Application of the Generic Fluidized-Bed Reactor Model to the

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Application of the Generic Fluidized-Bed Reactor Model to the Fluidized-Bed Membrane Reactor Process for Steam Methane Reforming with Oxygen Input Ibrahim A. Abba, John R. Grace,* and Hsiaotao T. Bi Fluidization Research Centre, Department of Chemical and Biological Engineering, University of British Columbia, 2216 Main Mall, Vancouver, British Columbia V6T 1Z4, Canada

A generic fluidized-bed reactor model (Abba et al. Chem. Eng. Sci. 2002, 57, 4797-4807; AIChE J. 2003, in press) is adapted to evaluate the performance of a fluidized-bed membrane reactor for steam reforming with oxygen input in a large-scale unit (16 m high and 2 m wide) described by Adris and Grace (Ind. Eng. Chem. Res. 1997, 36, 4549-4556). This allows flow regimes beyond bubbling to be modeled and facilitates the treatment of the impacts of changes in volumetric flow due to variations in molar flow, temperature, and hydrostatic pressure. Improvement in the reactor performance is shown when one considers these changes. Permselective membrane tubes are shown to substantially improve the performance of the reactor. The simulation results show that an ultrathin membrane coating could result in reversal in hydrogen diffusion with height, especially at elevated temperatures. The influences on the reactor performance of several other parameters such as the superficial gas velocity and steam-to-carbon ratio are also examined. Given the right combinations of key operating parameters such as the methane-to-oxygen ratio, feed temperature, and reactor temperature, the reactor can be operated autothermally. Introduction Steam methane reforming has been widely studied4-7 as a means of generating hydrogen, a key industrial commodity that is expected to assume critical importance as fuel cells gain ascendancy. Few models in the literature address the fluidized-bed membrane reactor (FBMR) process, now being commercialized in Canada for the generation of pure hydrogen. When such models have been considered,6,8,9 the investigations were limited to the bubbling flow regime of fluidization and to isothermal and isobaric conditions; the earlier models have also not fully accounted for the change in volumetric flow with reaction along the reactor height, although the reforming reactions are accompanied by a significant increase in the gas volumetric flow with the consequence of increased entrainment and decreased gas residence time, both of which have a negative impact on the reactor performance. In previous work (Abba et al.1,2), we have proposed a generic fluidized-bed model based on a probabilistic averaging technique, which covers the bubbling, turbulent, and fast fluidization flow regimes. In its most recent form,1 the model is applicable to cases where the volumetric gas flow changes as a result of variations in molar flow, pressure, and temperature. As a case study, the ethylene oxychlorination process, which is accompanied by a reduction in the gas volumetric flow due to reaction, was treated. Equilibrium constraints are important in steam methane reforming. Hence, high pressures and the increase in the molar flow rate due to reaction lead to lower conversions. Higher temperatures and lower pressures * To whom correspondence should be addressed. Tel.: 1-604822-3121. Fax: 1-604-822-6003. E-mail: [email protected].

Figure 1. Equilibrium methane conversion as a function of temperature at different reactor pressures. Steam-to-methane molar ratio: 3.0. Oxygen input: none.

favor the thermodynamics of the reforming reactions as shown in Figure 1, where the equilibrium compositions are computed using HYSIS software, taking into account the inlet reactor temperatures and pressures while fixing the inlet composition and setting the steamto-methane ratio to 3. Efficient removal of hydrogen through a permselective membrane along the reactor overcomes the equilibrium limitations. In this paper, we adapt the generic model to evaluate the performance of a FBMR for steam reforming with oxygen supply, which incorporates in situ permselective removal of hydrogen along the reactor as the reaction proceeds. The reforming reactions are accompanied by

10.1021/ie020780f CCC: $25.00 © 2003 American Chemical Society Published on Web 05/17/2003

Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 2737

of the oxygen inlet molar flow rate, the reactor temperature as well as the feed temperature, and the sweep gas inlet temperature. In addition, a sensitivity analysis is carried out to investigate the influence of key operating variables such as the reactor temperature and pressure. Table 1 lists the variables and the ranges over which they are varied.

