Static Bifurcation Characteristics of an Autothermal Circulating

reaction engineering theory and practice for solving a variety of practical and ... productivity of this autothermic process in relation to its static...
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Ind. Eng. Chem. Res. 2005, 44, 4871-4883

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Static Bifurcation Characteristics of an Autothermal Circulating Fluidized Bed Hydrogen Generator for Fuel Cells S. S. E. H. Elnashaie,* Pradeep Prasad, and Zhongxiang Chen Chemical Engineering Department, 230 Ross Hall, Auburn University, Auburn, Alabama 36849

Professor Milorad P. Dudukovic is the Chairman of the Chemical Engineering Department at Washington University in St. Louis, MO, and a leading figure in multiphase reactors. He has authored several highly cited papers on chemical reaction engineering involving kinetictransport interactions in multiphase systems. He has a commitment to the development of reaction engineering theory and practice for solving a variety of practical and fundamental problems. He is the director of the Chemical Reaction Engineering Laboratory (CREL) at Washington University, which is supported by over a dozen major chemical and petroleum companies. Some of his recent research accomplishments include the development of computerassisted radioactive particle tracking for studies of multiphase flows for improving computational fluid dynamics (CFD) models for multiphase systems and for selecting environmentally friendly reactors for the conversion of natural and synthesis gas to fuels and chemicals and novel coupling of exothermic and endothermic reactions in a reverse flow reactor to achieve potential improved efficiencies and energy savings. My students, Dr. Pradeep Prasad and Zhongxiang Chen, and I are very proud to contribute this paper to this special issue of Ind. Eng. Chem. Res. on the occasion of the 60th birthday of this outstanding academician, Professor Milorad P. Dudukovic, and we all wish him a long and healthy continuation of his productive and innovative career. sSaid Elnashaie Reforming reactions are endothermic and reversible. The present paper proposes a novel concept of an autothermic reactor-regenerator type of circulating fluidized bed. Carbon is optimally allowed to form on the catalyst in the riser reactor section through the use of relatively low steam-to-methane ratios. Coke formation occurs through the methane cracking and Boudouard coking reactions. The deactivated catalyst is regenerated in the regenerator by the burning of carbon. From the methane cracking and coke burning reactions, there can be a net energy production of 318.5 kJ per mole of CH4 cracked and carbon burned [CH4 f C + 2H2 (∆H2r ) 75 kJ/mol), C + O2 f CO2 (∆H3r ) -393.5 kJ/mol)]. This concept of carbon formation and burning is very well suited to the proposed novel autothermic circulating fluidized bed (CFB) configuration. By using a carefully controlled low steam-to-methane ratio, both the carbon formation and steam reforming reactions can be made to occur simultaneously, ensuring relatively high hydrogen productivity under autothermal conditions. However, this mode of operation exhibits static bifurcation behavior (multiplicity). This paper presents an introductory investigation of the hydrogen productivity of this autothermic process in relation to its static bifurcation characteristics. The paper also investigates an alternate configuration in which the off-gases from the reactor are combusted along with the carbon in the regenerator. The effects of hydrogenpermeable membranes and in situ CO2 sequestration on the performance of this autothermic CFB reformer are discussed, and it is shown that, despite the considerable improvements, certain complexities arise when in situ CO2 sequestration is used in this CFB configuration. 1. Introduction The classical industrial process for steam reforming (fixed bed) consists of hundreds of parallel catalyst tubes surrounded by a very large top- or side-fired furnace supplying heat for the highly endothermic reaction. The reaction is carried out at temperatures in the range of 800-1000 K and at pressures in the range of 20-25 bar. Relatively large Ni-based catalyst particles are used to avoid excessive pressure drop along the reformer tubes. This design, which we call the first-generation reformer * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: (334)844-2060. Fax: (334)8442063.

(FGR), is the dominant configuration in industry at present. It suffers from a number of limitations that lead to the lack of efficiency and huge size of the equipment. Because of the large size of the catalyst pellets, intraparticle diffusion limitations reduce the apparent catalyst activity and hence effectiveness factors to values as low as 10-2-10-3.1 The reversible nature of the reaction limits the conversion to that of the thermodynamic equilibrium and necessitates the use of elevated temperatures to achieve acceptable levels of conversion. Carbon formation increases with increasing temperature and with the use of higher hydrocarbon feeds, leading to deactivation of the catalyst and necessitating the use of high steam-to-hydrocarbon ratios.

10.1021/ie049304a CCC: $30.25 © 2005 American Chemical Society Published on Web 02/09/2005

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Figure 1. Schematic diagram of the proposed novel configuration.7-11

