Numerical Investigation of Sorption Enhanced Steam Methane

Ind. Eng. Chem. Res. 2010, 49, 1561–1576

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Numerical Investigation of Sorption Enhanced Steam Methane Reforming Process Using Computational Fluid Dynamics Eulerian-Eulerian Code A. Di Carlo,* E. Bocci, F. Zuccari, and A. Dell’Era CIRPS-InteruniVersity Research Center for Sustainable DeVelopment, UniVersity of Rome “La Sapienza”, Rome, Italy

This paper highlights the use of a fluidized bed reactor of 10 cm i.d. for producing hydrogen by sorptionenhanced steam methane reforming (SE-SMR). The model used for the hydrodynamic behavior of the bed is Eulerian-Eulerian. The kinetics of the steam methane reforming, water-gas shift, and carbonation reactions are based on literature values. Intra- and extraparticle mass transfer effects are considered together with the kinetics in the chemical models. The bed is composed of an Ni catalyst and calcined dolomite. A static bed height of 20 cm is investigated. A volume ratio of dolomite/catalyst is varied from 0-5 during the simulation. Dry hydrogen mole fraction of >0.93 is predicted for temperatures of 900 K and a superficial gas velocity of 0.3 m/s with a dolomite/catalyst ratio >2. Furthermore, the bubble formation in the fluidized bed influence product yields and product oscillations are observed. Another important aspect is that when the dolomite/ catalyst ratio is higher than 2 the necessary heat for the reforming endothermic reaction can be almost entirely supplied by the exothermic reaction of carbonation. Introduction Hydrogen is considered to be an important potential energy carrier; however, its advantages are unlikely to be realized unless efficient means to produce it with reduced generation of CO2 can be found. Sorption-enhanced steam methane reforming (SE-SMR) is a potential route to energy efficient hydrogen production with CO2 capture. The reactions with CaO as sorbent are CH4 + H2O S 3H2 + CO - 206.2 kJ/kmol

(1)

CO + H2O S H2 + CO2 + 41.2 kJ/kmol

(2)

CaO + CO2 S CaCO3 + 178 kJ/kmol

(3)

when a kinetic approach is used the following reaction must also be considered: CH4 + 2H2O S 4H2 + CO2 - 165.0 kJ/kmol

(4)

CO2 is converted into 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 reaction 3) releases relatively pure CO2, suitable for geological and deep-ocean storage or industrial usage. The CaO-CO2 reaction has been found to consist of two stages, a fast stage followed by an extremely slow stage.1 As the reaction produces an expanded solid product, the slow stage is believed to be controlled by product-layer diffusion. The sudden change from a fast to a slow stage of reaction is of interest with respect to CaO-based sorbents for CO2 removal. Alvarez and Abanades1 attributed the sharp transition to a critical thickness of the product layer. The findings of Abanades and Alvarez2 suggest that the pore size distribution plays a crucial role for the CaO-CO2 reaction. When the pore size distribution changes during calcination/carbonation cycles, the reactivity of the sorbent is altered accordingly. The proportion of the maximum conversion attributable to the reaction-controlled * To whom correspondence should be addressed. E-mail: [email protected].

phase diminishes with the number of capture-and-release cycles due to a change in the particle morphology resulting from sintering. Thus, the maximum conversion achieved during carbonation of a fixed duration decreases with cycle number as it is limited by the rate of conversion during the (slow) diffusioncontrolled phase. Bhatia and Perlmutter3 first suggested that the diffusion-controlled phase may involve a solid-state mass transfer mechanism. Strategies for enhancing multicycle performance include steam hydration and thermal treatments (e.g., the works of Manovic and Anthony4,5 and Lysikov et al.6). In the work of Kuramoto et al.,7 an intermediate hydration treatment was found to enhance the reactivity and durability of the sorbents for multicycle CO2 sorption. Because of the presence of eutectics in the CaO-Ca(OH)2-CaCO3 ternary system, the formation of sorbent melts was observed in repetitive calcination-hydration-carbonation reactions at elevated pressures at 923 and 973 K. Even under eutectic conditions, the sorbents retained their high reactivity for CO2 sorption. Tailored CaO-based sorbents, whereby the active material is supported on high surface area solids, such as alumina (Al2O3) or mayenite (Ca12Al14O33) have also been proposed (e.g., the works of Li et al.8 and Feng et al.9). In order to be competitive with the alternative strategy of simply using large quantities of limestone, tailored sorbent materials must achieve a significantly enhanced average conversion through a much larger number of cycles, in order to offset the economic penalties associated with their manufacture. For example, Li et al.10 estimated that CaO/Ca12Al14O33 (75/25 wt %) was approximately on par with CaO in terms of the cost of electricity and CO2 mitigation for coal combustion with CO2 removal from the flue gas. Calcium-based natural sorbents have the advantage of being low cost and readily available, but as mentioned previously, they have been proven to be unable to maintain their capture capacity over multiple reforming/regeneration cycles.11 Recently, it has been reported that lithium-containing materials (mainly Li2ZrO3 and Li4SiO4) are promising candidates with high CO2 capture capacity and high stability. Numerical studies have already been carried out with these new sorbents by Rusten et al.,12,13 Ochoa-Fernandez et al.14 and Lindborg et al.15 However, kinetic limitations are still the main drawback as

10.1021/ie900748t  2010 American Chemical Society Published on Web 01/19/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010

shown by Ochoa-Fernandez et al.14 Furthermore, the cost of synthetic sorbents, such as Li2ZrO3, would require them to sustain >10 000 cycles to compete with natural sorbents.11 The sorbent used in this study is instead dolomite, because of its favorable multicycle properties, compared to calcite. Initial calcination completely decomposes both the MgCO3 and CaCO3; however, the 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. In any case, dolomite does not show such high stability compared with synthetic sorbents and also demonstrates fragmentation behavior at elevated temperature, but its low cost makes it preferable for this study. Considering that only CaO is 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. Regarding modeling of SE-SMR using Ca-based sorbents, Lee et al.16 modeled the transient behavior in a packed-bed reactor, using their own apparent kinetics that were determined using thermogravimetric analysis (TGA) for carbonation. Xiu et al.17 developed a model for separation- enhanced steam reforming, using a pressure swing adsorption (PSA) system with a hydrotalcite-based CO2 sorbent. Ding and Alpay18 investigated a tubular reactor, both experimentally and theoretically, for the enhanced steam reforming reaction, again using a hydrotalcite based CO2 sorbent and a nonlinear (Langmuir) adsorption equilibrium. Fixed-bed reactors are the predominant type 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 the 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 operate in different flow regimes such as bubbling or fast fluidization. Prasad et al.19 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 a reformer and found that increasing the CaO particle size, by implementing a slip-factor to their model, gave a 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 fast fluidized beds, as well as low rates of attrition, because of low gas and particle velocities. Johnsen et al.20 conducted an experimental investigation on a bubbling fluidized-bed reactor. 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 873 K and 1 atm, with Arctic dolomite as the CO2 acceptor. On the basis of the reforming conditions used in the reformer of the experimental study, a steady-state model of a dual bubbling fluidized bed reactor system was then investigated21 using the Davidson bubble model22 in order to consider the interaction between the bubble and emulsion phase. The aim of this work, by contrast, is to evaluate the behavior of the fluidized bed reformer/carbonization reactor in an unsteady state condition using the recent CFD Eulerian-Eulerian (E-E)23 multiphase model, adopting the above-mentioned calcined dolomite as sorbent. The kinetic and mass transfer effect of the reforming and carbonization reaction are therefore

