4954
Ind. Eng. Chem. Res. 1997, 36, 4954-4964
Pneumatically Controlled Transport and Reaction in Inorganic Membranes Vasilis Papavassiliou,† Chin Lee,‡ Joseph Nestlerode, and Michael P. Harold* Central Research & Development, DuPont Company, Experimental Station, Wilmington, Delaware 19880
The pneumatic-control concept involves the application of a pressure gradient across a nonpermselective porous inorganic membrane to control the trans-membrane flux of a permeate while minimizing the backdiffusion of another component. In this study the concept was investigated for a series of inorganic membranes. Tubular, macroporous, sintered metal membranes were impregnated or coated with colloidal silica. Binary and ternary transport experiments reveal that the morphology can be tailored to achieve the desired trans-membrane flux with minimal backdiffusion. Simulations of the multicomponent transport in the membranes using the Dusty Gas Model are in good agreement with the data. The imposed pressure gradient creates a convective flow of the permeate across the membrane which inhibits the backdiffusion of the second component. The pneumatic-control transport was tested in a membrane reactor using the catalytic combustion of ethylene as the test reaction. A membrane reactor having catalytic pellets inside a porous tube (packed-bed membrane reactor, PBMR) was experimentally tested. The measured temperature rise shows the effect of distributing the oxygen along the length of the catalyst zone. Multiple steady states were observed for the PBMR. Transmembrane pressure drop was found to have a significant effect on conversion and reactant and product partitioning between the core and shell sides of the membrane. Introduction In recent years the use of porous inorganic films as transport barriers has been demonstrated to provide unique performance features in reaction applications (Zaspalis and Burggraaf, 1991; Tsotsis et al., 1993; Saracco and Specchia, 1994; Harold et al., 1994a). Sloot et al. (1992) have shown that a high-temperature, bimolecular reaction can be carried out within a catalytic, inorganic “porous wall”, which separates two flowing streams containing the two main reactants. The nonpermselective wall serves as a diffusional barrier, thereby creating a reaction plane at which point the two reactants are consumed. The location of the interface within the wall depends on the relative bulk concentrations and intraparticle diffusion coefficients of the two reactants. The key advantage is added flexibility in the molar feed ratio for reactions requiring strict stoichiometric control. Cini and Harold (1991) demonstrated improved catalyst utilization during liquid phase catalytic reaction between volatile (gaseous) and nonvolatile reactants, such as olefin hydrogenation. The porous catalytic wall in the system establishes a gas-liquid interface adjacent to the flowing gas stream, thereby eliminating external mass-transfer limitations of the volatile reactant. More recently, van Swaaij and coworkers (Veldsink et al., 1992, 1994, 1995; Saracco et al., 1995a,b) have extended the stoichiometric control concept to catalytic combustion. Modeling studies have revealed that the maximum yield of the desired intermediate (oxygenate) in a membrane reactor can exceed the maximum yield in a packed-bed reactor provided certain kinetic features are * To whom correspondence should be addressed. Phone: 302-695-8290. Fax: 302-695-3501. Email: HAROLDMP@ esvax.dnet.dupont.com. † Present address: PRAXAIR, 777 Old Saw Mill River Rd., Tarrytown, NY 10591. ‡ Present address: Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003. S0888-5885(97)00066-3 CCC: $14.00
satisfied (Harold et al., 1993, 1994b; Lee et al., 1995). The pneumatic-control concept involves the controlled supply of oxygen through the pores of a nonpermselective membrane, to react with a hydrocarbon on a catalyst on the other side of the membrane. This operating strategy offers the potential for optimizing the profile of oxygen along a catalyst bed to maximize oxygenate yield, while minimizing the mixing of hydrocarbon and oxygen in the flowing streams. Experimental demonstration of the nonpermselective membrane concept has been reported for the oxidative coupling of methane and oxidative dehydrogenation of ethane (Lafarga et al., 1994; Coronas et al., 1994; Tonkovich et al., 1995). Veldsink et al. (1994) successfully applied the Dusty Gas Model to nonisobaric, multicomponent transport in a macroporous R-Al2O3 membrane. The two-part study by Saracco et al. (1995a,b) examined the coupling between transport and reaction, complete oxidation of propane, in a cooled catalytically-impregnated membrane reactor. Reactor model predictions were in good agreement with experimental data which showed the beneficial and detrimental effects of supplying either reactant to the membrane under an imposed total pressure gradient. Dense oxygen ionic conductor membranes have been used to control the oxygen supply to the reaction zone on the other side of the membrane (Eng and Stoukides, 1991). They offer the advantage of oxygen permselectivity with minimal hydrocarbon backdiffusion to the oxygen supply side of the membrane. However, high temperatures are needed (>600 °C) to achieve a reasonable membrane oxygen flux. Therefore, at this time dense membranes are unsuitable for use for partial oxidation of hydrocarbons (C2-C6) which take place at lower temperatures, 200-500 °C. In this study methods for modifying the permeability of tubular macroporous, sintered metal supports are developed. We show that suitably modified porous supports can be obtained, which have the requisite morphological features for use in the aforementioned © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4955
Figure 1. SEM (left) and X-ray (right) micrographs of a silica thrice-impregnated stainless-steel membrane (sample 6). Red color in the X-ray micrograph indicate areas with silica.
membrane reactor applications. We report morphological characterization and permeation measurements for several membranes. Using independently-measured morphological parameters, a transport model based on the Dusty-Gas constitutive relations is used to simulate the transport experiments. The pneumatic-control concept is then tested under reaction conditions using the catalytic combustion of ethylene as the test reaction. Performance comparisons are made between the conventional packed-bed reactor and packed-bed membrane reactors.