Elnashaie and Adris2 were the first to propose the use of a bubbling fluidized bed steam reformer using powdered catalyst, to overcome the diffusional limitations of the catalyst pellets and thus increase the effectiveness factor by 100-1000-fold. Adris et al.3-5 further studied, validated, and patented6 the fluidized bed membrane reformer (FBMR) after building a pilot plant and undertaking experimental and modeling studies of the system. The FBMR configuration (secondgeneration reformer, SGR), although very efficient, still suffers from limitations with regard to the flow rate that can be used in a bubbling fluidized bed, thereby preventing the full exploitation of the increase in the catalyst effectiveness factor. Furthermore, it is not optimal for higher hydrocarbons because it does not have the best provision for handling the excessive carbon formation associated with higher hydrocarbons. A circulating fluidized bed configuration that we call the third-generation reformer (TGR) has been proposed in order to overcome these deficiencies.7 2. Main Features of the Present Novel Configuration The proposed novel configuration (See Figure 1) is a circulating fluidized bed (CFB) using powdered catalyst particles to overcome both the diffusional and hydrodynamic limitations. The small catalyst particles are carried along by the process gases in the riser part of the fluidized bed. In previously published studies,7,8 the effect of hydrogen-permselective membranes and the use of CaO as a CO2 adsorbent have been investigated for breaking of the thermodynamic equilibrium limitations. Oxygen introduction into the reformer has been used to achieve autothermal operation.9 The present novel design is quite versatile in terms of the feedstock that can be used because of this provision for handling excessive carbon formation.10,11 A more detailed description of the configuration can be found in the above-cited papers. Catalyst deactivation due to carbon formation occurs at low steam-to-hydrocarbon ratios.12,13 This problem can be addressed by separating the catalyst from the gas stream and regenerating it by burning off the carbon

as the catalyst is on its way back to the reforming section. The present investigation aims to explore the possibility of autothermal operation using regeneration of a catalyst that has been deactivated by carbon formation and to explore the static bifurcation characteristics of the configuration. The endothermic reforming reactions are accompanied by the mildly exothermic water-gas shift reaction, and the net process is highly endothermic.

CH4 + H2O h CO + 3H2

(∆H1r ) 206 kJ/mol)

CO + H2O h CO2 + H2

(∆H2r ) -41 kJ/mol) (2)

CH4 + 2H2O h CO2 + 4H2 (∆H3r ) 165 kJ/mol)

(1)

(3)

This process is also affected by carbon deposition at low steam-to-hydrocarbon ratios. Carbon deposition is undesirable in fixed beds, but it can be used advantageously in a CFB where one can allow the carbon to be deposited (reaction 4) in the riser section and then regenerate the catalyst by burning the carbon off (reaction 5) in the regenerator (similar in principle to the FCC process14,15).

CH4 h C + 2H2 (∆H4r ) 75 kJ/mol) C + O2 f CO2

(∆H5r ) -393.5 kJ/mol)

(4) (5)

It is clear from reactions 4 and 5 that there is a net production of 318.5 kJ from the process per mole of methane cracked and carbon burned. However, the maximum theoretical hydrogen yield attainable through the cracking of methane and oxidation of carbon is only 2 mol per mole of methane reacted. In contrast, steam reforming through reactions 1-3 can give a maximum theoretical hydrogen yield of 4 mol per mole of methane reacted, albeit at the cost of the energy input required. It can thus be expected that an optimal balance is possible between the above two extreme cases, giving the maximum possible hydrogen yield at zero external energy consumption.

Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 4873 Table 1. Rate Expressions reaction

rate expression

steam reforming

r1 )

shift reaction

r2 )

steam reforming

r3 )

k1 pH22.5

(

(

pCH4pH2O -

r4 )

K1

)

r6 )

/DEN2

16

pH2pCO k2 CO p pH2O /DEN2 pH2 K2 k3 pH23.5

(

2

pCH4pH2O -

(

(

K1K2 1 pH K/M 2

)

1 1+ p 3/2 + KC,CH4pCH4 Kr′′ H2

(

(

1 + KB,COpCO +

(

(

16

)

pH24pCO2

k+ B KC,CO pCO Boudouard reaction

)

pH23pCO

k+ MKC,CH4 pCH4 methane cracking

ref

/DEN2

16

)

19

2

)

1 pCO2 K/B pCO pCO2 1

KO,CO2KCO pCO

)

)

20

2

(

′ pH2O k+ k+ 7 1 1 H pH22 - / pCH4 + - / pCO KG,r ′′ KO,H2O pH2 K K H

H2O

coke gasification

r7′ )

lime-CO2 reaction

r8 ) k8(1 - XCaO)x1 - φ ln(1 - XCaO)(CCO2 - CCO2,e)

)

1 1 pH2O 1+ pH23/2 + KG,CH4pCH4 + KG,COpCO + KG,r ′′ KO,H2O pH2

3. The Model The present paper is an investigation of the basic static characteristics of the autothermic CFB configuration. Such a study is required in this case because of the thermal sensitivity of the system. The catalyst is assumed to be completely regenerated in the regenerator section by burning off all of the carbon formed in the riser section. The main reactions in the riser include steam reforming and methane cracking; Boudouard coking (reaction 6) and carbon gasification (reaction 7) are also included for a more accurate representation of the processes that can occur in the riser.