Figure 1. Schematic representation of a fluidized bed reactor.

interfaced with the hydrodynamic E-E model in order to consider the interaction between the emulsion and bubble phases and to assess the influencing factor for the bubble formation in the reaction yields (gas bypass, reaction products decreasing due to the low contact between reagent, catalyst, and sorbent). Reactor Configuration A schematic illustration of a continuous SE-SMR process, based on a bubbling fluidized bed reformer (BFBR), appears in Figure 1. The reforming catalyst and CO2 acceptor particles are mixed in the reformer. The catalyst is a commercial, nickel-based steam reforming catalyst ground to a mean particle diameter of 300 µm. The reformer was fed with methane and steam. Fluidized beds permit the use of smaller particles than fixed beds, hence overcoming diffusion limitations. However, the fluidization properties of the catalyst/sorbent mixture must be considered when deciding the particle diameters, to minimize segregation. Sorbent density can vary during the process between 1580 and 2300 kg/m3, and catalyst density is in the range of 2000-2200 kg/m3. Segregation can be avoided by also choosing a diameter of 300 µm for calcined dolomite. In fluidized beds, the 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 2 and 3) are slightly exothermic, reducing the heat required by the reformer. The resulting gas products from the reformer/ carbonator mainly consist of hydrogen and steam, with only minor quantities of CO, CO2, and unconverted CH4. A batch reactor is considered in this study. In particular, the sorbent and catalyst are continuously invested by the mix of methane and steam but no solid recirculation is considered: hence, only reforming/carbonization has been considered in this work. The desorption reaction has not been considered since it shows a faster kinetic. While this fundamental stage will certainly be studied in future research, it remains beyond the scope of this study. An adiabatic condition is considered at the reactor wall to evaluate to what extent the reactions are exothermic or endothermic. This is achieved by monitoring the increase or decrease


of the outlet gas temperature and temperature distribution in the reactor. The use of one particle as sorbent and catalyst, as depicted in similar study developed by Lindborg et al.,15 would be preferable; internal resistance to mass transport would be reduced. Satrio et al.24 previously prepared small spherical pellets having a layered structure such that each pellet consists of a highly reactive lime or dolime core enclosed within a porous but strong protective shell made of alumina in which a nickel catalyst was loaded. The material served two functions catalyzing the reaction of hydrocarbons with steam to produce hydrogen while simultaneously absorbing carbon dioxide formed by the reaction. In the work of Martavaltzi and Lemonidou,25 a new hybrid material, NiO-CaO-Ca12Al14O33, for application in SE-SMR has been synthesized. Development of a particle that can work at the same time as both sorbent and catalyst is a promising technology. Further numerical and experimental tests at the particle and microreactor level should certainly be carried out to prove this technology and to apply it at the benchscale and industrial fluidized bed level. In this research the use of two different particles was preferred for the two different purposes: Ni/MgAl2O4 as a catalyst for steam methane reforming and calcined dolomite as sorbent for CO2 capture. The use of a multifluid model for enabling the distinction of particles with different physical and chemical properties is therefore necessary as also confirmed by Lindborg et al.15 For instance differentiation between catalytic and CO2-accepting particles may introduce an extra diffusional limitation in the transport of CO2 from the catalyst to the sorbent which may in turn affect conversion.15

1563

where ε is the volume fraction of each phases, V the velocity vector, and F the density. Mass exchanges between phases m ˙ i, due to the carbonation reaction are explained below. The momentum balance for the gas phase is given by the Navier-Stokes equation, modified to include an interphase momentum transfer term. Due to CO2 capture reaction, mass is transferred from the gas phase to the dolomite phase. This affects the continuity equation (eq 5) and a source (or sink) term must be considered for both phases. At the same time, the mass transfer from the gas phase to the dolomite phase varies the phase momentum and a source (or sink) term in the momentum transport equation must be also considered (see the work of Gidaspow23). The approach illustrated in ref 26 was adopted in this work. The gas momentum balance is ∂ (ε F Vj ) + ∇ · (εgFgVjgVjg) ) ∇ · τg + εgFggj - εg∇p ∂t g g g βgs(Vjg - Vjs) - m ˙ gVjg

∑

(6)

s)c,d

Where g refers to the gas phase, c, to the catalyst, and d, to the dolomite solid phases, p is the thermodynamic pressure, β is the interface momentum transfer coefficient, and τg is the gas phase viscous stress tensor. The solid phase momentum balance for dolomite is ∂ (ε F Vj ) + ∇ · (εsFsVjdVjd) ) ∇ · τs + εsFsgj - εs∇p - ∇pd ∂t s s d βdj(Vjd - Vjj) + m ˙ gVjg (7)

∑

j)g,c

Model The model adopted is based on the fundamental concept of interpenetrating continua for multiphase mixtures. According to this theory, different phases can be present at the same time in the same computational volume. Such an idea is made possible by the introduction of a new dependent variable, the concentration, εi, of each phase i. In this study, the phases considered were the gas phases and two particle phases: one for the catalyst particles and a second one for the dolomite particles. The fundamental equations of mass, momentum, chemical species, and energy conservation are then solved for each considered phase. Appropriate constitutive equations must be specified in order to describe the physical rheological properties of each phase and to complete the conservation equations. In this model, solids viscosity and pressure are derived by considering the random fluctuation of particle velocity and its variations due to particle-particle collisions and the actual flow field. Such a random value of kinetic energy, or granular temperature, can be predicted by solving, in addition to the mass and momentum equations, a fluctuating kinetic energy equation for the particles. Solids viscosity and pressure can then be computed as a function of granular temperature at any time and position. Particles are considered smooth, spherical, inelastic, and undergoing binary collisions. The adoption of the second approximation distribution function allows us to apply the theory to both dense and diluted two-phase flows. A more complete discussion of the implemented kinetic theory model can be found in the work of Gidaspow.23 Hydrodynamic Model. The accumulation of mass in each phase is balanced by the convective mass flow and the source term due in this case to the CO2 capture and CaCO3 formation (i ) gas, solid(catalyst), solid(dolomite)): ∂ (ε F ) + ∇ · (εiFiVji) ) m ˙i ∂t i i

(5)

The solid phase momentum balance for the catalyst is ∂ (ε F Vj ) + ∇ · (εsFsVjcVjc) ) ∇ · τs + εsFsgj - εs∇p - ∇pc ∂t s s c βcj(Vjc - Vjj) (8)

∑

j)g,d

Where s refers to the solid phases (catalyst, c, and dolomite, d). The conservation of energy for the three phases are for gas, g, catalyst, c, and dolomite, d: ∂ ∂p + τ¯ i:∇ · Vji + ∇ki∇Ti + (ε F H ) + ∇ · (εiFiVjiHi) ) -εi ∂t i i i ∂t [hij(Tj - Ti) - βij(Vjj - Vji)2] + Sk∆Hk (9)

∑

∑

i*j

k

Where H is the specific enthalpy of the different phases, k is the thermal conductivity, h is the convection coefficient between phases, T is the temperature of the phases, and S is the rate of the reactions which occur in the different solid phases: • reactions 1, 2, and 4 in catalyst particles • reaction 3 in dolomite particles Lastly ∆H is the heat of reaction. The fluctuation energy conservation of solid phases (dolomite and catalyst) is 3 ∂ (ε F Θ ) + ∇ · (εsFsVjsΘs) ) (-psjI + τ¯ s):∇ · Vjs + 2 ∂t s s s ∇ · (kΘs∇Θs) - γΘs

[

]