Table 1. Membrane Geometric Parameters Calculated from Mercury Porosimetry and He Pychnometry Experimentsa
1: 2: 3: 4: 5: 6: 7:
membrane sample
pore size dp, µm
pore volume Vp, cm3/g × 10-2
porosity
unmodified one impregnation two impregnations three impregnations one impregnation three impregnations coated with γ-Al2O3b
0.2a 2.4 1.5 1.2 1.9 1.1 5 × 10-3
2.6 2.4 2.1 2.2 2.1
0.20a 0.16 0.15 0.14 0.14 0.13 0.50
Membrane Synthesis and Characterization
a Parameters given by Mott. b Film parameters provided by U.S. Filter.
Large-pore tubular sintered stainless-steel membranes (SSM) were used as supports (acquired from Mott Corp., Devon, PA). Unless otherwise noted, results are reported for 0.2-µm pore diameter, 0.375-in. inner diameter tubes with 0.2-cm wall thickness (note that the pore diameter value (0.2 µm) is based on a filtration measurement carried out by the supplier, so that this value underestimates the pore size). The support tubes were modified by impregnation with silica sol or by coating with boehmite and silica sols. The membranes thus prepared were further characterized by permeability measurements with nitrogen gas. U.S. Filter (Warrendale, PA) membrane supports were used in the membrane reactor studies (specifications given below). Asymmetric membranes were prepared by coating the SSM supports with alumina and silica/alumina mesoporous layers. The coating of the SSM was performed using standard sol-gel techniques (Zaspalis and Burggraaf, 1991). Calcination was carried out by heating from room temperature at a rate of 0.5 °C/min to a final temperature of 450-600 °C and continuing calcination at that temperature for 6 h. Examination of representative samples with scanning electron microscopy (SEM) showed an approximate 5-µm-thick γ-Al2O3 layer covering the porous metal support. The coating was essentially defect-free based on gas permeation measure-
ments. For some samples an additional silica layer was deposited on the γ-Al2O3 layer in order to further reduce the overall permeability. Uniformly-impregnated membranes were prepared by filling the pore structure of SSM tubes with colloidal silica suspensions. This approach is similar to the procedures of Lafarga et al. (1994). The impregnation was done by connecting one end of the SSM to a reservoir filled with the silica sol, while the other end was sealed with Swagelok fittings. Nitrogen gas was used to pressurize (100-150 kPa) the reservoir, resulting in the flow of sol through the membrane. This was carried out for about 15 min. The membrane was then disconnected from the reservoir, dried in air at room temperature, and calcined at 400 °C for 3 h. The permeability of the membrane was measured after this procedure, and the impregnating procedure was repeated if desired. With each impregnation (up to three consecutive treatments) the weight gain after calcination was approximately 0.5% for unmodified tubular supports with an initial weight of 15 g. The membranes were further characterized with mercury porosimetry, helium pychnometry, SEM, and X-ray microprobe. Table 1 reports the mercury porosimetry and helium pychnometry results of various
4956 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
controlled. The system is designed so that the operator never enters the ventilated reactor enclosure during runs. The safety interlock system for the reactor consists of five computer-independent, mechanical/electronic interlocks: over-temperature, over-pressure, nitrogen flow stoppage, hood failure, and manual intervention. If any of these are tripped, the reactor shuts down and is purged with “house” nitrogen. Theoretical Analysis Figure 2. Pore diameter distribution (from mercury porosimetry) comparison of a membrane after one and three silica impregnations.
membranes, and Figure 1 presents the SEM picture of a thrice-impregnated membrane (sample 6). The SEM reveals that the silica is uniformly distributed across the SSM pore structure, a fact that was also supported by the X-ray microprobe analysis. Three silica impregnations reduced the SSM tube pore average diameter (dp) by a factor of about 2 and the porosity () by about 10%. Pore diameter distributions obtained from mercury porosimetry are shown in Figure 2. The filling of the pores by the silica with one and three treatments is apparent. Asymmetric alumina membranes supplied by U.S. Filter were also used in reaction studies. The membrane tubes used were 10 cm long with 0.635-cm inner diameter and 0.25-cm wall thickness. The pore structure was asymmetric with a final 5-µm-thick microporous γ-Al2O3 coating with 5-nm pores. These membranes were used as received. Experimental Unit Overview The membrane reactor facility used for this study was constructed with “Safety First” in mind. The facility consists of a gas feed system, membrane reactor unit, gas chromatograph/mass spectrometer, control and data acquisition equipment, and a comprehensive interlock system. A schematic representation of the overall flow system, data acquisition, and control system is provided in Figure 3. As shown in Figure 3, the flow rates of the core- and shell-side gases are metered and controlled by electronic mass flow controllers. The stainless-steel membrane holder is immersed in a heated sand (silicon carbide) bath apparatus, the temperature of which is computercontrolled and the heating of which automatically stops if fluidization stops. The shell and core feed gas streams enter the top of the sand bath and into the fluidized sand. The feed lines are coiled within the sand bath to allow for preheating prior to the reactor. Control of core- and shell-side pressure is provided by a manual needle valve located on the effluent lines. Effluent stream compositions and flow rates are measured by gas chromatography and electronic flow meters, respectively. The control and data acquisition system (Figure 3) consists of a PC with Labtech (LTC, Wilmington, MA) data acquisition software, a backplane for thermocouple and pressure transducer signal conditioning, and a relay board for valve control. Gas flows are metered and controlled in a bank of electronic mass flow controllers. A bank of solenoids control the pneumatic on-off valves on the gas supply pipes. The reactor unit is computer-