2CO h C + CO2

)

(∆H6r ) -172 kJ/mol) (6)

C + H2O h CO + H2 (∆H7r ) 131 kJ/mol)

(7)

For reforming reactions 1-3, the nonmonotonic rate expressions proposed by Xu and Froment16 for Ni/Al2O3 catalyst and analyzed in detail by Elnashaie et al.17 are used in the present study. The kinetics of the methane cracking (reaction 4), Boudouard coking, and steam gasification reactions on a nickel catalyst have been studied by Snoeck et al.18-20 The loss of activity of the catalyst because of carbon deposition has been explained by Chen et al.11 through an exponential relation between carbon deposition and catalyst activity. The reaction of CaO with CO2 wherever considered is assumed to be in the reaction control regime because of the small particles used and the relatively short contact time in the riser reformer, as well as the relatively low levels of CaO conversion. The corresponding kinetic expression and constants have been ex-

2

20

21

tracted from the work of Bhatia and Perlmutter.21 The rate expressions used are collected in Table 1, along with the corresponding references. (The rate expression for coke gasification in Table 1 includes gasification by both steam and hydrogen.) It is assumed here that the catalyst that enters the riser is in reduced form. There are reports in the literature of the oxidation of Ni catalyst and the consequent loss in activity for reforming and its ability to get reduced.22-24 Most of these studies, however, were carried out in fixed beds for the partial oxidation reaction. It is not clear what effect the circulating fluidized bed reactor-regenerator configuration will have on the oxidation state and stability of the catalyst. Some possible alternative solutions to this problem include (among others) the use of more stable but more expensive catalysts such as Pt and Rh. The following simplifying assumptions are included in the model development: (1) All parts of the system are at steady state. (2) The flow is well-developed, with the gas flowing in plug flow through the reformer with catalyst slip. (3) Ideal gas laws are applicable. (4) Heat losses are negligible. (5) The regenerator and gas-solid separator are 100% efficient. Reformer Model. The mass balance involves seven components, viz., CH4, H2O, CO, CO2, H2, CaO, and CaCO3. Thus, there are seven mass balance equations and one energy balance equation for the reactor side and one mass balance for the hydrogen-permeable membrane side. The heat balance equation considers the heat capacities of both the gases and the solids (CaO, CaCO3, and catalyst). The partial pressures involved are calculated using the ideal gas relation.

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dFi ) Fcat(1 - R)(1 - )ArRi - mJi dl (i ) CH4, H2O, CO, H2, Hm 2 ) (8) dFCO2 dl

) Fcat(1 - R)(1 - )Ar(r2 + r3) F′CaOR(1 - )Arr8 (9)

dFi ) F′CaOR(1 - )Arr8 (i ) CaO, CaCO3) dl

∑i

Fi

d(Hi) dl

(10)

7

) Fcat(1 - R)(1 - )Ar

rj(-∆Hj) + ∑ j)1

F′CaOR(1 - )Arr8(-∆H8) + Q/r (11) The exponential catalyst activity model11 φ ) exp(-RcCk) takes into account the loss in the activity of the catalyst because of carbon deposition. Chen et al.11 estimated the value of Rc to be 28.8 g of catalyst per gram of coke. In eq 8, Ri ) 0 for the hydrogenmembrane-side mass balance equations, and Ji ) 0 for all components in the reactor-side equations except hydrogen, for which Ji is the corresponding molar permeation term depending on the type of membrane used. The value of m is +1 in the reactor-side equation and -1 in the membrane-side equation for hydrogen. For a supported Pd membrane tube, the hydrogen permeation term25 is given by eq 12. Values of parameters extracted from Nam and Lee26 are used in the present investigation. nt ) 0 when membranes are not used.

JH2 ) QH2

( ) ( )

-EH2 πdmnt exp (pH2,rn - pH2,mn) δH2 RTR

(12)

R is the volumetric ratio of CaO to total solids (CaO + catalyst) in the reactor. It is calculated from the feed mass ratio of CaO to catalyst (γ) and slip factors (ψ1 and ψ2) as described in Appendix A. γ ) 0 when CaO is not used. Particle sizes of 174 µm for the catalyst (which is the average particle diameter of steam reforming catalyst particles in the bubbling fluidized bed pilot-plant study by Adris et al.4) and 1000 µm for CaO (based on the results from earlier work by Prasad and Elnashaie8) have been assumed for calculations. Regenerator Model. A simplified model is used here wherein the regenerator is considered to be 100% efficient in burning all of the combustibles fed to it. It is assumed that air at 298 K is fed in stoichiometric proportion to the combustibles fed to the regenerator. Thus the temperature from the regenerator can be calculated by a simple energy balance

∑k FkCp,k(TG - Tref) ) ∑k FkCp,k(Tf,G - Tref) + ∑k (-∆Hc,k0)Fk,G + Qg

(13)

where k ) CH4, H2O, CO2, CO, H2, CaO, CaCO3, C, O2, N2, and catalyst. Solution of the Model. When solving for the riser reactor alone, the set of nine nonlinear initial-value differential equations for the riser reformer are integrated using the IVPAG subroutine from the IMSL

libraries using the feed methane flow rate (3.953 kmol/ hour) per tube of an industrial fixed bed reformer described by Elnashaie and Elshishini.1 A small amount of hydrogen is required in the feed mathematically to avoid division by zero in the reaction rate expressions and physically to reduce any oxidized nickel. In all of the results of the present investigation, the generalized map of gas/solid contacting reported by Grace27 and by Kunii and Levenspiel28 is used to ensure that the reactor is in either the fast fluidization or the pneumatic transport regime. The following data are used unless otherwise stated: the cross-sectional area (Ac) of the reactor available for flow of reactants is 75.12 cm2, the reactor pressure (P) is 5 atm, the catalyst flow rate (Fcat) is 20000 kg/h, the number of membranes (nt) is 0, and the CaO-to-catalyst ratio (γ) is 0. The total hydrogen yield is calculated as the total amount of hydrogen produced (appearing at the exit of the membranes and a remainder amount in the exit of the riser) per mole of methane fed