(10)

Where Θ is the granular temperature of dolomite and catalyst, kΘ is the diffusion coefficient for granular temperature, and γΘ is the collision dissipation of energy. Constitutive equations are required to complete the governing relations. The momentum

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Table 1. Drag Coefficient

Table 2. Constitutive Equations for Internal Momentum Transfer

Gidaspow drag coefficient 3 εsεgFg · |Vjg - Vjs | -2.65 εg βgs ) CD 4 ds

βgs ) 150

εs2µg εsds2

+ 1.75

εsFg |Vjg - Vjs | ds

solid phase stress tensor 2 τ¯ s ) εsµs(∇Vjs + ∇VjsT) + εs λs - µs ∇ · VjsjI 3

(

for εg g 0.8

[ ( )]

g°ss ) 1 -

24 [1 + 0.15(εgRes)0.687] εgRes

and Res )

with s ) c, d

radial distribution function for εg < 0.8

where CD )

)

Fgds |Vjg - Vjs | µg

1/3 -1

εs εs,max

diffusion coefficient of granular temperature (Gidaspow)

kΘs )

150Fsds√πΘs 6 1 + εsg°ss(1 + ess) 384(1 + ess)g°ss 5

[

2

]

+ 2Fsdsεs2g°ss(1 + ess)

Θs π

collision dissipation energy symmetric Syamlal and O’Brien

βdc )

3(1 + edc)

(

8

)

γΘs )

π fr π + Cdc ε ε F F (d + dc)2g°dc 2 4 c d c d d |Vjd - Vjc | 2π(Fddd3 + Fcdc3)

where

12(1 - ess2)g°ss ds√π

Fsεs2Θs3/2

solid pressure ps ) εsFsΘs + 2Fs(1 + ess)εs2g°ssΘs

fr Cdc

) coefficient of friction between particle phases solid shear viscosity g°dc ) radial distribution of particle phases µs ) µscoll + µskin

exchange coefficients can be calculated by specifying drag functions. In this study, the Gidaspow23 model for gas-solid phases interaction was applied while the symmetric Syamlal and O’Brien27 model was applied for the solid-solid phase interaction. The correlations for momentum exchange coefficients are provided in Table 1. Other constitutive equations are summarized in Table 2. Regarding thermal conductivity, a modification of the form proposed by Kuipers et al28 was applied in order to use it for two solid phases (catalyst and dolomite) and one gas phase. Regarding heat transfer coefficient, a correlation proposed by Gunn29 for granular flows was chosen (see Table 3. Values of 0.9 were selected for the restitution coefficients of dolomite and catalyst. Values of 0.9 can give good predictions of fluidized bed behavior as demonstrated by Lindborg et al30 and Taghipour et al.31 Chemical Model Reforming. In order to compute the kinetic expression of catalyzed reactions, various processes which act as resistances to the reactions must be considered. For a single porous particle, these are • Gas film layer resistance: reagents and products diffused from the gas to the external surface or from the external surface to the gas of the catalytic particle, respectively. • Pore diffusion resistance: As the interior of the particle contains the highest catalytic surface area, the reactions occur primarily inside the particle. Reagents and products must diffuse inside the particle.

solid collision viscosity

( )

Θs 4 µscoll ) εsFsdsg°ss(1 + ess) 5 π

1/2

kinetic viscosity (Gidaspow)

µskin )

10Fsds√Θsπ 4 1 + g°ssεs(1 + ess) 96εs(1 + ess)g°ss 5

[

2

]

bulk viscosity

( )

Θs 4 λs ) εsFsdsg°ss(1 + ess) 3 π

1/2

• Surface phenomena resistance: the reagents moving inside the catalyst must be absorbed on a solid surface and react following the kinetic mechanism, and then, the products must be deabsorbed from the solid surface to the gas phase. The three phenomena are summarized in Figure 2. As shown in Figure 2, the gas film layer resistance can be considered in series, with the parallel composed of pore diffusion resistance and surface phenomena resistance. Therefore to consider the different mechanisms, two types of the same chemical species must be considered one in the gas phase (g) and the other in the solid-catalyst phase (c). The following chemical species balance can be derived:

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010 Table 3. Constitutive Equations for Internal Heat and Mass Transfer

Dm(g) )

thermal conductivity28

kg )

kc,d

Γ)

kg0 (1 - √εc + εd) εg

k0g

,

B ) 1.25

( ) εc,d εg

10/9

,

)

dp

2

)

1 1 1 + Mm(g) Mn(g) pσ 2Ω mn mn

(14)

Sc )

6 dc

(15)

Finally hm(gc) is the mass transfer coefficient deduced using the Ranz-Marshall correlation:

heat transfer coefficient hsg )

T3

where the expressions to calculate the required parameters can be found in the work of Bird.34 Sc is the catalyst surface per unit volume:

ω ) 7.26 × 10-3

29

6kgεsεgNus

∑

(

Dmn(g) ) 0.0018583

0 kc,d ) (ωA + (1 - ωΓ)) εc,d

(

0 kc,d

(13)

The binary diffusion coefficient Dmn(g) has been calculated using the Chapman-Enskog33 equation:

B-1 1 2 A-1 B B ln - (B + 1) 1 - B/A (1 - B/A)2 A A 1 - B/A 2

A)

1 yn(g) D n*m mn(g)

1565

hm(gc)dc ) 2 + 0.6(Sc)1/3(Res)1/2 Dm(g)

where s ) c, d

Nus ) (7 - 10εg + 5εg2)(1 + 0.7Res0.2Pr1/3) + (1.33 - 2.4εg + 1.2εg2)Res0.7Pr1/3

∂ (ε F y ) + ∇ · (εgFgVjgym(g)) ) ∇ · (εgFgDm(g)∇ym(g)) + ∂t g g m(g) Fghm(gc)Sc(ym(c) - ym(g)) (11) where m ) H2, H2O, CH4, CO. While for CO2, another source (Scarb) term must be considered due to capture the reaction: ∂ (ε F y ) + ∇ · (εgFgVjgyCO2(g)) ) ∇ · (εgFgDCO2(g)∇yCO2(g)) + ∂t g g CO2(g) Fghm(gc)Sc(yCO2(c) - yCO2(g)) + Scarb (12)

The Scarb term will be discussed in the next section. The terms yg and yc refer to the mass fraction of species m in the gas phase (g) and in the solid-catalyst phase (c), respectively, Dm(g) is the effective diffusion coefficient of the species in bulk, calculated using the Wilke32 equation:

(16)

A simpler model to consider pore diffusion resistance and surface phenomena is based on the calculation of a so-called effectiveness factor. The effectiveness factors ηk are found from simulations of catalyst particle with typical bulk gas phase compositions as boundary conditions and were found to be 0.7 for reaction 1, 0.8 for reaction 2, and 0.4 for reaction 4. In order to define the problem, the kinetic mechanism for reforming reactions 1, 2, and 4 must be set up. For this purpose a Xu and Froment35 formulation was used: R1 )

k1 pH2(c)2.5

R2 )

R4 )

k2 pH2(c) k4 3.5

pH2(c)

(

)

pH2(c)3pCO(c) 1 pCH4(c)pH2O(c) Keq,1 Qr2

)

(

pH2(c)pCO2(c) 1 Keq,2 Qr2

(

p 2 H2(c)

pCO(c)pH2O(c)

(17)

pCH4(c)pH2O(c)

3

(18)

)

pCO2(c) 1 Keq,4 Qr2

Qr ) 1 + KCOpCO(c) + KCH4pCH4(c) + KH2pH2(c) +

(19)

KH2OpH2O(c) pH2(c)

(20) Where the necessary coefficients to define the kinetic Arrhenius k, the equilibrium constants Keq, and the absorption-desorption Arrhenius Km can be found in the work of Xu and Froment.35 The reaction rate of the species in the solid phase rm(c) are defined using the stoichiometry of the reactions: rCH4(c) ) -η1εcFcR1 - η4εcFcR4 rH2(c) ) 3η1εcFcR1 + η2εcFcR2 + 4η4εcFcR4 rH2O(c) ) -η1εcFcR1 - η2εcFcR2 - 2η4εcFcR4 rCO(c) ) η1εcFcR1 - η2εcFcR2 rCO2(c) ) η2εcFcR2 + η4εcFcR4 Figure 2. Section of a catalytic particle containing an ideal pore.