Generic Membrane Reactor Model

Figure 2. Schematic of a generalized one-dimensional, two-phase/ region fluidized-bed reactor model with freeboard and membrane tubes. Table 1. Variables and Ranges over Which They Are Varied variable

base value

range explored

reactor temperature, T (K) reactor inlet pressure, Po (kPa) membrane thickness, δ (µm) inlet superficial gas velocity, Uo (m/s) steam-to-carbon ratio

873 2600 25 ∼0.17 3

773-1073 600-3000 5-100 0.15-0.6 2.5-3.5

significantly larger net changes in the gas volumetric flow than in the oxychlorination process previously studied so that a more demanding test of the generic fluidized-bed reactor model is achieved here. In addition, the continual withdrawal of hydrogen poses an interesting challenge with respect to the changes in the number of moles and how they are tracked along the reactor. The reactor is supplied with oxygen to generate heat via oxidation reactions to match the heat required for the endothermic reforming reactions, thereby obviating the need for an external heat supply. It has also been shown in separate studies without oxygen10 and with oxygen input8 that, for U > 10Umf, a FBMR operates essentially isothermally, with a slight drop in temperature in the freeboard region. Here, we assess the impacts on the reactor performance of (i) changes in volumetric flow due to variations in molar flow, pressure, and temperature, (ii) membrane-tube permeation flux capacities, and (iii) pure oxygen input versus air input to provide the heat needed by the endothermic reforming reactions. The conditions for autothermal operation of the reactor are also investigated in terms

A schematic representation of the generic model with the membrane tubes incorporated is shown in Figure 2. The model involves mole balances in the low-density (L) and high-density (H) phases applicable to all three fluidization flow regimes, with hydrodynamic and dispersion variables continuously averaged probabilistically as one spans the flow regimes with increasing superficial gas velocity. The reactor is divided into dense bed (with L and H phases) and freeboard (single-phase) regions. Membrane tubes, permeable to hydrogen but impermeable to all other species, are stacked together vertically in the reactor spanning its entire length. The tubes are in modular form, with each module consisting of 100 tubes of 2 m length, with hydrogen withdrawn from the membrane tubes only at the exit of the last module; in practice, hydrogen is likely to be withdrawn at the exit of each module. The steady-state two-phase/region mole balances representing the two-phase bubbling bed model in the low-velocity limit, axially dispersed plug-flow model at intermediate velocities, and the core-annulus model in the high-velocity limit, incorporating bulk transfer of gas between phases1 and hydrogen diffusion through the membrane tubes, can be written as

L phase: dFiL d2(FiL/uL) + [(K + β -L)FiL/uLψL - Dz,g,L dz dz2 (K + β -H)FiH/uHψH] + JiL + AFLRateiL ) 0 (1) H phase: dFiH d2(FiH/uH) - Dz,g,H + [(K + β -H)FiH/uHψH dz dz2 (K + β -L)FiL/uLψL] + JiH + AFHRateiH ) 0 (2) Overall balances: Fi ) FiL + FiH

(3)

Hydrogen fluxes through the permselective (e.g., palladium or palladium alloy) membrane tubes in the L and H phases are given by11

L phase: JiL ) kh(PiLn - Pi,Pn)

(4)

H phase: JiH ) kh(PiHn - Pi,Pn)

(5)

where

kh ) PMπdoNtube/δ

(6)

PM ) ηpPMo exp(-Ep/RT)

(7)

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Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 Table 2. Base Operating Conditions, Hydrodynamic Properties, and Reactor Geometry parameter

value

inlet temperature, To inlet pressure, Po total inlet gas flow rate, FTo feed molar fractions, yo [CH4/H2O/O2] inlet superficial gas velocity, Uo expanded bed height, Ld average particle diameter, d hp initial solids inventory, Mso catalyst density, Fp inside diameter of the reactor, Dt column overall height, Lt

