Modeling of Sorption-Enhanced Steam Reforming in a Dual Fluidized

Ind. Eng. Chem. Res. 2006, 45, 4133-4144

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Modeling of Sorption-Enhanced Steam Reforming in a Dual Fluidized Bubbling Bed Reactor Kim Johnsen,*,† John R. Grace,‡ Said S. E. H. Elnashaie,‡ Leiv Kolbeinsen,§ and Dag Eriksen† Institute for Energy Technology (IFE), P.O. Box 40, NO-2027 Kjeller, Norway, Department of Chemical and Biological Engineering, UniVersity of British Columbia, 2360 East Mall, VancouVer, Canada V6T 1Z3, and Department of Materials Science and Engineering, Norwegian UniVersity of Science and Technology (NTNU), NO-7491 Trondheim, Norway

This paper highlights the use of a dual fluidized bed reactor system for producing hydrogen by sorptionenhanced steam methane reforming. Hydrogen concentrations of >98% are predicted for temperatures of ∼600 °C and a superficial gas velocity of 0.1 m/s, using a simple two-phase bubbling bed model for the reformer. The kinetics of the steam methane reforming and water-gas shift reactions are based on literature values, whereas experimentally derived carbonation kinetics are used for the carbonation of a dolomite. It is shown that the reformer temperature should not be 630 °C for carbon capture efficiencies to exceed 90%. Operating at relatively high solids circulation rates to reduce the need for fresh sorbent is predicted to give higher system efficiencies than for the case where fresh solid is added. This finding is attributed to the additional energy required to decompose both CaCO3 and MgCO3 in fresh dolomite. Introduction Fossil fuels will continue to be a major source of energy for decades to come. To reduce greenhouse gas (GHG) emissions, energy systems that are energy-efficient and also capture CO2 are attractive. Hydrogen is considered to be an important potential energy carrier; however, its advantages are unlikely to be realized unless efficient means can be found to produce it with reduced generation of CO2. Sorption-enhanced steam methane reforming (SE-SMR) is a potential route to energyefficient hydrogen production with CO2 capture. The reactions with CaO as sorbent are

CH4 + H2O h CO + 3H2

(∆H0298 ) 206.2 kJ/mol)

(1)

CO + H2O h CO2 + H2

(∆H0298 ) - 41.2 kJ/mol)

(2)

CH4 +2H2O h CO2 + 4H2

(∆H0298 ) 165 kJ/mol)

(3)

CaO(s) + CO2 h CaCO3(s)

(∆H0298 ) -178 kJ/mol) (4)

where reaction 3 is the summation of reactions 1 and 2. CO2 is converted to a solid carbonate as soon as it is formed, shifting the reversible reforming and water-gas shift reactions beyond their conventional thermodynamic limits. Regeneration of the sorbent (the reverse of reaction 4) releases relatively pure CO2, suitable for geological and deep-ocean storage or industrial usage. SE-SMR with calcium-based CO2 sorbents has been demonstrated in several investigations (e.g., Balasubramanian et al.,1 Brun-Tsekhovoi et al.,2 Han and Harrison,3 Ortiz and Harrison,4 Silaban and Harrison,5 Silaban et al.6). More recently, lithium-based sorbents have received increased attention, because of their promising multicycle behavior (e.g., Kato and Nakagawa7), as determined by thermogravimetric analysis (TGA). * To whom correspondence should be addressed. E-mail: [email protected]. † Institute for Energy Technology (IFE). ‡ Department of Chemical and Biological Engineering, University of British Columbia. § Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU).

The literature that is available on modeling of SE-SMR is rather sparse. Lee et al.8 modeled the transient behavior of steam methane reforming with simultaneous CO2 removal by CaO pellets in a packed-bed reactor, using their own apparent kinetics that were determined using TGA for carbonation. Xiu et al.9 developed a model for separation-enhanced steam reforming, using a pressure swing adsorption (PSA) system with a hydrotalcite-based CO2 sorbent. Ding and Alpay10 investigated a tubular reactor, both experimental and theoretically, for the enhanced steam reforming reaction, again using a hydrotalcitebased CO2 sorbent and a nonlinear (Langmuir) adsorption equilibrium. Fixed-bed reactors have been the predominant reactors in the literature for both experimental and modeling investigations. However, they are unlikely to be applied to the SE-SMR process on an industrial scale where continuous regeneration of sorbent is required. Fluidized-bed reactors are common in processes where catalysts must be continuously regenerated, while also facilitating heat transfer, temperature uniformity, and higher catalyst effectiveness factors. Fluidized beds can be operated in different flow regimes, e.g., in bubbling or fast fluidization. Prasad and Elnashaie11 modeled a novel reactor-regenerator configuration in which a sorbent was added to assist hydrogen permselective membranes in “breaking” the thermodynamic equilibrium of SMR. They chose a fast fluidized bed as reformer and found that increasing the CaO particle size, by implementing a slip-factor to their model, gave higher hydrogen yield, as the residence time for carbonation increased. Coupling two bubbling beds would have the advantage of a relatively long residence time for the sorbent, compared to fastfluidized beds, as well as low rates of attrition, because of low gas and particle velocities. We previously conducted an experimental investigation in a bubbling fluidized-bed reactor.12 The reactor was operated cyclically and batchwise, alternating between reforming/carbonation conditions and higher-temperature calcination conditions to regenerate the sorbent. An equilibrium H2 concentration of ∼98% on a dry basis was reached at 600 °C and 1 atm, with Arctic dolomite (Franzefoss A/S) as the CO2-acceptor. Based on the reforming conditions used in the reformer of the experimental study, a steady-state

10.1021/ie0511736 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/11/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006

Figure 1. Schematic diagram of the sorption-enhanced steam methane reforming (SE-SMR) process.

Figure 2. Equilibrium pressure of CO2 over a CaO/CaCO3 mixture, as a function of temperature.

model of a dual bubbling fluidized bed reactor system is investigated in this paper. Reaction rate expressions for both the catalytic reforming/shift reactions and the carbonation reaction are used to predict the steady-state product composition, with special attention to the expected energy efficiency and carbon capture performance of a continuous system. The steadystate model is also used for sensitivity analysis and to provide useful guidance for screening potential new sorbents. To make the system evaluation as close to reality as possible, an experimental reaction rate expression and multicycle performance of the dolomite are included in the model.

difference in loss of multicycle durability for different regeneration atmospheres with dolomite as the sorbent, except when regeneration was conducted in pure nitrogen at 950 °C. Multicycling was performed in the presence of the reforming catalyst, which also seemed to maintain its activity. The choice of fluidizing gas in the calciner influences the decomposition temperature of the carbonate. In pure CO2, the decomposition temperature is ∼900 °C, based on an equation proposed by Baker:15

PEq )

1 ) 10(-8308/T)+7.079 KEq

(5)

