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Assessing High-Temperature Water-Gas Shift Membrane Reactors Donghao Ma and Carl R. F. Lund* Chemical Engineering Department, University at Buffalo (SUNY), Buffalo, New York 14260-4200
A simple two-step microkinetic model for the high-temperature water-gas shift was developed using existing experimental data. This two-step redox model uses only three adjustable parameters, and it is capable of predicting the inhibitory effect of CO2 on the kinetics of the reaction. It was used to simulate the performance of an adiabatic membrane reactor for the water-gas shift where the membrane is based on Pd. The simulations show that excess steam in the feed is desirable to control the adiabatic temperature rise; a 3:1 ratio of steam to carbon monoxide was found to be near optimum. The simulations further suggest that the rate of reaction is the limiting process in the membrane reactor, not the permeation of hydrogen through the membrane. At 90% hydrogen yield, finding a perfect membrane would only reduce the reactor size by 12%, whereas eliminating the inhibitory effect of CO2 would reduce the reactor size by 76%. Introduction The water-gas shift, eq 1, is a well-established and long-practiced process1-3 that is being revisited as a potential component of next-generation fuel cell and coal conversion technology. In this context, a membrane reactor process offers some attractive features,4-6 particularly the ability to generate 100% pure H2 while simultaneously producing a stream of predominantly CO2 that could be sequestered to mitigate globalwarming effects. This paper examines a few of the issues that arise when one considers utilizing commercial hightemperature water-gas shift catalysts in a packed-bed membrane reactor with a Pd membrane, and it presents a convenient methodology for identifying the ratecontrolling processes in such systems.
CO + H2O / CO2 + H2
(1)
In conventional applications, the reaction is run in adiabatic stages with cooling between the stages and with excess steam in the feed. The first stage operates at a higher average temperature, using a promoted ferrochrome catalyst that has an operating range of ca. 600-750 K.3 The final stage operates at a lower average temperature using a CuZn-based catalyst that has a maximum operating temperature of ca. 530-560 K.1 Figure 1a presents a schematic representation of a conventional process. Several factors have contributed to the adoption of a process such as that of Figure 1a. The first is the tradeoff between reaction rate and equilibrium conversion. The water-gas shift is exothermic and reversible, so a higher temperature leads to a higher rate of reaction but a lower final (equilibrium) conversion. In the process shown, most of the conversion would take place in the first reactor where the rates are higher; then, in the final, lower-temperature stage, a high conversion is realized. Often, the water-gas shift feed stream comes from a steam reformer where the outlet * To whom correspondence should be addressed. E-mail:
[email protected]. Voice: (716) 645-2911 ext. 2211. Fax: (716) 645-3822.
Figure 1. Schematic representation of (a) a two-stage conventional water-gas shift process and (b) one stage of an adiabatic membrane reactor process for the water-gas shift.