(21)

In order to solve the problem for the reforming reaction, the flux of the consumed/produced species in the solid phase was

1566


set as equal to the flux from the gas phases to the solid phases and vice versa: Fghm(gc)Sc(ym(c) - ym(g)) ) rm(c)Mm

(22)

In previous work by Rusten et al.,12 a different sorbent Li2ZrO3 has been investigated for the SE-SMR. In their paper, Rusten et al.12 simulate SE-SMR using heterogeneous models and pseudohomogeneous models that include an efficiency factor. SMR has been determined to be strongly intraparticular diffusion-controlled, and to check whether this is also the case for SE-SMR, heterogeneous models were formulated. Dry hydrogen mole fractions did not show significant differences in the reactor performances for the pseudohomogeneous, oneparticle heterogeneous, and two-particle heterogeneous models. No advantage of heterogeneous models was therefore observed under standard conditions, because the capture of CO2 is the limiting step of the process. In contrast with SMR, where the reactions are very fast, the capture kinetics are slow, compared with diffusion processes. If CO2 acceptors with faster kinetics were used, heterogeneous or pseudoheterogeneous models with efficiency factors would be necessary. As shown by Rusten et al.12 the use of a heterogeneous model would be useless, albeit not wrong, if the same conditions were applied. In this study, the use of a heterogeneous model was preferred because different materials and conditions were used in the simulation. In the current work, calcined dolomite is used instead of Li2ZrO3. Calcined dolomite can work at higher temperature (873-973 K) than Li2ZrO3 (858 K). Johnsen36 has demonstrated a faster kinetic of calcined dolimite compared to that of Li2ZrO3. Ochoa-Fernandez et al.14 report that the slow sorption kinetics of Li2ZrO3 at low partial carbon dioxide pressures are caused by a second-order concentration dependency, a different scenario compared with the sorption kinetics of CaO. Further investigation is required to evaluate if the same results obtained by Rusten et al.12 could also be applied to CaO based sorbents. This is however beyond the scope of the present work. Term Sk in eq 9 for reactions 1, 2, and 4 is Sk ) ηkεcFcRk

(23)

CO2 Capture. To describe the chemical mechanism for CO2 capture, a shrinking unreacted core model (SCM) was chosen. A recent comprehensive literature review of carbonation models was provided by Stanmore and Gilot.37 For noncatalytic reactions, two simple idealized models are widely used: the progressive-conversion model (PCM) and the shrinking unreacted-core model (SCM).38 The PCM assumes that intraparticle diffusion is fast compared to the chemical reaction, making a uniform reacting particle. It is well-known that carbonation proceeds through a slow diffusional limited regime at higher conversion levels. The noncatalytic gas-solid reaction between CaO and CO2 is known to proceed through two rate-controlling regimes.39,40,3 Initially, a rapid chemically controlled stage is rate-determining, before the rate of reaction decreases due to diffusion limitations caused by the very slow diffusion through the product layer. The PCM model is not suitable for describing this regime. The classic SCM model however assumes that the reaction occurs first at the outer skin of the particle. The zone of reaction then moves into the solid, leaving behind completely converted material, known as the product layer in the case of the carbonation. Thus, at any time, there exists an unreacted core of material which shrinks in size during the reaction. During formation of the product layer, the CO2 in the exterior of the particle has an extra diffusion limitation and reacts with more

Table 4. Carbonation Experimental Parameters Adopted Dpl (m2/s)21 k0 (m/s)21 Ea (kJ/mol)21 VCaCO3 (cm3/mol)41 VCaO (cm3/mol)41 VMgCO3 (cm3/mol)41 VMgO (cm3/mol)41 f41 FD (kg/m3)41 δCaO, MgO41 (m)

7.7 × 10-9 3.05 32.6 36.9 16.9 27.5 11.1 0.574 2851 1.50 × 10-6

difficulty with the unreacted core. This mechanism may explain the two rate-controlling regimes discussed above. More complex mechanisms could probably be applied,37 but SCM applied to CO2 capture has been demonstrated to give acceptable results, as shown by Johnsen.36 Three resistances to reaction for the gas-solid reaction between CO2 and calcined dolomite must be considered: • external mass transfer • intraparticle diffusion taking into consideration the internal mass transfer due to resistance to the product layer • chemical reaction. In this case, the three resistances occur in series and the algebraic combination is simply handled by the classic Ohm’s law treatment of resistances in series, eliminating intermediate concentration terms, and yielding a relationship for the rate of reaction with the driving force expressed in terms of bulk concentration. The following assumptions were applied: • CaO and inert material (mainly MgO) are uniformly distributed in the dolomite pellet. Carbonation of MgO is thermodynamically unfavorable at temperatures above 500 °C at ambient pressure and is therefore considered inert. However, MgO is still a significant part of the total volume of the particle. • single spherical particle • constant particle size. To account for a nonlinear dependency of partial pressure, the SCM rate expression was modified using the formulation proposed by Johnsen et al.21 to include a parameter, n ) 0.66. Considering X as the conversion of CaO, the final rate expression, Scarb of eq 12 is Scarb ) εdFdMCO2 × 6 1 (1 - X)2/3 (pCO2 - pCO2,eq)0.66 dd RT dd [(1 - X)1/3 - (1 - X)2/3] 1 2 (1 - X)2/3 + + k3 De hCO2(gd)

(24)

Where PCO2 and PCO2,eq are the partial pressures (Pa) in the bulk phase and at equilibrium respectively, k3 is the Arrhenius of reaction 3, De is the effective diffusivity, hCO2(gd) is the external mass transfer coefficient, and X is the CaO conversion. The equilibrium pressure of carbon dioxide (in atmospheres) is expressed as a function of temperature pCO2,eq ) 4.137 × 107e[20474/(T-273.15)]

(25)

The three denominator groups of eq 24 are calculated as follows: Chemical Reaction. k3 is calculated as an Arrhenius type expression defined as: k3 ) k0e-Ea/RT

(26)

The pre-exponential factor and the activation energy are defined in Table 4


Intraparticle Diffusion. The model in Stendardo and Foscolo41 was used. It is assumed that the fresh solid sorbent contains only CaCO3, with mass fraction f, and MgCO3, with mass fraction (1 - f). Before calcination, the particle internal porosity, ε0, is zero, and the dolomite theoretical density, Fd, is obtained from knowledge of the molar volumes of CaCO3 and MgCO3: Fdf Fd(1 - f) VCaCO3 + V ) N0CaVCaCO3 + MCaCO3 MMgCO3 MgCO3 N0MgVMgCO3 ) 1

(27)