The transport phenomenon membrane unit was modeled by integrating the differential material balances of the species on the core and shell sides of the membrane. The steady-state material balances for species i are given by
core:
dGc,i 4Ni )0 dl dc
(1)
shell:
dGs,i 4ds + 2 Ni ) 0 dl ds - dt2
(2)
where Gc,i and Gs,i are the species i axial molar fluxes on the core- and shell-side, respectively, dc is the inner diameter of the porous tube, dt is the outer diameter of the tube, and ds is the inner diameter of the outer membrane holder. The radial fluxes of species i, Ni, must be determined locally by solving the one-dimensional, steady-state constitutive flux relations. Mechanisms that may simultaneously contribute to the overall transport within the porous membranes used in this study include Knudsen diffusion, molecular diffusion, viscous flow, and surface diffusion. The “Dusty Gas Model” (DGM) developed by Mason et al. (1967) and Mason and Malinauskas (1983) accounts for the first three mechanisms and is given by the expressions
Ni
∑i D ∑ i*j
1 )RT
Ki
zjNi - ziNj
(
p )RT
∆ij
B0 p
zi
∇zi -
)
zi
∑i D
η
1
)
∇p
( )
RT
1
1 ∆ij
1+
Ki
1/DKi
1-
∑l D
+ Dij,eff
DKiDij,eff
zl
zi
∑i D
(3)
∇p (4)
Kl
(5)
Ki
where Ni is the total molar flux of species i, zi is the mole fraction of i, p is the total pressure, η is the viscosity of the gas mixture, and DKi is the effective Knudsen diffusion coefficient of species i which is given by
x
4 DKi ) K0 3
8RT πMi
(6)
The morphological parameters B0 and K0 are given by
K0 ) dp/4τ
B0 ) dp2/32τ
(7)
where , τ, and dp is porosity, tortuosity, and the average
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4957
Figure 3. Schematic representation of the experimental setup.
pore radius, respectively, of the porous medium. Dij,eff are the binary effective bulk diffusion coefficients defined as Dij,eff ) ∆ij/τ. The binary molecular diffusion coefficients Dij used in our simulations were calculated using the equation of Fuller, Schettler, and Giddings (Reid et al., 1977):
10-3T1.75 Dij )
x
Mi + Mj MiMj
p(ui1/3 + uj1/3)2
(8)
Viscosity was assumed constant and was calculated following methods suggested in Perry’s Chemical Engineers’ Handbook (1996). Two types of solutions were carried out. A semianalytical solution corresponding to the linearized form of the Dusty Gas Model (LDGM) and a numerical solution of the complete Dusty Gas Model (DGM) relationships (Mason et al., 1967; Mason and Malinauskas, 1983). The LDGM assumes that the trans-membrane concentration profiles of all species are linear. Similar solutions for catalytic pellet pore structures have been presented by Krishna (1993). The LDGM can be solved analytically if one further assumes that the viscous transport term and mixture diffusion coefficients are dependent on an average composition of the gas mixture. Papavassiliou (1995) describes in detail the LDGM solution for multicomponent transport in membranes. In this paper we mostly report results using the DGM and comment on the applicability of the LDGM solution. Our analysis was of a two-dimensional system. Concentration variations in the core and cell channels were calculated by integrating the steady-state mass balances given by eqs 1 and 2. In solving the DGM equations for either case we assumed continuity of total pressure
and composition at the core- and shell-side surfaces of the membrane tube. Moreover, the membrane domain was approximated by Cartesian geometry. Finally, total pressure gradients in the axial direction were assumed negligible, and the system was assumed to be at a uniform temperature T. The model is similar to the models used by Veldsink et al. (1994) and Saracco et al. (1995a,b). The Newton method was used to perform the lengthwise integration. We used COLSYS, a boundary value ordinary differential equation algorithm developed by Ascher et al. (1981), to solve the intramembrane transport problem at a given axial position. Asymmetric membrane structures were also modeled with the DGM. Harold and Lee (1997) describe how the DGM can be used to include more than one membrane layer. One particular problem that arises in that numerical solution is the discontinuity point at the interface between two membrane layers that may have very different transport characteristics. The COLSYS code was effective in handling the numerical difficulties of multicomponent transport in asymmetric membranes. In the Appendix we describe in more detail our treatment of the DGM for the asymmetric membrane. Results and Discussion Single-Component Transport. Single-component (N2) transport measurements were carried out to monitor the effect of repeated silica impregnations (samples 1, 5, and 6) and of a single slip-cast γ-Al2O3 film (sample 7). The dependence of the nitrogen permeability on the average total pressure is shown in Figure 4. The nitrogen permeability is defined as NN2δ/∆P, where δ is the support tube wall thickness and ∆P is the transmembrane pressure difference.
4958 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 2. Membrane Geometric Parameters Calculated by Methods I and II method I membrane sample
/τ
1: unmodified 0.093 5: one impregnation 0.072 6: three impregnations 0.027
Figure 4. Permeabilities vs mean pressure for unmodified and modified membranes.