YH2 )

m 0 FH + FH2 - FH 2 2 0 FCH 4

(14)

The solution of the entire reformer-regenerator system leads to a boundary-value problem that requires an iterative solution procedure. Initially, the inlet temperature to the riser reformer is assumed, and the nine nonlinear initial-value ordinary differential equations for the reformer are solved. At the exit of the reformer, we have the products of the gaseous reforming reaction and the carbon deposited on the catalyst. The hydrogen is assumed to be separated from the rest of the process gases. The gaseous products of the reformer are then separated from the solids (carbon + catalyst) in the gas-solid separator, which is assumed to be 100% efficient in the present case. The solids are then fed to the regenerator where combustion of the carbon (and in some cases, a part of the reactor off-gases) occurs and generates heat that raises the temperature of the solid. The temperature is obtained from the algebraic regenerator heat balance, eq 13. The burning of the carbon releases heat that regenerates and heats the catalyst, which mixes with the feed, which is fed at room temperature. The heat vaporizes the water to form steam and heats the feed to the reformer inlet temperature. This completes one cycle of the process. If the reformer inlet temperature thus calculated is the same as the value assumed initially, then the problem has converged. Otherwise, the difference between the two temperatures constitutes an error that has to be reduced to a preset level of tolerance. The bisection method was utilized to solve this two-point boundary-value problem. The routine requires two initial guesses for the reactor inlet temperature that “bracket” the solution. The interval between these two guesses is then progressively halved while still bracketing the solution, until the error decreases to below the desired tolerance. The bisection method was chosen because of its stability and the possibility of multiple solutions in such types of problems involving exothermic reaction in the regenerator and feedback from the exit of the reformer to the inlet via the regenerated catalyst. Two different configurations are investigated in this paper. In configuration A, after the reformer product gases are separated from the solids, the solids are fed

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Figure 2. Schematic representation of the reformer-regenerator boundary-value problem.

to the regenerator while the gases are released as offgases after hydrogen separation (i.e., δ ) 0). In configuration B, some of the off-gases are recycled (dotted line in Figure 2) and fed to the regenerator where they undergo combustion along with carbon (i.e., δ * 0). It is assumed here that the product hydrogen is separated before any off-gases are recycled to the regenerator. The fraction of the off-gases recycled (δ) is investigated as one of the bifurcation parameters. 4. Results and Discussion From a thermodynamic point of view, the methane cracking and steam reforming reactions show similar dependences on temperature and pressure (see Figure 3). The reforming reaction has slightly higher equilibrium conversions than the cracking reaction at lower temperatures. At high temperatures (>900 K), the equilibrium conversions are almost equal. Of course, at the same equilibrium conversion of methane, the steam reforming reaction has a higher hydrogen yield than the cracking reaction because of the hydrogen that is abstracted from water. The kinetics of carbon formation in comparison to that of steam reforming also plays an important role in the feasibility of the concept. This aspect has been investigated using a kinetic model for the riser reactor. In reality, the reactor-regenerator system will reach a steady state based on a balance between the heat required by the process and the heat generated in the process. The modeling of the complete reformerregenerator system leads to the boundary-value problem described in the previous section. The solution for such a process involving an exothermic reaction in the regenerator and feedback of “information” via the recirculation stream is expected to show a multiplicity of steady states.14,15 Configuration A. Because the concept involves a balance between the steam reforming and carbon formation reactions such that the carbon formed when burned is able to satisfy the energy needs for the

Figure 3. Equilibrium conversions: (a) methane cracking (steamto-methane ratio ) 0), (b) methane steam reforming (steam-tomethane ratio ) 1). P ) (s) 1, (- - -) 3, (- - -) 5, and (- ‚ -) 10 atm.

process, the steam-to-methane ratio is the most important parameter. Figure 4 considers the steam-tomethane ratio as the bifurcation parameter when no reactor off-gases are used in the regenerator (configuration A as described earlier with δ ) 0). As expected, a multiplicity of steady states is observed, in this case

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Figure 4. Multiple steady states: Effect of steam-to-methane ratio for configuration A (δ ) 0). (s) High-temperature steady state, (- - -) middle-temperature steady state, (s) low-temperature steady state.

Figure 5. Effect of feed temperature for configuration A (δ ) 0). Tf ) (s) 298.15, (4 400, (0) 600, and (]) 900 K.

Figure 6. Effect of pressure for configuration A (δ ) 0). P ) (s) 2, (4) 5, and (0) 10 atm.

at steam-to-methane ratios below 0.22 as shown in Figure 4. The high-temperature steady-state branch is stable and shows the highest methane conversion and hydrogen yield among the three branches. Below a

steam-to-methane ratio of about 0.1, the high-temperature branch tends toward very high temperatures, which will lead to a temperature runaway and also makes computation quite difficult. Therefore, the high-

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Figure 7. Effect of reactor off-gases on the bifurcation behavior (configuration B). δ ) (0) 0, (]) 0.05, and (4) 0.1.

