isothermal, isobaric, steady-state, and plug-flow conditions through the whole reactor. Into the reaction side, a gas mixture containing hydrogen, methanol, carbon monoxide, and argon is introduced and into the separation side pure argon is fed cocurrently in the sweep mode. All the gases are assumed to obey the ideal gas law. The permeation properties of the membrane tube has been intensively investigated for pure hydrogen in the previous study8 where hydrogen flux has been proportional to the difference of the square roots of the hydrogen partial pressures across the membrane. The permeability derived from the slope, P h , has been found to obey the Arrhenius form in the range of 200-300 °C:
P h )P h 0 exp(-Ep/RT)
(1)
On the other hand, the reaction behavior also has been characterized mainly at 220 °C. Because the selectivity of methanol to carbon monoxide has always been larger than 94%, in this calculation only the main reaction can be assumed to occur in the reaction side. The reaction rate, rM, has already been determined from experimental conversion without hydrogen removal as the following formula:8
rM )
k(KpMr/pHr2 - pCr) 1 + KCKpMr/pHr2
(2)
All the parameters appearing in the above two equations are listed in Table 1, where other parameters are also summarized. It is noted that though the following formulas are constructed for methanol decomposition, those for hydrogen separation without reaction can be easily obtained by setting rM to be zero throughout. In the differential equations described below, the following dimensionless parameters are used:
φ ) p/Pstd, U ) u/u0, V ) v/u0, L ) l/l0
(3)
where Pstd is a standard pressure for normalization. In this study the hydrogen partial pressure in the inlet of
PTr u˜
0
2πl0P h
xPstd ln(r1/r3)
)
Arl0PTr
(6)
(7)
u˜ 0Pstd
Because methanol produces the same molar of carbon monoxide, the total flow rate of molecules except hydrogen is unchanged throughout in the reaction side, leading to the following representation of U:
U)1+
Pstd {(UφHr) - φ0Hr} PTr
(8)
From U obtained by eq 8 as well as UφHr and UφMr, φHr and φMr can be obtained. φCr and φHs can be calculated by
φCr )
1 0 {φ + φ0Mr - (UφMr)} U Cr
(9)
PTs VH Pstd V 0 + V
(10)
φHs )
H
where
VH )
ArPstd 0 {φ + 2φ0Mr - (UφHr) - 2(UφMr)} AsPTs Hr
(11)
Thus obtained dimensionless pressures, φ’s, are utilized in the right sides in eqs 4 and 5. B. Diffusion Model. In this model unidirectional diffusion of hydrogen in the radial direction of the packed bed is considered, by which Itoh et al. have successfully described hydrogen separation behavior from gas mixtures.10 On the separation side, the ideal flow conditions are applied. Because the basic partial differential equation describing the changes of hydrogen partial pressure in the feed side cannot be solved analytically, the feed side is uniformly divided by W in the radial direction and the central finite difference
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approximation is applied, which brings the following (W + 1) differential equations:
{
d(UφHr)m
) dL 1 [2(φHr)1 - 2(φHr)0 M ˜
(
1 ( (φ ) - φ ) + 2rM a x Hr 0 x s
1+
1 (φHr)m+1 - 2(φHr)m + 2(a + m)
(β∆R) 2 -
1 M ˜
[{ {
1-
)
]
} }
]
1 (φHr)m-1 + 2rM 2(a + m)
1 [2(φHr)W-1 - 2(φHr)W] + 2rM M ˜
(m ) 0)
(1 e m e W - 1) (m ) W)
(12)
where
(r2 - r1)2 2 M ˜ ) Per ∆R d pl0 β)
(13)
P h RT(r2 - r1)
(14)
DerxPstdr1 ln(r1/r3)
Because unidirectional diffusion of hydrogen is assumed, the differential equations for methanol and carbon monoxide can be given by the following simple forms:
d(UφMr)m ) -rM dL
(m ) 0, 1, ..., W)
d(UφCr)m ) rM dL
(15)
(m ) 0, 1, ..., W)
(16)
U and VH can be written in terms of the averages of UφXr’s:
U)1+ VH )
[
{
Pstd 1 PTr Ar
∫rr
2
1
(UφHr) 2πr dr - φ0Hr
ArPstd 0 1 φ + 2φ0Mr AsPTs Hr Ar
∫rr
2
1
}
(17)
{(UφHr) +
]
2(UφMr)}2πr dr (18) Equation 10 is still valid to obtain φHs for the diffusion model. Peclet number appearing in eq 13 was determined by Wen and Fans’ equation:11
1/Per ) 0.4/(PepSc)0.8 + 0.09/{1 + 10/(RepSc)}
(19)
The effective radial diffusion coefficient, Der, was obtained as follows:
Der ) uidp/Per
(20)
The sets of differential equations, eqs 4 and 5 for the ideal model and eqs 12, 15, and 16 for the diffusion model, were numerically solved by the fourth-order
Figure 2. Permeability for pure hydrogen (b) and apparent permeability for Ar-66.7%H2 for the open (0), sweep (]), and vacuum (4) modes. (u˜ 0 ) 2.0 × 10-5 mol/s; PTr ) 0.2 MPa.)
