- Email: [email protected]
3D Simulation of bubbling fluidized bed reactors for sorption enhanced steam methane reforming processes
Journal of Natural Gas Science and Engineering 2 (2010) 105e113
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
3D Simulation of bubbling fluidized bed reactors for sorption enhanced steam methane reforming processes Yuefa Wang, Zhongxi Chao, Hugo A. Jakobsen* Department of Chemical Engineering, Norwegian University of Science and Technology, NTNU, Sem Sælands vei 4, NO-7491 Trondheim, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 February 2010 Received in revised form 19 April 2010 Accepted 19 April 2010 Available online 14 May 2010
Hydrogen production by the Sorption Enhanced Steam Methane Reforming (SE-SMR) process was studied with a numerical two-fluid model. The process was simulated in a three dimensional bubbling fluidized bed reactor. The effects of pressure, steam-to-carbon ratio and inlet gas flow rate on the reactions are studied. High pressure and low steam-to-carbon ratio will decrease the conversion of methane. But the high pressure makes the adsorption of CO2 faster. Compared to the standard SMR process, the methane conversion and heat utility are enhanced by CO2 adsorption. The CO2 produced in the methane reforming process is adsorbed almost totally in a relative long period of time in the bubbling fluidized bed. It means that the adsorption rate of CO2 is fast enough compared with the SMR rate. In a certain range of gas flow rates, the mass transfer and reaction kinetics can reach the equilibrium, and the reaction efficiency is independent of gas flow rate. The temperature distribution is almost uniform over the whole reactor. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Methane reforming Carbon dioxide capture SE-SMR CaO sorbent 3D simulation Fluidized bed
1. Introduction
CH4 þ H2 O5CO þ 3H2
Natural gas is both an important source of energy and an important precursor for chemical materials. Compared to other fossil fuels, natural gas is a clean energy which produces negligible emissions of carcinogen mutagenic hydrocarbon species in combustion (Barros Zárante and Sodré, 2009). The carbon dioxide is the main product in the natural gas combustion. However, with the increasing impact of global warming caused mostly by increasing concentrations of greenhouse gases, the emission control of CO2 as the most important anthropogenic greenhouse gas was concerned by many researchers. Hydrogen is considered to be a potential clean energy source. As a raw material of chemical industry, natural gas can be converted to hydrogen and synthesis gas by the steam methane reforming (SMR) process (Al-Qahtani, 1997; Pedernera et al., 2007). Actually, there are several ways of catalytic reforming of methane to produce hydrogen, i.e. steam reforming, dry reforming, oxidative reforming, and autothermal reforming, by using Ni-based catalyst. The steam reforming of methane is the main industrial route (Ávila-Neto et al., 2009). It usually includes the following three reactions:
CO þ H2 O5CO2 þ H2
* Corresponding author. E-mail address: [email protected] (H.A. Jakobsen). 1875-5100/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jngse.2010.04.004
DH298 ¼ 206 kJ=mol DH298 ¼ 41 kJ=mol
CH4 þ 2H2 O5CO2 þ 4H2
DH298 ¼ 165 kJ=mol
(1) (2) (3)
Xu and Froment (1989) developed a model for the SMR reaction kinetics considering all the three reactions as independent, although at equilibrium the third reaction is dependent as it is the sum of the first two reactions. It is an endothermic process usually carried out at high temperature of 1000e1200 K and pressure of 20e35 bar (Rusten et al., 2007a). Recently the process of sorption enhanced steam methane reforming (SE-SMR) is becoming an important topic due to its integration of hydrogen production and CO2 separation. In this process, carbon dioxide is captured by an on-line sorbent, and the chemical equilibrium is shifted to the product side of the SMR reaction. Therefore, the product obtained may be almost pure hydrogen (Han and Harrison, 1994). The carbon dioxide adsorbed by the sorbent can be separated from sorbent by desorption later for storage or other treatment. The SE-SMR reactions can proceed at temperatures of about 200 C lower than that for standard SMR process (Hufton et al., 1999). The integration of heat between the exothermic sorption reaction and the endothermic reforming reactions improves the energy efficiency of the SE-SMR process. The regeneration of the sorbent requires the largest energy supply
106
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
considering both the SE-SMR and regeneration processes. However, considering the SE-SMR reactor unit solely, the energy supply by the sorption reaction and by the circulating hot solid particles from the regeneration vessel is important to avoid considerable additional energy supply requirements for the SE-SMR reactor unit. The overall heat integration including regeneration must be considered in future investigations. In the SE-SMR process, the performances of the sorbents and the reactors are the main factors studied in the current investigations. Ca-based sorbents are more widely studied and used because of their high CO2 capacity and rapid reaction, as well as lower cost (Balasubramanian et al., 1999; Lopez Ortiz and Harrison, 2001; Yi and Harrison, 2005; Grasa and Abanades, 2006; Sun et al., 2008). Lithium-containing materials were investigated recently as CO2 sorbent due to its promising stability and high adsorption capacity (Xiong et al., 2003; Kato et al., 2004; Kimura et al., 2005; Lindborg and Jakobsen, 2009). However, kinetic limitations and high cost are the main drawback of Lithiumbased sorbents (Ochoa-Fernandez et al., 2005). A CaO-based CO2 sorbent is used in this study. The adsorption reaction is:
CaO þ CO2 5CaCO3
DH298 ¼ 178 kJ=mol
(4)
It is an exothermic reaction being able to provide a large part of the energy required by the steam reforming reactions. The fixed bed reactors have been used since 1930s and are currently widespread for tranditional SMR process. At the early stages of the SE-SMR research, most studies on the reactor performance for the SE-SMR process were focused on fixed bed reactors both in experiments (Hufton et al., 1999; Balasubramanian et al., 1999; Lopez Ortiz and Harrison, 2001; Yi and Harrison, 2005; Li et al., 2006) and in numerical simulations (Ding and Alpay, 2000; Xiu and Rodrigues, 2002; Lee et al., 2004; Ochoa-Fernández et al., 2005; Rusten et al., 2007a,b; Li and Cai, 2007). In view of the adsorption/regeneration cycles of sorbents needed in SE-SMR process, the fixed bed reactors must be switched periodically between two operating conditions, and the heat integration is not sufficient to avoid cold spots at the inlet area. Such operation is not preferable for industrial purpose. The solid particles can be circulated between two reactors continuously in the fluidized bed reactors. Thus fluidized bed reactors are favorable for SE-SMR process thanks to the continuous operation, as well as effective heat transfer, thereby temperature uniformity, and low mass transfer resistance (Lindborg and Jakobsen, 2009). The experimental results of CaO carbonation in a pilot-scale fluidized-bed reactor by Abanades et al. (2004) showed that high CO2 capture efficiencies from combustion flue gas are obtained in a fluidized bed. Hughes et al. (2004) investigated cyclic carbonation and calcination reactions for CO2 capture from combustion and gasification processes. Their approach may reduce the CO2 emissions from coal- and petroleum coke-fired fluidized bed combustors by up to 85%. Several papers have reported studies on the performance of the SESMR process in fluidized bed reactors. Prasad and Elnashaie (2004) proposed a circulating fluidized-bed membrane reactor for steam methane reforming with CO2 sequestration using the CO2-lime reaction, and studied the reactor performance with a one-dimensional model. Johnsen et al. (2006a) conducted an experimental investigation on reforming and sorbent calcination in cyclic operation in a bubbling fluidized bed reactor. Johnsen et al. (2006b) studied the SESMR and sorbent regeneration processes conducted continuously in two coupled bubbling beds with a homogeneous model. Lindborg and Jakobsen (2009) studied the process performance and analyzed the reactor design for SE-SMR in a bubbling fluidized bed reactor by using a two-dimensional model, and pointed out that investigations of SESMR process using a three-dimensional multifluid model are needed.
This paper is focused on the performances of the SE-SMR process with CaO sorbent conducted in a bubbling fluidized bed reactor. A 3D numerical two-fluid model was developed to implement our work. The bubbling regime in the beds provided a relatively long residence time and low rates of attrition for sorbent because of the low gas and particle velocities.
2. Models 2.1. Hydrodynamic model The two-fluid model is a popular approach for dense gas-solid systems. Kinetic theory of granular flow (KTGF) is applied to obtain the governing equations and closures of the particle phase while retaining the standard Eulerian formulation for the continuous phase. The mass balance, species mass balance and momentum balance equations of the particle phase have a similar form as those of the gas phase, as shown in Eqs. (5)e(7):
v ða r Þ þ V$ðak rk vk Þ ¼ Gk vt k k
k ¼ c; d
(5)
v ar6 þ V$ ak rk vk 6k;j ¼ V$ ak rk Deff k;j V6k;j vt k k k;j þ Mj Rij k ¼ c; d
ð6Þ
v ða r v Þ þ V$ðak rk vk vk Þ ¼ ak Vp þ V$sk þ ak rk g vt k k k þ Mk k ¼ c; d
ð7Þ
The KTGF postulates that the dispersed particulate phase (granular material) can be represented by a collection of identical, smooth, rigid spheres with similarities to gas molecules (Jakobsen, 2008). The granular temperature was difined as the mean kinetic energy of the particle fluctuations to describe the random motion of the granular particles. The governing equation for the granular temperature is:
3 v ðad rd QÞ þ V$ðad rd vd QÞ ¼ sd : Vvd þ V$ðkd VQÞ 2 vt D E 3 ~ 0c $Cd þ Gk Q g 3bQ þ b v 2
ð8Þ
Molecular temperature equations for gas and particle phase are as follows:
ac rc Cp;c
DTc i ¼ V$ ac keff c VTc þ Qc Dt
ad rd Cp;d
X DTd DHiR RR;i VTd þ Qci ¼ V$ ad keff d i Dt i
(9)
(10)
The standard ke3 turbulence models are used to describe the gas phase turbulence quantities (Pfleger et al., 1999). The drag correlation of Benyahia et al. (2006) is used in this work to account for the gas-solid interactions. Constitutive equations for internal momentum transfer are given in Table 1. The KTGF model only accounts for particle streaming and short term particle-particle contacts. However, in dense flows of particles as in the bubbling fluidized bed, the frictional stresses have significant effects on the hydrodynamic properties of the two phases (Boemer et al., 1997; Lu et al., 2004; Patil et al., 2005). In this paper the kinetic-frictional stress model was used for particle phase. This effective particulate stress tensor is assumed equal to
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113 Table 1 Constitutive equations for internal momentum transfer.