temperature is already high, making for relatively easy integration of the two reactions. The use of excess steam favors a higher equilibrium conversion, reduces the adiabatic temperature rise in the reactor, and helps prevent carbon deposition at the reactor inlet. A representative design for a membrane reactor process is shown schematically in Figure 1b. The reaction would likely take place adiabatically and at higher temperature and pressure. The higher pressure provides the driving force for permeation of the H2 product through the Pd membrane. Although the reactor would likely still be operated in stages to keep the temperature within the operating range of the catalyst, there is no need to use lower temperatures in the final stage because in situ separation will lead to a high H2 yield even at higher temperatures. It would not be necessary to use an excess of steam to favor higher conversion4 either, although it might still be useful with
10.1021/ie020679a CCC: $25.00 © 2003 American Chemical Society Published on Web 01/23/2003
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respect to lowering the adiabatic temperature rise and preventing carbon deposition. The primary purpose of the present study is to assess the performance of a membrane reactor similar to that just described through mathematical simulation. The specific objectives include determining whether excess steam in the feed is beneficial; determining, as a function of position along the reactor, whether the rate of reaction or the rate of permeation is rate-limiting; and assessing the significance of the known rateinhibiting effect of CO2 on membrane reactor performance. This is accomplished through the development of an adiabatic membrane reactor model that is used to simulate membrane reactor performance. The development of a simple kinetic model for use in the simulation is also presented. Methods Bohlbro reported an extensive study of the kinetics of high-temperature water-gas shift over iron-chrome catalysts.3 In that work, the kinetics were modeled using power-law rate expressions, and different kinetic parameters were used at different temperatures. Here, Bohlbro’s data have been used to develop a simple microkinetic model for the water-gas shift over an iron-chrome catalyst. The kinetics have been described in terms of the simple redox mechanism presented in eqs 2 and 3. The fitting procedure is similar to that used by Dumesic et al.7,8 Briefly, an expression for the net rate, rj,net, of each mechanistic step was written using simple transition state theory, e.g., eq 4 gives the net rate of reaction 2, where k02 represents the preexponential factor of the forward rate coefficient, E2 represents the activation energy, ∆S2 represents the standard entropy change associated with reaction 2, and ∆H2 represents the standard enthalpy change. In eq 4, Pi represents the partial pressure of species i, θi represents the fractional catalyst surface coverage of species i, R is the ideal gas constant, and T is the temperature. The standard entropy and enthalpy changes of the reaction steps were then expressed in terms of the standard entropies and enthalpies of formation of the participant species. Thus, the standard entropy and enthalpy changes for reaction 2 were expressed using eqs 5 and 6. The entropies of formation, S0i , and enthalpies of formation, ∆fH0i , for the gas-phase species, i, are known functions of temperature. Here, these quantities were represented using the Shomate equation, with appropriate parameters obtained from the NIST Chemistry Webbook.9 The entropy of formation for the surface oxygen was estimated starting with its gas-phase value at the average experimental temperature, 688 K, and then subtracting its ideal gas translational entropy. The resulting entropy of formation was held constant during the fitting process. Similarly, the enthalpy of formation for the surface oxygen was estimated starting with its gas-phase value at 688 K and then subtracting the net strength of the bond or bonds holding it to the surface, 0 -∆HO . The preexponential factors, k0j , for each of gasfO* the reactions, j, were estimated on the basis of simple transition state theory or collision theory and then held constant during the fitting process, as well. This left the 0 two activation energies, E1 and E2, and -∆HO as gasfO* the three adjustable parameters that were used to fit
the microkinetic model to the experimental data.
r2,net ) k02 exp
CO + O/ / / + CO2
(2)
H2O + / / O/ + H2
(3)
[
( )
-E2 PCOθO* RT
PCO2θ/
exp
( ) (
]
)
∆S2 -∆H2 exp R RT (4)
0 ∆S2 ) S0/ + SCO - S/0O - S0CO 2
(5)
0 - ∆fH/0O - ∆fH0CO ∆H2 ) ∆fH0/ + ∆fHCO 2
(6)