Figure 8. Fraction of reactor off-gases recycled (δ) as the bifurcation parameter (configuration B). (s) High-temperature steady state, (- - -) middle-temperature steady state, (s) lowtemperature steady state.

temperature branch is not shown below a steam-tomethane ratio of 0.1 in Figure 4. The middle steady state is a saddle-type unstable steady state.14 The lowtemperature branch is stable and corresponds to zero conversion with the reactor temperature as the feed temperature itself (quenched state). The high-temperature and intermediate-temperature branches meet at the bifurcation point (static limit point), beyond which the system shows a unique, stable, quenched state with zero methane conversion and hydrogen yield. The highest hydrogen yield (∼2.04) is obtained by operating on the high-temperature branch, at a steam-to-methane ratio of 0.15. As the steam-to-methane ratio is increased along the high-temperature branch, the temperature decreases until the bifurcation point is reached and the system reaches a quenched state. To obtain a reasonable yield of hydrogen under autothermal conditions, the system needs to be operated on the high-temperature branch, and tight control is required from both operational and safety points of view. Figure 5 shows the effect of varying the feed temperature on the static bifurcation characteristics of the system. Increasing the process feed temperature means an increase in the heat input and leads to a quantitative and qualitative change in the behavior of the system. Higher feed temperatures cause the static limit point to move toward higher steam-to-methane ratios and the region of multiplicity to shrink. Most importantly, higher feed temperatures bring about an increase in the hydrogen yield of the process (high-temperature steady state). This also means that the low-temperature steady states are no longer necessarily giving zero methane conversion and hydrogen yield. Of course, the higher hydrogen yield is brought about at the expense of the energy requirement

of preheating the feed to the corresponding feed temperature. This subject is explored in more detail in a later section of this paper. Reforming and cracking reactions involve an increase in the number of moles and are favored by lower pressures. This is evident in Figure 6, which shows an increase in hydrogen yield with decreasing pressure in the system. The maximum hydrogen yield at 2 atm is 2.12 at a steam-to-methane ratio of 0.21, whereas that at 10 atm is 1.96 at a 0.1 steam-to-methane ratio. Pressure also has an effect on the static limit point, which moves to a lower steam-to-methane ratio as the pressure changes from 2 to 5 atm but then moves to a higher value when pressure further increases to 10 atm. This nonmonotonic behavior of the static limit point is the net result of the complex nonlinear dependence of the reactions on pressure. Configuration B. The reactor off-gases contain combustible components such as unreacted methane and products including hydrogen and carbon monoxide. These can also be combusted in the regenerator along with the carbon to provide additional heat. It is assumed here that the product hydrogen is separated before any off-gases are recycled to the regenerator. Combustion of some or all of the off-gases releases extra energy as a result of the oxidation of methane and carbon monoxide. Figure 7 shows the effect of recycling the reactor off-gases. As the fraction of reactor off-gases recycled (δ) is increased, the bifurcation curve (Figure 7) shifts to the right, and the region of multiplicity (in terms of steam-to-methane ratio) shrinks from 0.27 for δ ) 0.05 to 0.1 for δ ) 0.1. The system shows two static limit points (SLPs) for δ * 0 as compared to a single SLP for δ ) 0. Also in the previous figures corresponding to δ )

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Figure 9. Effect of steam-to-methane ratio for configuration B (δ ) 1.0). (s) Tf ) 298.15 K, P ) 5 atm; (4) Tf ) 400 K, P ) 5 atm; (]) Tf ) 900 K, P ) 5 atm; (O) Tf ) 900 K, P ) 2 atm.

0 (Figures 4-6), the SLP is located at relatively small steam-to-methane ratios, which itself limits the hydrogen yield that can be attained. Figure 8 shows the investigation of δ as the bifurcation parameter at a steam-to-methane ratio of 0.15. δ ) 0 is the case with no recycle, and the values correspond to those in Figure 5. The combustion of off-gases in the regenerator changes the nature of the low-temperature steady state from a quenched state, and thus the temperature along this branch increases with δ (likewise for methane conversion and hydrogen yield) for the high- and lowtemperature steady states, whereas they decrease for the middle steady state. The system reaches a bifurcation point at 5.4% reactor off-gases recycled, beyond which only one stable high-temperature steady state exists. Higher recycle ratios than shown in Figure 8 are also possible at higher steam-to-methane ratios. Figure 9 shows the existence of a single stable steady state when 100% of the reactor off-gases are recycled. The temperature decreases with increasing steam-to-methane ratio because of the increase in the amount of water that needs to be vaporized and/or heated. As explained earlier, fresh feed at temperature Tf is brought into direct contact with hot catalyst from the regenerator. As the feed temperature (Tf) is lowered, the heat absorbed by the feed from the hot catalyst stream becomes greater. This becomes obvious especially for the case where the feed is at Tf ) 298.15 K, where the heat absorbed from the catalyst is used for vaporizing the water and then further heating the feed to the reactor inlet temperature. This leads to a maximum in the