Table 2 Constitutive equations for internal heat and mass transfer.
Gas phase stress:
Effective conductivity:
sc ¼ 2ac mc Sc
(11)
Solid phase stress:
sd ¼ ð pd þ ad zd V$vk ÞI þ 2ad md Sd Deformation rate: 1 1 Vvk þ ðVvk ÞT ðV$vk ÞI Sk ¼ 2 3 Solid phase bulk viscosity (Lun et al., 1984): rffiffiffiffi Q 4 zd ¼ ad rd dd g0 ð1 þ eÞ p 3 Conductivity of the granular temperature: rffiffiffiffi 2 Q 15 mdilute 6 d kd ¼ 1 þ ad g0 ð1 þ eÞ þ2a2d rd dd g0 ð1 þ eÞ p 2 g0 ð1 þ eÞ 5 Collisional energy dissipation (Jenkins and Savage, 1983): ! rffiffiffiffi 4 Q g ¼ 3a2d rd g0 Q 1 e2 V$vd dd p
(12)
m keff k ¼ kk þ
1 þ 2:5ad þ 4:5904a2d þ 4:515439a3d h 3 i0:67802 d 1 aamax
k0c
km c ¼
ac
D
Rs ¼
E
¼
b2 dp jvd hvc ij2 Rs pffiffiffiffiffiffiffi 4a4c ad rd pQ
1 pffiffiffiffiffiffi g0 1 þ 3:5 ad þ 5:9ad
pffiffiffiffiffiffi
ad Þ
(29)
(30)
ad
(14)
(15)
"
#
2 A1 B A B1 1 ln ðB þ 1Þ 1 B=A ð1 B=AÞ2 A B 1 B=A 2 10=9 k0 a A ¼ d0 ; B ¼ 1:25 d ; f ¼ 7:26 103 ac kc
L ¼
ð31Þ
Effective diffusivity:
(16)
m Deff k;j ¼ Dk;j þ
mtk rk Sct
(32)
Molecular diffusion coefficient (Wilke, 1950): 16 P 6j Mm Mj Dij
Dm c;j ¼ (17)
(18)
(33)
jsi
Binary diffusion coefficient (Fuller et al., 1966): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tc1:75 1=Mj þ 1=Mi Dij ¼ h P P 1=3 i2 1=3 101:325P ð VÞj þ ð VÞi
(34)
(19) (20)
the sum of the kinetic stress tensor and the frictional stress tensor (Srivastava and Sundaresan, 2003): f sd ¼ sk;c þ sd d
ð1
k0c km d ¼ pffiffiffiffiffiffiðfA þ ð1 fLÞÞ
Dissipation of granular energy due to fluid turbulence (Lindborg et al., 2007):
b v~0c $Cd
(28)
(13)
d
Dilute viscosity (Gidaspow, 1994): pffiffiffiffiffiffiffi 5 mdilute r d Qp ¼ d 96 d d
mtk rk Prt
Molecular conductivity (Bauer and Schlünder, 1978):
Radial distribution function (Ma and Ahmadi, 1986): g0 ¼
107
(21)
Thus the solid pressure and viscosity were calculated by the following equations:
pd ¼ pk;c þ pfd d
(22)
md ¼ mk;c þ mfd d
(23)
The internal heat and mass transfer equations can be found in Table 2. The constitutive equations concerning the interfacial momentum and heat coupling are given in Table 3. More detailed descriptions of the model and solution methods can be found in Lindborg et al. (2007) and Lindborg and Jakobsen (2009).
2.2. Chemical model Steam methane reforming on nickel-based catalysts is the main process for industrial production of hydrogen or synthesis gas. Numerous studies have been reported on the kinetics of these reactions (Akers and Camp, 1955; Allen et al., 1975; Hou and Hughes, 2001). Xu and Froment (1989) investigated a large number of detailed mechanisms and derived the intrinsic rate equations for the steam reforming of methane on nickel-alumina
The kinetic and collisional pressure (Lun et al., 1984) and the viscosity (Gidaspow, 1994) are:
pkc d ¼ ad rd Q½1 þ 2ð1 eÞad g0
mkc d
rffiffiffiffi 2 2mdilute Q 4 4 d 1 þ ad g0 ð1 þ eÞ þ ad rd g0 ð1 þ eÞ ¼ p ad g0 ð1 þ eÞ 5 5
(24)
Interfacial force:
(25)
8 r < F ðad amin d Þ if ad > amin s d ad Þ ðamax ¼ d : 0 if ad amin d
mfd ¼
f pffiffiffi pd 2sinf qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2ad Sd : Sd þ Q=d2p
Mc [ Md ¼ FD ¼ bðvd vc Þ
(35)
Interfacial heat transfer (spherical particles):
Frictional pressure (Johnson et al., 1990) and viscosity (Ocone et al., 1993) are:
pfd
Table 3 Interfacial momentum and heat transfer equations.
Qc ¼
6ad h ðT -Tc Þ dd cd d
(36)
Interfacial heat transfer coefficient (Gunn, 1978):
(26)
hcd ¼
kc h
7 10ac þ 5a2c
1=3 1 þ 0:7Re0:2 p Pr i 1=3 þ 1:33 2:4ac þ 1:2a2c Re0:7 p Pr
ad
ð37Þ
Particle Reynolds number and Prandtl number:
(27)
Rep ¼
m Cp;c ac rc jvd vc jdd ; Prp ¼ c mc kc
(38)
108
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
catalysts which have been widely used. Their rate equations were also used in our simulations:
" # 3 k1 pCH4 pH2 O pH2 pCO =K1 R1 ¼ 2:5 p H2 DEN2 R2 ¼
(39)
k2 pCO pH2 O pH2 pCO2 =K2 2 p H2 DEN
(40)
" # 2 4 k1 pCH4 pH2 O pH2 pCO2 =K3 R3 ¼ 3:5 p H2 DEN2
(41)
where
DEN ¼ 1 þ KCO pCO þ KH2 pH2 þ KCH4 pCH4 þ KH2 O pH2 O =pH2
(42)
R1, R2 and R3 correspond to the reactions (1), (2) and (3) respectively. The rate equation for CO2 adsorption by the CaO sorbent is taken from Sun et al. (2008):
Ra ¼
n dX ¼ 56ka ð1 XÞ pCO2 pCO2;eq S dt
(43)
where n is the reaction order with the following values:
n ¼ 1 n ¼ 0
when when
pCO2 pCO2 ;eq 10 KPa pCO2 pCO2 ;eq > 10 KPa
3. Results The catalytic steam methane reforming reactions and the CO2 adsorption by sorbent are performed simultaneously in the bubbling flow regime to provide sufficient residence time for the solid phase processes. The solid phase consists of the identical particles. The catalyst and the sorbent are assumed to be mixed uniformly in the particles with the same mass ratio. Table 4 lists the simulation parameters. 3.1. Hydrodynamics of the bubbling fluidized bed The model is built up and solved in three-dimensional cylindrical coordinates. Fig. 1 presents the contour of the voidage and the solid velocity vector profiles in an vertical plane. The simulation results revealed the heterogeneous structure of the bed and the non axial symmetric behavior of the solid flow.
Fig. 1. Instantaneous contour of voidage (a) and solid velocity vector profiles (b) in a vertical plane in the bubbling fluidized bed (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1, p ¼ 1 bar).
of solids hence the solid circulation flux is zero. The gas phase consisting of CH4 and steam flows into the reactor from the bottom uniformly and flows out of the reactor from the top of the reactor. Figs. 2 and 3 give the dry concentration profiles of the components along the axis for SMR and SE-SMR respectively. The temperature and pressure are 848 K and 1 bar. The superfacial inlet gas velocity is 0.3 m/s, and the steam-to-carbon ratio is 5. In the SMR results, the outlet concentration of H2 is only 76%, and a lot of CO2 is emitted out of the reactor. However in the simulations of SE-SMR process, both the conversion of methane and the adsorption of CO2 are larger than 99% even after 210 s. In this case the amount of CO2 produced in methane reforming reactions can be considered to be adsorbed totally by the sorbent, the methane reforming and hydrogen production are greatly enhanced. The sorbent capacity is large enough for the simulated conditions.