773 K 2600 kPa 218.8 mol/s 0.222/0.667/0.111 0.17 m/s 11.2 m 100 µm 61800 kg 3550 kg/m3 2m 16 m

with corresponding boundary conditions

at z ) 0 -kg,P at z ) L,

Figure 3. H2 diffusion through a membrane tube around a control volume of thickness ∆z.

dTP ) Cpg,PFg,PUP(To,sg - TP) dz

dTP )0 dz

(13) (14)

The net rate of consumption of component i in the jth phase participating in Nr reactions can be written as Nr

For all other species, Ji ) 0. The permeate-side mole balance is (see Figure 3)

dFi,P ) ψLJiL + ψHJiH dz

(8)

with the inlet condition Fi,P ) 0 at z ) 0. The species conversions, yields, etc., are computed based on the total molar flow rates of all species. The steady-state energy balance for the fluidized-bed reactor incorporating heat losses to the membrane tubes and to the surroundings can be approximated (neglecting any temperature differences between the L and H phases at a given level) by

d dz

( ) ke

dT dz

dT

∑

mAsrσ(Ts4 - Tsur4) ) 0 (9) with corresponding boundary conditions

at z ) 0 -ke at z ) Lt

dT ) UFgCpg(To - T) dz

dT )0 dz

(10) (11)

The insulation outer surface temperature, Ts, is assigned a value corresponding to the protective safety temperature limit of 60 °C, while a value of 25 °C is assumed for both the temperature of the surroundings, Tsur, and the ambient temperature, T∞. The steady-state energy balance for the membranetube (permeate) side is given by

(

)

∑ νikrk

d(Cpg,PFg,PUPTP) dTP d kg,P - UAAst(TP - T) ) 0 dz dz dz (12)

(15)

k)1

where the stoichiometric coefficients νik are positive for products, negative for reactants, and zero for nonreacting species. The pressure in the reactor is calculated by assuming that the only contribution to the axial pressure drop is the hydrostatic head of solids. Boundary conditions and the correlations used to estimate the model parameters (K, Dz,g, etc.) are given elsewhere.1,2 The solids concentration in the freeboard is assumed to decay exponentially as proposed by Kunii and Levenspiel:12

φ ) φ* + (φd - φ*)e-azf

Nr

+ φ (∆Hk,iRatei) dz k UAAst(T - TP) + hAsr(Ts - T∞) + - CpgFgU

Ratei )

(16)

Full details of the model equations and the freeboard implementation within the context of the generic approach are given by Abba et al.2 A summary of the bed hydrodynamics, operating conditions, and reactor geometry used for the simulation, corresponding to the base case, is given in Table 2; Table 3 gives the sweep gas inlet conditions and assumed details of membrane tubes based on Adris and Grace,3 while the permeation properties are obtained from an in-house study conducted in our laboratory. All other hydrodynamic and thermophysical properties are evaluated within the model using the correlations and equations summarized by Abba et al.2 The complete steam reforming process with oxygen input involves complex equilibrium-constrained reactions with nonlinear temperature-dependent kinetics as shown in Table 4, with the reaction rates for reactions (R1)-(R3) as suggested by Xu and Froment13 and those for reactions (R4) and (R5) as suggested by Yermakova et al.14 Table 5 gives the complete rate expressions, while the rate and adsorption parameters are listed in Table 6. The complete model was solved using gPROMS software from Process Systems Enterprise Limited,

Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 2739 Table 3. Sweep Gas Inlet Conditions and Membrane-Tube Details parameter

value

sweep gas inlet temperature, To,sg sweep gas inlet pressure, Po,sg sweep gas inlet flowrate, Fo,sg outside diameter of tubes, do inside diameter of tubes, di tube length, Ltube total number of tubes, Ntube intertube spacing membrane layer thickness, δ permeation preexponential constant, PMO permeation activation energy, Ep permeability effectiveness factor, ηp permeation capacitya exponent in eqs 4 and 5, n

773 K 200 kPa 48.6 mol/s 4.85 × 10-3 m 4.22 × 10-3 m 16 m 1825 0.024 m 25 µm 3.82 × 10-7 mol/m‚s‚Pa0.5 9.18 × 103 J/mol 1 1.8 × 107 m 0.5

Figure 4. Predicted axial gas velocity profiles for case 4. Other conditions are given in Table 2.

a Permeation capacity ) outside surface area of membrane tubes/membrane layer thickness.