Significant reduction in the permeability (about 1 order of magnitude or more) was achieved with the silica impregnation and the alumina coating. These results are similar to those of Lafarga et al. (1994), who reported a significant reduction in the permeability of a ceramic tube modified with silica. At first glance the permeability reduction shown in Figure 4 does not appear consistent with the modest reduction in the pore size and porosity of the membrane (see Table 1). Insight into the permeability reduction can be gained from an analysis of the pure component data. Application of the DGM to a single component gives expression (9). Assuming the pores are cylindrical, an estimate of the average pore diameter (dp) and porosity/ tortuosity ratio (/τ) for a sample can be made from the slope and intercept of the permeability line (e.g., Figure 4), following Mason and Malinauskas (1967) and Veldsink et al. (1994); i.e.,
(
)
Niδ pT0 + pTδ )m +b pT0 - pTδ 2
(9)
where
m ) B0/ηRT
(10a)
b ) DKN2/RT
(10b)
The average pore diameter (dp) and porosity/tortuosity ratio (/τ) are obtained from
method I:
dp )
x
32mη 3b
32ηRT ) m (11) τ d2
8RT πMi
p
A second method is to use the average pore diameter provided by mercury porosimetry, in lieu of the B0 expression in eq 7, together with the intercept (i.e., to estimate /τ). Using the expression for the Knudsen diffusion coefficient, this gives
method II:
) τ
3
x
dp
8RT πMi
b
(12)
The results of applying methods I and II for samples 1, 5, and 6 are given in Table 2. The estimate of the pore diameter provided by method I for the unmodified support tube (sample 1) is larger than the value
B 0, cm2 × 10-11 32.57 3.163 0.836
method II dp, µm
dp, µm
/τ
3.30 1.20 1.89 0.046 1.00 1.07 0.025
measured by mercury porosimetry. On the other hand, the pore size estimates for the impregnated tubes (samples 5 and 6) are somewhat below the measured values. Both methods estimate a significant decrease in /τ with sequential silica impregnations. Given the relatively small decrease in the porosity, this implies a significant increase in the tortuosity of the porous materials. For example, in a comparison of the singleimpregnation (sample 5) and three-impregnation (sample 6) membranes, only a 7% decrease in porosity is noted. However, the tortuosities for samples 5 and 6 are 3.1 to 5.4, respectively, a 170% difference. This suggests that silica blocks pore passages, thereby increasing the effective transport length. Lafarga et al. (1994) used a ceramic tube with a much larger initial porosity (0.29) and pore volume (0.1 cm3/g) compared to ca. 0.20 and 0.03 cm3/g for the sintered metal tube used in this study. A larger reduction in porosity, the average pore diameter, and permeability was achieved by Larfarga et al. for the ceramic tube silica modification. Multicomponent Transport. The success of the pneumatic-control concept depends on the ability to supply oxygen through the membrane to a catalyst with a flux which maximizes the local oxygenate selectivity during a hydrocarbon oxidation and which minimizes the backdiffusion of hydrocarbon and/or oxygenate to the oxygen side of the membrane. In this section we first test the concept with a simulation and then validate the theoretical findings with experimental tests. Simulations reveal that both the membrane morphology and trans-membrane pressure gradient must be tailored to achieve a desired supply flux of oxygen while minimizing backdiffusion losses. Suppose for the reaction system of interest that the local oxygen consumption rate, which maximizes oxygenate selectivity, is known a priori. At steady state this rate is set equal to the flux of oxygen supplied through the membrane:
RAFb ) NA
() dt 2
(13)
where RA is the reaction rate, Fb is the catalyst bed density, dt is the inside diameter of the tube containing the catalyst, and NA is the trans-membrane flux of A. Our objective is to determine the requisite membrane morphology (pore size, porosity, tortuosity, and thickness) and trans-membrane pressure gradient to achieve the requisite oxygen flux and minimize the backdiffusion of hydrocarbon. Figure 5 presents a set of simulations of the pneumatic-control concept. Consider that a gas A (oxygen) flows on the shell side (x ) 0), while a mixture of 10% A, 20% B (ethylene), and balance nitrogen flows on the core side (x ) δ) of a porous membrane. In Figure 5 the ratio of the core- to shell-side total pressure, pTδ/ pT0, is plotted as a function of the dimensionless oxygen flux, NA/Nr (top plot), and the flux ratio of B to A, NB/ NA, is plotted as a function of NA/Nr (bottom plot). A
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4959
Figure 5. Total pressure ratio (top) and normalized flux (NB/NA) ratio (bottom) vs normalized species A flux for membranes with different pore radius.