3.2. Comparison between SE-SMR and standard SMR The CO2 adsorption by CaO was carried out in a bubbling fluidized bed. The solid particles are restrained in a constant amount in the bubbling fluidized bed reactor. There is no exchange Table 4 Simulation parameters. Particle diameter Particle density Initial bed height Initial solid fraction Reactor size Grid cell number Time step Convergence criterion Sorbent capacity Sorbent-to-catalyst mass ratio
500 mm 1500 kg/m3 1.2 m 0.58 R ¼ 0.1 m, z ¼ 4 m 10 12 80 (BFB) 1 104s krm k < 3kbk 3 ¼ 1010 0.25 g(CO2)/g (CaO) 4
Fig. 2. Axial distributions of components concentration in gas phase in the bubbling fluidized bed for the standard SMR process at time 49 s.
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
109
Fig. 3. Axial distributions of components concentration in gas phase and CO2 concentration in solid phase in the bubbling fluidized bed for SE-SMR process at time 210 s.
3.3. Influence of pressure
3.4. Influence of steam-to-carbon ratio
Figs. 4e7 show the different effects of the reaction pressure on the SMR and SE-SMR process. The concentrations of methane and hydrogen are increased and decreased respectively with increasing the pressure in both processes. However the change in SMR is much larger than that in SE-SMR (Figs. 4 and 6). The smaller effects of pressure in the SE-SMR process may be owing to the CO2 adsorption by the sorbents. CO2 adsorption can make the conversion of methane almost complete and counteract the influence of the higher pressure. The CO2 concentrations in the gas phase decreased with increasing pressure in both the SMR and SE-SMR processes, but to a less degree (Fig. 5). This trend is due to the combined effects of lower methane conversion and higher CO2 adsorption rate by sorbents at higher pressure. Fig. 7 shows that the adsorption rate of carbon dioxide by sorbents is higher at higher pressure. It is a natural result of the adsorption process.
Steam-to-carbon ratio is an important factor for the steam methane reforming reactions because it may influence the equilibrium of these reactions. For the SE-SMR process, the outlet methane concentration is increased a little (from 0.3% to 0.7%) when the steam-to-carbon ratio is decreased from 5 to 4, but increased much more (from 0.7% to 3%) when the steam-to-carbon ratio is decreased from 4 to 3 (Fig. 8(a)). A similar effect was obtained for the hydrogen concentration, the variation is about the same but the changes are in the opposite direction (Fig. 8(b)). However, the outlet concentration of carbon dioxide was less influenced by the steam-to-carbon ratio as shown in Fig. 9(a). The CO2 concentration within the sorbents decreased with the increasing steam-to-carbon ratio (Fig. 9(b)). For the standard SMR process, the effects of steam-to-carbon ratio on the reactions are much larger than that in SE-SMR process.
Fig. 4. Average outlet concentration of methane for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
Fig. 5. Average outlet concentration of carbon dioxide for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
110
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
Fig. 6. Average outlet concentration of hydrogen for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
All concentrations of methane, hydrogen and carbon dioxide in gas phase changed clearly with the variation of steam-to-carbon ratio. The reason may be that the integration of CO2 adsorption to SMR promoted the conversion of methane largely. This effect and the in situ removal of CO2 weaken the influence of steam-to-carbon ratio to the reforming reactions in the SE-SMR process.
Fig. 8. Average outlet concentrations of methane (a) and hydrogen (b) for both SMR and SE-SMR at different steam-to-carbon ratios (p ¼ 1 bar, u0 ¼ 0.3 m/s, T ¼ 848 K, t ¼ 49 s).
3.5. Influence of inlet gas flow rate In order to simulate the bubbling flow at higher gas flow rates, the particles of higher density 2400 kg/m3 was used in this part. The diameter of particles is still 500 mm. Fig. 10 shows that the components concentrations in the gas phase are almost the same for different gas flow rates after the initial unstable period (about 10s). Actually, the concentrations of methane and CO2 are close to zero (0.6% and 0.3% respectively), and that of hydrogen is near 99%. In this case the methane reforming, the CO2 adsorption can be considered completed for all gas flow rates investigated. It indicates the mass transfer and reaction kinetics are fast enough to reach equilibrium under the simulated conditions. The CO2 adsorption rate is increased as the gas flow rate increased (Fig. 11). This trend occurs because the reaction rate of CO2 adsorption depends on the partial pressure of CO2 and the specific surface area of sorbent. At the reactor startup and at lower gas flow rates, the SMR CO2 production rate is relatively low, thus
Fig. 7. Average concentration of carbon dioxide in sorbents for SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
Fig. 9. Average outlet concentration of carbon dioxide for SMR and SE-SMR (a) and carbon dioxide fractionin sorbents for SE-SMR (b) at different steam-to-carbon ratios (p ¼ 1bar, u0 ¼ 0.3 m/s, T ¼ 848 K, t ¼ 49 s).
Fig. 10. Average outlet concentration of hydrogen (a) and carbon dioxide (b) for SESMR at different inlet gas flow rates (p ¼ 1 bar, T ¼ 848 K, rsc ¼ 5:1).
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
111
process in the fluidized bed is quite uniform since the released heat by CO2 adsorprion is close to the absorbed heat by methane reforming, and the gas and solid phases in the bubbling bed are well-mixed. 4. Conclusion
Fig. 11. Average concentration of carbon dioxide in sorbents for SE-SMR at different inlet gas flow rates (p ¼ 1 bar, T ¼ 848 K, rsc ¼ 5:1).
the partial pressure of CO2 in the gas phase is low and only a fraction of the surface area of the sorbent is occupied by CO2. Under these SMR conditions the adsorption rate is low and far from its equilibrium. As a result, the adsorption rate will increase with the increase of partial pressure of CO2 at the higher gas flow rates. A higher adsorption rate will reduce the time to reach the equilibrium of the adsorption, thus decrease the total production time for the same amount of sorbents. Similar conclusions were drawn by Johnsen et al. (2006a) evaluating experimentally the effects of variations in the superficial gas velocity. 3.6. Temperature distribution Fig. 12 presents the temperature distributions in SE-SMR process. The temperature of the inlet gas was set to 848 K. As the gas goes through the bed, the SMR and adsorption reactions take place, the temperature decreased gradually to about 845.5 K. It means that the CO2 adsorption can supply some of the heat required by the SMR reactions, but still not enough under the simulated conditions. After a peak value in the bed at about 0.2 m above the inlet, the temperature increased to about 847.5 K at the upper surface, which is possibly a result of a reduction of the SMR reaction rates. As a whole, the temperature distribution for SE-SMR
Fig. 12. (a) Temperature distribution in a vertical cross section, (b) average axial temperature distribution, (c) average axial distribution of solid fraction for SE-SMR in bubbling fluidized bed (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1, t ¼ 49 s, p ¼ 10 bar).