Table 4. Steam Reforming Reactions with Oxygen Input kr1

CH4 + H2O {\} CO + 3H2

(R1)

kr2

CO + H2O {\} CO2 + H2

(R2)

kr3

CH4 + 2H2O {\} CO2 + 4H2

(R3)

kr4

CH4 + 2O2 {\} CO2 + 2H2O

(R4)

kr5

CH4 + 1.5O2 {\} CO + 2H2O

(R5)

Table 5. Reaction Kinetics for the Steam Reforming Process reaction

reaction rate equation

R1 R2 R3 R4 R5

r1 ) kr1(PCH4PH2O/PH22.5 - PH20.5PCO/Keq,1)/κ2 r2 ) kr2(PCOPH2O/PH2 - PH20.5PCO2/Keq,2)/κ2 r3 ) kr3(PCH4PH2O2/PH23.5 - PH20.5PCO2/Keq,1Keq,2)/κ2 r4 ) kr4xCH40.5xO2 r5 ) kr5xCH40.5xO20.75 where κ ) 1 + KCOPCO + KH2PH2 + KCH4PCH4 + KH2OPH2O/PH2

Table 6. Reaction Rate Parameters13,14 rate/adsorption constants

preexponential factor

activation energy/ eat of adsorption (kJ/mol)

kr1 kr2 kr3 kr4 kr5 KCO KCH4 KH2O KH2 Keq,1 Keq,2

8.34 × 1017 [mol‚Pa0.5/kg‚s] 1.22 × 101 [mol/kg‚s‚Pa] 2.01 × 1017 [mol‚Pa0.5/kg‚s] 1.26 × 1012 [mol/kg‚s] 3.08 × 1010 [mol/kg‚s] 8.23 × 10-10 [Pa-1] 6.65 × 10-9 [Pa-1] 1.77 × 105 6.12 × 10-14 [Pa-1] 1.2 × 1023 [Pa2] 1.77 × 10-2

240.1 67.1 243.9 170.3 139.7 -70.65 -38.28 88.68 -82.90 223.10 -36.58

which is configured to seamlessly exchange input data and simulation results with Excel spreadsheets. Results and Discussion The steam reforming reactions are accompanied by a significant increase in the gas volumetric flow due to changes in the number of moles as well as to decreasing hydrostatic pressure, augmented or offset to some extent by changes in temperature. To rigorously simulate the

reactor, we consider that the system operates nonisothermally. As a result, we treat the effect of the volumetric flow change accounting for changes in the total molar flow rate, temperature, and pressure along the reactor height, with their impacts on the reactor performance examined for the four cases listed in Table 7. Figure 4 shows predicted axial profiles of phase and reactor average gas velocities for case 4 with the operating conditions as identified in Table 2. An increase in the cross-sectional average superficial gas velocity of about 18% (from ∼0.17 to ∼0.2 m/s) is observed immediately at z ) 0 owing to the step change in oxygen and methane conversions due to axial dispersion. One would expect a further increase immediately above the distributor due to the reaction-generated increase in the number of moles, but the increase is offset by diffusion of hydrogen through the membrane tubes resulting in a net decrease in the volumetric flow. The subsequent flat profile is mainly due to the decrease in the driving force for hydrogen diffusion. As shown in Figure 4, in the freeboard region (0.73 < z/Lt e 1), the probabilistic approach merges the gas velocities in the L and H phases and models the region as a single-phase axially dispersed plug flow. Figure 5a shows the predicted conversions of methane and oxygen for the four cases corresponding to the base conditions in Table 2. Rapid conversions of all reactants are observed, with oxygen reaching complete conversion almost immediately above the distributor in all four cases. A slightly higher conversion of methane is predicted for case 4. A decrease in the superficial gas velocity in case 4, for example, due to decreased molar flow leads to increased conversion of methane because of the higher gas residence time in the bed, and this results in an increased hydrogen yield as shown in Figure 5b. (Permeate, retentate, and total hydrogen yields are defined as the ratio of permeate, retentate, and total molar flow of hydrogen to the molar flow of methane fed.) Both the conversions and hydrogen yields for all cases are profoundly affected by the steep temperature rise at the distributor due to the exothermic methane combustion reactions and the subsequent drop along the rest of the reactor due to the endothermic reforming reactions as shown in Figure 6. Exit model predictions for the four cases with 25-µm membrane thickness are compared in Table 8 to case 1 without membrane tubes. The improvement in the reactor performance when one considers the volume change due to molar flow changes is clear; the table also highlights the improvement due to the membrane tubes. From the