wide range of pore sizes are considered (i.e., 10 nm to 0.4 µm). Nr is a reference diffusive flux defined by
DABpT0 Nr ) RT τδ
(14)
Nr represents the maximum bulk diffusive flux of oxygen across the membrane of porosity , tortuosity τ, and thickness δ. Also, Nr is independent of the total pressure because DAB is inversely proportional to pressure. The magnitude of NA/Nr provides a convenient way of assessing the extent of convective relative to diffusive transport. For example, for NA/Nr . 1 convection dominates diffusion. The results in Figure 5 enable one to place bounds on the morphology of the membrane and to estimate the catalyst tube diameter. The specific algorithm is as follows: i. The desired oxygen flux (NA) is specified. ii. The tolerable loss of hydrocarbon is specified, |NB/ NA|. iii. The membrane pore size is assumed. iv. Figure 5 is used to determine the trans-membrane pressure gradient and NA/Nr ratio. v. Using eqs 13 and 14, together with known values for DAB and pT0, the parameter group (/τδ) and dt are determined. vi. If pT0, /τδ, or dt is not acceptable because of materials constraints, then return to step iii. A few key features are evident for the simulation shown in Figure 5. As the pore size increases, NA becomes much more sensitive to small changes in the imposed pressure gradient. For this reason too large a pore size is not desirable. On the other hand, too small a pore size may require a prohibitive pressure gradient to achieve the desired NA and minimize backdiffusion. Thus, sufficient flexibility in /τδ is essential to meet the flux and materials constraints. The simulation results in Figure 5 agree qualitatively with experiments for nonreactive multicomponent transport. We performed binary and ternary transport experiments with both symmetric and asymmetric membranes.
Figure 6. Total pressure ratio (top) and normalized flux (NN2/ NO2) ratio (bottom) vs normalized O2 flux for modified membranes (samples 5-7).
Binary transport experiments involved flowing pure N2 and O2 on opposite sides of the tubular membrane. The inlet mass flow rates were held constant while the pressure on the O2 side (shell) was increased. For each pressure difference the effluent compositions of the shell and core streams were measured using a gas chromatograph equipped with a thermal conductivity detector. In all the binary experiments the inlet flow rates of each gas were fixed at 250 cm3/min and the tube length was 2.3 cm. Figure 6 compares the results of three modified membranes (samples 5-7). In Figure 6 (top) the ratio of the core- to shell-side total pressure, pTδ/pT0, is plotted as a function of the dimensionless oxygen flux, NO2/Nr. Using eq 13, Nr ) 1.1 × 10-4 mol/cm2‚min is a reference binary diffusion flux for the unmodified membrane (sample 1). By ratioing the actual flux to Nr, the extent of convective transport can be assessed. In Figure 6 (bottom) the flux of N2 to O2, NN2/NO2, is plotted as a function of NO2/Nr. This plot conveys the extent of backdiffusion of N2 from the low-pressure (pTδ) side to the high-pressure (pT0) side. A comparison of the membranes reveals the extent of permeability reduction in Figure 6. Both silica impregnation (samples 2 and 4) and film coating are effective in reducing the overall permeability. A wide range of oxygen flux is achieved, spanning primarily diffusive transport (NO2/Nr < 1) with no applied pressure gradient (pTδ/pT0 ) 1) to primarily convective transport (NO2/Nr . 1) with a pressure gradient that is about 10% of the total core-side pressure. The data shown in Figure 6 demonstrate that application of a total pressure gradient across the membrane leads to convective transport of O2, which, in turn, inhibits the backdiffusion of N2. This is the key feature of the pneumatic-control concept. Successful application of this to oxidation would require that the trans-membrane flux of oxygen match the reaction requirements for maximal oxygenate selectivity together with minimal backdiffusion of hydrocarbon. A quantitative comparison between experiment and theory is made in Figure 7 for the thrice-impregnated
4960 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 7. Total pressure ratio (top) and normalized flux (NN2/ NO2) ratio (bottom) vs normalized O2 flux comparison of experimental results (with sample 6) with theoretical results.
membrane (sample 6). The geometrical parameters of the porous membrane that were calculated from the permeability experiments were used in the calculations (Table 2). The membrane parameters using method II were used in the calculations. No other adjustable parameters were used in the simulations. The dashed and solid curves in Figure 7 are the predictions of the linearized Dusty Gas Model (LDGM) and exact Dusty Gas Model (DGM), respectively. At low applied pressure gradient LDGM and DGM simulate binary transport equally well. As the pressure gradient increases, the LDGM predictions diverge from the data while the DGM predictions improve. The failure of LDGM is not unexpected because the species profiles become progressively nonlinear as the fraction of transport flux due to convection increases. Discrepancies between experimental and theoretical results (with the DGM) may be attributable to approximations of the membrane geometrical parameters (e.g., mean pore radius used instead of a pore size distribution), approximations involving the Cartesian geometry, the assumption of constant viscosity, and, finally, experimental error. Ternary transport experiments were carried out to more closely mimic the transport features of a reactive system. Figure 8 shows a comparison between data and simulations for the case in which a 22% O2 in CO2 mixture was flowed on the shell side (227 cm3/min of total flow) and pure N2 was flowed on the core side (250 cm3/min) of a thrice-impregnated membrane (not characterized but with similar permeability as sample 6). Morphological parameters for a similar membrane (sample 6) were used to simulate the ternary experiment. The model predicts satisfactorily the dependencies of the total pressure ratio (Figure 8, top) and the N2/O2 flux ratio (Figure 8, bottom) on the dimensionless O2 flux. The dependence of the CO2/O2 flux ratio on the dimensionless O2 flux is also provided in Figure 7 (bottom). NCO2/NO2 is a monotonically increasing function of NO2/Nr. At sufficiently high applied pressure gradient NCO2/NO2 approaches a constant value of approximately 3.6. This is close to the ratio of the CO2 and O2 bulk concentrations (78/22 ) 3.55). The asymp-
Figure 8. Total pressure ratio (top) and normalized flux (NN2/ NO2 or NCO2/NO2) ratio (bottom) vs normalized O2 flux comparison of experimental results (with sample 6) for a ternary system with theoretical results.