To fit the microkinetic model to the experimental data, material balance equations were written for every species except the vacant site, assuming the reactor to have operated in isothermal, isobaric plug flow. This resulted in a model that consisted of a set of coupled algebraic and ordinary differential equations to which was added the requirement that the sum of the fractional coverages over all surface species, including the vacant site, must equal 1. For given values of the 0 , this adjustable parameters E1, E2, and -∆HO gasfO* model could be solved to predict the CO conversion in each experiment. This was repeated, varying the values of these adjustable parameters, until the sum of the squares of the differences between the predicted CO conversions and Bohlbro’s experimentally measured CO conversions was minimized. This process was automated using Athena Visual Workbench.10 The schematic diagram of Figure 1b formed the basis for simulation of membrane reactor performance. It was assumed that the catalyst would be packed inside a cylindrical membrane tube and that it would operate adiabatically, at constant pressure, at steady state, and in plug flow. The microkinetic model just described was used to represent the reaction kinetics. Ferrochrome high-temperature shift catalysts have an operational temperature range of ca. 600-750 K, so it was assumed that the feed would enter at 600 K and that, when the temperature reached 750 K, the process stream would be cooled back to 600 K and then fed to the next adiabatic stage of the membrane reactor. The figure shows only a single stage. In other words, no attempt was made to optimize the temperature profile. The diameter of the membrane tube was assumed to be 0.25 in., and the Pd thickness to be 10 µm. The latter value is reasonable for a thin film of Pd supported on a porous alumina or glass substrate.4,11,12 It was assumed that the pressure inside the membrane tube (where reaction occurs) was 1000 psia and that the pressure outside the membrane tube was 1 atm (14.7 psia). This pressure differential was assumed to provide the driving force for hydrogen permeation through the membrane, so no inert sweep gas would be needed on the receiving, or permeate, side of the membrane. The permeability of hydrogen through the Pd membrane was assumed to follow Sievert’s law using the temperature-dependent permeance reported by Shu et al.13 With these assumptions, the membrane reactor model consisted of a set of seven coupled algebraic and ordinary differential equations given as eqs 7-13. In these equations, n˘ i represents the molar flow rate of species i, m denotes the catalyst mass, Am represents the membrane area per
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mass of catalyst, P0 is the preexponential term of the permeance, EP is the activation energy of the permeance, PP is the permeate-side pressure (1 atm), and C ˆ p-i is the molar specific heat capacity of species i (calculated using the Shomate equation and NIST Chemistry Webbook data9). The inlet molar flow rates were used as the initial conditions for eqs 7-10, and 600 K was used as the initial condition for eq 11. The model equations were solved using Athena Visual Workbench.10
dn˘ CO ) -r2,net dm dn˘ H2O dm
) -r3,net
dn˘ CO2 dm dn˘ H2 dm
) r2,net
) r3,net - AmP0 exp
(7)
(8)
(9)
( )x
-Ep ( PH2 - xPP) (10) RT
dT ) dm
-r2,net∆H2 - r3,net∆H3 n˘ COC ˆ p-CO + n˘ H2OC ˆ p-H2O + n˘ CO2C ˆ p-CO2 + n˘ H2C ˆ p-H2 (11) r2,net ) r3,net
(12)
1 ) θO/ + θ/
(13)
To assess the performance of the membrane reactor, comparisons were made to three idealized situations. The first corresponded to a perfect membrane. In this case, permeation was assumed to occur instantaneously. As a consequence, the partial pressure of H2 on the reaction side of the membrane was set equal to the permeate-side pressure of 1 atm, and eq 10 was removed from the set of model equations. The second idealized situation corresponded to a perfect catalyst. In this case, the model consisted of only eq 14. The other molar flow rates and the temperature were calculated by assuming that the reaction was always at thermodynamic equilibrium (with a corresponding adiabatic temperature rise).
dn˘ H2 dm
) -AmP0 exp
( )x
-Ep ( PH2 - xPP) RT
(14)
The third idealized situation was related to the known inhibition of ferrochrome high-temperature shift catalysts by CO2. Figure 2 shows plots of a series of kinetic runs from Bohlbro’s data set wherein the inlet partial pressures of CO and H2O were held constant along with the total flow rate and temperature. The partial pressure of CO2 and that of the N2 makeup gas were the only parameters varied. The figure shows that, while the reaction was far from thermodynamic equilibrium, the experimental CO conversion decreased from over 20% in the absence of CO2 to less than 5% when CO2 was added. This is due to inhibition by CO2; Bohlbro found the order of the reaction with respect to CO2 to be ca. -0.6. The figure shows that the microkinetic mod-
Figure 2. With the overall reaction far from thermodynamic equilibrium (filled triangles), inhibition of the water-gas shift catalyst activity by CO2 at 653 K and 1 atm total pressure is evident in Bohlbro’s data (filled circles) and is captured by the two-step microkinetic model (filled squares). The unfilled squares show the behavior of a hypothetical catalyst where the inhibition by CO2 has been mathematically eliminated as described in the text.