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Table 7. Four Different Cases for Simulating the Effects of Changes in the Number of Moles and Pressure on the Reactor Performance

a

case 1a

uj ) ujo (j ) L and H)

case 2

uj ) ujo

FT,j FTo

accounts for change in number of moles effects of T and P on U are ignored thermophysical properties vary with P

case 3

uj ) ujo

FT,j Po FTo P

accounts for change in number of moles accounts also for effect of P on U thermophysical properties vary with P

case 4

uj ) ujo

FT,j Po T FTo P To

accounts for change in number of moles accounts also for effects of both T and P on U thermophysical properties vary with T and P

neglects volume change due to reaction effects of T and P on U are ignored all thermophysical properties are based on average values of P and T

Base case.

Figure 7. Axial profiles of species molar fractions for case 4. Conditions are given in Table 2.

Figure 5. Axial profiles of (a) methane and oxygen conversions and (b) hydrogen yields for conditions given in Table 2.

Figure 8. Axial conversion profiles of methane conversion when the energy balance is included in the model (see temperature profile) vs when it is ignored (T ) 873 K throughout). Other conditions are given in Tables 2 and 3. Table 8. Comparison of Exit Model Predictions for Base Conditions and the Four Cases (Table 7) with 25-µm Membrane Thickness to Case 1 without Tubes, Based on the Conditions in Tables 2 and 3 conversion case 1 case 2 case 3 case 4 no tubes (case 1)

Figure 6. Axial profiles of the reactor temperature for conditions given in Table 2.

axial profiles of species mole fractions, shown in Figure 7, sharp changes are observed near the distributor, with most profiles almost leveling off over the rest of the

H2 yield

CH4

O2

permeate

retentate

total

0.757 0.645 0.688 0.771 0.473

1.000 1.000 1.000 1.000 1.000

1.433 1.178 1.269 1.440 NA

0.446 0.367 0.398 0.452 0.849

1.879 1.545 1.667 1.892 0.849

reactor height. The exception is hydrogen, whose molar flow is seen to decrease somewhat with height due to its continual withdrawal through the membrane tubes, leading to a slight further conversion of methane along the reactor. Figure 8 compares predicted methane conversion for isothermal and nonisothermal cases. The lower conver-

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Figure 9. Predicted methane conversions at different reactor temperatures compared to other simulation results of Dogan et al.9 for identical conditions given in Figure 3 and Tables 2-4 of Dogan et al.9

Figure 11. (a) Predicted methane conversions and hydrogen yields and (b) axial profile of permeate hydrogen yield at different membrane thicknesses. Other conditions are listed in Table 2.

Figure 10. Axial conversion profiles of (a) methane conversion and (b) permeate hydrogen molar flow rate with pure oxygen input vs air input. Other conditions are given in Tables 2 and 3

sion predicted from the nonisothermal case is due to the decreasing temperature profile predicted by the energy equation. Because of the large impact of temperature on the reactor performance, subsequent analyses are based on fixed reactor temperature (i.e., isothermal condition), so that the influences of the various parameters listed in Table 1 can be examined without being obscured by the secondary effects of reactor temperature gradients. Therefore, except where stated otherwise, all subsequent simulation results and discussion are based on isothermal operation for the base conditions in Table 2.