Figure 9. Total pressure ratio (top) and normalized flux (NN2/ NO2) ratio (bottom) vs normalized O2 flux comparison of experimental results for an asymmetric membrane (sample 7) with theoretical results.
totic behavior merely reflects the loss of any membrane permselectivity between O2 and CO2 when convective transport dominates. On the other hand, the decrease in NCO2/NO2 as the applied pressure gradient is decreased reflects the slower diffusion of CO2 in the multicomponent mixture. Figure 9 presents the results of the multicomponent transport experiment with an asymmetric membrane (sample 7). For the membrane support geometrical parameters of an unmodified membrane (sample 1 in Table 1) were used. For the film geometrical param-
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4961
Figure 10. Schematic representation of the system used for the ethylene combustion studies.
eters of sample 7 in Table 1 were used. The transport conditions were similar to those in Figure 5, and a similar transport behavior is observed as well. The numerical simulation qualitatively describes the experimentally observed behavior, but the quantitative agreement is not as good as that in the case of symmetric membranes. Veldsink et al. (1994) used a similar procedure to evaluate multicomponent transport in a ceramic membrane contained in a Wicke-Kallenbach arrangement. The Dusty Gas Model was shown to be necessary in order to predict the membrane transport, especially in the case of an imposed pressure gradient. Transport and Reaction Studies. Optimum operation of membrane reactors for hydrocarbon oxidation requires balancing the amount of oxygen that is supplied through the membrane with the needs of the catalytic reaction. Also, loss of reactant and product from the reaction side to the oxygen side, due to backdiffusion, must be minimized. In the previous sections, we examined theoretically and experimentally how both factors can be controlled in nonreactive cases by regulating the trans-membrane pressure (pneumatic control). Here we examined reactive cases as well using the oxidation of ethylene on Pd catalyst as the test reaction. Saracco et al. (1995a,b) carried out a systematic study of propane combustion in a ceramic membrane impregnated with Pt/Al2O3. With catalyst located in the membrane there are a few operating issues that are unique. For example, the imposition of too large of a pressure gradient to supply one reactant can reduce the overall conversion because backdiffusion of the second reactant to the catalytic zone is effectively blocked. Saracco et al. reported very good agreement between reactor data and model predictions. Their findings also underscore the need to use the Dusty Gas constitutive relations to describe the multicomponent intramembrane transport. We describe the results of the experiments with catalytic pellets (2.8 g of 0.5% Pd on Al2O3) packed inside a ceramic (U.S. Filter) tube. Figure 10 presents a schematic of the experimental reactor configuration. The PBMR was operated by distributing the oxygen from the shell side through the membrane pores (distributed feed), with an applied pressure gradient, to the core side containing the catalyst and flowing hydrocarbon. Comparison was made with conventional reactors by co-
Figure 11. Ethylene conversion vs core inlet temperature for a reactor operating with mixed feed (top) and distributed feed (bottom).
feeding oxygen and hydrocarbon (mixed feed) from the membrane core with the same experimental configuration. The overall feed composition and flow rate was fixed in the experiments described here (2.7 vol % ethylene, 9 vol % oxygen, remainder nitrogen; ca. 500 std. cm3/min). Control experiments were performed with an inert membrane and without catalyst (with feed conditions similar to those used in the catalytic reactor experiments). These runs revealed that there was about 5% ethylene conversion to CO2 at 350 °C. In these reaction experiments a commercial ceramic support was used. The fact that the 50 Å pores do provide Knudsen permselectivity is not important in this application for two reasons. First, as was made evident in the transport experiments, a γ-aluminasupported membrane performs similarly to that of the silica-modified membrane (Figures 4 and 6). Second, the species used in the reaction study all have similar molecular weights, so that Knudsen diffusivity differences are negligible. Figure 11 presents the ethylene conversion as a function of the reactant inlet temperature for a fixed feed for the mixed feed (top) and distributed feed (bottom). In experiments with distributed feed the shell-side valve was closed so a fixed oxygen amount was supplied through the membrane to the reaction side. Multiple steady states were observed for both feed configurations. Ignition from a low conversion state occurred at a core feed temperature of about 110 °C. The ignited state persisted at a core feed temperature as low as 35 °C. The multiplicity is not unexpected for this fast and exothermic reaction with axial conduction (feedback) of heat. Saracco et al. (1995b) reported multiplicity for propane oxidation with a distributed feed of propane and air to a catalytically impregnated membrane. While the conversion dependence on the inlet temperature was similar for both configurations, there was a noted difference when comparing the temperature rise (∆T) defined as the difference between the outlet and inlet core (catalyst) side temperatures. In Figure 12 we plot ∆T as a function of the inlet temperature when the reactor is in the ignited state (Figure 11). For the mixed
4962 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 12. Temperature rise vs core inlet temperature for a reactor operating with mixed feed and distributed feed.
Figure 14. Oxygen flow rates (top) and ethylene flow rates (bottom) at the core and shell outlets vs trans-membrane pressure drop.