Reactor Configuration A schematic illustration of a continuous SE-SMR process, based on parallel fluidized-bed reactors, appears in Figure 1. Bubbling Fluidized Bed Reformer (BFBR). The reforming catalyst and CO2 acceptor particles are mixed in the reformer (with λ as the volumetric ratio of sorbent to the total volume of particles). The catalyst is a commercial, nickel-based steam reforming catalyst ground to a mean particle diameter of 200 µm. It is not separated from the sorbent before being transferred to the calciner. Methane and steam are fed to the reformer. Fluidized beds allow smaller particles than fixed beds, hence overcoming diffusional limitations.13 However, the fluidization properties of the catalyst/sorbent mixture must be considered when deciding the particle diameters , to minimize segregation. Temperature is relatively uniform due to rapid solid mixing, and solids are transferred easily between the two reactors. With almost complete CO2 capture, the combined reactions (reactions 1-4) are slightly exothermic, eliminating the need for additional heat to the reformer. The product gas from the reformer/ carbonator then mainly consists of hydrogen and steam, with only minor quantities of CO, CO2, and unconverted CH4. Calciner. Carbonated sorbent is transferred to the calciner/ regenerator, where heat (Q) is supplied for the endothermic calcination reaction (the reverse of reaction 4). Heat can be supplied either by burning fuel in the regenerator or by indirect heating from an external heat source. Indirect heating has the advantage of producing essentially pure CO2 for further sequestration, e.g., suited to geological storage or enhanced oil recovery, eliminating the need for downstream purification. The SE-SMR process, illustrated in Figure 1, is based on pure CO2 to be produced by the calciner. To avoid separation processes downstream, CO2 and/or H2O can be used as the fluidizing gas in the regenerator. Ortiz and Harrison14 report no significant

This equation is originally based on experimental data for CO2 partial pressures in the range of 1-300 atm, but it was also observed, by comparing with thermodynamic data from HSC thermodynamic software package, to describe lower partial pressures (Outokumpu Research Oy, Finland). Figure 2 shows the equilibrium partial pressure of CO2 as a function of calcination temperature, calculated from this equation. Steam as a fluidization medium has the advantage of reducing the partial pressure of CO2, hence reducing the temperature required for calcination, and it is therefore likely to be preferred over CO2. Carbon Dioxide Acceptor. Calcium-based sorbents have the advantage of being available at a low cost, but they have been proven to be unable to maintain their capture capacity over multiple reforming/regeneration cycles.16 A make-up stream of fresh sorbent (Fs,0) must be included to maintain the capture capacity. The fresh sorbent is added to the calciner, whereas withdrawal is from the reformer, as indicated in Figure 1. Synthetic sorbents, such as Li2ZrO3, have better multicycle stability, but their cost would require them to withstand close to 10 000 cycles to compete with natural sorbents for CO2 capture.17 Dolomite is used as the sorbent in this study, because of its favorable multicycle properties, compared to calcite. Initial calcination completely decomposes both the MgCO3 and CaCO3; however, carbonation conditions are at such high temperatures that only CaO forms carbonate. The extra pore volume created by MgCO3 decomposition is thought to be responsible for the more favorable cycling performance. Because only CaO is considered as the active part of dolomite for CO2 capture at the reforming temperatures, the dolomite is often referred to as CaO when considering sorbent conversion in this paper.

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4135 Table 1. Kinetic Parameters from Xu and Froment18

parameter

activation energy and heat of chemisorption [kJ/mol]

pre-exponential factor

rate constants k1 9.49 × 1016 kmol kPa0.5 kg-cat-1 h-1 k2 4.39 × 104 kmol kg-cat-1 h-1 kPa-1 k3 2.29 × 1016 kmol kPa0.5 kg-cat-1 h-1 KCH4 6.65 × 10- 6 kPa-1 KCO 8.23 × 10- 7 kPa-1 KH2O 1.77 × 105 KH2 6.12 × 10- 11 kPa-1 equilibrium constants K1 K1 ) 10267 × 10(-26830/T)+30.11 kPa2 K2 K2 ) 10(4400/T)-4.036

240.1 67.13 243.9 38.28 70.65 -88.68 82.90

Model Development In the present paper, a steady-state model of a dual fluidized bubbling bed SE-SMR reactor system is investigated. The model predictions are then compared with previous SE-SMR experiments in a bubbling fluidized bed.12 Kinetic Rate Equations for SMR. The rate expressions for catalytic steam reforming of methane over a nickel-based catalyst are those proposed by Xu and Froment,18 who used the same Ni/MgAl2O4 catalyst as that used in this study and investigated temperatures in the range of 773-848 K, which are typical of temperatures for SE-SMR. The rate expressions were obtained under pressurized conditions, and validity in the atmospheric carbonator-reformer is assumed. The rate expressions for reactions 1-3 are, respectively, given by

r1 )

k1 pH22.5

[

pCH4pH2O -

]

pH23pCO K1

[

]

/DEN2

(6)

pH2pCO k2 r2 ) pCOpH2O /DEN2 pH 2 K2 r3 )

[

k3 pH2

3.5

pCH4pH2O 2

]

pH24pCO2 K1K2

(7)

/DEN2

(8)

where

DEN ) 1 + KCOpCO + KH2pH2 + KCH4pCH4 +

KH2OpH2O pH2

The values of the kinetic parameters are listed in Table 1. Carbonation Reaction Kinetics. Several models and reaction rate expressions have been proposed for the carbonation of CaO.19-21 The ultimate conversion reported in the literature found by TGA for calcium-based sorbents varies from 60% to 100%. This great variation is associated with different morphologies of the sorbents. Pore blockage and buildup of a solid product layer retard the reaction at high conversions, so that complete conversion is never achieved for some sorbents. Rate equations for carbonation reactions in the literature differ greatly in form and complexity. For example, Lee20 proposed the simple rate expression

(

)

X dX )k 1dt Xu

2

where k is a kinetic rate constant and Xu is the ultimate conversion. This equation suggests that the rate of reaction is

independent of the partial pressure of CO2. Kyaw et al.21 studied the reaction rate for both calcite and dolomite, and they proposed

dX ) kx(1 - X)2/3(P - Pe)n dt where kx is a reaction rate constant, X the conversion at time t, P the partial pressure of CO2, and Pe the equilibrium partial pressure of CO2. The authors determined the reaction order to be n ) 0.1, whereas the activation energies of calcite and dolomite were ∼78 and 35 kJ/mol, respectively. Bhatia and Perlmutter19 found zero activation energy for the temperature range of 550-725 °C for the reaction-controlled regime by using a random pore model. A recent comprehensive literature review of carbonation models was provided by Stanmore and Gilot.22 Because of the unique morphology of different sorbents, rate expressions should be developed for the specific sorbent at hand. Literature values of diffusion constants and apparent activation energies could lead to huge errors for other sorbents. For this work, a shrinking core model23 (SCM) was chosen to describe the rate of carbonation. This choice was based on findings from scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM/EDS),24 where the concentration of oxygen at the exterior of a partially carbonated particle was determined to be approximately twice that in the interior, indicating that CO2 does not react uniformly throughout the particle. Further justification of the choice of the SCM model is given by Johnsen.24 To account for a nonlinear dependency of partial pressure, the SCM rate expression was modified to include a parameter, n:

r4 )