N0Ca and N0Mg indicate the number of calcium and magnesium carbonate moles respectively per unit volume of dolomite particle. We also consider that both carbonates are completely transformed into the respective oxides as a result of a calcination process, so the particle porosity at the beginning of the gas decarbonation step is given by (1 - ε0) ) N0CaVCa + N0MgVMg

(28)

Magnesium carbonate decomposes at a much lower temperature than calcium carbonate, so at the temperature envisaged for this application (about 873 K), it would not contribute to CO2 capture (it stabilizes the particle structure and provides additional voidage); as a result, the particle void fraction as a function of CaO conversion, X, is given by (1 - ε) ) N0Ca[VCaO(1 - X) + VCaCO3X] + N0MgVMgO ) 1 - ε0 + N0CaX(VCaCO3 - VCaO) (29) The mass transport rate within the pore volume is governed by two different phenomena: bulk diffusion and Knudsen diffusion. The first is a function of temperature and pressure (the molecular velocity and the mean free path). Bulk diffusivity is evaluated using eqs 13 and 14. Knudsen diffusion, Dk, depends on the molecular velocity and the pore radius:

2 Dk ) rav 3

8RT πMCO2(c)

(30)

Assuming a cylindrical pore structure for the solid particle allows rav to be related to the void fraction ε and the pore surface per unit particle volume, σ: rav ) 2

ε σ

(31)

In our idealized picture of dolomite, σ is in turn obtainable as a function of the grain size (of CaO and MgO, respectively) and calcium oxide conversion:

[

σ ) N0CaVCaO

6 δCaO

(1 - X) + N0MgVMgO

6 δMgO

]

(32)

δCaO and δMgO are the average diameters of calcium and magnesium oxide grains, respectively. It is worth noting here that, as has been assumed above, when a calcium oxide grain is fully carbonated the associated porosity and pore surface are brought to zero. From eqs 32 and 28, it is possible to calculate rav (eq 31) and therefore Dk with eq 30 The overall pore diffusivity is calculated using the Bosanquet equation as reported in the work of Hayes42 combining molecular and Knudsen diffusion:

1

Dov )

1 DCO2(g)

+

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(33)

1 Dk

This equation is probably not as rigorous as the dusty gas model but gives consistent predictions as indicated in the works of Stendardo and Foscolo,41 Johnsen et al.,21 and Zevenhoven et al.43 when applied to a SCM sorption reaction. The advantage of this equation is faster computation compared with the rigorous dusty gas model. Finally, it was possible to calculate the De,0 as De,0 ) Dov

ε τ

(34)

Equation 34 may be simplified using the assumption of Smith44 for macropore particles such as dolomite. De,0 ) Dovε2

(35)

As shown in the work of Zevenhoven,43 it is possible to calculate De of eq 24 as a function of X: De ) De,0

1 + AX 1 + BX

with A )

1 - ε0 ε0

B)

ADe,0 Dpl

(36) The parameters for finally defining intraparticle diffusion are given in Table 4 External Mass Transfer. For the calculation of h a Ranz-Marshall correlation was used similar to eq 16. A similar species balance equation can be written for CaCO3 and CaO referring to the solid-dolomite phase: Mk ∂ (ε F y ) + ∇ · (εdFdVjdyk(d)) ) νk S ∂t d d k(d) MCO2 carb

(37)

where k ) CaO, CaCO3 and νk is equal to 1 for CaCO3 and -1 for CaO. It is now possible to define m ˙ of eqs 5-7: it is the mass flow rate of CO2 subtracted from the gas phase and accumulated in the solid-dolomite phase as CaCO3: m ˙ ) Scarb

(38)

The carbonation rate parameters to solve the equation system as indicated in Johnsen et al.21 and Stendardo and Foscolo41 are given below in Table 4. The term of eq 9 is S3 )

Scarb MCO2

(39)

The partial differential equation system (eqs 5-12 and 37) was solved with a finite volume method, using Fluent software coupled with a Newton-Raphson method for the algebraic system 22 developed in C language and interfaced as a user defined function (UDF) in Fluent. A k-ε realizable method model was used for turbulence. In Table 5, the initial and boundary condition used that was used. A quadratic mesh of ∆x ) ∆y ) 2.5 mm was evaluated to give accurate results. The Euler implicit method was chosen for time integration, while a second order upwind discretization scheme was used for space discretization. To give an asymmetric condition, a heterogeneity was introduced into the bed by tilting the gravity vector 1% during the first second of simulation. The

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Table 5. Initial and Boundary Conditions

Table 6. Bed Main Parameters for Tests

I.C. umf (m/s) yH2O(g) yH2O(c) Tg,c,d (K) Θ0d,c (m2/s2) yCaO(d) yMgO(d) εmf,g

0.06 1 1 900 1 × 10-4 0.48 0.52 0.4 B.C. (inlet)

usuperficial (m/s) Tg (K) yCH4(g) yH2O(g) Iturb dreac (m)

0.3 900 0.2 0.8 5% 0.1

effect of this had only minor effects on the statistical behavior of the fluid flow. Model ValidationsEntire Process In order to validate the model, some preliminary calculations were carried out and the results were compared with experimental data. As shown in Figure 3, the physical rig consisted of • a pipeline for water, steam generation, and methane feeding • fluidized bed reactors composed of a windbox of 20 cm high and 10 cm i.d. and a zone of reaction 60 cm high and 10 cm i.d. A sintered steel plate was used as distributor to guarantee the required pressure drop in order to maintain a homogeneous velocity at the inlet to the bed. • cooling and drying system • gas chromatography analyzersVarian microGC. The columns used were CP-Molsieve 5 and PoraPLOT U. The gas carrier type was N2. A thermal conductivity detector was used. A Watson Marlow series 400 pump was used to feed the plant with deionized water. The flow rate was controlled by a Dwyer variable area flowmeter. Water was vaporized at 190 °C. The steam generator employed was a single-loop proportional-integral-derivative (PID) controller series 96 Watlow to maintain constant temperature. In particular, a J thermocouple was used as temperature sensor. The methane flow rate was controlled by a Dwyer variable area flowmeter. Steam and methane were mixed to feed the fluidized bed reactor. The mix (steam and methane) was first heated to 823 K by electrical resistance, in the windbox: here, another single-loop PID controller series 96 Watlow with a K thermocouple was used. Finally, the mix was fed to the reactor bed, where the process temperature (873-973 °C) was controlled by a further series 96 Watlow with a K thermocouple. Two further K thermocouples were installed to monitor the temperature inside the fluidized bed: one at a 2 cm distance from the distributor and the other at 15 cm from the distributor. The uniformity of temperature monitored by these two sensors assured the fluidization of the bed and therefore the perfect mixing condition. A pressure probe was then installed to monitor the process pressure. At the exit of the reactors, a cyclone and an antiparticulate filter were installed for particulate abatement, thereby preventing pipe plugging at the rig outlet.

static bed height bed diameter total bed material catalyst particle size dolomite particle size dol/cat ratio vol

20 [cm] 8 [cm] 1004.8 [cm3] 180-425 [µm] 180-425 [µm] 4

The syngas was finally cooled and dried by three impingement bottles in a water bath and a silica gel fixed bed, respectively. The dried syngas was then analyzed by the Varian microGC system. A Ni-based steam-reforming catalyst by Haldor Topsoe was used with calcined Pilkington dolomite. The catalyst and sorbent were first ground and then sieved to obtain, for both, a granulometric distribution with a Sauter diameter of around 300 µm. Before the real tests, a cold test was developed at 2.5 times umf using just nitrogen for 30 min to evaluate if segregation would occur. No segregation was observed at the end of the experiment. At startup H2/N2 (30/70%) was fed to the reactor, to reduce NiO to Ni and to ensure an active catalyst. This operation continued for 30 min at 873 K at umf. The true test was then started. A fluidization velocity 3 times umf (= 0.15 m/s) and an S/C ratio of 4 were chosen for the real tests. Table 6 gives a summary of the parameters chosen for the tests. The model was run using the same experimental conditions. The reactor was simulated for 1 min, and the results of simulation were then averaged. Figures 4 and 5 show experimental data and simulation results at different process temperatures. The results of the simulation showed a slight overestimation of the conversion of methane. The maximum relative error

Figure 3. Layout of the experimental rig in the laboratory.