The temperature distribution is quite uniform in the bubbling fluidized bed reactors for the SE-SMR reactions due to the heat integration of the SMR and the CO2 capture processes. The Higher pressure is favorable for adsorption of CO2, but unfavorable for methane reforming. The steam-to-carbon ratio is important to the conversion of methane in the reactor. Sufficient steam concentration in the feed is a necessary condition for complete conversion of methane. When the ratio is lower than 4, the conversion of methane is reduced markedly. Under the investigated conditions, the reaction efficiency is independent of the inlet gas flow rate. This trend occurs because the mass transfer and reaction kinetics are fast enough to reach the chemical equilibrium. The production time will decrease with increasing gas flow rates. The simulation results show that the integration of CO2 sorption into the SMR process can increase the methane conversion to about 100% and allows more effective energy utility. The adsorption rate of CO2 is fast enough compared with the SMR rate to completely adsorb the CO2 produced in the bubbling fluidized bed investigated. Acknowledgement The PhD fellowship (Chao, Z.) financed through the GASSMAKS program (Advanced Reactor Modeling and Simulation) and the Post doc fellowship (Wang, Y.) financed through the RENERGI program (Hydrogen Production by Sorbent Enhanced Reforming) of the Norwegian Research Council are gratefully appreciated. Nomenclature
Latin letters drag coefficient for a particle CD heat capacity of phase k Cp,k s CO2 fraction in sorbent CCO 2 particle diameter dd, dp binary diffusion coefficient Dji diffusion coefficient for component j in phase k Dk,j e coefficient of restitution F constant g gravity radial distribution function g0 interfacial heat transfer coefficient hcd reaction enthalpy for reaction i HiR k rate coefficient thermal conductivity of phase k kk K1, K2, K3 equilibrium constant adsorption constants for component Y (Y ¼ CH4, CO2, H2, KY H2O) M mole mass interfacial heat transfer to phase k Qki n reaction order of CO2 adsorption p pressure particle pressure pd Pr Prandtl number r constant steam-to-carbon ratio rsc
112
Re Ri Rj Rs s S Sh t T X ydry Cd FD I Mk S ~ 0c v vk
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
Reynolds number reaction rate of reaction i formation rate of component j energy source constant specific surface area of sorbent Sherwod number time temperature conversion dry mole fraction in gas phase peculiar velocity drag force unit tensor interfacial momentum transfer of phase k deformation rate tensor of phase k fluctuating component of fluid velocity velocity of phase k
Greek letters ak volume fraction of phase k (k¼c,d) b interfacial drag coefficient g collisional energy dissipation f angle of internal friction zd solid phase bulk viscosity kd conductivity of granular temperature mdilute dilute viscosity d mk viscosity of phase k rk density of phase k sk stress tensor of phase k u mass fraction G averaged interfacial mass flux Q granular temperature Superscripts dilute dilute c collisional eff effective f frictional i interfacial k kinetic m molecular max maximum min minimum Subscripts a adsorption c continuous phase d dispersed phase, desorption eq equilibrium i reaction number j component number k phase (k ¼ c,d) p particle References Abanades, J.C., Anthony, E.J., Lu, D.Y., Salvador, C., Alvarez, D., 2004. Capture of CO2 from combustion gases in a fluidized bed of CaO. AIChE J. 50, 1614e1622. Akers, W.W., Camp, D.P., 1955. Kinetics of the methane-steam reactions. AIChE J. 1, 471e475. Allen, D.W., Gerhard, E.R., Likins, M.R., 1975. Kinetics of the methane-steam reaction. Ind. Eng. Chem. P.D.D. 14, 256e259. Al-Qahtani, H., 1997. Effect of aging on a steam reforming catalyst. Chem. Eng. J. 65, 51e56. Ávila-Neto, C.N., Dantas, S.C., Silva, F.A., Franco, T.V., Romanielo, L.L., Hori, C.E., Assis, A.J., 2009. Hydrogen production from methane reforming:
thermodynamic assessment and autothermal reactor design. J. Nat. Gas Sci. Eng. 1 (6), 205e215. Balasubramanian, B., Lopez Ortiz, A., Kaytakoglu, S., Harrison, D.P., 1999. Hydrogen from methane in a single-step process. Chem. Eng. Sci. 54, 3543e3552. Barros Zárante, P.H., Sodré, J.R., 2009. Evaluating carbon emissions reduction by use of natural gas engine fuel. J. Nat. Gas Sci. Eng. 1 (6), 216e220. Bauer, R., Schlünder, E.U., 1978. Effective radial thermal conductivity of packings in gas flow. Part II. Thermal conductivity of the packing fraction without gas flow. Int. Chem. Eng. 18, 189e204. Benyahia, S., Syamlal, M., O’Brien, T.J., 2006. Extension of Hill-Koch-Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technol. 162, 166e174. Boemer, A., Qi, H., Renz, U., 1997. Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed. Int. J. Multiphase Flow 23, 927e944. Ding, Y., Alpay, E., 2000. Adsorption-enhanced steam-methane reforming. Chem. Eng. Sci. 55, 3929e3940. Fuller, E.N., Schettler, P.D., Giddings, J.C., 1966. A new method for prediction of binary gas-phase diffusion coefficients. Ind. Eng. Chem. 58, 18e27. Gidaspow, D., 1994. Multiphase Flow and Fluidization. Academic Press, Boston. Grasa, G.S., Abanades, J.C., 2006. CO2 capture capacity of CaO in long series of carbonation/calcination cycles. Ind. Eng. Chem. Res. 45, 8846e8851. Gunn, D.J., 1978. Transfer of heat or mass to particles in fixed and fluidised beds. Int. J. Heat Mass Transfer 21, 467e476. Han, C., Harrison, D.P., 1994. Simultaneous shift reaction and carbon dioxide separation for the direct production of hydrogen. Chem. Eng. Sci. 49, 5875e5883. Hou, K., Hughes, R., 2001. The kinetics of methane steam reforming over a Ni/ aeAl2O catalyst. Chem. Eng. Sci. 82, 311e328. Hufton, J.R., Mayorga, S., Sircar, S., 1999. Sorption enhanced process for hydrogen production. AIChE J. 45, 248e256. Hughes, R.W., Lu, D., Anthony, E.J., Wu, Y., 2004. Improved long-term conversion of limestone derived sorbents for in-situ capture of CO2 in a fluidized bed combustor. Ind. Eng. Chem. Res. 43, 5529e5539. Jakobsen, H.A., 2008. Chemical Reactor Modeling, Multiphase Reactive Flows. Springer-Verlag, Berlin. Jenkins, J.T., Savage, S.B., 1983. A theory for the rapid flow of identical, smooth, nearly elastic spherical particles. J. Fluid Mech. 130, 187e202. Johnsen, K., Ryu, H.J., Grace, J.R., Lim, C.J., 2006a. Sorption-enhanced steam reforming of methane in a fluidized bed reactor with dolomite as CO2-acceptor. Chem. Eng. Sci. 61, 1195e1202. Johnsen, K., Grace, J.R., ELnashaie, S., Kolbeinsen, L., Eriksen, D., 2006b. Modeling of sorption-enhanced steam reforming in a dual fluidized bubbling bed reactor. Ind. Eng. Chem. Res. 45, 4133e4144. Johnson, P.C., Nott, P., Jackson, R., 1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 510e535. Kato, M., Essaki, K., Yoshikawa, S., Nakagawa, K., Uemoto, H., 2004. Reproducibility of CO2 absorption and emission for cylindrical pellet type lithium orthosilicate. J. Ceram. Soc. Jpn. 112, S1338eS1340. Kimura, S., Adachi, M., Noda, R., Horio, M., 2005. Particle design and evaluation of dry CO2 recovery sorbent with a liquid holding capacity. Chem. Eng. Sci. 60, 4061e4071. Lee, D.K., Baek, I.H., Yoon, W.L., 2004. Modeling and simulation for the methane steam reforming enhanced by in situ removal utilizing the CaO carbonation for H2 production. Chem. Eng. Sci. 59, 931e942. Lindborg, H., Lysberg, M., Jakobsen, H.A., 2007. Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds. Chem. Eng. Sci. 62, 5854e5869. Lindborg, H., Jakobsen, H.A., 2009. Sorption enhanced steam methane reforming process performance and bubbling fluidized bed reactor design analysis by use of a two-fluid model. Ind. Eng. Chem. Res. 48, 1332e1342. Li, Z., Cai, N., Yang, J., 2006. Continuous production of hydrogen from sorptionenhanced steam methane reforming in two parallel fixed-bed reactors operated in a cyclic manner. Ind. Eng. Chem. Res. 45, 8788e8793. Li, Z., Cai, N., 2007. Modeling of multiple cycles for sorption-enhances steam methane reforming and sorbent regeneration in fixed bed reactor. Energy Fuels 21, 2909e2918. Lopez Ortiz, A., Harrison, D.P., 2001. Hydrogen production using sorption-enhanced reaction. Ind. Eng. Chem. Res. 40, 5102e5109. Lu, H., He, Y., Liu, W., Ding, J., Gidaspow, D., Bouillard, J., 2004. Computer simulations of gasesolid flow in spouted beds using kinetic-frictional stress model of granular flow. Chem. Eng. Sci. 59, 865e878. Lun, C.K.K., Savage, S.B., Jefferey, D.J., Chepurniy, N., 1984. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223e256. Ma, D., Ahmadi, G., 1986. An equation of state for dense rigid sphere gases. J. Chem. Phys. 84, 3449e3450. Ochoa-Fernández, E., Rusten, H.K., Jakobsen, H.A., Rønning, M., Holmen, A., Chen, D., 2005. Sorption enhanced hydrogen production by steam methane reforming using Li2ZrO3 as sorbent: Sorption kinetics and reactor simulation. Catal. Today 106, 41e46. Ocone, R., Sundaresan, S., Jackson, R., 1993. Gas-particle flow in a duct of arbitrary inclination with particle-particle interactions. AIChE J. 39, 1261e1271. Patil, D.J., van Sint Annaland, M., Kuipers, J.A.M., 2005. Critical comparison of hydrodynamic models for gas-solid fluidized beds e Part I: bubbling gas-solid fluidized beds operated with a jet. Chem. Eng. Sci. 60, 57e72.
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113 Pedernera, M.N., Pina, J., Borio, D.O., 2007. Kinetic evaluation of carbon formation in a membrane reactor for methane reforming. Chem. Eng. J. 134, 138e144. Pfleger, D., Gomes, S., Gilbert, N., Wagner, H.G., 1999. Hydrodynamic simulations of laboratory scale bubble columns fundamental studies of EulerianeEulerian modelling approach. Chem. Eng. Sci. 54, 5091e5099. Prasad, P., Elnashaie, S.S.E.H., 2004. Novel circulating fluidized-bed membrane reformer using carbon dioxide sequestration. Ind. Eng. Chem. Res. 43, 494e501. Rusten, H.K., Ochoa-Fernández, E., Chen, D., Jakobsen, H.A., 2007a. Numerical investigation of sorption enhanced steam methane reforming using Li2ZrO3 as CO2-acceptor. Ind. Eng. Chem. Res. 46, 4435e4443. Rusten, H.K., Ochoa-Fernández, E., Lindborg, H., Chen, D., Jakobsen, H.A., 2007b. Hydrogen production by sorption-enhanced steam methane reforming using Lithium oxides as CO2-acceptor. Ind. Eng. Chem. Res. 46, 8729e8737.