)

number of moles reacted s (m3 of dolomite) 3 1 (1 - XCaO)2/3 (PCO2 - PCO2,eq)n RP RT 1/3 2/3 2/3 1 RP[(1 - XCaO) - (1 - XCaO) ] (1 - XCaO) + + k4 De kg (9)

where De is the effective diffusivity (given in units of m2/s), Rp the particle radius (in meters), kg the external mass-transfer coefficient (expressed in terms of m/s), XCaO the conversion of CaO, and k4 the chemical reaction constant (given in units of m/s). Note that n accounts for the nonlinear partial pressure difference between CO2 in the bulk phase and the equilibrium pressure and should not be considered as a reaction order. By inspection, one can see that eq 9 contains a driving force in the numerator, represented by the difference between the partial pressure of CO2 and its equilibrium pressure at the reaction temperature. The denominator contains three resistances in series, with their relative importance varying as the reaction progresses. A major challenge with the shrinking unreacted core model is to specify the effective diffusivity, De. Zevenhoven et al.25 modeled the particle conversion of limestone and dolomite sulfidation, using a variable effective diffusivity. Because of the build-up of a solid product layer as the reaction proceeds, intraparticle transport of CO2 was strongly affected by the conversion. Their effective diffusivity accounts for both (i) diffusion in the pores of the particle (gas-phase diffusion and Knudsen diffusion) and (ii) diffusion through a solid product layer. The effective diffusivity can be described by

De ) De,0

(

)

1 + AXCaO 1 + BXCaO

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Table 2. Carbonation Reaction Rate Parameters parameter

value

k4,0 [m/s] Ea [kJ/mol] Dpl [m2/s] n

3.05 32.6 7.7 × 10-9 0.66

Table 3. Analysis of Arctic Dolomite SHB, Data from Franzefoss AS

where

A)

1 - 0 0

B)

ADpore Dpl

species

concentration [wt %]

CaO MgO SiO2 Al2O3 Fe2O3 Na2O TiO2 K2O loss by ignition

32 20.3 0.7 0.1 0.1 0.003 0.005 0.004 46.3

conversion after N cycles (XN) and the cycle number (N) was proposed:

XN ) fN+1 + b

and

(11)

Here, Dpore is the diffusivity in the pores (due to both gas-phase diffusion and Knudsen diffusion), 0 the porosity, τ the tortuosity factor, and Dpl the product layer diffusivity. The carbonation reaction rate constant (k4), which can be described as k4 ) k4,0 exp[-Ea/(RT)], and the product layer diffusivity (Dpl), and the value of n used in this study are listed in Table 2. These values were found experimentally from TGA for the Arctic dolomite sorbent. The thermogravimetric reactor was operated under nonisothermal conditions, and the kinetic parameters were obtained by fitting the conversion as a function of time, with multiple experimental temperatures as input.24 Figure 3 shows how the reaction rate expression from TGA predicts the CaO conversion as a function of time for three different CO2 partial pressures. The model seems to predict lower conversions (up to ∼30%) very well, whereas predictions at higher conversions are less reliable but still acceptable. However, solid residence times achieved in a circulating system may not be high enough for the entire sorbent particle to be utilized, because of the onset of the much slower diffusioncontrolled regime at higher conversions, which highlights the importance of the carbonation model at lower conversions. Sorbent Multicycle Capacity. Abanades26 reported that the decay in sorption capacity was strongly dependent on the number of carbonation/calcination cycles, and, to a lesser extent, the reaction conditions. A simple relationship between the CaO

where f and b are constants. This equation is used to describe the multicycle conversion of CaO in Arctic dolomite (Franzefoss A/S, Arctic Dolomite SHB) in this study. Composition data are given in Table 3. TGA was performed, with alternating carbonation and calcination, in a pure CO2 atmosphere at 850 and 925 °C, respectively. Ideally, steam should be used for calcination; however, CO2 was used for both carbonation and calcination, because of the lack of automatic operation of the gas flow controllers of the thermogravimetry reactor. The results appear in Figure 4. The loss of sorption capacity, as a function of carbonation/calcination cycling, is evident. The constants of eq 11 were determined to be f ) 0.82 and b ) 0.28 by fitting the experimental data. Model Assumptions. The following are simplifying assumptions for the reactor system in Figure 1: (a) Steady-state operation. (b) Both reformer and calciner/regenerator operate in the bubbling regime at ambient pressure. (c) Both reactors are isothermal, but they have different temperatures, T1 and T2. Gas and solids leave the reactor at the same temperature (T1 ) Ts,1 and T2 ) Ts,2). Heat loss associated with transfer of solids between the reactors is ignored, together with any other heat loss. (d) The reformer operates under autothermal conditions. All heat needed for the reforming/sorption reactions is supplied by the hot solids from the calciner. (e) The regenerator is assumed to be of the same size as the reformer. The volume of the calciner is sufficiently large to convert all CaCO3 entering the regenerator to CaO (Xcalc ) 1)

Figure 3. Comparison of experimental (points) and predicted (solid lines) conversions (average particle diameter, 250 µm; reactor temperature, 550 °C).

Figure 4. Loss of sorption capacity of CaO in dolomite as a function of the number of cycles (carbonation conditions: 850 °C in pure CO2 for 2 h; calcination conditions: 925 °C in pure CO2 for 3 h).

[

0 1 De,0 ) Dpore ) τ (1/D) + (1/DKn)

]

(10)

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4137 Table 4. Hydrodynamic and Mass-Transfer Relationships parameter

relationship

bubble size (evaluated at z ) 0.4Hmf)

( )

[

interfacial bubble area per unit volume

reference

-0.3z db ) dbm - (dbm - db0) exp dt 2.78 (U - Umf)2 where db0 ) g 0.4 π and dbm ) 0.65 dt2(U - Umf) 4 6 ab ) db

Mori and Wen28

]

U - Umf UA

voidage fraction of bubbles in bed

b )

absolute bubble rise velocity

UA ) 0.711xgdb + (U - Umf)

minimum fluidization velocity of a binary system

Ar )

Davidson and Harrison29

dp,mix3Ff(Fm - Ff)g

Wen and Yu30

µ2

dp,mixUmfFf ) [(33.7)2 + 0.0408Ar]0.5 - 33.7 µ ωc ωd 1 where ) + Fmix Fcat Fdolomite ωc ωd 1 and ) + Fmixdp,mix Fcatdp,cat Fdolomitedp,dolomite

at the given temperature. The fluidizing gas velocity in the reformer is set at 0.05 m/s. (f) The calciner temperature (T2) is calculated from the equilibrium pressure of CO2 for the calcination reaction, with 50 °C added to this temperature to ensure complete calcination. (g) Catalyst is not separated from the sorbent before entering the calciner. (h) The reaction rates are not affected by the number of reforming/calcination cycles. (i) A make-up flow of fresh sorbent is added to compensate for the loss of sorbent capacity, and the decay is described by eq 11 with f ) 0.82 and b ) 0.28, based on fitting of the experimental data, as noted previously. (j) The purge stream from the reformer is assumed to consist only of sorbent (no catalyst), requiring a dry classifier to be used in the process. Brun-Tsekhovoi et al.2 used relatively large dolomite particles to facilitate their physical separation from the catalyst. Model Equations. To solve the system that involves both catalytic reactions and a consumable solid, it is necessary to write separate mole balances for the gaseous phase and the solid phase. There are five gas species involved in the reactions, i.e., CH4, H2O, CO, CO2, and H2. The two-phase model of Orcutt et al.27 is used to model the reformer, because of its simplicity. This assumes the gas to be perfectly mixed in the dense phase, whereas it is in plug flow in the bubble phase. No reactions occur in the bubble phase (no solid present). Mass transfer between the two phases is represented by an interphase masstransfer coefficient, kq:

kq ) 0.75Umf +

0.975g0.25D0.5 db0.25

(12)