hydrogen yield with respect to the steam-to-methane ratio. The maximum is not seen when the water is fed in the form of steam because of the lower heat requirements. As shown previously, lower pressures favor the reforming reactions, and the hydrogen yield increases to around 2.98 mol of H2/mol of CH4 fed at a steam-tomethane ratio of 1.5 (when Tf ) 900 K and P ) 2 atm). As the steam-to-methane ratio increases, the carbon formation drops and ultimately becomes zero. At this stage, the heat requirement for reforming is provided solely by the combustion of the reactor off-gases. Of course, this requires less than complete conversion of methane. It is thus possible to operate the reactor autothermally even without carbon formation at the expense of a part of the methane feed. Figure 9 shows that higher feed temperatures give better hydrogen yield, but higher feed temperatures come at a price because the feed has to be raised from room temperature to feed temperature (Tf) outside the CFB reformer. A major portion of the energy required is for heating water to generate steam. This energy requirement should, in fact, be considered when evaluating a process for hydrogen production. Likewise, when examining the energy requirement, it is also important to consider the hot off-gases from the regenerator. These can be utilized to preheat the feed to some extent and thus decrease the dependence of the CFB reformer on external energy. The preheating requirement over and above the capability of the regenerator off-gas stream is the net external energy dependence of the CFB reformer. This net external energy requirement should be taken into account in the definition of the hydrogen

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Figure 10. Energy-based hydrogen yield: (a) configuration A, (b) configuration B. (s) Tf ) 298.15 K, P ) 5 atm; (4) Tf ) 400 K, P ) 5 atm; (]) Tf ) 900 K, P ) 5 atm; (O) Tf ) 900 K, P ) 2 atm.

yield to provide a realistic measure of the hydrogen production efficiency of the system. This has been accomplished here using an energy-based hydrogen yield as described in the Appendix B. When Tf is 298.15 K, the heat required to increase the feed temperature (Q1) is zero and EH (see Appendix B) is negative. This means that the process is producing surplus energy in the form of heat in addition to producing hydrogen. At higher Tf values, EH can take positive or negative values depending on the relative magnitudes of Q1 and Q2. EH is reflected in the energybased hydrogen yield (EYH2) as a bonus or penalty on the hydrogen yield from the reactor. Figure 10a shows the EYH2 values for the high- and middle-temperature steady states for configuration A. There is no drastic difference between the hydrogen yield and EYH2 values in this case because of the small steam-to-methane ratios. The difference is appreciable in the case of configuration B as can be observed by comparing the hydrogen yield values in Figure 9c to the EYH2 values in Figure 10b. In general, for both configurations, lower feed temperatures give higher EYH2 values. Of course, this is not to say that one should necessarily operate at lower feed temperatures. The above figure just shows that there is a penalty associated with obtaining a higher hydrogen flow rate from the process by operating at high feed temperatures. Effect of Breaking the Thermodynamic Equilibrium Barrier for the Steam Reforming Reactions. The effect of reaction equilibrium breaking

techniques such as the use of hydrogen-permeable membranes and/or calcium oxide has earlier been investigated for the riser reactor alone.7,8 These techniques “break” the thermodynamic equilibrium by selective removal of products and force the reaction to proceed beyond the equilibrium. They also allow operation of the reformer at lower temperatures. The cases discussed in this paper thus far did not consider these techniques. Figure 11a,b shows the effect of these techniques on the reactor-regenerator system for configuration A (δ ) 0), and Figure 11c,d shows the effect of these techniques on the reactor-regenerator system for configuration B (δ ) 1). As expected, the hydrogenpermeable membranes push the thermodynamic equilibrium forward and increase the hydrogen yield as compared to the case without membranes. A potential problem with the hydrogen-permeable membranes could be the deactivation of the Pd-based membranes. Gases consisting of hydrogen, carbon monoxide, carbon dioxide, and lower saturated hydrocarbons such as methane do not strongly affect the hydrogen permeance of thin palladium and palladium-silver alloy membranes.25 However, there is the possibility of deactivation, but by the deposition of coke and other carbonaceous material such as unsaturated hydrocarbons,25 especially at low steam-to-methane ratios. The use of calcium oxide leads to some different complexities. The use of CaO in the absence of membranes gives a hydrogen yield slightly higher than but largely comparable to that in the no-CaO, no-membrane case. the no-CaO, no-membrane case is not shown in Figure 12a and b for better readability of the figures, but the corresponding data can be found in Figure 5. The presence of hydrogen-permeable membranes increases the region of operability of the process and also increases the hydrogen yield. Use of CaO along with membranes further increases the hydrogen yield in the regions where the temperature is lower than ∼1150 K, a region where the formation of CaCO3 is favored. Higher temperatures will favor the decomposition of CaCO3; therefore, for the steady states above this temperature, the case with CaO behaves similar to that with membranes only. In Figure 11c and d, the use of membranes increases the hydrogen yield as expected. Also the use of CaO increases the hydrogen yield over the case with neither CaO nor a membrane for a certain range of steam-tomethane ratios. The yield starts to decrease, however, beyond a certain critical point. When CaO is used together with membranes, we expect the hydrogen yield to be further enhanced. Simulations of the riser alone and comparison to cases with and without CaO at the same feed temperatures have shown an increase in hydrogen yield with the use of CaO.8 However, for configuration B of the circulating fluidized bed case, we observe that the use of CaO only gives comparable or smaller hydrogen yields than the case with membranes alone. As seen previously, the performance of the cases with CaO is dependent on the steady-state temperature. For some ranges of steam-to-methane ratios, the temperature increases above ∼1150 K, and this makes CaO ineffective as a means of pushing the equilibrium forward. The reason for the decreased hydrogen yields for other steam-to-methane ratios is not clear but could be an effect of several factors. One factor is the added heat capacity due to CaO that leads to lower steadystate temperatures in the CFB. Another important