Runge-Kutta method. W was chosen to be 16, which required more than 100 000 axial steps to converge the results. It took several seconds for a Power Macintosh G3 DT266 to complete the program written by FORTRAN 77. 4. Results and Discussion 4.1. Hydrogen Separation from Gas Mixtures. First, we tried to represent hydrogen separation from gas mixtures assuming complete mixing in both sides, where apparent permeability was determined for each condition so that the ideal model reproduced experimental flow rates. Figure 2 shows the apparent permeability for separation from 0.2-MPa Ar-66.7%H2 as well as permeability for pure hydrogen determined in the open mode, which corresponds to eq 1. It should be noted that the apparent permeability for the gas mixture is always smaller than the permeability for pure hydrogen and the difference from that for pure hydrogen increases in the order of open, sweep, and vacuum modes. However, inert gas such as argon does not seem to cause such a large decrease in permeability of the membrane. The most probable origin of the decrease is concentration polarization in the reactor. Generally, its influence becomes significant when the hydrogen permeation rate is large, i.e., in the vacuum mode, which is in good agreement with the above phenomenon. Therefore, we analyzed the raw data again, taking into account the hydrogen diffusion in the reaction side. A comparison between the experimental flow rates and calculated results by using several models is made in Figure 3. This figure shows the limitation of the ideal model, too. On the other hand, the diffusion model can reproduce the experiment for the argon hydrogen mixture, which indicates the importance of radial diffusion under the experimental conditions as shown by Itoh et al.10 The Schmidt number for hydrogen diffusion in argon is rather close to that in carbon monoxide so that the broken lines calculated by the diffusion model can be considered to be not only for Ar-H2 but also for COH2. Nevertheless, the experimental results for the COcontaining gas mixture are always larger than those for Ar-H2 in the low-temperature range. The difference between them can be considered to be due to CO hindrance to hydrogen permeation of the membrane. Because the decrease in hydrogen permeation during the separation from CO-H2 recovers in several minutes after changing the feed to pure hydrogen, the hindrance may be attributed to adsorption of carbon monoxide on the membrane surface. Therefore, we supposed that the permeability for CO-containing gas mixtures can be
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Figure 4. Coefficient κ to represent the CO hindrance to hydrogen permeation.
Figure 3. Hydrogen flow rates at the outlet of the feed side with Ar-66.7%H2 (O) or CO-66.8%H2 (b) as a feed normalized at the inlet and calculated results. (220 °C; u˜ 0 ) 2.0 × 10-5 mol/s; PTr ) 0.2 MPa.)
described by the following form instead of P h for pure hydrogen:
(
)
pCr 1-κ P h PTr
(21)
where the coefficient κ was determined so that the diffusion model with κ reproduces the experimental plots for the CO-containing gas mixture in Figure 3b. On the other hand, at 280 and 300 °C κ can be regarded as zero because the flow rates for these gas mixtures are almost the same at these temperatures in any mode. Thus, the determined κ is shown in Figure 4 as a function of temperature. κ decreases with temperature, which relates to the decrease in CO adsorption. Moreover, this tendency is consistent with the other results in the literature.9 Furthermore, the diffusion model with κ-modified permeability was applied to the other modes. The results, shown in Figure 3a,c, are in agreement with the experiments in absolute value as well as in difference between the gas mixtures. A comparison between the calculation and experiment was made for various concentrations, too. The results are shown in Figure 5, where the data for the open mode is not shown because high feed pressures are necessary to carry out hydrogen separation due to a high hydrogen
Figure 5. Calculated hydrogen flow rates at the outlet of the feed side for various concentrations of CO-H2 mixtures normalized at the inlet as well as experimental results. (220 °C; u˜ 0 ) 2.0 × 10-5 mol/s; PTr ) 0.2 MPa.)