el captures this inhibition effect as well. In the third idealized situation, this inhibition by CO2 was removed from the kinetic behavior. To do this, the rate expressions in eq 3 and 4 were evaluated at prevailing conditions, except that the partial pressure of CO2 was set to an arbitrary low partial pressure where inhibition by CO2 was minimal. This CO2 partial pressure (0.0288 atm) was selected so that the predicted conversion at CO2/CO ) 0 in Figure 2 would match the experimental conversion. The rate expressions that result can be denoted as rj,net|PCO2)0.0288atm, where j can correspond to either reaction 2 or reaction 3. In doing this, rj,net| PCO2)0.0288atm would not display the proper limiting behavior as the conversion approaches equilibrium, so the resulting rate was multiplied by the quantity (1 PH2PCO2/KPCOPH2O)3, which ensures that the rate goes to 0 at thermodynamic equilibrium. The result is shown in eq 15, where K denotes the temperature-dependent equilibrium constant for the overall water-gas shift reaction and rj,NI represents the rate in the absence of CO2 inhibition. Figure 2 shows that the use of this rate expression matches the experimental results at low CO2/ CO, but as the CO2/CO ratio is increased, the conversion holds essentially constant, i.e., inhibition by CO2 is mathematically eliminated.
(
rj,NI ) 1 -
PH2PCO2 KPCOPH2O
)
3
rj,net|PCO2)0.0288atm
(15)
Results and Discussion Figure 3 shows plots of the CO conversions predicted by the microkinetic model against those measured experimentally. The figure shows that the fit is generally good, taking the experimental uncertainty into consideration. Indeed, in the original work, Bohlbro
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Figure 3. Carbon monoxide conversion predicted by the two-step microkinetic mode compared to that measured experimentally by Bohlbro. Bohlbro’s data have been grouped into sets with a common temperature and pressure. Table 1. Microkinetic Modeling Parameters parameter
adjusted or fixed
resulting value
0 -∆HO gasfO* 0 S/O 0 k2 k03 E2
adjusted fixed fixed fixed adjusted adjusted
602 kJ mol-1 18.2 J mol-1 K-1 106 atm-1 s-1 106 atm-1 s-1 72.5 kJ mol-1 27.5 kJ mol-1
E3
grouped experimental runs according to temperature, pressure, etc., and used different sets of power-law parameters for different groups of results; here, all of the data were fit using only three adjustable parameters. The optimized values of the adjustable parameters, along with the microkinetic modeling parameters that were held fixed, are presented in Table 1, and their values are seen to be reasonable. In this work, it is not claimed that the simple two-step mechanistic model truly represents the molecular phenomena involved in the reaction; all that is desired is a kinetic model that accurately predicts the rate of reaction. The figure shows that this has been achieved. Most importantly, the microkinetic model predicts the inhibitory effect of CO2, as can be seen in Figure 2. The membrane reactor model used here is relatively simple. Nonetheless, similar models have been successfully used to simulate an isothermal Pd membrane reactor,13,14 giving very good agreement between the model’s predictions and actual measurements from a laboratory membrane reactor. Here, the reactor is assumed to operate adiabatically, adding one additional equation to the model. Marigliano et al.15 used a model very similar to the present model in the successful simulation of a steam reformer. In that model, energy transfer was included; the present model is less complicated, as the reactor is assumed to operate adiabatically. In light of the demonstrated accuracy of the such models, it is believed that the present simulations offer a very reasonable first-order approximation of adiabatic membrane reactor performance.
Figure 4. Effect of inlet steam to carbon monoxide ratio on the hydrogen yield and number of adiabatic stages.