113
Srivastava, A., Sundaresan, S., 2003. Analysis of a frictional-kinetic model for gasparticle flow. Powder Technol. 129, 72e85. Sun, P., Grace, J.R., Lim, C.J., Anthony, E.J., 2008. Determination of intrinsic rate constants of the CaO-CO2 reaction. Chem. Eng. Sci. 63, 47e56. Wilke, C.R., 1950. Diffusional properties of multicomponent gases. Chem. Eng. Prog. 46, 95e104. Xiong, R., Ida, J., Lin, Y., 2003. Kinetics of carbon dioxide sorption on potassiumdoped lithium zirconate. Chem. Eng. Sci. 58, 4377e4385. Xiu, G., Rodrigues, A.R., 2002. Sorption-enhanced reaction process with reactive regeneration. Chem. Eng. Sci. 57, 3893e3908. Xu, J., Froment, G.F., 1989. Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AIChE J. 35, 88e96. Yi, K.B., Harrison, D.P., 2005. Low pressure sorption enhanced hydrogen production. Ind. Eng. Chem. Res. 44, 1665e1669.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
3D Simulation of bubbling fluidized bed reactors for sorption enhanced steam methane reforming processes Yuefa Wang, Zhongxi Chao, Hugo A. Jakobsen* Department of Chemical Engineering, Norwegian University of Science and Technology, NTNU, Sem Sælands vei 4, NO-7491 Trondheim, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 February 2010 Received in revised form 19 April 2010 Accepted 19 April 2010 Available online 14 May 2010
Hydrogen production by the Sorption Enhanced Steam Methane Reforming (SE-SMR) process was studied with a numerical two-fluid model. The process was simulated in a three dimensional bubbling fluidized bed reactor. The effects of pressure, steam-to-carbon ratio and inlet gas flow rate on the reactions are studied. High pressure and low steam-to-carbon ratio will decrease the conversion of methane. But the high pressure makes the adsorption of CO2 faster. Compared to the standard SMR process, the methane conversion and heat utility are enhanced by CO2 adsorption. The CO2 produced in the methane reforming process is adsorbed almost totally in a relative long period of time in the bubbling fluidized bed. It means that the adsorption rate of CO2 is fast enough compared with the SMR rate. In a certain range of gas flow rates, the mass transfer and reaction kinetics can reach the equilibrium, and the reaction efficiency is independent of gas flow rate. The temperature distribution is almost uniform over the whole reactor. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Methane reforming Carbon dioxide capture SE-SMR CaO sorbent 3D simulation Fluidized bed
1. Introduction
CH4 þ H2 O5CO þ 3H2
Natural gas is both an important source of energy and an important precursor for chemical materials. Compared to other fossil fuels, natural gas is a clean energy which produces negligible emissions of carcinogen mutagenic hydrocarbon species in combustion (Barros Zárante and Sodré, 2009). The carbon dioxide is the main product in the natural gas combustion. However, with the increasing impact of global warming caused mostly by increasing concentrations of greenhouse gases, the emission control of CO2 as the most important anthropogenic greenhouse gas was concerned by many researchers. Hydrogen is considered to be a potential clean energy source. As a raw material of chemical industry, natural gas can be converted to hydrogen and synthesis gas by the steam methane reforming (SMR) process (Al-Qahtani, 1997; Pedernera et al., 2007). Actually, there are several ways of catalytic reforming of methane to produce hydrogen, i.e. steam reforming, dry reforming, oxidative reforming, and autothermal reforming, by using Ni-based catalyst. The steam reforming of methane is the main industrial route (Ávila-Neto et al., 2009). It usually includes the following three reactions:
CO þ H2 O5CO2 þ H2
* Corresponding author. E-mail address: [email protected] (H.A. Jakobsen). 1875-5100/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jngse.2010.04.004
DH298 ¼ 206 kJ=mol DH298 ¼ 41 kJ=mol
CH4 þ 2H2 O5CO2 þ 4H2
DH298 ¼ 165 kJ=mol
(1) (2) (3)
Xu and Froment (1989) developed a model for the SMR reaction kinetics considering all the three reactions as independent, although at equilibrium the third reaction is dependent as it is the sum of the first two reactions. It is an endothermic process usually carried out at high temperature of 1000e1200 K and pressure of 20e35 bar (Rusten et al., 2007a). Recently the process of sorption enhanced steam methane reforming (SE-SMR) is becoming an important topic due to its integration of hydrogen production and CO2 separation. In this process, carbon dioxide is captured by an on-line sorbent, and the chemical equilibrium is shifted to the product side of the SMR reaction. Therefore, the product obtained may be almost pure hydrogen (Han and Harrison, 1994). The carbon dioxide adsorbed by the sorbent can be separated from sorbent by desorption later for storage or other treatment. The SE-SMR reactions can proceed at temperatures of about 200 C lower than that for standard SMR process (Hufton et al., 1999). The integration of heat between the exothermic sorption reaction and the endothermic reforming reactions improves the energy efficiency of the SE-SMR process. The regeneration of the sorbent requires the largest energy supply
106
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
considering both the SE-SMR and regeneration processes. However, considering the SE-SMR reactor unit solely, the energy supply by the sorption reaction and by the circulating hot solid particles from the regeneration vessel is important to avoid considerable additional energy supply requirements for the SE-SMR reactor unit. The overall heat integration including regeneration must be considered in future investigations. In the SE-SMR process, the performances of the sorbents and the reactors are the main factors studied in the current investigations. Ca-based sorbents are more widely studied and used because of their high CO2 capacity and rapid reaction, as well as lower cost (Balasubramanian et al., 1999; Lopez Ortiz and Harrison, 2001; Yi and Harrison, 2005; Grasa and Abanades, 2006; Sun et al., 2008). Lithium-containing materials were investigated recently as CO2 sorbent due to its promising stability and high adsorption capacity (Xiong et al., 2003; Kato et al., 2004; Kimura et al., 2005; Lindborg and Jakobsen, 2009). However, kinetic limitations and high cost are the main drawback of Lithiumbased sorbents (Ochoa-Fernandez et al., 2005). A CaO-based CO2 sorbent is used in this study. The adsorption reaction is:
CaO þ CO2 5CaCO3
DH298 ¼ 178 kJ=mol
(4)
It is an exothermic reaction being able to provide a large part of the energy required by the steam reforming reactions. The fixed bed reactors have been used since 1930s and are currently widespread for tranditional SMR process. At the early stages of the SE-SMR research, most studies on the reactor performance for the SE-SMR process were focused on fixed bed reactors both in experiments (Hufton et al., 1999; Balasubramanian et al., 1999; Lopez Ortiz and Harrison, 2001; Yi and Harrison, 2005; Li et al., 2006) and in numerical simulations (Ding and Alpay, 2000; Xiu and Rodrigues, 2002; Lee et al., 2004; Ochoa-Fernández et al., 2005; Rusten et al., 2007a,b; Li and Cai, 2007). In view of the adsorption/regeneration cycles of sorbents needed in SE-SMR process, the fixed bed reactors must be switched periodically between two operating conditions, and the heat integration is not sufficient to avoid cold spots at the inlet area. Such operation is not preferable for industrial purpose. The solid particles can be circulated between two reactors continuously in the fluidized bed reactors. Thus fluidized bed reactors are favorable for SE-SMR process thanks to the continuous operation, as well as effective heat transfer, thereby temperature uniformity, and low mass transfer resistance (Lindborg and Jakobsen, 2009). The experimental results of CaO carbonation in a pilot-scale fluidized-bed reactor by Abanades et al. (2004) showed that high CO2 capture efficiencies from combustion flue gas are obtained in a fluidized bed. Hughes et al. (2004) investigated cyclic carbonation and calcination reactions for CO2 capture from combustion and gasification processes. Their approach may reduce the CO2 emissions from coal- and petroleum coke-fired fluidized bed combustors by up to 85%. Several papers have reported studies on the performance of the SESMR process in fluidized bed reactors. Prasad and Elnashaie (2004) proposed a circulating fluidized-bed membrane reactor for steam methane reforming with CO2 sequestration using the CO2-lime reaction, and studied the reactor performance with a one-dimensional model. Johnsen et al. (2006a) conducted an experimental investigation on reforming and sorbent calcination in cyclic operation in a bubbling fluidized bed reactor. Johnsen et al. (2006b) studied the SESMR and sorbent regeneration processes conducted continuously in two coupled bubbling beds with a homogeneous model. Lindborg and Jakobsen (2009) studied the process performance and analyzed the reactor design for SE-SMR in a bubbling fluidized bed reactor by using a two-dimensional model, and pointed out that investigations of SESMR process using a three-dimensional multifluid model are needed.
This paper is focused on the performances of the SE-SMR process with CaO sorbent conducted in a bubbling fluidized bed reactor. A 3D numerical two-fluid model was developed to implement our work. The bubbling regime in the beds provided a relatively long residence time and low rates of attrition for sorbent because of the low gas and particle velocities.