Figure 4. Comparison of H2 obtained by model and by experiment.


Figure 5. Comparison of CH4 and CO2 obtained by model and by experiment.

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Figure 6. Comparisons of bubble diameter as a function of position above the distributor obtained from simulations and the correlation of Darton et al.46

between experimental and simulated data was 24% for CO2, 15% for CH4, and 1.5% for H2. It can therefore be stated that the simulation results are in good agreement with the experimental results. It must be noticed that during experimental activities significant fine powders generation was observed only during the first period, while it could be neglected, even if persistent, in the remaining test period. Model ValidationsHydrodynamic Bubble Size and Bubble Rise Velocity. In validating the model, some preliminary calculations were carried out in order to verify if the model can predict bubble size and bubble rise velocity. Bubble size has always been considered an important variable in fluidized beds, since it controls most of the rate phenomena in the bed such as particle circulation rate, gas dispersion and heat transfer, and bubble rise velocity. As stated in the Davidson and Harrison22 model, if the fast bubble condition is achieved, a gas cloud is formed around bubbles and the gas contained in the bubble phase may miss the opportunity to mix with the solid present in the emulsion phase. The particles used in the simulation, in all operative conditions, were Geldart B particles as depicted in the scaling relations of Gibilaro.45 The system was simulated using a similar composition to the one expected by a chemical equilibrium calculation of the process. The control volume was therefore fed with a syngas composed of 60% H2, 35% H2O, 1% CH4, 2% CO, and 2% CO2. Only hydrodynamic behavior was investigated in this simulation, not the chemistry of the process. A dol/cat ratio of 5 was chosen and a static bed of 20 cm. The superficial velocity was set to 0.3 m/s at 873 K. A bubble was defined as an area where the solid volume fraction is below 20%. Similar procedures developed by Lindborg et al.30 were used. The control volume was divided into four convenient zones of different heights: 0-0.05, 0.05-0.1, 0.1-0.2, and 0.2 m bed expanded surface height. A simulation of a 7 s run was carried out, with the results of the last 3 s recorded every 0.02 s. This was sufficient to obtain a large quantity of data. In each section, the bubble diameter was determined from an ensemble average of area equivalent diameters of circular bubbles (db ) 2/N∑i(Ai/ π)1/2). The results obtained were compared with the equation proposed by Darton et al.46,40 db ) 0.54(us - umf)0.4(h + 4√A0)0.8 /g0.2

(40)

Figure 7. Predicted bubble rise velocity as a function of bubble size compared with both the works of Davidson et al.22 and Lim et al.47

The results of the predicted bubble versus height above the distributor are reported in Figure 6. Error bars indicate the standard deviation of bubble size. The simulations underestimated the bubble diameter in the upper part of the fluidized bed, but generally they were in agreement with correlation of Darton et al.46 Bubble rise velocity was determined from an ensemble average of the individual changes in mass center positions of the bubbles in consecutive recordings. Figure 7 illustrates the bubble rise velocity versus bubble diameter obtained by simulation and calculated using expressions of Davidson et al.,22 eq 41, and Lim et al.,47 eq 42: ub ) us - umf + 0.711√gdb

(41)

ub ) us - umf + 0.4√gdb

(42)

As also depicted by Lindborg et al.,30 large variations in bubble rise velocities were seen in the simulations due to significant interactions with neighboring bubbles. The simulations showed that small bubbles accelerate in the wakes of larger bubbles, while larger tend to slow down when the trailing bubbles are about to catch them up. Coalescence also affected the rise velocity in addition to the gulf stream effect as also shown in Figure 8. Bubbles rose particularly fast, apparently independent of bubble size, if they entered upflowing particle streams. In contrast, bubble rise was significantly reduced in downflowing streams. For larger bubbles far away from the distributor,

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Figure 9. Calculated inlet tracer concentration profiles with a superficial inlet velocity of 0.30 m/s.

Figure 8. Coalescence disturbance in the computation of bubble rise velocity.

variations in rise velocities could also occur due to uncertainties in the determination of the bubble mass center locations. Despite this, bubble rise velocity as a function of bubble diameter was generally in fair agreement with the correlations of Davidson et al.22 and Lim et al.47 Gas Mixing in a Freely Bubbling Bed. In order to evaluate the magnitude of gas mixing in the fluidized beds and validate the reactor model, a further investigation was developed. The concentration profile of a tracer gas pulsed in the wind chamber was measured at different radial positions in the freeboard, in order to evaluate the back mixing of the fluidized bed. To simulate similar conditions stemming from the process, hydrogen was chosen as the tracer gas and steam as the carrier gas, a dol/cat ratio of 5 was selected and a static bed of 20 cm. The superficial velocity used was 0.3 m/s, and the temperature was set to 873 K. As shown by Lindborg et al.,30 the inlet concentration of tracer gas in the bed can be approximated as the outlet concentration of a tracer pulse from a stirred tank (wind chamber) with a space-time expressed by τw ) Hw/us. Hw was set to 0.2 m while the mass fraction of hydrogen in a pulse was set to 0.003. Simulations were conducted over 15 s with a timestep size of 0.1 ms. The hydrogen pulse was introduced after 5 s simulation time to avoid any influence from the startup phase. Figure 9 illustrates the inlet tracer concentration profiles used in the simulation with a superficial inlet velocity of 0.30 m/s. In Figure 10 is reported the computed tracer concentration in the freeboard for three different radial positions: on the axis (0 cm), near wall (4 cm), and between wall and axis (2 cm). As also observed by Lindborg et al.,30 a radial concentration profile was seen at the outlet. The lowest measured concentration was close to the wall. The simulations showed that gas backmixing, and thus the residence time, was clearly affected by the motion of the particle phase. The tail in the concentration profiles was caused by descending particles which were withdrawing gas. In contrast with the results of Lindborg et al.,30 a symmetric concentration profile was observed. The main differences obtained by this work and that of Lindborg et al.30 may be due to the different reactor diameter used in the

Figure 10. Calculated tracer concentration profiles in the freeboard with a superficial inlet velocity of 0.30 m/s.

simulation. In the current research, a smaller reactor diameter was used. This implies that a bubble originating near a wall near the distributor while rising can more easily reach the center of the bed surface, as also shown in Figure 8. In this simulation, a downward flow of particles was mainly seen along the wall, and so, the backmixing was mainly due to the descending particle motion near the wall. A gradient and a tail in concentration profile was observed in this study as confirmed in the work of Lindborg et al.,30 but these were less pronounced. The explanation for these differing results can be due to the smaller reactor diameter once again and to the different kinds of particle adopted (Geldart B). It is well-known that under these conditions the bubble can not reach a stable maximum bubble size but grows continuously and can reach a diameter of the same order as the reactor diameter (slug condition). Gas backmixing and radial dispersion are therefore greatly reduced.48 The radial variations in both concentration and residence time were also caused by large velocity gradients in the freeboard zone due to wall friction. Segregation. The hydrodynamic behavior of gas-solid flow in the bubbling fluidized beds depends upon the particle properties. In a system consisting of particles of different density and different sizes, the larger (heavier) particles tend to reside at the bottom of the bed and are in this case referred to as jetsam. The smaller (lighter) fractions show the tendency to float and reside at the bed surface. These particles are referred to as flotsam. Mixing/segregation phenomena have always played an


Figure 11. Mass fraction profile of jetsam showing segregation behavior.