Figure 9 compares predictions from this model at different temperatures with the simulation results of Dogan et al.,9 who based their simulation on the twophase bubbling bed model, without allowance for axial dispersion. Their model also does not account for the influence of volumetric flow changes with reaction. Nonetheless, the predictions are similar, with the present case somewhat higher, probably because of the improved gas-solid contacting in the bed as the bed enters the turbulent fluidization flow regime. The generic model is able to simulate this important change in the hydrodynamics. Enriched air or pure oxygen input to the reactor has the advantage of facilitating the supply of heat required for the endothermic reforming reactions by causing exothermic oxidation reactions. However, for the same total feed molar flow rate, pure oxygen gives lower methane conversion compared to air input as shown in Figure 10a, primarily because of the dilution by N2 leading to decreased inlet molar compositions of the reactant species and hence higher conversions as well as yields. The net molar flow of permeate hydrogen is, however, higher for the case with oxygen input (see Figure 10b). Figure 11 compares model predictions for different membrane thicknesses. It is shown that palladium membrane layer thicknesses greater than about 40 µm lead to a decrease in both methane conversion and hydrogen yields due to decreased permeability. For values less than about 40 µm, however, hydrogen yields are predicted to slightly decrease with decreasing

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Figure 13. Predicted methane conversions, hydrogen yields, and permeate-side hydrogen molar flows at different reactor inlet pressures. Other conditions are in Tables 2 and 3.

Figure 12. Predicted (a) methane conversions and (b) total hydrogen yield at different reactor temperatures. Other conditions are listed in Table 2.

membrane thickness. This is due to a reversal in the hydrogen driving force as one goes up the reactor height, resulting in reduced net permeate hydrogen exiting the membrane tubes. Clearly, this could be countered in practice by removing the hydrogen in stages from the membrane tubes or by limiting the palladium coating to the lower part. The reversal is better captured by the axial profiles of permeate hydrogen yield for different membrane layer thicknesses shown in Figure 10b. Close to the distributor, the predicted yields are well apart for all four values of the membrane thickness, with the difference diminishing along the reactor height, resulting in a slightly lower yield at the reactor exit for the 5-µm thickness compared to the 25-µm case. Figure 12 examines the effects of temperature on the conversion of methane and the yield of hydrogen and compares the model predictions for different membrane thicknesses to the case without membrane tubes. An increase in the reactor temperature favors both the conversion of methane and the hydrogen yield for all cases because of three factors: (i) increases in the kinetic rate constants, (ii) positive equilibrium shift, and (iii) increased permeability with increasing temperature. At lower temperatures, conversions for the 10- and 25µm-thick membranes are consistently higher than those for the 100-µm-thick membranes and for the case without membrane tubes, with the difference decreasing at higher temperatures. There is a substantial increase in both the conversion and yield as hydrogen is selectively removed through the membrane tubes. This figure captures the dual impacts of hydrogen withdrawal and temperature increase, both enhancing the reactor per-

Figure 14. Predicted methane conversions and total hydrogen yields at different superficial gas velocities based on inlet conditions. Other conditions are given in Table 2.