2. Models 2.1. Hydrodynamic model The two-fluid model is a popular approach for dense gas-solid systems. Kinetic theory of granular flow (KTGF) is applied to obtain the governing equations and closures of the particle phase while retaining the standard Eulerian formulation for the continuous phase. The mass balance, species mass balance and momentum balance equations of the particle phase have a similar form as those of the gas phase, as shown in Eqs. (5)e(7):
v ða r Þ þ V$ðak rk vk Þ ¼ Gk vt k k
k ¼ c; d
(5)
v ar6 þ V$ ak rk vk 6k;j ¼ V$ ak rk Deff k;j V6k;j vt k k k;j þ Mj Rij k ¼ c; d
ð6Þ
v ða r v Þ þ V$ðak rk vk vk Þ ¼ ak Vp þ V$sk þ ak rk g vt k k k þ Mk k ¼ c; d
ð7Þ
The KTGF postulates that the dispersed particulate phase (granular material) can be represented by a collection of identical, smooth, rigid spheres with similarities to gas molecules (Jakobsen, 2008). The granular temperature was difined as the mean kinetic energy of the particle fluctuations to describe the random motion of the granular particles. The governing equation for the granular temperature is:
3 v ðad rd QÞ þ V$ðad rd vd QÞ ¼ sd : Vvd þ V$ðkd VQÞ 2 vt D E 3 ~ 0c $Cd þ Gk Q g 3bQ þ b v 2
ð8Þ
Molecular temperature equations for gas and particle phase are as follows:
ac rc Cp;c
DTc i ¼ V$ ac keff c VTc þ Qc Dt
ad rd Cp;d
X DTd DHiR RR;i VTd þ Qci ¼ V$ ad keff d i Dt i
(9)
(10)
The standard ke3 turbulence models are used to describe the gas phase turbulence quantities (Pfleger et al., 1999). The drag correlation of Benyahia et al. (2006) is used in this work to account for the gas-solid interactions. Constitutive equations for internal momentum transfer are given in Table 1. The KTGF model only accounts for particle streaming and short term particle-particle contacts. However, in dense flows of particles as in the bubbling fluidized bed, the frictional stresses have significant effects on the hydrodynamic properties of the two phases (Boemer et al., 1997; Lu et al., 2004; Patil et al., 2005). In this paper the kinetic-frictional stress model was used for particle phase. This effective particulate stress tensor is assumed equal to
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113 Table 1 Constitutive equations for internal momentum transfer.
Table 2 Constitutive equations for internal heat and mass transfer.
Gas phase stress:
Effective conductivity:
sc ¼ 2ac mc Sc
(11)
Solid phase stress:
sd ¼ ð pd þ ad zd V$vk ÞI þ 2ad md Sd Deformation rate: 1 1 Vvk þ ðVvk ÞT ðV$vk ÞI Sk ¼ 2 3 Solid phase bulk viscosity (Lun et al., 1984): rffiffiffiffi Q 4 zd ¼ ad rd dd g0 ð1 þ eÞ p 3 Conductivity of the granular temperature: rffiffiffiffi 2 Q 15 mdilute 6 d kd ¼ 1 þ ad g0 ð1 þ eÞ þ2a2d rd dd g0 ð1 þ eÞ p 2 g0 ð1 þ eÞ 5 Collisional energy dissipation (Jenkins and Savage, 1983): ! rffiffiffiffi 4 Q g ¼ 3a2d rd g0 Q 1 e2 V$vd dd p
(12)
m keff k ¼ kk þ
1 þ 2:5ad þ 4:5904a2d þ 4:515439a3d h 3 i0:67802 d 1 aamax
k0c
km c ¼
ac
D
Rs ¼
E
¼
b2 dp jvd hvc ij2 Rs pffiffiffiffiffiffiffi 4a4c ad rd pQ
1 pffiffiffiffiffiffi g0 1 þ 3:5 ad þ 5:9ad
pffiffiffiffiffiffi
ad Þ
(29)
(30)
ad
(14)
(15)
"
#
2 A1 B A B1 1 ln ðB þ 1Þ 1 B=A ð1 B=AÞ2 A B 1 B=A 2 10=9 k0 a A ¼ d0 ; B ¼ 1:25 d ; f ¼ 7:26 103 ac kc
L ¼
ð31Þ
Effective diffusivity:
(16)
m Deff k;j ¼ Dk;j þ
mtk rk Sct
(32)
Molecular diffusion coefficient (Wilke, 1950): 16 P 6j Mm Mj Dij
Dm c;j ¼ (17)
(18)
(33)
jsi
Binary diffusion coefficient (Fuller et al., 1966): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tc1:75 1=Mj þ 1=Mi Dij ¼ h P P 1=3 i2 1=3 101:325P ð VÞj þ ð VÞi
(34)
(19) (20)
the sum of the kinetic stress tensor and the frictional stress tensor (Srivastava and Sundaresan, 2003): f sd ¼ sk;c þ sd d
ð1
k0c km d ¼ pffiffiffiffiffiffiðfA þ ð1 fLÞÞ
Dissipation of granular energy due to fluid turbulence (Lindborg et al., 2007):
b v~0c $Cd
(28)
(13)
d
Dilute viscosity (Gidaspow, 1994): pffiffiffiffiffiffiffi 5 mdilute r d Qp ¼ d 96 d d
mtk rk Prt
Molecular conductivity (Bauer and Schlünder, 1978):
Radial distribution function (Ma and Ahmadi, 1986): g0 ¼
107
(21)
Thus the solid pressure and viscosity were calculated by the following equations:
pd ¼ pk;c þ pfd d
(22)
md ¼ mk;c þ mfd d
(23)
The internal heat and mass transfer equations can be found in Table 2. The constitutive equations concerning the interfacial momentum and heat coupling are given in Table 3. More detailed descriptions of the model and solution methods can be found in Lindborg et al. (2007) and Lindborg and Jakobsen (2009).
2.2. Chemical model Steam methane reforming on nickel-based catalysts is the main process for industrial production of hydrogen or synthesis gas. Numerous studies have been reported on the kinetics of these reactions (Akers and Camp, 1955; Allen et al., 1975; Hou and Hughes, 2001). Xu and Froment (1989) investigated a large number of detailed mechanisms and derived the intrinsic rate equations for the steam reforming of methane on nickel-alumina
The kinetic and collisional pressure (Lun et al., 1984) and the viscosity (Gidaspow, 1994) are:
pkc d ¼ ad rd Q½1 þ 2ð1 eÞad g0
mkc d
rffiffiffiffi 2 2mdilute Q 4 4 d 1 þ ad g0 ð1 þ eÞ þ ad rd g0 ð1 þ eÞ ¼ p ad g0 ð1 þ eÞ 5 5
(24)
Interfacial force:
(25)
8 r < F ðad amin d Þ if ad > amin s d ad Þ ðamax ¼ d : 0 if ad amin d
mfd ¼
f pffiffiffi pd 2sinf qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2ad Sd : Sd þ Q=d2p
Mc [ Md ¼ FD ¼ bðvd vc Þ
(35)
Interfacial heat transfer (spherical particles):
Frictional pressure (Johnson et al., 1990) and viscosity (Ocone et al., 1993) are:
pfd
Table 3 Interfacial momentum and heat transfer equations.
Qc ¼
6ad h ðT -Tc Þ dd cd d
(36)
Interfacial heat transfer coefficient (Gunn, 1978):
(26)
hcd ¼
kc h
7 10ac þ 5a2c
1=3 1 þ 0:7Re0:2 p Pr i 1=3 þ 1:33 2:4ac þ 1:2a2c Re0:7 p Pr
ad
ð37Þ
Particle Reynolds number and Prandtl number:
(27)
Rep ¼
m Cp;c ac rc jvd vc jdd ; Prp ¼ c mc kc
(38)
108
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
catalysts which have been widely used. Their rate equations were also used in our simulations:
" # 3 k1 pCH4 pH2 O pH2 pCO =K1 R1 ¼ 2:5 p H2 DEN2 R2 ¼
(39)
k2 pCO pH2 O pH2 pCO2 =K2 2 p H2 DEN
(40)
" # 2 4 k1 pCH4 pH2 O pH2 pCO2 =K3 R3 ¼ 3:5 p H2 DEN2
(41)
where
DEN ¼ 1 þ KCO pCO þ KH2 pH2 þ KCH4 pCH4 þ KH2 O pH2 O =pH2
(42)
R1, R2 and R3 correspond to the reactions (1), (2) and (3) respectively. The rate equation for CO2 adsorption by the CaO sorbent is taken from Sun et al. (2008):
Ra ¼
n dX ¼ 56ka ð1 XÞ pCO2 pCO2;eq S dt
(43)
where n is the reaction order with the following values:
n ¼ 1 n ¼ 0
when when
pCO2 pCO2 ;eq 10 KPa pCO2 pCO2 ;eq > 10 KPa
3. Results The catalytic steam methane reforming reactions and the CO2 adsorption by sorbent are performed simultaneously in the bubbling flow regime to provide sufficient residence time for the solid phase processes. The solid phase consists of the identical particles. The catalyst and the sorbent are assumed to be mixed uniformly in the particles with the same mass ratio. Table 4 lists the simulation parameters. 3.1. Hydrodynamics of the bubbling fluidized bed The model is built up and solved in three-dimensional cylindrical coordinates. Fig. 1 presents the contour of the voidage and the solid velocity vector profiles in an vertical plane. The simulation results revealed the heterogeneous structure of the bed and the non axial symmetric behavior of the solid flow.
Fig. 1. Instantaneous contour of voidage (a) and solid velocity vector profiles (b) in a vertical plane in the bubbling fluidized bed (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1, p ¼ 1 bar).
of solids hence the solid circulation flux is zero. The gas phase consisting of CH4 and steam flows into the reactor from the bottom uniformly and flows out of the reactor from the top of the reactor. Figs. 2 and 3 give the dry concentration profiles of the components along the axis for SMR and SE-SMR respectively. The temperature and pressure are 848 K and 1 bar. The superfacial inlet gas velocity is 0.3 m/s, and the steam-to-carbon ratio is 5. In the SMR results, the outlet concentration of H2 is only 76%, and a lot of CO2 is emitted out of the reactor. However in the simulations of SE-SMR process, both the conversion of methane and the adsorption of CO2 are larger than 99% even after 210 s. In this case the amount of CO2 produced in methane reforming reactions can be considered to be adsorbed totally by the sorbent, the methane reforming and hydrogen production are greatly enhanced. The sorbent capacity is large enough for the simulated conditions.