pressure in the permeate side. It is worth noting that the contribution of the radial diffusion is comparable to that of the hindrance in any mode and both effects are necessary to explain the experiment, especially in the vacuum mode. Additionally, the figure also indicates that the diffusion model taking into account the CO hindrance is applicable to the wide concentration range and three different modes. 4.2. Influence of CO Hindrance on Methanol Decomposition in PMR. The models described above were applied to methanol decomposition in the same PMR and compared with the experimental results presented in the previous study.8 Typical radial concentration profiles calculated by the diffusion model with κ are illustrated in Figure 6. Although the decrease in the permeation rate due to the CO hindrance is to reduce the concentration polarization, the ununiformity still remains throughout the reactor. Figure 7 depicts the influence of such radial diffusion and hindrance on methanol decomposition. It is found that the influence is not so large around the inlet but accumulates to cause a significant decrease in conversion at the outlet. In addition, the hydrogen flow rate is also found to be very sensitive to the two factors.
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4917
Figure 6. Radial distribution profiles of hydrogen in the feed side during methanol decomposition calculated by the diffusion model with κ. (Vacuum mode; 100% methanol as a feed; GHSV ) 6 h-1; 220 °C; PTr ) 0.1 MPa.)
combination of these factors. This suggests that the decrease in conversion cannot be ascribed only to the diffusion or to the hindrance. Also, it is worth noting that the influence of the diffusion and hindrance is larger in the vacuum mode than in the sweep mode, which is consistent with the results in Figure 5. However, deviation between the experiment and simulation still remains so that another factor must be considered. One of the most possible factors is reaction temperature.12,13 Because the decomposition is endothermic, the promotion of the decomposition by hydrogen separation decreases the temperature in the reactor, resulting in a decrease in decomposition rate. Because the equilibrium conversion changes drastically around the temperature employed, the influence seems to be large. However, we did not monitor the temperature distribution along the reactor and therefore could not present further analysis. 5. Conclusions
Figure 7. Calculated flow rate profiles of methanol and hydrogen in the feed side during methanol decomposition normalized by the methanol feed rate. The experimental flow rates of methanol (9) and hydrogen (b) are also plotted.5 (Vacuum mode; 100% methanol as a feed; GHSV ) 6 h-1; 220 °C; PTr ) 0.1 MPa.)
We have investigated the effect of the radial hydrogen diffusion in the feed side and the CO hindrance to hydrogen permeation on hydrogen separation from gas mixtures using a double-tube type of palladium membrane reactor. Comparisons between the experiment and the simulation showed that the radial diffusion must be taken into account for separation from gas mixtures and CO hindrance is also important for COcontaining mixtures at temperatures less than 280 °C. To estimate the decrease in the hydrogen permeation rate by the presence of carbon monoxide, we introduced eq 21 instead of permeability for pure hydrogen, which enabled us to know the hydrogen permeation flux using the PMR for various concentrations and three different modes. Furthermore, the mathematical models were applied to methanol decomposition in the same PMR, showing that the combination of the radial diffusion and the CO hindrance causes a significant decrease in conversion in the PMR. The influence of these factors was also found to be larger in the vacuum mode than in the sweep mode. However, disagreement between the experiment and simulation still remains. To explain it, other factors should be considered, such as temperature distribution. Nomenclature
Figure 8. Comparison between calculated methanol conversions and experimental results (b).8 Experimental conversion without hydrogen separation (O) is also plotted. (100% methanol as a feed; 220 °C; PTr ) 0.1 MPa.)