Goossens et al.31

βU dCib ) kq(Cid - Cib)abb dz (for i ) CH4, H2O, CO, H2, CO2) (14) where ab is the interfacial bubble area per unit bubble volume and b is the fraction of bed volume occupied by bubbles. The boundary condition is

Cib ) Ci,in

(at z ) 0)

For the dense phase, a mole balance over the entire phase gives

(1 - β)U(Ci,in - Cid) +

∫0H kq(Cib - Cid)abb dz )

(1 - b)(1 - mf)(1 - λ)HFCatRi (for i ) CH4, H2O, CO, H2) (15) CO2 is the only gas species consumed in the gas-solid reaction. Its rate of disappearance via the carbonation reaction must be included in the dense phase mole balance:

(1 - β)U(Ci,in - Cid) +

∫0H kq(Cib - Cid)abb dz )

(1 - b)(1 - mf)(1 - λ)HFCatRi + (1 - b)(1 - mf)λHR′i (for i ) CO2) (16) The reaction rates for the catalytic reactions are denoted by Ri, whereas the gas-solid reaction rate is designated by R′i. Using the rate expressions from Xu and Froment18 and carbonation reaction given as expression 9, we write the total generation and removal rates as

RCH4 ) -r1 - r3

The fraction of gas that is flowing through the bubble phase at any height is given by

RH2O ) -r1 - r2 - 2r3

U - Umf β) U

RH2 ) 3r1 + r2 + 4r3

(13)

Other hydrodynamic and mass-transfer correlations that have been used in this study are listed in Table 4. A differential mole balance for species i at any height in the bubble phase gives

RCO ) r1 - r2

RCO2 ) r2 + r3 R′CO2 ) -r4

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Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006

as an input to the other reactor. For component, i, without any phase change, the enthalpy at temperature T is given by

Table 5. Solid Stream Relationships to reformer [kg/s]

to calciner [kg/s]

Fs,2 ) Fs,0 + Fs,r FCaO,2 ) Fs,2YCaOXcalc

Fs,1 ) Fs,r FCaO,1 ) Fs,rYCaOXcalc(1 - XCaO)

FCaCO3,2 ) 0

FCaCO3,1 ) Fs,rYCaO

FMgO,2 ) Fs,2YMgO

FMgO,1 ) Fs,rYMgO

( )

Fc,2 ) Fs,r a

ωc )

ωc 1 - ωc

(1 - λ)Fcat (1 - λ)Fcat + λFdolo

a

H0i (T) ) H0i (298) +

( ) MCaCO3 MCaO

(XCaO)

Fc,1 ) Fc,2

Mole Balances. Calcined dolomite consists of CaO and inert material (mainly MgO) that is uniformly distributed in the dolomite pellet. Carbonation of the MgO is thermodynamically unfavorable at the high temperatures of the system, and, therefore, the magnesium is not considered to contribute to CO2 removal. YCaO and YMgO represent the weight percentages of CaO and MgO, respectively, in calcined Arctic dolomite. Fs,2 is the total mass flow of calcined dolomite from the calciner and is the sum of recycled sorbent (Fs,r) and fresh added sorbent (Fs,0). Fresh sorbent is introduced to the calciner as CaCO3‚ MgCO3 and must be fully calcined before entering the reformer. Therefore, the calcination of freshly added dolomite adds to the energy requirement of the calciner. The catalyst is not separated from the mixture before entering the calciner, so that the solid circulation includes the catalyst. The solid streams between the reactors are listed in Table 5. A mole balance on CaO in the solid dolomite continuously added and withdrawn from the reformer must be included:

number of moles CaO in - number of moles CaO out ) number of moles CaO reacted

(

)

1 FCaO,2 X ) -r4Vdolomite MCaO CaO

(17)

The CO2 conversion in the gas phase and solids conversion satisfies the equation

number of moles CO2 consumed ) number of moles CaO consumed XCO2(CCH4,in)UAc ) FCaO,2

( )

1 X MCaO CaO

(18)

The solid conversion is calculated based on the reaction kinetics. However, there is an upper limit for solid conversion, because the CaO sorption capacity dramatically decreases as a function of the number of cycles (as shown in Figure 4). The amount of fresh sorbent (Fs,0) to be added to the system is calculated from a population balance, combined with the empirical eq 11, based on the work of Abanades,26 and should satisfy the equation

XCaO )

fFs,0 Fs,0 + Fs,r(1 - f)

+b

(19)

If no fresh sorbent is added, this equation predicts that the steady-state conversion approaches 28%. Enthalpy Balances. Both reactors operate isothermally, and enthalpy balances are used to calculate the steady-state temperatures of the reactors. These balances must be solved simultaneously with the mole balances in an iterative manner, because the solid outlet temperature of each reactor is required

(20)

The heat capacity is a function of temperature expressed by

Cpi ) Ai + BiT +

.

∫298T Cpi dT Ci T2

+ D i T2

(21)

The constants in eq 21 are obtained from the thermodynamic software program HSC Chemistry (Outokumpu Research Oy, Finland). The enthalpy of the solids entering the reformer is calculated from

Hs,2 ) FCaO,2∆HCaO,2 + FCaCO3,2∆HCaCO3,2 + FMgO,2∆HMgO,2 + Fc∆Hcatalyst,2 (22) For the reformer, the enthalpy balance to be solved is

(Hs,1 + H1 + Hs,p) - (Hs,2 + H0,ref) + ∆Hrx,reformer ) 0 (23) where ∆Hrx,reformer is the sum of the heats of reaction for the endothermic reforming reactions,

∆Hrx,reformer ) VbedFcat‚(1 - λ)(1 - mf)(1 - b) × 3

∑j ∆Hrx,jRj + Vbed(λ)(1 - mf)(1 - b)R′4∆Hrx,4

(24)

with ∆Hrx,1 ) 206.2 kJ/mol, ∆Hrx,2 ) -41.1 kJ/mol, ∆Hrx,3 ) 164.9 kJ/mol, ∆Hrx,4 ) -178.8 kJ/mol, and ∆Hrx,5 ) -100.9 kJ/mol. For the calciner:

(Hs,2 + H2) - (H0,calc + Hs,1 + Hs,0) + ∆Hrx,calciner - Q ) 0 (25) The heat of reaction for ∆Hrx,calciner is the sum of the endothermic calcination reaction of CaCO3. Note that the heat of decomposition of MgCO3 (∆Hrx,5) is included for fresh dolomite that has been added to the system. Model Solution. The model consists of a set of highly nonlinear algebraic equations. Mole balances and enthalpy balances for both reactors were solved simultaneously to obtain steady-state solutions for the system. The calculation procedure was iterative, implemented in MATLAB. The numerical solution procedure is as follows: (i) Guess an initial temperature of solids entering the reformer from the calciner, Ts,2 (assumed equal to T2). (ii) Calculate T1 from the mole and enthalpy balances with the aforementioned temperature as input. (iii) Use calculated reformer temperature, T1, as input to the energy balance in the calciner to calculate an improved value of the calciner temperature T2. (No mole balance for the calciner is needed here, just the assumption that Xcalc ) 1.) (iv) Compare the calculated T2 from the energy balance with the initial guess value. A steady-state solution is reached when the calciner temperature is equal to the temperature of the solids entering the reformer. Unless otherwise stated, the reactor dimensions used in the previous batch experiments12 were applied for the calculations, as listed in Table 6. A SE-SMR unit has a limited number of independent variables, such as preheat temperature of gas feed, volumetric feed rates of solids to the reformer, and fresh sorbent addition