3.2. Comparison between SE-SMR and standard SMR The CO2 adsorption by CaO was carried out in a bubbling fluidized bed. The solid particles are restrained in a constant amount in the bubbling fluidized bed reactor. There is no exchange Table 4 Simulation parameters. Particle diameter Particle density Initial bed height Initial solid fraction Reactor size Grid cell number Time step Convergence criterion Sorbent capacity Sorbent-to-catalyst mass ratio
500 mm 1500 kg/m3 1.2 m 0.58 R ¼ 0.1 m, z ¼ 4 m 10 12 80 (BFB) 1 104s krm k < 3kbk 3 ¼ 1010 0.25 g(CO2)/g (CaO) 4
Fig. 2. Axial distributions of components concentration in gas phase in the bubbling fluidized bed for the standard SMR process at time 49 s.
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
109
Fig. 3. Axial distributions of components concentration in gas phase and CO2 concentration in solid phase in the bubbling fluidized bed for SE-SMR process at time 210 s.
3.3. Influence of pressure
3.4. Influence of steam-to-carbon ratio
Figs. 4e7 show the different effects of the reaction pressure on the SMR and SE-SMR process. The concentrations of methane and hydrogen are increased and decreased respectively with increasing the pressure in both processes. However the change in SMR is much larger than that in SE-SMR (Figs. 4 and 6). The smaller effects of pressure in the SE-SMR process may be owing to the CO2 adsorption by the sorbents. CO2 adsorption can make the conversion of methane almost complete and counteract the influence of the higher pressure. The CO2 concentrations in the gas phase decreased with increasing pressure in both the SMR and SE-SMR processes, but to a less degree (Fig. 5). This trend is due to the combined effects of lower methane conversion and higher CO2 adsorption rate by sorbents at higher pressure. Fig. 7 shows that the adsorption rate of carbon dioxide by sorbents is higher at higher pressure. It is a natural result of the adsorption process.
Steam-to-carbon ratio is an important factor for the steam methane reforming reactions because it may influence the equilibrium of these reactions. For the SE-SMR process, the outlet methane concentration is increased a little (from 0.3% to 0.7%) when the steam-to-carbon ratio is decreased from 5 to 4, but increased much more (from 0.7% to 3%) when the steam-to-carbon ratio is decreased from 4 to 3 (Fig. 8(a)). A similar effect was obtained for the hydrogen concentration, the variation is about the same but the changes are in the opposite direction (Fig. 8(b)). However, the outlet concentration of carbon dioxide was less influenced by the steam-to-carbon ratio as shown in Fig. 9(a). The CO2 concentration within the sorbents decreased with the increasing steam-to-carbon ratio (Fig. 9(b)). For the standard SMR process, the effects of steam-to-carbon ratio on the reactions are much larger than that in SE-SMR process.
Fig. 4. Average outlet concentration of methane for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
Fig. 5. Average outlet concentration of carbon dioxide for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
110
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
Fig. 6. Average outlet concentration of hydrogen for SMR and SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
All concentrations of methane, hydrogen and carbon dioxide in gas phase changed clearly with the variation of steam-to-carbon ratio. The reason may be that the integration of CO2 adsorption to SMR promoted the conversion of methane largely. This effect and the in situ removal of CO2 weaken the influence of steam-to-carbon ratio to the reforming reactions in the SE-SMR process.
Fig. 8. Average outlet concentrations of methane (a) and hydrogen (b) for both SMR and SE-SMR at different steam-to-carbon ratios (p ¼ 1 bar, u0 ¼ 0.3 m/s, T ¼ 848 K, t ¼ 49 s).
3.5. Influence of inlet gas flow rate In order to simulate the bubbling flow at higher gas flow rates, the particles of higher density 2400 kg/m3 was used in this part. The diameter of particles is still 500 mm. Fig. 10 shows that the components concentrations in the gas phase are almost the same for different gas flow rates after the initial unstable period (about 10s). Actually, the concentrations of methane and CO2 are close to zero (0.6% and 0.3% respectively), and that of hydrogen is near 99%. In this case the methane reforming, the CO2 adsorption can be considered completed for all gas flow rates investigated. It indicates the mass transfer and reaction kinetics are fast enough to reach equilibrium under the simulated conditions. The CO2 adsorption rate is increased as the gas flow rate increased (Fig. 11). This trend occurs because the reaction rate of CO2 adsorption depends on the partial pressure of CO2 and the specific surface area of sorbent. At the reactor startup and at lower gas flow rates, the SMR CO2 production rate is relatively low, thus
Fig. 7. Average concentration of carbon dioxide in sorbents for SE-SMR at different pressures (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1).
Fig. 9. Average outlet concentration of carbon dioxide for SMR and SE-SMR (a) and carbon dioxide fractionin sorbents for SE-SMR (b) at different steam-to-carbon ratios (p ¼ 1bar, u0 ¼ 0.3 m/s, T ¼ 848 K, t ¼ 49 s).
Fig. 10. Average outlet concentration of hydrogen (a) and carbon dioxide (b) for SESMR at different inlet gas flow rates (p ¼ 1 bar, T ¼ 848 K, rsc ¼ 5:1).
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
111
process in the fluidized bed is quite uniform since the released heat by CO2 adsorprion is close to the absorbed heat by methane reforming, and the gas and solid phases in the bubbling bed are well-mixed. 4. Conclusion
Fig. 11. Average concentration of carbon dioxide in sorbents for SE-SMR at different inlet gas flow rates (p ¼ 1 bar, T ¼ 848 K, rsc ¼ 5:1).
the partial pressure of CO2 in the gas phase is low and only a fraction of the surface area of the sorbent is occupied by CO2. Under these SMR conditions the adsorption rate is low and far from its equilibrium. As a result, the adsorption rate will increase with the increase of partial pressure of CO2 at the higher gas flow rates. A higher adsorption rate will reduce the time to reach the equilibrium of the adsorption, thus decrease the total production time for the same amount of sorbents. Similar conclusions were drawn by Johnsen et al. (2006a) evaluating experimentally the effects of variations in the superficial gas velocity. 3.6. Temperature distribution Fig. 12 presents the temperature distributions in SE-SMR process. The temperature of the inlet gas was set to 848 K. As the gas goes through the bed, the SMR and adsorption reactions take place, the temperature decreased gradually to about 845.5 K. It means that the CO2 adsorption can supply some of the heat required by the SMR reactions, but still not enough under the simulated conditions. After a peak value in the bed at about 0.2 m above the inlet, the temperature increased to about 847.5 K at the upper surface, which is possibly a result of a reduction of the SMR reaction rates. As a whole, the temperature distribution for SE-SMR
Fig. 12. (a) Temperature distribution in a vertical cross section, (b) average axial temperature distribution, (c) average axial distribution of solid fraction for SE-SMR in bubbling fluidized bed (u0 ¼ 0.3 m/s, T ¼ 848 K, rsc ¼ 5:1, t ¼ 49 s, p ¼ 10 bar).