The conversions calculated by these models are compared in Figure 8. For example, the conversion at a GHSV of 8 h-1 in the vacuum mode calculated by the ideal model without respect to the hindrance is 92%, which decreases by 4% because of the hindrance, by 9% because of the diffusion, and by 11% because of the
a ) r1/{(r2 - r1)∆R} A ) sectional area perpendicular to the axis (m2) dp ) size of catalyst pellets (m) Der ) effective radial diffusion coefficient of hydrogen in a packed bed (m2/s) DHX ) molecular diffusivity of hydrogen in gas X (m2/s) Ep ) activation energy for hydrogen permeation through a palladium alloy membrane tube (J/mol) Eps ) porosity of the packed bed k ) rate constant appearing in eq 2 (mol/m3‚s‚Pa) KC ) equilibrium adsorption coefficient of carbon monoxide on the catalyst surface (1/Pa) K ) equilibrium constant for methanol decomposition (Pa2) l ) length of the palladium alloy membrane tube (m) l0 ) entire length of the palladium alloy membrane tube (m) L ) dimensionless length, l/l0 ∆L ) axial increment for the Runge-Kutta method m ) radial grid point
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M ˜ ) modulus appearing in differential equations for the diffusion model p ) partial pressure (Pa) P h ) hydrogen permeability of the palladium alloy membrane tube (mol/m‚s‚Pa1/2) P h 0 ) pre-exponential factor of hydrogen permeability of the palladium alloy membrane tube (mol/m‚s‚Pa1/2) Pstd ) standard of pressure for normalization (Pa) PT ) total pressure (Pa) Per ) Peclet number, uidp/Der r ) distance from the axial center of the membrane reactor (m) r1 ) outer radius of the membrane tube (m) r2 ) inner radius of the shell tube (m) r3 ) inner radius of the membrane tube (m) rM ) methanol decomposition rate (mol/m3‚s) R ) gas constant (J/mol‚K) R ) dimensionless radius, (r - r1)/(r2 - r1) ∆R ) radial increment, 1/W Rep ) Reynolds number, Favudp/µav Sc ) Schmidt number for hydrogen diffusion in gas X, µX/ (FXDHX) T ) temperature (K) u ) superficial gas velocity on the reaction side (m/s) ui ) interstitial gas velocity on the reaction side (m/s), u/Eps u˜ ) total gas flow rate on the reaction side (mol/s) U ) dimensionless gas velocity on the reaction side, u/u0 v ) gas velocity on the separation side (m/s) V ) dimensionless gas velocity on the separation side, v/u0 VH ) contribution of hydrogen to V W ) number of radial increments R˜ ) dimensionless permeability of hydrogen β ) modulus appearing in eq 12 ) coefficient for normalization of rM (m3‚s/mol) φ ) dimensionless pressure, p/Pstd κ ) reduction factor describing CO hindrance µ ) viscosity (kg/m‚s) F ) density (kg/m3) Subscripts av ) average C ) carbon monoxide H ) hydrogen M ) methanol r ) reaction side s ) separation side T ) total
X ) any species of gas Superscript 0 ) inlet value
Literature Cited (1) Itoh, N. A Membrane Reactor Using Palladium. AIChE J. 1987, 33, 1576. (2) Kikuchi, E.; Uemiya, S.; Sato, N.; Inoue, H.; Ando, H.; Matsuda, T. Membrane Reactor Using Microporous Glass-Supported Thin Film of Palladium. Application to the Water Gas Shift Reaction. Chem. Lett. 1989, 489. (3) Uemiya, S.; Matsuda, T.; Kikuchi, E. Aromatization of Propane Assisted by Palladium Membrane Reactor. Chem. Lett. 1990, 1335. (4) Champagnie, A. M.; Tsotsis, T. T.; Minet, R. G. A HighTemperature Catalytic Membrane Reactor for Ethylene Dehydrogenation. Chem. Eng. Sci. 1990, 45, 2423. (5) Zaika, Z. D.; Minet, R. G.; Tsotsis, T. T. A High-Temperature Catalytic Membrane Reactor for Propane Dehydrogenation. J. Membr. Sci. 1993, 77, 221. (6) Edlund, D. J.; Pledger, W. A. Thermolysis of Hydrogen Sulfide in a Metal-Membrane Reactor. J. Membr. Sci. 1993, 77, 255. (7) Shu, J.; Grandjean, B. P. A.; Kaliaguine, S. Methane Steam Reforming in Asymmetric Pd- and Pd-Ag/Porous SS Membrane Reactors. Appl. Catal. A 1994, 119, 305. (8) Hara, S.; Xu, W.-C.; Sakaki, K.; Itoh, N. Kinetics and Hydrogen Removal Effect for Methanol Decomposition. Ind. Eng. Chem. Res. 1999, 38, 488. (9) Amano, M.; Nishimura, C.; Komaki, M. Effects of High Concentration CO and CO2 on Hydrogen Permeation through the Palladium Membrane. Mater. Trans. JIM 1990, 31, 404. (10) Itoh, N.; Xu, W.-C.; Haraya, K. Radial Mixing Diffusion of Hydrogen in a Packed-Bed Type of Palladium Membrane Reactor. Ind. Eng. Chem. Res. 1994, 33, 197. (11) Kulkarni, B. D.; Doraiswamy, L. K. Estimation of Effective Transport Properties in Packed Bed Reactors. Catal. Rev.-Sci. Eng. 1980, 22, 431. (12) Itoh, N. Simulation of Bifunctional Palladium Membrane Reactor. J. Chem. Eng. Jpn. 1990, 23, 81. (13) Ali, J. K.; Baiker, A. Dehydrogenation of Methylcyclohexane to Toluene in a Pilot-Scale Membrane Reactor. Appl. Catal. A 1997, 155, 41.
Received for review March 19, 1999 Revised manuscript received September 8, 1999 Accepted September 16, 1999 IE990200N