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4139 Table 6. Base Values from Previous Experimental Conditions12

a

parameter

value

total mass of particles in bed static bed height catalyst particle size range dolomite particle size range catalyst density calcined dolomite density reactor diametera

3.1 kg 0.3 m 150-250 µm 125-300 µm 2200 kg/m3 1540 kg/m3 0.1 m

For both reformer and calciner reactors.

rate. The steady-state reformer temperature (T1) is influenced by the circulation rate of solids, which, in turn, affects the gas conversion, CO2 capture efficiency, calciner heat requirements, etc. Although the process layout is rather simple, with only two interconnected vessels, the process is complex; proper design and operation require knowledge of the response to changes in the various process parameters. Evaluation Parameters. Product gas purity and dry gas hydrogen concentration are key parameters in evaluating the performance of the process. Other important parameters include hydrogen yield (moles hydrogen produced/moles methane fed), denoted as YH2, and carbon capture efficiency (moles CO2 captured/moles carbon fed), denoted as XCO2. The reformer efficiency is defined as in the work of Ryde`n and Lyngfelt,32 who compared chemical looping with conventional steam reforming. A H2-equivalent term, H2,eq, describes the amount of hydrogen remaining per mole of CH4 fed if all external heat and power demands were to be met using the produced H2 for heating and power production.

H2,eq ) YH2 - H2,calciner + H2,steam - H2,compression (26) Reformer efficiency is defined as

ηr ) H2.eq

( ) LHVH2

LHVCH4

(27)

where

H2,calciner ) H2,steam )

QH LHVH2

0.9QS LHVH2

and

H2,compression )

Qc LHVH2

QH is the heating demand of the calciner (J/mol CH4) and Qs is the heating excess of the streams entering and leaving the system. A steam generation efficiency of 90% is assumed. Qc is the electricity needed to compress the product gases (both H2 and CO2). If the process produces excess heat and power, then H2,eq exceeds the actual hydrogen product. The lower heating values (LHVs) for hydrogen and methane are 241.8 and 802.3 kJ/mol, respectively. Ryde`n and Lyngfelt assumed that the electrical energies required to compress CO2 and H2 are 15 and 13 kJ/mol, respectively, and these values have also been adopted in this study. Results and Discussion Effect of Sorbent Addition. Hydrogen concentration is predicted as a function of reactor length for three values of λ in

Figure 5. Effect of sorbent addition on hydrogen concentration (T1 ) 600 °C, steam-to-carbon (S/C) ratio of 3, fluid velocity (U) of 0.1 m/s).

Figure 5 for a reformer temperature of 600 °C, a steam-carbon ratio (S/C) of 3, and a superficial gas velocity of 0.1 m/s. An equilibrium dry hydrogen concentration of 73.8% is reached after traversing ∼0.07 m when no sorbent is added (λ ) 0). When sorbent is added to the reactor, the hydrogen concentration increases to 95.8% and 97.0% for λ ) 0.36 and λ ) 0.90, respectively, showing the shift in equilibrium product composition. A previous experimental investigation12 in a low-velocity bubbling bed reactor gave a dry hydrogen concentration of ∼98% for λ ) 0.36 under the same reaction conditions as those listed in Table 6. The underprediction by the model may be related to the hydrodynamic model, in particular, the fact that solids are not taken into account in the bubbles. Improved models are available,33,34 which include a small portion of the solids within the bubbles. However, given the predicted stabilization of all three curves, with regard to height, the difference between the predictions and experimental results in this case is primarily related to the equilibrium approached, not the kinetic model. The temperature in the freeboard region was hotter than the actual bed temperature for the experimental investigation, and additional reactions in this region of the reactor are likely to be the cause of the increased methane conversion. The relatively low ratio of λ ) 0.36 was chosen to give reasonable production times, because the experiments were conducted in batch mode. Previous workers, e.g., Ortiz and Harrison,4 used a dolomite-catalyst mass ratio of 2.2-2.7, corresponding to λ ≈ 0.8. To minimize the requirement for expensive catalyst, operation with high λ is desirable. For λ ) 0.90, a hydrogen concentration of 97% is predicted in the product gas. Further increases led to a decrease in the predicted hydrogen concentration, indicating that at least 10% catalyst (by volume) is required to maximize the hydrogen yield and reduce the catalyst cost. Our previous experimental batchwise investigation12 contains product composition data from the reformer as a function of time, with an observed “breakthrough” being observed to occur between 40 and 55 min for U ≈ 0.1 m/s. For this superficial gas velocity, the total carbon feed rate is calculated to 2.9 × 10-3 mol/s. Assuming that 95% of the carbon fed to the reformer is converted to CO2 and reacted to form CaCO3, the amount of unreacted sorbent at the point before the experimental breakthrough (40 min) is 280 g, corresponding to a solid conversion of 69%. Figure 6 shows the experimental hydrogen concentration, compared with model predictions, at different degrees of sorbent conversion using the steady-state model. The point of breakthrough at 55 min is also modeled, corresponding to 95%

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Figure 6. Experimental and predicted hydrogen concentrations (T1 ) 600 °C, S/C ) 3, U ) 0.1 m/s).

Figure 7. Effect of the S/C ratio on reformer hydrogen purity (λ ) 0.90, T1 ) 600 °C, U ) 0.1 m/s).

conversion. The predicted dry hydrogen outlet concentration is somewhat lower than the experimental for the pre-breakthrough period. However, the kinetics and model predictions are quite consistent with the batch experiments. Effect of the Steam-to-Carbon (S/C) Ratio. The effect of an increased S/C ratio on the outlet hydrogen concentration is shown in Figure 7. The ratio is varied over the range of 3-4, which is the likely range of interest to minimize carbon formation while not requiring excessive energy for steam generation. The hydrogen concentration is predicted to increase from 97.0% to 98.4% as the S/C ratio is varied from 3 to 4. This increase is related to the positive effect on the water-gas shift reaction (WGS) equilibrium, which favors the production of H2 and CO2. Increased CO2 partial pressure increases the rate of carbonation, further enhancing the steam reforming reaction. System Considerations. Based on the aforementioned findings, values of S/C ) 4 and λ ) 0.90 were chosen for the remaining simulations. The scale of the reformer/regenerator system was increased to a reactor diameter of 1 m, which is equivalent to a power output of ∼250 kW (H2-LHV based) at a superficial gas velocity of 0.1 m/s. The static bed height of the shallow bubbling bed was slightly increased to 0.35 m to compensate for bigger bubbles. The velocity of 0.1 m/s is low when considering the practical application of the process. However, the velocity is within the bubbling regime, suiting the hydrodynamic two-phase model. Higher velocities and other