In a membrane reactor, the use of excess steam can have at least three effects: it can help prevent carbon deposition at the inlet to the reactor, it can reduce the adiabatic temperature rise, and it can reduce the reaction rate (Bohlbro’s power law models show the rate to be approximately 0.9 order in CO and ca. 0.25 order in H2O). As already noted, excess steam leads to a greater equilibrium conversion in a conventional reactor, but that is not needed in a membrane reactor. To assess the effect of excess steam on membrane reactor performance, four adiabatic membrane reactor simulations are compared in Figures 4 and 5. Figure 4 shows plots of the final yield of H2 (the number of moles of H2 recovered through the membrane relative to the number of moles of H2 that would be produced at 100% conversion of the limiting reagent) as a function of the number of adiabatic stages. In constructing this figure, additional stages were added until, in the final stage, the outlet temperature no longer reached 750 K. The figure shows that, for the conditions of the simulation, a H2O/ CO feed ratio of 3 is optimum with respect to the number of adiabatic stages. Figure 5 shows the H2 yield as a function of the cumulative mass of catalyst (equivalent to reactor size). It can again be seen that a H2O/ CO feed ratio of 3 is optimum, reaching its ultimate final conversion with the least amount of catalyst. The differences between ratios of 2 and 3 in Figure 5 is not large, but it must be remembered that a H2O/CO feed ratio of 2 requires three adiabatic stages whereas a ratio of 3 only uses two stages. Clearly, the role of excess steam in reducing the adiabatic temperature rise overshadows any negative effect on the reaction kinetics. Hence, in all remaining simulations in the present investigation, the inlet H2O/CO ratio was set equal to 3. When seeking to develop a better high-temperature water-gas shift membrane reactor, it is useful to be able to identify the rate-limiting process at any point within the reactor. Specifically, it is useful to know whether the rate of the chemical reaction or the rate of permeation through the membrane is rate-determining. In the present work, two approaches to making such an assessment have been employed. The first attempts to
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Figure 5. Hydrogen yield as a function of catalyst volume for staged adiabatic membrane reactors with varying inlet steam to carbon monoxide ratios.
Figure 6. Variation in the percent of reaction equilibration and the percent of permeation equilibration along the length of an adiabatic staged membrane reactor.
quantify the extent to which the reaction and permeation processes are locally equilibrated. To understand this approach, consider an adiabatic membrane reactor similar to that described previously and shown schematically in Figure 1b. One can define a local percent of reaction equilibration, PRE, as given in eq 16. If the local composition corresponds to thermodynamic equilibrium, PRE will equal 100%. If no reaction has taken place, PRE will equal 0%. For any single adiabatic stage, PRE will always lie between these two extremes. Furthermore, because the reaction is exothermic and there is cooling between stages, there will always be a decrease in PRE in passing from the outlet of one stage to the inlet of the next, but it will never fall below 0%. Hence, PRE represents a useful metric for assessing the local degree of reaction equilibration at any point in the multistage membrane reactor train.
the partial pressure of H2 has reached the permeateside pressure, PPE will vary between 0 and 100%, and it will be unaffected by cooling between stages, so it is a useful metric for assessing the local degree of permeation equilibration at any point in a multistage membrane reactor train.