formance by overcoming the equilibrium constraints. The impact of reversed hydrogen diffusion, discussed above, is seen to be even more pronounced at elevated temperatures, resulting in significantly higher predicted hydrogen yields for the largest membrane thickness considered here. In general, predictions from the different thicknesses are within about 5% of each other, with the case without tubes remaining considerably lower. As shown in Figure 13, increasing the reactor inlet pressure leads to predicted decreases in both methane conversions and hydrogen yields because high pressures are thermodynamically unfavorable to the equilibrium of the reforming reactions. The predicted increase in the molar flow of hydrogen on the permeate side, FH2,P, is due to the increased driving force with increasing pressure. Note that changes in the reactor inlet pressure are reflected in the feed conditions by fixing the inlet superficial gas velocity to the base value of 0.17 m/s and letting the feed molar flow rates vary while maintaining the steam-to-methane and oxygen-to-methane ratios constant at 3 and 0.5, respectively. This allows the influence of the reactor pressure to be clearly observed without being obscured by changing the gas velocity, which is explored separately below. Note that the impact of pressure on the hydrodynamic regime probabilities is negligible for the range considered. Figure 14 shows the model exit predictions as a function of the superficial gas velocity based on the reactor temperature. With increasing Uo, the decrease in the gas residence time causes a decrease in the

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Figure 17. Predicted heat inputs to the reactor at different inlet oxygen flow rates. Other conditions are given in Table 2. Figure 15. Predicted regime probabilities averaged over dense bed height vs superficial gas velocities based on inlet conditions. Other conditions are given in Tables 2 and 3.

Figure 16. Predicted methane conversions and hydrogen yields at different steam-to-carbon ratios. Other conditions are given in Table 2.

methane conversion, leading to a reduced hydrogen yield. With increasing Uo, the selectivity ()ratio of the total molar flow produced to the molar flow of methane consumed) of methane to hydrogen initially drops steeply and then continues to drop mildly beyond 0.3 m/s. Therefore, there is little incentive to operate at high Uo, even when recycle of unreacted methane is considered because both the conversion and yield drop with no reduction in the oxidation products (CO and CO2). As shown in Figure 15, at high Uo, Pturb approaches unity, meaning that the fluidization is predominantly turbulent where the dispersed single-phase plug-flow model is approached.1,15 It is also seen that fast fluidization is barely a factor for the range of gas flow rates under consideration. Figure 16 shows the influence of the steam-to-carbon ratio on the reactor performance. The ratio was varied by changing the steam molar flow rate while maintaining the oxygen-to-methane ratio constant at 0.5 and fixing the inlet superficial gas velocity. As expected, increasing the steam-to-carbon ratio leads to an increase in the methane conversion and the molar flow of hydrogen in both the permeate and nonpermeate streams. Figures 17-19 show the net heat input to the reactor required to operate at different oxygen flow rates, inlet temperature of reactants and sweep gas (assumed to be the same), and reactor temperature. The net heat input is calculated from an overall energy balance, taking into account the net heat generated due to

Figure 18. Predicted heat inputs to the reactor as a function of inlet reactor and sweep gas temperatures at different oxygen flow rates. Other conditions are given in Table 2.

Figure 19. Predicted heat inputs to the reactor at different reactor temperatures. Other conditions are given in Table 2.

reaction, heat introduced by the inlet gases (including sweep gas), heat removed through the exit stream, and any heat lost to the surroundings. The condition for autothermal operation corresponds to zero on the ordinate scale, with negative/positive values signifying that excess heat generated from the combustion reactions needs to be removed from/added to the reactor. For the conditions simulated, it is seen that the reactor can be operated autothermally given the right combination of oxygen flow rate and reactor and inlet temperatures. For example, Figure 17 indicates that the inlet oxygen flow rate required for autothermal operation is 28 mol/s (100 kmol/h) when the other conditions are as identified in Table 2.