Figure 8. (a) Reformer temperature, (b) solid conversion, and (c) dry hydrogen mole concentration in the reformer product gas, as a function of the circulation rate for S/C ) 4, λ ) 0.9, and T0,ref ) 250 °C.

fluidization regimes, e.g., fast fluidization (CFB reactors), would give higher gas throughput and be more attractive for largescale applications. The concentration of hydrogen in the reformer is dependent on the rate of reaction of the combined reactions, which are strongly related to reformer temperature and solid conversion. Increasing the solid circulation rate leads to increased reformer temperature as more hot solids are added from the calciner. Figure 8 shows how the reformer temperature, solid conversion, and dry hydrogen mole concentration in the product gas are affected by the increased circulation rate. Figure 8 shows that a reformer temperature in the range of 550-620 °C is optimal for obtaining a high hydrogen concentration in the product gas (>98%). To achieve this, the circulation rate of calcined dolomite must be within the 3-5 kg/min range for this size of reactor and a preheating temperature of 250 °C. The temperature effect on the combined reactions is rather complex. Increasing the temperature leads to an increased steam reforming reaction rate, whereas the rate of carbonation increases to a certain point before the reaction rate decreases, because of the decreased equilibrium constant (i.e., due to the reverse calcination reaction), as can be seen from the rate expression for carbonation (eq 9) used in the modeling, where the difference in partial CO2 pressure and the equilibrium pressure at the given temperature represents the driving force for reaction. The circulation rate not only influences the reformer temperature, but also the solid conversion (Figure 8b). Solid conversion is dependent on the residence time in the reformer, and a low solids conversion of 20%-30% is achieved for the circulation rates, giving the maximum hydrogen concentration observed at >98% H2. High circulation gives a low fractional conversion of the sorbent, in addition to increased temperature. The reformer temperature can also be adjusted by varying the reactant preheating. Using higher preheating temperatures (T0,ref), the circulation rate can be reduced to reach the optimum reaction temperature for the combined reactions. Figure 9 shows how the dry hydrogen concentration is affected by solid conversion and reformer temperature for two different preheating temperatures. The higher preheating temperature of 500 °C requires a lower solid circulation to achieve proper reaction temperatures; hence, a steady-state solid conversion of 50%-60% is reached at reforming temperatures close to 600 °C. For a preheating temperature of 250 °C, the same reforming temperature is reached at lower solid conversions of 20%-30%. The maximum hydrogen concentration is also somewhat higher for the lowest

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4141 Table 7. Process Parameters for T0,ref ) 250 °C, Steam-to-Carbon (S/C) Ratio of 4, and λ ) 0.90 solids circulation rate, Fs,2 [kg calcined dolomite/min] solid make-up ratio, fresh sorbent/recyled sorbenta T1 [°C] T2 [°C] XCaO XCH4 XCO2 H2 dry concentration [%] YH2 H2,calciner H2,steam H2,compression H2,eq ηr [%] a

Figure 9. Reformer temperature and dry hydrogen concentration in the reformer product gas, as a function of CaO conversion for preheating values, T0,ref, of 250 °C (solid line) and 500 °C (dashed line) (S/C ) 4 and λ ) 0.9).

Figure 10. Reformer efficiency and solid conversion, each as a function of circulation rate for S/C ) 4, λ ) 0.9, and T0,ref ) 250 °C.

preheating temperature. This can be understood by looking at the nature of the carbonation reaction, with a rapid initial reaction rate followed by a slower regime in which the rate is controlled by CO2 diffusion through the CaCO3 product layer. A reaction temperature of ∼600 °C can be maintained by adjusting the circulation rate of hot solids entering the reformer in combination with preheating of the feed gas. If an increased circulation rate is used to increase the reformer temperature, more heat must be supplied to the calciner, thereby reducing the total system efficiency. However, this leads to a lower sorbent conversion in the reformer, utilizing the fast reaction regime, and the need for fresh sorbent addition is reduced. The effect of circulation rate on solid conversion and reformer efficiency is shown in Figure 10. It seems that reformer efficiencies of ∼86% can be achieved for moderate circulation rates of calcined dolomite of 4-6 kg/min. Efficiencies are reduced at low circulation rates, because of the need to add more fresh sorbent to the calciner, requiring more heat to precalcine fresh dolomite. This is clearly seen in Figure 10, where there is a marked decrease in reformer efficiency for CaO conversions exceeding 28%. The MgCO3 in uncalcined dolomite also contributes to increased energy demand in the calciner, compared to the case where the sorbent is pure limestone. The reformer efficiency also is strongly dependent on the temperature difference between the reformer and calciner. A high reformer temperature reduces the energy needed to heat the solids to the

2.7

3.6

0.11

0.03

542 887 0.40 0.92 0.90 97.4 3.65 1.60 0.70 0.27 2.48 74.7

578 881 0.31 0.96 0.94 98.4 3.84 1.47 0.66 0.27 2.76 83.1

5.1

8.4

619 874 0.22 0.98 0.92 98.0 3.89 1.39 0.65 0.27 2.88 86.7

665 869 0.12 0.99 0.82 95.5 3.86 1.42 0.68 0.26 2.84 85.6

Based on calcined dolomite.

calcination temperature. However, the reformer temperature has an upper limit, as shown in Figure 8, because CO2 capture decreases as its equilibrium shifts toward calcination with increasing reformer temperature. The overall system performance for a preheat temperature of 250 °C, S/C ratio of 4, and λ ) 0.90 is presented in Table 7. This table shows that increasing the solids circulation rate causes the sorbent conversion (XCaO) to decrease, because of the shorter residence time in the reformer, whereas the temperature (T1) increases due to the increased flow of hot solids from the regenerator. The regenerator temperature (T2) always equals the thermodynamic equilibrium decomposition temperature of CaCO3 at the given partial pressure, with 50 °C added to this temperature, to ensure complete calcination, and therefore slightly decreases as the degree of carbonation is reduced, so that less CO2 is being released. The temperature difference between the reformer and calciner is critical for high system efficiencies. A higher temperature of the solids leaving the reformer means that less energy is needed for the calciner, hence increasing the efficiency. In addition, a lower CaO conversion means that less CO2 is released in the calciner, reducing its partial pressure and decreasing the carbonate decomposition temperature. Clearly there is a trade-off in choosing the reaction conditions if both high energy efficiencies and high purity of H2 are sought. This is a major motivation for exploring other sorbents, which could release CO2 at lower temperatures. The carbon capture efficiency is plotted as function of reformer temperature in Figure 11. The capture efficiency also is dependent, to some extent, on the sorbent conversion, as well as the temperature, and for a gas feed preheat temperature of 250 °C, the sorbent conversion ranges from 5 to 50% in the reformer temperature interval shown in Figure 11. Note that >90% of the carbon entering the reformer (assuming no carbon deposition on the catalyst) can be captured for reforming temperatures in the range of 540-630 °C. Fresh Sorbent Addition. Abanades26 incorporated a fresh sorbent make-up feed for CO2 capture from combustion flue gases when evaluating carbon capture efficiency and claimed that there would be a compromise between moderate recycling rates and low addition of fresh sorbent to achieve high capture efficiencies. Figure 10 clearly shows that the addition of fresh sorbent reduces the efficiency of the system. Initial calcination of the fresh dolomite requires the decomposition of MgCO3, partially nullifying the favorable multicycle properties of dolomites, compared to limestone. The addition of fresh sorbent is only required for lower circulation rates to give steady-state CaO conversions of >28%. However, the model suggests that

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Figure 11. Carbon capture efficiency (XCO2), as a function of reformer temperature for S/C ) 4, λ ) 0.9, and T0,ref ) 250 °C.