PRE ) 100%
(
PH2PCO2
)
KPCOPH2O
(16)
The permeation process is equilibrated when the local H2 partial pressure (in the reaction zone) is equal to the permeate-side pressure, PP. At the opposite extreme, if no permeation has taken place, then the local partial pressure of H2 is determined by the inlet H2 partial 0 pressure, PH ; the inlet CO partial pressure, P0CO; and 2 the CO conversion, xCO. Using these two points of reference, a local percent of permeation equilibration, PPE, can be defined as in eq 17. Examination of eq 17 shows that PPE will equal 100% whenever the partial pressure of H2 is equilibrated across the membrane; it will equal 0% if no permeation has taken place. However, it should be noted that it is possible for PPE to assume a negative value. This can happen near the inlet to the reactor where the conversion of CO is low and, consequently, the H2 partial pressure has not yet built up to equal the permeate-side pressure. At such a location, H2 might actually permeate from the permeate side of the membrane to the reaction side, and if this happens, PPE will have a negative value. However, once
(
PPE ) 100% 1 -
PH2 - PP
)
0 PH + xCOP0CO - PP 2
(17)
As already noted, an inlet H2O/CO ratio of 3 leads to a membrane reactor that requires only two adiabatic stages (Figure 4) and that reaches equilibrium with the least amount of catalyst (Figure 5). The variations in the percent of reaction equilibration and the percent of permeation equilibration along the length of this reactor are plotted in Figure 6, which also reproduces the H2 yield results. Near the inlet to the reactor, the percentage of permeation equilibration is indeed negative as just described, but these data are not plotted in Figure 6. The most striking observation from Figure 6 is that the permeation process is far closer to being equilibrated than the reaction process almost everywhere within the reactor. More specifically, the percent permeation equilibration becomes greater than 90% at a catalyst mass of only 875 g, whereas the percent reaction equilibrium only reaches 10% at a catalyst mass of ca. 4500 g. This result might seem surprising at first. It is often assumed that the rate of permeation through dense membranes such as Pd is too slow for practical applications. The membrane thickness used here in the simulations is within the range of experimentally studied membranes, however. The conclusion that the reaction rate is the limiting process is also drawn upon examination of Figure 7. That figure shows that, if the membrane in the reactor model is made perfect (instantaneous transport of the hydrogen through it), there is only a marginal gain in the hydrogen yield from the reactor. On the other hand, if the catalyst in the reactor model is made perfect (instantaneous equilibration of the reaction), there is a tremendous gain in hydrogen
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Conclusions
Figure 7. Comparison of the simulated membrane reactor yield to idealized membrane reactors where either the membrane is perfect, the catalyst is perfect, or the catalyst does not suffer from CO2 inhibition.
yield. For example, at a catalyst mass of ca. 1000 g, the membrane reactor model predicts approximately 50% hydrogen yield with either a perfect membrane or a more realistic membrane. At the same catalyst mass, the membrane reactor model predicts over 90% hydrogen yield for a realistic membrane with a perfect catalyst. These results suggest that the most dramatic improvement in high-temperature, adiabatic water-gas shift membrane reactor performance will be realized by finding improved catalysts, not by finding improved membranes. This can be seen in Figure 7 for the third idealized case, that where inhibition by CO2 is removed. Simply eliminating the inhibition by CO2 without changing the catalyst activity or anything associated with the membrane gives 90% hydrogen yield at a catalyst mass of ca. 1000 g; inhibition by CO2 lowers the yield from 90 to ∼50%. Stated in another way, the simulations predict that, for a 90% hydrogen yield, finding a perfect membrane would reduce reactor size by 12%, whereas eliminating the inhibiting effect of CO2 would reduce reactor size by 76%. Ferrochrome hightemperature water-gas shift catalysts have been used for a long time, and they have been studied extensively. As a consequence, it would not be a trivial task either to improve such catalysts or find a more suitable one. Nonetheless, the present results indicate that catalyst improvement will have a much greater impact on membrane reactor performance than will membrane improvements. More generally, the approach utilized here is generally applicable to the assessment of membrane reactors in so-called “equilibrium shifting” situations. Through membrane reactor modeling and simulation, one can compare the system of interest to idealized cases where either the catalyst is perfect or the membrane is perfect. Such a comparison might then suggest that development efforts should be focused either on the membrane or on the catalyst.