Figure 13. Ethylene conversion vs trans-membrane pressure drop for a reactor operating with distributed feed.
feed configuration ∆T remains relatively flat as the inlet temperature decreases from 160 to 40 °C. In comparison, for the distributed feed configuration ∆T increases as the inlet temperature decreases over the same range. This difference in behavior suggests the following. In the mixed feed configuration the reaction takes place close to the packed-bed entrance. The exothermic reaction raises the temperature of the flowing gaseous components to a temperature higher than the feed temperature. Heat losses to the sand bath reservoir result in a cooling. In the distributed feed case, due to lack of sufficient oxygen near the reactor entrance, the temperature maximum occurs further down the bed and the gaseous components have less distance to cool before they exit the reactor. As a result, the outlet temperature is higher than the inlet temperature. These results indicate that not only is oxygen distributed along the membrane but also heat may be distributed more uniformly as well. Of particular relevance to the current study is the effect of trans-membrane pressure drop on the reactor performance. Figure 13 shows the dependence of ethylene conversion on the pressure drop with the inlet temperature fixed at 110 °C. In our apparatus pressure drop was regulated by adjusting a control valve on the shell-side exit of the membrane. From Figure 13 we observe that for high-pressure drops across the membrane ethylene conversion approaches 100%. As pressure drop decreases, conversion decreases. This trend is due to a loss of ethylene by backdiffusion from the catalytic zone and a decreasing supply of oxygen to the catalytic zone. Thus there is a optimum shell-side pressure that maximizes hydrocarbon conversion. The ability to exploit membrane reactors industrially for a particular reaction will depend on predicting the membrane properties and operating conditions that maximize conversion while supplying only the required oxygen and minimize backdiffusion.
The product partitioning between the core and shell side is presented in Figure 14. Shown are the flow rates of oxygen and ethylene at the core and shell outlet as a function of pressure drop (∆P). Predictably, oxygen flow rate on the shell side decreases as ∆P increases, whereas the oxygen flow rate on the core side increases as ∆P increases. The ethylene flow rate on the shell side increases as ∆P decreases due to backdiffusion losses. The ethylene flow rate on the core side increases as ∆P decreases. This is a result of less oxygen being available for reaction due to the decreasing oxygen flux to the catalyst side as ∆P decreases. Conclusions This study provides a detailed examination, both theoretical and experimental, of the pneumatic-control concept in inorganic membranes. Using nonreactive transport experiments and comparing theoretical and experimental results, we conclude that it is possible to synthesize a porous membrane that will supply oxygen necessary for reaction and at the same time minimize backdiffusion of the hydrocarbon. Porous membranes behave like dense membranes, under the appropriate conditions, without the temperature limitations of the dense oxygen conductors known today. Good agreement of theoretical and experimental results was obtained for multicomponent transport with symmetric and asymmetric membranes. Utilizing ethylene combustion as a model reaction, we found that membranes operating with distributed feed gave rise to higher temperatures at the membrane core exit. In the mixed feed configuration most of the heat is generated close to the reactor entrance and is removed to the surroundings before reactants exit the reactor. In the segregated feed configuration the lengthwise distribution of oxygen results in a distribution of the heat generated in the membrane reactor. The more uniform heat distribution is another characteristic of the membrane reactor operation, and simulations are necessary to prove the validity of our interpretation of the experiments. Indeed, the findings underscore the importance of addressing the heat management issues during the design of membrane reactors for hydrocarbon oxidation.
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4963
Reactant losses due to backdiffusion are critical and result in decreasing the overall effectiveness of the membrane reactor (decrease conversion). When the pressure on the shell side of the membrane and the flows of the core- and shell-side of the membrane are regulated, an optimum performance can be achieved. Application of the conclusions of this study to selective oxidation of hydrocarbons is underway to investigate if selectivity, safety, and heat removal benefits justify the use of membrane reactors on an industrial scale.
physical constants are evaluated as described in previous paragraphs. Since there is no reaction and the system is at steady state, the fluxes of species i are constant in the two layers (NiI ) NiII ) Ni), i.e.
∇Ni ) 0 The DGM equations for layer I are
Ni
∑i
Acknowledgment The authors thank Chip Michel for performing the SEM and microprobe measurements and Rick Maynard for carrying out the mercury porosimetry and He pychnometry measurements. The authors also thank Dr. Jan Lerou for his enthusiastic support of the membrane reactor program at DuPont.