Figure 12. CaO conversion as function of the number of carbonationcalcination cycles.

circulation rates can be relatively high while maintaining highpurity hydrogen and reformer efficiency. Note that the 28% conversion limit in the current model is based on a limited number of thermogravimetry cycles (see Figure 4), and that a larger number of cycles is likely to give a lower conversion limit, which would require an increased addition of fresh sorbent to the calciner, reducing the energy efficiency. For example, if the conversion limit (b) were to be reduced from 28% to 10%, and the circulation rate of sorbent remained constant at 6 kg/ min, the reformer efficiency would be reduced from 86.6% to 72.1%. Separation of catalyst from sorbent between the reactors should be avoided, because this would add extra components and complexity to the system, lead to additional attrition, and cause extra heat losses. The catalyst density in the current study was 2200 kg/m3, whereas the sorbent density was dependent on the degree of carbonation, with a range from 1560 kg/m3 (fully calcined) to 2230 kg/m3 (completely carbonated), the latter being similar to the catalyst density. Therefore, efficient separation of catalyst from the sorbent purge is likely to be difficult, meaning that the addition of fresh sorbent should be minimized to reduce the loss of expensive catalyst from the purge stream. Ideally, the lifetime of the sorbent should be similar to the expected catalyst lifetimesmonths, or even years. Effect of Partial Carbonation. Abanades and Alvarez16 included previously published multicycle results when they reported an unavoidable decay in carbonation conversion that was dependent on the number of cycles. However, they did not consider any loss of absorption capacity if CaO is not fully carbonated upon cycling. In a continuous fluidized bed reformercalciner system, the degree of carbonation is strongly dependent on the circulation rate of solids, as shown by the model. TGA was used to investigate the effect of partial carbonation of CaO in Arctic dolomite. The condition of 10 cycles with the dolomite exposed to 10% CO2 for 80 min was utilized as a reference case (denoted by TG-1). Next, a new batch of dolomite was placed in the TGA apparatus and exposed to 10% CO2 for only 8 min (with 100% N2 for the remaining 72 min, to give the same total time of exposure) for the first 9 cycles, whereas, for the 10th cycle, the carbonation time was 80 min (referred to as TG-2a, where TG-2b is a replication). The carbonation temperature was 600 °C. Calcination was in a pure N2 atmosphere at 850 °C for both TG-1 and TG-2. The results of these experiments appear in Figure 12. The characteristic decay with cycling is observed for TG-1, with a final conversion of 48.4% for the 10th cycle. For TG-2, where the carbonation time was

8 min, a smaller decay is observed for the first nine cycles. This is probably due to somewhat slower reaction kinetics as the number of cycles increased. When carbonation proceeded for 80 min in the 10th cycle of TG-2, the CaO conversion increased to 77.4% and 82.2% for TG-2a and TG-2b, respectively; these values are significantly higher than the observed conversion of 44.8% after the same number of cycles in TG-1. The ultimate conversion seems to be strongly dependent on the carbonation history of the sample, with partial carbonation of the sorbent being favorable for maintaining the sorption capacity. The reason for this may be attributed to the structural properties of the dolomite, which experiences mechanical stresses when alternating between the oxide and fully carbonated states, with very different molar densities. This finding is important when evaluating sorbents for circulating systems where circulation rates are relatively high, with typical conversions of 20%-30% (see Figure 8), because it suggests that the sorbent can maintain its capacity much better, with partial carbonation, than if the entire sorbent is utilized. Conclusions Dry hydrogen concentrations of >98% can be achieved for temperatures of ∼600 °C and a superficial gas velocity of 0.1 m/s, using a simple two-phase bubbling bed model for the reformer, coupled with steam methane reforming and watergas shift reaction kinetics from the literature, combined with values that have been experimentally determined from the carbonation kinetics for Arctic dolomite. The model delineates important features of the system. Sorbent properties such as reactivity, multicycle capacity, and reformer temperature determine the overall process performance. The dolomite seems to be sufficiently reactive to approach the equilibrium hydrogen concentration for the gas velocity used. The catalytic reactions are faster than the gas-solid carbonation reaction. A mixture that contains 10% catalyst is predicted to obtain maximum hydrogen yield for the reactor conditions that have been investigated. The reformer temperature should not be less than 540 °C nor greater than 630 °C to achieve carbon capture efficiencies of >90%. The multicycle capacity of natural sorbents such as dolomites is rather poor, such that fresh sorbent must be added to the system to reduce the recycle flow. Operating at a relatively high circulation rate is calculated to give the highest system efficiencies, because the reaction rate of natural sorbents is slow at high conversions, compared to the initial carbonation stage, whereas the addition of fresh

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dolomite requires energy to decompose both CaCO3 and MgCO3. The addition of fresh sorbent is also likely to result in catalyst loss in the purge stream, requiring sorbents with lifetimes comparable to those of the catalyst. Further work is required on the cycling capacity property of dolomites and other sorbents, in particular, with respect to the sorption capacity after many more cycles than investigated in the current study or found in the literature, because of the importance of the conversion limit, with respect to the practicality and optimization of the sorption-enhanced reforming process. Notation ab ) interfacial bubble are per unit volume [m-1] Ac ) cross-sectional area of reformer [m2] Ci,b ) molar concentration in bubble phase [mol/m3] Ci,d ) molar concentration in dense phase [mol/m3] db ) bubble diameter [m] D ) gas-phase diffusivity [m2/s] De ) effective diffusivity [m2/s] DKn ) Knudsen diffusivity [m2/s] dp,catalyst ) average particle diameter of catalyst [m] dp,dolomite ) average particle diameter of dolomite [m] dp,mix ) average particle diameter of mixture [m] Dpl ) product layer diffusion constant [m2/s] dt ) diameter for bed [m] Fs ) sorbent circulation rate [kg dolomite/s] g ) acceleration of gravity [m/s2] H ) enthalpy of streams [J/mol] Hmf ) bed height at minimum fluidization velocity [m] H2,eq ) hydrogen yield [mol H2/(mol CH4)] KE ) equilibrium constant for carbonation [atm-1] kg ) external mass transfer coefficient [m/s] kq ) interphase mass transfer constant [m/s] k4 ) rate constant of carbonation [m/s] k4,0 ) Arrhenius constant [m/s] LHV ) Lower Heating Value [kJ/mol] QH ) heating demand of calciner [J/(mol CH4)] Qs ) heating demand/excess of streams [J/(mol CH4)] Qc ) energy of compression [J/(mol CH4)] PEq ) equilibrium partial pressure of CO2 [atm] PCO2 ) partial pressure of CO2 [Pa] PCO2,eq ) equilibrium partial pressure of CO2 [Pa] R ) gas constant [J mol-1K-1] Rp ) sorbent particle radius [m] r1, r2, r3 ) reaction rate of catalytic reactions [kmol (kg-cat h)-1] r4 ) rate of carbonation [mol (m3 dolomite s)-1] T1 ) reformer temperature [°C] T2 ) calciner temperature [°C] U ) superficial gas velocity [m/s] UA ) bubble rise velocity [m/s] Umf ) minimum fluidization velocity [m/s] Vdolomite ) total volume of calcined dolomite in reformer [m3] XCaO ) conversion of CaO in reformer XCalc ) conversion of CaCO3 in calciner YCaO, YMgO ) weight percentage in Arctic dolomite z ) vertical coordinate [m] Greek Letters 0 ) initial voidage of calcined dolomite  ) voidage of static bed height b ) voidage of bubbling bed λ ) volumetric ratio of sorbent [m3 sorbent/m3 total solid] β ) gas fraction in bubble phase