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Figure 12. Mass fraction profile of jetsam showing no segregation.

important role in bubbling fluidized beds consisting of particles of different sizes and/or densities. The model proposed in this work used two different particles of different density: sorbent and catalyst. A further validation of the model was carried out to verify if it can predict segregation of particles. Two cases were investigated: (1) A binary mixture composed of 50% by weight of 500 µm catalyst and 50% by weight of 200 µm sorbent. A superficial velocity of 0.18 m/s was chosen. The superficial velocity chosen is 1.2-1.4 times the minimum fluidization velocity of the jetsam (catalyst) and 11-13 times the minimum fluidization velocity of the flotsam (sorbent). (2) A binary mixture composed of 20% by weight of 300 µm catalyst and 80% by weight of 300 µm sorbent, similar to that used in the SE-SMR simulations of the next sections. A superficial velocity of 0.2 m/s was chosen. The superficial velocity chosen is 4.5-5.5 times the minimum fluidization velocity of the jetsam (catalyst) and 6-7.5 times the minimum fluidization velocity of the flotsam (sorbent). The temperature for both cases was set to 900 K while the static bed height was 20 cm. The control volume was fed with a syngas composed of 60% H2, 35% H2O, 1% CH4, 2% CO, and 2% CO2. This composition is similar to that expected from a SE-SMR process. For each binary system there is a critical velocity UT0 below which the system rapidly segregates and above which it rapidly mixes. The empirical equation proposed in ref 49 was used to estimate the UT0 (eq 43):

[ ]

UT0 Umf,J ) Umf,F Umf,F

1.2

+ 0.9

(

FJ -1 FF

)() 1.1

dJ - 2.2xj-1/2H* dF (43)

A critical velocity of 0.2-0.22 m/s was obtained for the first case (1): under such conditions, the system segregates; the model should predict segregation. The profile of the mass fraction of the jetsam obtained by simulation is shown in Figure 11 after 4 s. As shown the model predicted the segregation of heavier and larger particles. A critical velocity of 0.01-0.02 m/s was obtained for the second case (2). In this case the system should not show significant segregation of heavier particles. This result was confirmed by the simulation (Figure 12) where no significant segregation was observed. As shown in Figures 11 and 12, the model was able to predict the segregation even if further experimental investigations are necessary in order to verify this assumption. Results and Discussion A first simulation of the process was carried out using a superficial velocity of 0.3 m/s, a static bed of 20 cm high, and

Figure 13. (a) Void fraction and (b) H2 molar fraction (wet) for 20 cm of static bed and dol/cat ) 5 at 15 s.

a steam to carbon ratio of 4. An initial simulation of a bed completely filled with catalyst particles was carried out merely to verify if it is possible to achieve SMR equilibrium composition. The SE-SMR was then simulated using two different dol/ cat ratios, the first equal to 2 and the second equal to 5. A dol/ cat ratio of 5 is probably more suitable for a cost-effective process. Figures 13-15 clearly show the effect of bubbles on product yields and in particular on H2 production. The gas flowing through the bubbles did not react because of the lower mass of

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solid in the bubble; this reduced the H2 concentration produced by the process and generated oscillations in the outgoing gas composition. The H2 fraction in the outgoing gas is shown in 16 during 48 s of simulation, while residual CH4 fraction is shown in Figure 17. As indicated in Figures 16 and 17, a chemical equilibrium composition was obtained with a static bed of 20 cm completely filled solely with Ni-catalyst particles. In this case, the residual CH4 at the equilibrium condition for 900 K is shown in the graph by a dashed line. The increase of CH4 over time was due to the endothermic reactions 1 and 4 which reduced the temperature of the process, decreasing overall reaction rate and changing the equilibrium composition. This is clear when looking at the temperature of the outgoing gas with time (Figure 18). When dolomite was added (reducing catalyst), the carbonation reaction (reaction 3) increased the H2 produced (Figure 16), but equilibrium (0.96-0.97) was not achieved. Looking at Figure 17, it can be seen that with a dol/cat ratio of 2 the amount of catalyst was sufficient to have a residual CH4 near the equilibrium composition (dotted line). The lower hydrogen produced can therefore be explained by the slower reaction of carbonation due to the small amount of dolomite and lower residence time of reacting gases when large bubbles are present. An increase in the amount of dolomite in the bed (dol/cat ) 5), slightly decreased the hydrogen produced (Figure 16) while it increased


Figure 16. Hydrogen mole fraction produced by 20 cm of static bed.

the residual CH4 (Figure 17). The main reason for this trend is believed to be connected with the reduced steam methane reforming reaction rates due to the lower amount of catalyst used, giving rise to a decreased CH4 conversion. In this case, the H2 decrease was however less than the increase of residual CH4: the carbonation reaction rate was thus improved. The reduction of hydrogen purity is acceptable, however, given the lower amount of high cost catalyst used. Moreover in this last case (dol/cat ) 5), the simulated outgoing temperature was more


Figure 17. Residual methane mole fraction with 20 cm of static bed, equilibrium composition SMR (- - -), equilibrium composition SE-SMR ( · · · ).

Figure 18. Outlet syngas temperature for a reactor with 20 cm of bed.

Figure 19. Gas temperature profile on the reactor axis.

stable than in other cases investigated (see Figure 18). During all the time of the simulation, the temperature of the outgoing gas did not show a significant decrease. Figure 19 gives the area-averaged temperature profile at 48 s for the case dol/cat ) 5. As shown, the temperature in the reactor remained homogeneous and constant, with a difference of only 5 K. This result was also confirmed by the experimental result of Johnsen at al.,20 where calcined dolomite was used as sorbent for the SE-SMR. The results of Lindborg et al.15 showed by contrast a temperature difference of 20-25 K. As explained by Lindborg et al.,15 the main reason of this temperature difference was the result of the fast endothermic reforming reactions and the low internal particle reaction rate. The great

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Figure 20. Hydrogen mole fraction obtained by varying the static bed height at different times.