It was found that a simple two-step microkinetic model offered a reasonable simulation of the kinetics of the water-gas shift over a high-temperature ferrochrome catalyst. This simple model used only three adjustable parameters. Importantly, it properly captured the experimentally observed inhibitory effect of CO2 on the rate of water-gas shift. A simple mathematical model was used to simulate the performance of an adiabatic membrane reactor. On the basis of this simulation, it was found that excess steam, although not necessary to push equilibrium conversion, was still highly beneficial in controlling the adiabatic temperature rise in a high-temperature watergas shift membrane reactor. For the situation studied herein, an inlet feed composition of 3 H2O per CO was optimum; it required only two adiabatic stages and achieved its ultimate conversion with the least catalyst. Further simulation suggests that the limiting factor, in the kind of high-temperature water-gas shift membrane reactor studied here, is the rate of reaction and not the rate of permeation through the membrane. The simulation shows that the inhibition of the reaction rate by CO2 has a dramatic effect on the overall performance of the membrane reactor. Removing this inhibitory effect of CO2 would lead to much greater gains in H2 yield than would finding a perfect membrane material. Acknowledgment This material is based on work supported by the U.S. Department of Energy, University Coal Research Program under Award DE-FG26-99FT40590. Literature Cited (1) Rase, H. F. Chemical Reactor Design for Process Plants; John Wiley: New York, 1977; Vol. Two. (2) Newsome, D. S. The water-gas shift reaction. Catal. Rev.Sci. Eng. 1980, 21, 275. (3) Bohlbro, H. An Investigation on the Conversion of Carbon Monoxide with Water Vapour over Iron Oxide Based Catalysts; Haldor Topsøe: Gjellerup, Copenhagen, Denmark, 1969. (4) Uemiya, S.; Sato, N.; Ando, H.; Kikuchi, E. The Water Gas Shift Reaction Assisted by a Palladium Membrane Reactor. Ind. Eng. Chem. Res. 1991, 30, 585. (5) Damle, A. S.; Gangwal, S. K.; Venkataraman, V. K. A simple model for a water gas shift membrane reactor. Gas Sep. Purif. 1994, 8, 101. (6) Criscuoli, A.; Basile, A.; Drioli, E. An analysis of the performance of membrane reactors for the water-gas shift reaction using gas feed mixtures. Catal. Today 2000, 56, 53. (7) Dumesic, J. A.; Milligan, B. A.; Greppi, L. A.; Balse, V. R.; Sarnowski, K. T.; Beall, C. E.; Kataoka, T.; Rudd, D. F.; Trevino, A. A. A Kinetic Modeling Approach to the Design of Catalysts: Formulation of a Catalyst Design Advisory Program. Ind. Eng. Chem. Res. 1987, 26, 1399. (8) Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoske, J. E.; Trevino, A. A. The Microkinetics of Heterogeneous Catalysis; American Chemical Society: Washington, DC, 1993. (9) NIST Standard Reference Database Number 69; National Institute of Standards and Technology (NIST): Gaithersburg, MD, 2001; Vol. 2002. (10) Athena Visual Workbench, ver. 7.0; Stewart and Associates, Inc.: Madison, WI, 1997. (11) Keuler, J. N.; Lorenzen, L. Comparing and Modeling the Dehydrogenation of Ethanol in a Plug-Flow Reactor and a PdAg Membrane Reactor. Ind. Eng. Chem. Res. 2002, 41, 1960. (12) Way, J. D.; McCormick, R. L. Palladium/Copper Alloy Composite Membranes for High-Temperature Hydrogen Separa-
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 717 tion From Coal-Derived Gas Streams. Presented at the University Coal Research Contractors Review Conference, Pittsburgh, PA, Jun 5-6, 2001. (13) Shu, J.; Grandgean, B. P. A.; van Neste, A.; Kaliaguine, S. Catalytic Palladium-based Membrane Reactors: A Review. Can. J. Chem. Eng. 1991, 69, 1036. (14) Barbieri, G.; Di Maio, F. P. Simulation of the Methane Steam Re-forming Process in a Catalytic Pd-Membrane Reactor. Ind. Eng. Chem. Res. 1997, 36, 2121.
(15) Marigliano, G.; Barbieri, G.; Drioli, E. Effect of energy transport on a palladium-based membrane reactor for methane steam reforming process. Catal. Today 2001, 67, 85.
Received for review August 30, 2002 Revised manuscript received December 3, 2002 Accepted December 4, 2002 IE020679A