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Figure 11. Effect of breaking thermodynamic equilibrium for Tf ) 900 K, P ) 5 atm: (a,b) configuration A, (c,d) configuration B. (]) nt ) 0, γ ) 0; (4) nt ) 10, γ ) 0; (0) nt ) 0, γ ) 0.05; (×) nt ) 10, γ ) 0.05.

Figure 12. Hydrodynamic limitation on the use of CaO: u* vs d/p profile along the length of the reactor from 0 to 0.815 m (δ ) 0, steam-to-methane ratio ) 0.8, nt ) 10, γ ) 0.06).

factor that can lower the overall temperature (especially keeping in mind that the riser off-gases are combusted in the regenerator in configuration B) is that the CO content of the riser off-gases is lower in the presence of CaO. Also, we found that supplying heat to the reactor and removing an equal amount of heat from the regenerator actually decreases the hydrogen yield. Yet this is exactly what happens when CaO combines with CO2 and releases heat in the reactor and CaCO3 absorbs heat to decompose in the regenerator A hydrodynamic limitation is observed in configuration A to the efficient breakage of the thermodynamic equilibrium. When both CaO and membranes are used, both of the reaction products are being simultaneously removed from the gas phase. Under certain conditions, this leads to a dramatic decrease in velocity inside the riser, so that it falls out of the fast fluidization regime. Figure 12 shows an example of this behavior for configuration A for a steam-to-methane ratio of 0.8, γ ) 0.06, and nt ) 10. A profile of u* and d/p along the length of the riser as a thick dashed line on the generalized map of gas-solid contacting published by Kunii and Levenspiel24 and Grace et al.28 is shown in Figure 12. It clearly shows u* falling below the terminal velocity (ut). Such behavior is more likely in configuration A than in configuration B. In configuration B, the system can adjust itself and negate the effect of CaO by operating at different combinations of conversion and temperature (thus controlling the combustion of unreacted and product gases in the regenerator). This intelligent self-adjustment is not possible in configuration A, because it solely depends on the formation of carbon, which in turn is dictated by the steam-tomethane ratio used.

Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 4881

5. Conclusion A novel autothermal methane reformer concept with a combination of steam reforming, carbon formation, and burning of carbon and other combustibles is proposed for the production of hydrogen. Such an operation is difficult to attain in a conventional fixed bed type of reactor but the novel circulating fluidized bed configuration is quite suitable for this purpose. The reactorregenerator type of configuration has been simulated using a reaction-engineering model and an iterative solution algorithm for the resulting two-point boundaryvalue problem. The results show that autothermal operation of the reactor-regenerator system is possible with high hydrogen yield and using water as feed to the reformer instead of steam. The system shows multiplicity of steady states and undergoes bifurcation to reach a quenched state at steam-to-methane ratios higher than the bifurcation point. In an alternate configuration, autothermal operation is achieved through recycling the reactor off-gases. It is shown using this configuration that the system can also be operated autothermally at higher steam-to-methane ratios where there is no carbon formed. Higher feed temperatures and lower pressures are shown to favor the hydrogen productivity of the system. An energy-based definition of hydrogen yield has been introduced to quantify the energy requirements of the process when operating at higher feed temperatures. The use of hydrogen-permeable membranes increases the hydrogen yield, which has been shown to reach ∼3.15 mol of H2 per mole of CH4 fed. The use of CaO in the circulating fluidized bed is observed to lead to some complexities in behavior when used along with membranes. For the configuration where reactor off-gases are recycled to the regenerator, we observe lower hydrogen yield when both CaO and membranes are used as compared to the case with hydrogen-permeable membranes alone. A hydrodynamic limitation to the efficiency of breaking thermodynamic equilibrium was also observed, when the use of CaO and membranes together in some cases causes the riser to fall out of the fast fluidization regime. Acknowledgment This research was supported by Auburn University through Grant 2-12085.