difference between this work and that of Lindborg et al.15 can be explained by different conditions and materials used in the simulation of the process. In the work of Lindborg et al.,15 particles A were used as the bed material while in this work particles B were used. It is well-known that particle B exhibits a more vigorous fluidization, improving bed mixing and therefore also improving temperature homogeneity in the bed. In Lindborg et al.,15 the sorbent used was Li2ZrO3. As also noticed by Johnsen,36 the kinetics of CO2 sorption of the CaO are faster than that of Li2ZrO3.The operating temperature in this work (with CaO) was higher than that in the work of Lindborg et al.15 (with Li2ZrO3); consequently, the reaction rate of CO2 sorption was further improved. Moreover, it should be noted that the carbonation reaction of CaO is 11% more exothermic than the Li2ZrO3 reaction, so a higher amount of heat is released by CaCO3 formation. A further interesting observation is that an increase of dolomite (reducing catalyst) increased oscillations in product yields (see Figures 16 and 17). The bubbles in the fluidized bed grow in size while rising, thereby increasing their negative effect on reaction rates. If the gas does not react quickly near distributor, where bubbles are still small, the growing bubbles remove gas from the reactions, increasing oscillations of the outgoing gas composition. Thus an increase of the dol/cat ratio reduced the reaction rates of reactions 1, 2, and 4, so the required CO2 to start reaction 3 was achieved later and bubbles became large enough to remove gas from the reactions. The hydrogen dry fraction was then investigated by varying the static bed between 10 and 20 cm for a dol/cat ) 5, steamto-carbon S/C ) 4, and a superficial velocity of 0.3 m/s at three different times (see Figure 20). An increase of bed height increased gas residence time and improved hydrogen production. Moreover, a more stable H2 molar fraction, very close to 0.92 for all the simulated times, was obtained. This can be explained by the more stable temperatures due to the exothermicity of the carbonation reaction and the higher amount of CaO that was available to react. Finally, the effect of varying the steam-to-carbon (S/C) ratio on the final dry hydrogen fraction was investigated. The results are shown in Figure 21. The hydrogen fraction was predicted to increase from 0.89 to 0.92 as the S/C ratio varies from 3 to 4. This increase was related to the positive effect on the water-gas shift reaction (WGS) equilibrium, which favors H2 and CO2 production. As is known, an increase of CO2 partial

1574


reaction. The SE-SMR showed great advantages if compared to the traditional SMR. However further investigations to increase the scale of the process to an industrial level should be carried out. Regeneration of sorbent, multicycle effects and attrition should also be considered in the future work. The use of a double bubbling bed reactor or circulating fluidized bed should be evaluated using a Eulerian-Eulerian approach. The use of a bubbling bed for the reforming reactor seemed the right choice because of the slow reaction rates. A similar investigation should be carried out for the calcination reactor to evaluate if a riser or a bubbling bed is needed. Fragmentation is also a parameter which should be considered as part of this. In addition, more stable and more resistant sorbents should be evaluated and compared with calcined dolomite. Figure 21. Hydrogen mole fraction at the outlet of a reactor with 20 cm of bed for varying S/C ratios.

Acknowledgment

pressure increases the rate of carbonation, further enhancing the steam reforming reaction.

The author is particularly indebted to Prof. Pier Ugo Foscolo and Ing. Katia Gallucci of the University of L’Aquila for their enormous help on the subject of fluidization.

Conclusions

Notation

In the present paper, a numerical investigation of a fluidized bed reactor for steam methane reforming with CO2 capture was carried out using a CFD Eulerian-Eulerian model to evaluate the fluidization behavior of the bed. A multifluid approach was used in order to model a solid phase composed of two different particles: catalyst and sorbent. The extra- and intraparticle diffusion were coupled to kinetic mechanisms of reactions. The mass transfer coefficient for the extraparticle diffusion was calculated by literature correlations while the intraparticle diffusion was considered by the use of an effectiveness factor. Further investigations are necessary to evaluate the importance of mass transfer in the process when CaO is used as sorbent. Slower reaction rates of CO2 capture could justify the use of an effectiveness factor equal to 1, because CO2 capture is probably the controlling step. SCM was preferred for evaluating the CO2 capture reaction. This model is simple and solved quickly. SE-SMR process simulations were validated by experimental results and hydrodynamic considerations. Further experimental validation must be carried out however at a higher superficial velocity. During the experimental work, whereas significant finepowder generation was only observed during the first period, this effect was seen to be negligible, albeit persistent, in the remaining test period. Finally, a small-scale reactor of 10 cm i.d. was simulated. Three different cases were investigated: in the first, only SMR was simulated; in the other two cases, the SE-SMR process was investigated with dol/cat ratios of 2 and 5. An equilibrium composition was obtained for SMR. A high molar fraction of H2 was observed during simulations of SESMR. The model showed that at 900 K a molar fraction >0.93 can be achieved using a dolomite/catalyst ratio higher than 2, with a bed height of 20 cm, a superficial gas velocity of 0.3 m/s, and a steam to carbon ratio higher than 3. In the simulation of a dol/cat ratio of 5, a reduction of molar fraction of H2 was observed. This is mainly due to the reduced steam methane reforming reaction rates. However, a high molar fraction of H2 was obtained (∼0.92). During all the time of the simulation, the temperature of the outgoing gas did not show a significant decrease and the temperature in the reactor remained homogeneous and constant with a difference of only 5 K. This result demonstrated that for the investigated period the sorption reaction can provide all the required heat for the steam reforming

Latin Letters A0 ) catchment area of distributor Dm(g) ) molecular diffusivity coefficient of species m in gas phase g Dmn(g) ) binary diffusion coefficient of between species m and n in gas phase g Dk ) Knudsen diffusion for CO2 capture De ) effective diffusivity coefficient for CO2 in capture reaction Dpl ) product layer diffusivity coefficient Db ) bubble diameter ds ) particle diameter of solid phase s ess ) restitution coefficient of solid phase s f ) mass fraction of CaCO3 in dolomite g°ss ) radial distribution function of the solid phase s g°cd ) radial distribution function between catalyst c and dolomite d solid phase Hi ) specific enthalpy of phase i Hw ) height of the wind chamber h ) height on the fluidized bed hij ) heat transfer coefficient between phases hm(gs) ) mass transfer coefficient between gas (g) and solid (s) phases ki ) thermal conductivity of phase i kΘs ) diffusion coefficient of granular temperature of solid phase s Mm ) molecular weight of species m N0Ca ) number of Ca moles per unit volume of dolomite particle N0Mg ) number of Mg moles per unit volume of dolomite particle m ˙ i ) mass exchanges between phases i p ) pressure ps ) solid pressure Rk ) reaction rate (kg/(s m3 kgcat) for reactions 1, 2, and 4) rav ) pore radius of calcined dolomite rm(c) ) rate of formation of chemical species due to reactions 1, 2, and 4 Sc ) catalyst surface area per unit volum of catalyst particle c Sk ) heat source term due to reactions ub ) bubble rise velocity umf ) minimum fluidization velocity us ) superficial velocity Vgs ) -Vsg ) relative velocity between solid (s) and gas (g) phases Vi ) velocity of phase i

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010 X ) conversion of CaO due to reaction 3 ym(c) ) mass fraction of gas species m in catalyst solid phase c ym(g) ) mass fraction of gas species m in gas phase (bulk) g Greek Letters βij ) interfacial momentum transfer coefficient between phases γΘs ) collision dissipation of granular energy of solid phase s δCaO ) average diameters of CaO grains in dolomite δMgO ) average diameters of MgO grains in dolomite ∆Hk ) heat of reaction k εi ) volume fraction of phase i ε ) dolomite particle porosity ηk ) effectiveness factor for reactions 1, 2, and 4 µg ) gas viscosity µs ) solid viscosity Fi ) density of phase i σmn ) Lennard-Jones potential parameter σ ) dolomite pore surface per unit particle volume Ωmn ) collisional integral for diffusion τi ) stress tensor of phase i τw ) space-time of the wind chamber Θs ) granular temperature of solid phases s Subscripts b ) bubble c ) catalyst, first solid phase d ) dolomite, second solid phase e ) effective F ) Flotsam g ) gas phase J ) Jetsam k ) reactions or dolomite chemical species m ) chemical species mf ) minimum fluidization s ) solid phases or superficial (superficial velocity) w ) wind chamber 0 ) initial

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ReceiVed for reView May 8, 2009 ReVised manuscript receiVed December 21, 2009 Accepted December 29, 2009 IE900748T

Numerical Investigation of Sorption Enhanced Steam Methane

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