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Conclusions A FBMR with oxygen input has been evaluated using a generic fluidized-bed reactor model for cases with and without immersed permselective membrane tubes. The generic model extends the range of conditions that can be considered, for example, allowing operation within the turbulent flow regime to be simulated. Assessment of the impacts of changes in the volumetric flow due to variations in the molar flow, temperature, and hydrostatic pressure shows a clear improvement in the reactor performance when these changes are considered. Permselective membrane tubes show a substantial improvement in the reactor performance over the case without membrane tubes. For the conditions simulated, it is shown that, for very small membrane thickness, reversal in hydrogen diffusion could occur, especially at elevated temperatures. Withdrawal of hydrogen at intervals along the reactor or increased sweep gas can eliminate this effect. It is shown that the reactor can be operated autothermally given the right combination of key operating parameters such as the methane-tooxygen ratio and feed and reactor temperatures. Acknowledgment Funding from the Canada Research Chair program of the Government of Canada and from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. The authors also gratefully acknowledge valuable inputs from Dr. A. Adris, Dr. A. Li, and Dr. H. Zhao, all of Membrane Reactor Technologies, Vancouver, Canada. Nomenclature a ) freeboard decay constant, eq. 16, m-1 A ) reactor cross-sectional area, m2 Asr ) outer heat-transfer surface area per unit reactor volume, m-1 Ast ) membrane-tube heat-transfer surface area per unit reactor volume, m-1 Cpg ) specific heat of gas, J/mol‚K db ) volume-equivalent bubble diameter, m di ) membrane-tube inside diameter, m do ) membrane-tube outside diameter, m dp ) mean particle diameter, m Dt ) reactor diameter, m Dz,g ) gas axial dispersion coefficient, m2/s Ep ) permeation activation energy, J/mol Fi,P ) permeate-side molar flow rate of species i, mol/s FO2 ) oxygen inlet flow rate, mol/s Fo,sg ) sweep gas inlet flow rate, mol/s FTo ) total inlet gas flow rate, mol/s h ) free-convection heat-transfer coefficient of air, W/m2‚ K ∆Hk ) heat of reaction k, kJ/kmol J ) hydrogen flux through membrane tubes per unit length, mol/m‚s ke ) effective axial thermal conductivity of solids, W/m‚K kg ) thermal conductivity of gas, W/m‚K kr,i ) reaction rate constants (i ) 1-5) K ) volumetric interphase mass-transfer coefficient, s-1 Keq,i ) equilibrium constants (i ) 1-3) Ki ) adsorption constants (i ) CO, CH4, H2, H2O) Ld ) dense bed height, m Lf ) freeboard height, m Lt ) total column height, m Ms ) solids inventory, kg n ) exponent in eqs 4 and 5

Nr ) number of reactions Ntube ) total number of membrane tubes P ) pressure, Pa Pi ) partial pressure of species i, Pa Pi,j ) partial pressure of species i in the j phase, Pa Pturb ) probability of being in a turbulent fluidization flow regime PM ) permeability, mol/m‚s‚Pan PMO ) permeation preexponential factor, mol/m‚s‚Pan Po ) inlet pressure, Pa qi ) fraction of total flow passing through phase i Q ) gas volumetric flow rate, m3/s rk ) rate of reaction k, mol/kgcat‚s T ) reactor temperature, K To ) inlet temperature of the reactants, K TP ) permeate-side temperature, K T∞ ) ambient air temperature, K uj ) gas velocity in phase j, m/s U ) superficial velocity of gas at any level, m/s UA ) overall bed-to-membrane-tube heat-transfer coefficient, W/m‚K xi ) mole fraction of species i yo ) feed molar fraction z ) axial coordinate, positive upward, measured from the grid, m Greek Symbols β ) gas-transfer rate/control volume in eqs 1 and 2, s-1 s δ ) membrane-tube effective wall thickness, m m ) surface emissivity ηp ) permeability effectiveness factor φ ) solids volume fraction φ* ) saturation carrying capacity κ ) function defined in Table 5 F ) density, kg/m3 ψ ) phase volume fraction σ ) Boltzmann constant, W/m2‚K4 Subscripts bubb ) bubbling flow regime d ) dense phase f ) freeboard fast ) fast fluidization flow regime g ) gas H ) high-density phase L ) low-density phase mf ) minimum fluidization o ) initial/inlet p ) particle P ) permeate side s ) outer surface of insulation sur ) surroundings sg ) sweep gas t ) total turb ) turbulent flow regime z ) axial

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Received for review October 2, 2002 Revised manuscript received March 17, 2003 Accepted March 19, 2003 IE020780F