l ) distance along the reactor (m) pi ) partial pressure of component i (atm) q ) gas volumetric flow rate (m3 h-1) Qg ) rate of heat input to the regenerator (kJ h-1) Q/r ) rate of heat input to the reactor (kJ h-1 m-1) Qr ) rate of heat input to the reactor (kJ h-1) rj ) rate of reaction j (kmol h-1 kgcat-1 or h-1) Ri ) rate of generation of species i (kmol h-1 kgcat-1) ∆T ) temperature approach between the hot and cold streams in the preheater (K) ∆Tmax ) maximum temperature difference between the hot and cold streams at the preheater inlet (K) Te ) outlet temperature of the off-gas stream from preheater (K) Tf ) feed temperature (K) TR ) reactor outlet temperature (K) Tf,G ) regenerator inlet temperature (K) Tf,R ) reactor inlet temperature (K) U0 ) gas superficial velocity (m s-1) vp ) particle velocity (m s-1) vt ) terminal velocity of particle (m s-1) XCaO ) conversion of CaO YH2 ) yield of hydrogen [mol of H2 (mol of CH4 fed)-1] Greek Letters R ) volume (CaO + CaCO3) per unit volume of solids (CaO + CaCO3 + catalyst) δH2 ) thickness of hydrogen-permeable membrane (m) γ ) CaO-to-catalyst ratio [kg of CaO (kg of catalyst)-1]  ) void fraction η ) efficiency of heat recovery µ ) viscosity (kg m-1 s-1) φ ) catalyst activity function FCaO ) density of CaO (kg m-3) F′CaO ) molar density of CaO (kmol m-3) Fcat ) density of catalyst (kg m-3) Ff ) density of fluid (kg m-3) Fs ) density of solid (kg m-3) ψ ) slip factor

Appendix A. Calculation of CaO-to-Solids Volumetric Ratio (r) and Riser Voidage (E) The slip factor (ψ) is the ratio between the particle velocity (vp) and the actual gas velocity. Let ψ1 and ψ2 be the slip factors for the catalyst and CaO, respectively. Then

U0 ) ψ1vcat 

Notation Ar ) cross-sectional area of the reactor Dt ) reactor diameter (m) EYH2 ) energy-based yield of hydrogen [mol of H2 (mol of CH4 fed)-1] Fi ) molar flow rate of species i (kmol h-1) Fm i ) molar flow rate of species i on the membrane side (kmol h-1) F0i ) molar feed flow rate of species i (kmol h-1) Fcat ) catalyst flow rate (kg.h-1) FCaO ) CaO flow rate (kg.h-1) Fr ) Froude number [) U0/(gDt)0.5] Frt ) particle Froude number [) ut/(gDt)0.5] Hi ) molar enthalpy of species i (kJ mol-1) ∆Hrj ) standard heat of reaction for reaction j (kJ mol-1) 0 ∆Hc,k ) standard heat of combustion of component k (kJ mol-1) JH2 ) flux of hydrogen through the membrane (kmol h-1 m-1)

(A1)

(m2)

Equation A1 leads to

Ar(1 - )RFcatU0 ) ψ1Ar(1 - )RFcatvcat q(1 - )(1 - R)Fcat ) ψ1Fcat

(A2)

Equation A2 can be written for CaO particles as well (CaO and CaCO3 are considered together here)

q(1 - )RFCaO ) ψ2FCaO Dividing eq A1 by eq A2 gives

ψ1FcatFCaO 1 - R ) ψ2FCaOFcat R

(A3)

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Rearranging then leads to

R)

γψ2Fcat ψ1FCaO + γψ2Fcat

hydrogen (EH) using the standard heat of combustion of hydrogen (lower heating value)

(A4) EH )

Adding eqs A2 and A3 gives

q(1 - )[(1 - R)Fcat + RFCaO] ) (ψ1Fcat + ψ2FCaO) Rearranging, we obtain the voidage () as

)

q q + qs

(A5)

where

qs )

(1 - R)Fcat + RFCaO

Patience et have proposed a correlation based on the Froude number for calculating the slip factor in the fully developed region of fast fluidized and pneumatic transport risers

( )

U0 5.6 + 0.47Frt0.41 )1+ vp Fr

(A6)

The Froude number (Frt) is calculated using the terminal velocity of the particle from the correlation proposed by Haider and Levenspiel.31

v/t )

[

] ]

-1

18 0.591 + / 1/2 / 2 (dp) (dp)

d/p ) dp

[

gFf(Fs - Ff)

[

v/t ) vt

µ2 Ff2

gµ(Fs - Ff)

(A7)

1/3

]

(A8)

1/3

(A9)

Appendix B. Calculation of Energy Based Hydrogen Yield (EYH2) The total heat required for increasing the feed temperature from 298.15 K to Tf is calculated as Q1. The total heat that can be recovered from the regenerator off-gases is found as Q2. To calculate Q2 we require the regenerator off-gas outlet temperature (Te) from the preheater unit. This can be calculated using the concept of the efficiency of energy recovery (η) discussed by Goossens29 based on the second law of thermodynamics. The energy recovery efficiency is given by eq A1. A value of η ) 0.7 has been assumed for calculation purposes. The temperature differences ∆T and ∆Tmax were calculated assuming that the fresh feed side in the preheater consists of water at 373.15 K.

η)1-

∆T ∆Tmax

(B2)

FH2 - EH 0 FCH 4

(B3)

Literature Cited

al.30

ψ)

0 ∆Hc,H 2

The energy-based hydrogen yield (EYH2) is then obtained using the equivalent hydrogen subtracted from the hydrogen produced in the CFB reformer. EYH2 is a measure of the net hydrogen yield from the process after taking into account the net energy required for preheating the feed.

EYH2 )

ψ1Fcat + ψ2FCaO

Q1 - Q2

(B1)

Te can thus be calculated and then Q2. The difference between Q1 and Q2 is the net energy requirement for preheating, which here is converted to equivalent

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Received for review August 3, 2004 Revised manuscript received October 15, 2004 Accepted October 19, 2004 IE049304A