(A1)
1 )RT
I
DKi
∑ i*j
zjINi - ziINj
(
1+
pI RT
∆ij
η
I
)I
B0IpI
∇zi -
∑i
ziI RT
Appendix DGM Solution for a Two-Layer Membrane. In order to solve the DGM equations for a two-layer membrane of total thickness δ ) L1 + L2, we defined separate variables for each layer depicted by superscripts I and II. For a n component mixture we have n unknown fluxes (Ni), n unknown mole fractions for layer I (ziI), n unknown mole fractions for layer II (ziII), and total pressure in each layer (pI and pII) for a total of 3n + 2 unknowns. Each membrane layer has a different set of geometrical properties (B0, Rp, , and τ). The
1/DKi
1-
I
∇pI
zl
∑l
DKlI
1
1
Dij,eff
ziI
∑i
DKiIDij,effI
DKiI
We write similar equations for layer II:
Ni
∑i
(
1 )-
RT
II
DKi
∑ i*j
(A4)
+ I
∆ij
zjIINi - ziIINj
1+
pII )RT
II
∆ij
B0IIpII η
II
∇zi -
∑i
ziII
DKi
ziII RT
)
∇pII
( ) II
1/DKiII
1-
II
∑l
1
1
1
)
+ Dij,effII
DKiIIDij,effII
∑i
ziII
(A5)
∇pII
zl
DKlII
∆ijII
(A3)
1
) I
) porosity η ) viscosity (P) τ ) tortuosity δ ) membrane thickness (cm) Fb ) catalyst bed density (g of catalyst/cm3) i, j ) component c ) core s ) shell K ) Knudsen p ) pore I, II ) membrane layers r ) reference eff ) effective
(A2)
( )
Greek Symbols
Subscripts and Superscripts
∇pI
I
DKi
Nomenclature B0 ) morphological parameter (cm2) Dij ) binary bulk diffusion coefficients (cm2 s-1) DK ) effective Knudsen diffusion coefficient (cm2 s-1) dp ) membrane pore diameter (µm) dc ) inner diameter of the tube (cm) dt ) outer diameter of the tube (cm) ds ) inner diameter of the outside shell (cm) G ) axial molar flux (mol s-1) K0 ) morphological parameter (cm) M ) molecular weight N ) trans-membrane flux (mol cm-3 min-1) p ) pressure (atm) RA ) oxygen consumption rate (mol/g of catalyst s) Rp ) membrane pore radius (µm) R ) universal gas constant (J mol-1 K-1) T ) temperature (K) u ) molecular volume z ) mole fraction
)
ziI
(A6) (A7)
DKiII
It is also noted that
znj ) 1 -
zij ∑ i*n
j ) I or II
(A8)
For a n component mixture in the two layer membrane only n - 1 of eqs A3 and A5 are independent, giving 2n - 2 equations. We get n equations from eq A1, two from eqs A3 and A6, and two more from eq 8, for a total of 3n + 2. Boundary conditions complete the handling of the intramembrane transport. At any axial position the flow rate composition and pressure of the core- and shell-side streams are known. At the core side (inner tube wall) the following conditions are satisfied:
x ) 0:
ziI )
Gc,i
∑i
and pI ) pc
Gc,i
At the shell side (outer tube wall) we have
(A9)
4964 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
x ) δ:
ziI )
Gs,i
∑i Gs,i
and pII ) ps
(A10)
At the interface between layers I and II we have continuity of pressure and composition; i.e.,
x ) L1:
ziI ) ziII and pI ) pII
(A11)
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Mason, E. A.; Malinauskas, A. P.; Evans, R. B., III. Flow and Diffusion of Gases in Porous Media. J. Chem. Phys. 1967, 46, 3199. Papavassiliou, V. Transport and Catalysis in Inorganic Membranes. Ph.D. Dissertation, Tufts University, Medford, MA, 1995. Perry’s Chemical Engineers’ Handbook, 50th ed.; McGraw-Hill: New York, 1996. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties Of Gases And Liquids; McGraw-Hill: New York, 1977. Saracco, G.; Specchia, V. Catalytic Inorganic Membrane Reactors: Present Experience and Future Opportunities. Catal. Rev.-Sci. Eng. 1994, 36, 305. Saracco, G.; Veldsink, J. W.; Versteeg, G.; van Swaaij, W. P. M. Catalytic Combustion of Propane in a Membrane Reactor With Separate Feed of Reactants. I. Operation in Absence of TransMembrane Pressure Gradients. Chem. Eng. Sci. 1995a, 50, 2005. Saracco, G.; Veldsink, J. W.; Versteeg, G. F.; van Swaaij, W. P. M. Catalytic Combustion of Propane in a Membrane Reactor with Separate Feed of Reactants. II. Operation in Presence of Trans-Membrane Pressure Gradients. Chem. Eng. Sci. 1995b, 50, 2833. Sloot, H. J.; Smolders, C. A.; van Swaaij, W. P. M.; Versteeg, G. F. High-Temperature Membrane Reactors for Catalytic GasSolid Reactions. AIChE J. 1992, 38, 887. Tonkovich, A. L.; Secker, R. B.; Reed, E. L.; Roberts, G. L.; Cox, J. L. A Design for Bimolecular Reactant Addition. Sep. Sci. Technol. 1995, 30, 1609. Tsotsis, T. T.; Minet, R. G.; Champagnie, A. M.; Liu, P. K. T. In Computer-Aided Design of Catalysts; Becker, E. R., Pereira, C. J., Eds.; Marcel Dekker: New York, 1993; p 471. Veldsink, J. W.; van Damme, R. M. J.; Versteeg, G. F.; van Swaaij, W. P. M. A Catalytically Active Membrane Reactor for Fast Exothermic, Heterogeneously Catalyzed Reactions. Chem. Eng. Sci. 1992, 47, 2939. Veldsink, J. W.; Versteeg, G. F.; van Swaaij, W. P. M. An Experimental Study of Diffusion and Convection of Multicomponent Gases Through Catalytic and Non-Catalytic Membranes. J. Membr. Sci. 1994, 92, 275. Veldsink, J. W.; Versteeg, G. F.; van Swaaij, W. P. M. A Catalytically Active Membrane Reactor For Fast, Highly Exothermic, Heterogeneous Gas Reactions. A Pilot Plant Study. Ind. Eng. Chem. Res. 1995, 34, 763. Zaspalis, V. T.; Burggraaf, A. J. In Inorganic Membranes Synthesis, Characteristics, and Applications; Bhave, R. R., Ed.; Van Nostrand Reinhold: New York, 1991; p 171.
Received for review January 22, 1997 Revised manuscript received July 16, 1997 Accepted July 21, 1997X IE970066B X Abstract published in Advance ACS Abstracts, September 15, 1997.