Fcat ) density of catalyst [kg/m3] Fdolo ) density of Arctic dolomite [kg/m3] Fmix ) density of catalyst-dolomite mixture [kg/m3] Ff ) density of gas in bed [kg/m3] ηr ) reformer efficiency µ ) gas viscosity [Pa s] ωc ) weight fraction of catalyst ωd ) weight fraction of dolomite Subscripts 0 ) fresh make-up p ) purge flow Acknowledgment This work was financially supported by the Research Council of Norway (RCN). Literature Cited (1) Balasubramanian, B.; Ortiz, A. L.; Kaytakoglu, S.; Harrison, D. P. Hydrogen from methane in a single-step process. Chem. Eng. Sci. 1999, 54, 3543. (2) Brun-Tsekhovoi A. R.; Zadorin, A. N.; Katsobashvili, Ya. R.; Kourdyumov, S. S. The Process of Catalytic Steam Reforming of Hydrocarbons in the Presence of Carbon Dioxide Acceptor. In Hydrogen Energy Progress VII; Proceedings of the World Hydrogen Energy Conference; Pergamon Press: New York, 1988; p 885. (3) Han, C.; Harrison, D. P. Simultaneous shift reaction and carbon dioxide separation for the direct production of hydrogen. Chem. Eng. Sci. 1994, 49, 5875. (4) Ortiz, A. L.; Harrison, D. P. Hydrogen production using sorptionenhanced reaction. Ind. Eng. Chem. Res. 2001, 40, 5102. (5) Silaban, A.; Harrison, D. P. High-temperature capture of carbon dioxide: Characteristics of the reversible reaction between CaO(s) and CO2(g). Chem. Eng. Commun. 1995, 137, 177. (6) Silaban, A.; Narcida, M.; Harrision, D. P. Characteristics of the reversible reaction between CO2(g) and calcined dolomite. Chem. Eng. Commun. 1996, 146, 149. (7) Kato, M.; Nakagawa, K. New series of Lithium containing complex oxides, Lithium silicates, for application as a high-temperature CO2 absorbent. J. Ceram. Soc. Jpn. 2001, 109 (11), 911. (8) Lee, D. K.; Baek, I. H.; Yoon, W. L. Modeling and simulation for the methane steam reforming enhanced by in situ removal utilizing the CaO carbonation for H2 production. Chem. Eng. Sci. 2004, 59, 931. (9) Xiu, G.; Li, P.; Rodrigues, A. Sorption-enhanced reaction process with reactive regeneration. Chem. Eng. Sci. 2002, 57, 3893. (10) Ding, Y.; Alpay, E. Adsorption-enhanced steam methane reforming. Chem. Eng. Sci. 2000, 55, 3929. (11) Prasad, P.; Elnashaie, S. S. E. H. Novel circulating fluidized-bed membrane reformer using carbon dioxide sequestration. Ind. End. Chem. Res. 2004, 43, 494. (12) Johnsen, K.; Ryu, H.-J.; Grace, J. R.; Lim, J. Sorption-Enhanced Steam Reforming of Methane in a Fluidized Bed Reactor with Dolomite as CO2sAcceptor. Chem. Eng. Sci. 2006, 61, 1195-1202. (13) Elnashaie, S. S. E. H.; Adris, A. M. In Fluidization VI; Grace, J., Shemilt, L. W., Bergougnou, M. M., Eds.; Engineering Foundation: New York, 1989; p 318. (14) Ortiz, A. L.; Harrison, D. P. Hydrogen production using sorptionenhanced reaction. Ind. Eng. Chem. Res. 2001, 40, 5102. (15) Baker, E. H. The calcium oxide-carbon dioxide system in the pressure range 1-300 atm. J. Chem. Soc. 1962, 70, 464. (16) Abanades, J. C.; Alvarez, D. Conversion limits in the reaction of CO2 with lime. Energy Fuels 2003, 17, 308. (17) Abanades, J. C.; Rubin, E. S.; Anthony, E. J. Sorbent Cost and Performance in CO2 Capture Systems. Ind. Eng. Chem. Res. 2004, 43, 3462. (18) Xu, J.; Froment, G. F. Methane steam reforming, methanation and water gas shiftsI. Intrinsic kinetics. AIChE J. 1989, 35, 88. (19) Bhatia, S. K.; Perlmutter, D. D. Effect of the product layer on the kinetics of the CO2-lime reaction. AIChE J. 1983, 29, 79. (20) Lee, D. K. An apparent kinetic model for the carbonation of calcium oxide by carbon dioxide. Chem. Eng. J. 2004, 100, 71. (21) Kyaw, K.; Kanamori, M.; Matsuda, H.; Hansatani, M. Study of carbonation reaction of Ca-Mg oxides for high-temperature energy storage and heat transformation. J. Chem. Eng. Jpn. 1996, 29, 112.

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(22) Stanmore, B. R.; Gilot, P. Reviewscalcination and carbonation of limestone during thermal cycling for CO2 sequestration. Fuel Process. Technol. 2005, 86, 1707-1743. (23) Levenspiel, O. Chemical Reaction Engineering; Wiley: New York, 1972. (24) Johnsen, K. Sorption-enhanced steam methane reforming in fluidized bed reactors. PhD thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, to be published 2006. (25) Zevenhoven, C. A. P.; Yrjas, K. P.; Hipa, M. M. Hydrogen sulfide capture by limestone and dolomite at elevated pressure. 2. Sorbent particle conversion modeling. Ind. Eng. Chem. Res. 1996, 35, 943. (26) Abanades, J. C. The maximum capture efficiency of CO2 using a carbonation/calcination cycle of CaO/CaCO3. Chem. Eng. J. 2002, 90, 303. (27) Orcutt, J. C.; Davidson, J. F.; Pigford, R. L. Reaction time distributions in fluidized catalytic reactors. Chem. Eng. Prog. Symp. Ser. 1962, 58 (38), 1. (28) Mori, S.; Wen, C. Y. Estimation of Bubble Diameter in Gaseous Fluidized Beds. AIChE J. 1975, 21, 109. (29) Davidson, J. F.; Harrison, D. Fluidized Particles; Cambridge University Press: New York, 1963.

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ReceiVed for reView October 21, 2005 ReVised manuscript receiVed March 31, 2006 Accepted April 13, 2006 IE0511736