The temperature distribution is quite uniform in the bubbling fluidized bed reactors for the SE-SMR reactions due to the heat integration of the SMR and the CO2 capture processes. The Higher pressure is favorable for adsorption of CO2, but unfavorable for methane reforming. The steam-to-carbon ratio is important to the conversion of methane in the reactor. Sufficient steam concentration in the feed is a necessary condition for complete conversion of methane. When the ratio is lower than 4, the conversion of methane is reduced markedly. Under the investigated conditions, the reaction efficiency is independent of the inlet gas flow rate. This trend occurs because the mass transfer and reaction kinetics are fast enough to reach the chemical equilibrium. The production time will decrease with increasing gas flow rates. The simulation results show that the integration of CO2 sorption into the SMR process can increase the methane conversion to about 100% and allows more effective energy utility. The adsorption rate of CO2 is fast enough compared with the SMR rate to completely adsorb the CO2 produced in the bubbling fluidized bed investigated. Acknowledgement The PhD fellowship (Chao, Z.) financed through the GASSMAKS program (Advanced Reactor Modeling and Simulation) and the Post doc fellowship (Wang, Y.) financed through the RENERGI program (Hydrogen Production by Sorbent Enhanced Reforming) of the Norwegian Research Council are gratefully appreciated. Nomenclature
Latin letters drag coefficient for a particle CD heat capacity of phase k Cp,k s CO2 fraction in sorbent CCO 2 particle diameter dd, dp binary diffusion coefficient Dji diffusion coefficient for component j in phase k Dk,j e coefficient of restitution F constant g gravity radial distribution function g0 interfacial heat transfer coefficient hcd reaction enthalpy for reaction i HiR k rate coefficient thermal conductivity of phase k kk K1, K2, K3 equilibrium constant adsorption constants for component Y (Y ¼ CH4, CO2, H2, KY H2O) M mole mass interfacial heat transfer to phase k Qki n reaction order of CO2 adsorption p pressure particle pressure pd Pr Prandtl number r constant steam-to-carbon ratio rsc
112
Re Ri Rj Rs s S Sh t T X ydry Cd FD I Mk S ~ 0c v vk
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113
Reynolds number reaction rate of reaction i formation rate of component j energy source constant specific surface area of sorbent Sherwod number time temperature conversion dry mole fraction in gas phase peculiar velocity drag force unit tensor interfacial momentum transfer of phase k deformation rate tensor of phase k fluctuating component of fluid velocity velocity of phase k
Greek letters ak volume fraction of phase k (k¼c,d) b interfacial drag coefficient g collisional energy dissipation f angle of internal friction zd solid phase bulk viscosity kd conductivity of granular temperature mdilute dilute viscosity d mk viscosity of phase k rk density of phase k sk stress tensor of phase k u mass fraction G averaged interfacial mass flux Q granular temperature Superscripts dilute dilute c collisional eff effective f frictional i interfacial k kinetic m molecular max maximum min minimum Subscripts a adsorption c continuous phase d dispersed phase, desorption eq equilibrium i reaction number j component number k phase (k ¼ c,d) p particle References Abanades, J.C., Anthony, E.J., Lu, D.Y., Salvador, C., Alvarez, D., 2004. Capture of CO2 from combustion gases in a fluidized bed of CaO. AIChE J. 50, 1614e1622. Akers, W.W., Camp, D.P., 1955. Kinetics of the methane-steam reactions. AIChE J. 1, 471e475. Allen, D.W., Gerhard, E.R., Likins, M.R., 1975. Kinetics of the methane-steam reaction. Ind. Eng. Chem. P.D.D. 14, 256e259. Al-Qahtani, H., 1997. Effect of aging on a steam reforming catalyst. Chem. Eng. J. 65, 51e56. Ávila-Neto, C.N., Dantas, S.C., Silva, F.A., Franco, T.V., Romanielo, L.L., Hori, C.E., Assis, A.J., 2009. Hydrogen production from methane reforming:
thermodynamic assessment and autothermal reactor design. J. Nat. Gas Sci. Eng. 1 (6), 205e215. Balasubramanian, B., Lopez Ortiz, A., Kaytakoglu, S., Harrison, D.P., 1999. Hydrogen from methane in a single-step process. Chem. Eng. Sci. 54, 3543e3552. Barros Zárante, P.H., Sodré, J.R., 2009. Evaluating carbon emissions reduction by use of natural gas engine fuel. J. Nat. Gas Sci. Eng. 1 (6), 216e220. Bauer, R., Schlünder, E.U., 1978. Effective radial thermal conductivity of packings in gas flow. Part II. Thermal conductivity of the packing fraction without gas flow. Int. Chem. Eng. 18, 189e204. Benyahia, S., Syamlal, M., O’Brien, T.J., 2006. Extension of Hill-Koch-Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technol. 162, 166e174. Boemer, A., Qi, H., Renz, U., 1997. Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed. Int. J. Multiphase Flow 23, 927e944. Ding, Y., Alpay, E., 2000. Adsorption-enhanced steam-methane reforming. Chem. Eng. Sci. 55, 3929e3940. Fuller, E.N., Schettler, P.D., Giddings, J.C., 1966. A new method for prediction of binary gas-phase diffusion coefficients. Ind. Eng. Chem. 58, 18e27. Gidaspow, D., 1994. Multiphase Flow and Fluidization. Academic Press, Boston. Grasa, G.S., Abanades, J.C., 2006. CO2 capture capacity of CaO in long series of carbonation/calcination cycles. Ind. Eng. Chem. Res. 45, 8846e8851. Gunn, D.J., 1978. Transfer of heat or mass to particles in fixed and fluidised beds. Int. J. Heat Mass Transfer 21, 467e476. Han, C., Harrison, D.P., 1994. Simultaneous shift reaction and carbon dioxide separation for the direct production of hydrogen. Chem. Eng. Sci. 49, 5875e5883. Hou, K., Hughes, R., 2001. The kinetics of methane steam reforming over a Ni/ aeAl2O catalyst. Chem. Eng. Sci. 82, 311e328. Hufton, J.R., Mayorga, S., Sircar, S., 1999. Sorption enhanced process for hydrogen production. AIChE J. 45, 248e256. Hughes, R.W., Lu, D., Anthony, E.J., Wu, Y., 2004. Improved long-term conversion of limestone derived sorbents for in-situ capture of CO2 in a fluidized bed combustor. Ind. Eng. Chem. Res. 43, 5529e5539. Jakobsen, H.A., 2008. Chemical Reactor Modeling, Multiphase Reactive Flows. Springer-Verlag, Berlin. Jenkins, J.T., Savage, S.B., 1983. A theory for the rapid flow of identical, smooth, nearly elastic spherical particles. J. Fluid Mech. 130, 187e202. Johnsen, K., Ryu, H.J., Grace, J.R., Lim, C.J., 2006a. Sorption-enhanced steam reforming of methane in a fluidized bed reactor with dolomite as CO2-acceptor. Chem. Eng. Sci. 61, 1195e1202. Johnsen, K., Grace, J.R., ELnashaie, S., Kolbeinsen, L., Eriksen, D., 2006b. Modeling of sorption-enhanced steam reforming in a dual fluidized bubbling bed reactor. Ind. Eng. Chem. Res. 45, 4133e4144. Johnson, P.C., Nott, P., Jackson, R., 1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 510e535. Kato, M., Essaki, K., Yoshikawa, S., Nakagawa, K., Uemoto, H., 2004. Reproducibility of CO2 absorption and emission for cylindrical pellet type lithium orthosilicate. J. Ceram. Soc. Jpn. 112, S1338eS1340. Kimura, S., Adachi, M., Noda, R., Horio, M., 2005. Particle design and evaluation of dry CO2 recovery sorbent with a liquid holding capacity. Chem. Eng. Sci. 60, 4061e4071. Lee, D.K., Baek, I.H., Yoon, W.L., 2004. Modeling and simulation for the methane steam reforming enhanced by in situ removal utilizing the CaO carbonation for H2 production. Chem. Eng. Sci. 59, 931e942. Lindborg, H., Lysberg, M., Jakobsen, H.A., 2007. Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds. Chem. Eng. Sci. 62, 5854e5869. Lindborg, H., Jakobsen, H.A., 2009. Sorption enhanced steam methane reforming process performance and bubbling fluidized bed reactor design analysis by use of a two-fluid model. Ind. Eng. Chem. Res. 48, 1332e1342. Li, Z., Cai, N., Yang, J., 2006. Continuous production of hydrogen from sorptionenhanced steam methane reforming in two parallel fixed-bed reactors operated in a cyclic manner. Ind. Eng. Chem. Res. 45, 8788e8793. Li, Z., Cai, N., 2007. Modeling of multiple cycles for sorption-enhances steam methane reforming and sorbent regeneration in fixed bed reactor. Energy Fuels 21, 2909e2918. Lopez Ortiz, A., Harrison, D.P., 2001. Hydrogen production using sorption-enhanced reaction. Ind. Eng. Chem. Res. 40, 5102e5109. Lu, H., He, Y., Liu, W., Ding, J., Gidaspow, D., Bouillard, J., 2004. Computer simulations of gasesolid flow in spouted beds using kinetic-frictional stress model of granular flow. Chem. Eng. Sci. 59, 865e878. Lun, C.K.K., Savage, S.B., Jefferey, D.J., Chepurniy, N., 1984. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223e256. Ma, D., Ahmadi, G., 1986. An equation of state for dense rigid sphere gases. J. Chem. Phys. 84, 3449e3450. Ochoa-Fernández, E., Rusten, H.K., Jakobsen, H.A., Rønning, M., Holmen, A., Chen, D., 2005. Sorption enhanced hydrogen production by steam methane reforming using Li2ZrO3 as sorbent: Sorption kinetics and reactor simulation. Catal. Today 106, 41e46. Ocone, R., Sundaresan, S., Jackson, R., 1993. Gas-particle flow in a duct of arbitrary inclination with particle-particle interactions. AIChE J. 39, 1261e1271. Patil, D.J., van Sint Annaland, M., Kuipers, J.A.M., 2005. Critical comparison of hydrodynamic models for gas-solid fluidized beds e Part I: bubbling gas-solid fluidized beds operated with a jet. Chem. Eng. Sci. 60, 57e72.
Y. Wang et al. / Journal of Natural Gas Science and Engineering 2 (2010) 105e113 Pedernera, M.N., Pina, J., Borio, D.O., 2007. Kinetic evaluation of carbon formation in a membrane reactor for methane reforming. Chem. Eng. J. 134, 138e144. Pfleger, D., Gomes, S., Gilbert, N., Wagner, H.G., 1999. Hydrodynamic simulations of laboratory scale bubble columns fundamental studies of EulerianeEulerian modelling approach. Chem. Eng. Sci. 54, 5091e5099. Prasad, P., Elnashaie, S.S.E.H., 2004. Novel circulating fluidized-bed membrane reformer using carbon dioxide sequestration. Ind. Eng. Chem. Res. 43, 494e501. Rusten, H.K., Ochoa-Fernández, E., Chen, D., Jakobsen, H.A., 2007a. Numerical investigation of sorption enhanced steam methane reforming using Li2ZrO3 as CO2-acceptor. Ind. Eng. Chem. Res. 46, 4435e4443. Rusten, H.K., Ochoa-Fernández, E., Lindborg, H., Chen, D., Jakobsen, H.A., 2007b. Hydrogen production by sorption-enhanced steam methane reforming using Lithium oxides as CO2-acceptor. Ind. Eng. Chem. Res. 46, 8729e8737.
113
Srivastava, A., Sundaresan, S., 2003. Analysis of a frictional-kinetic model for gasparticle flow. Powder Technol. 129, 72e85. Sun, P., Grace, J.R., Lim, C.J., Anthony, E.J., 2008. Determination of intrinsic rate constants of the CaO-CO2 reaction. Chem. Eng. Sci. 63, 47e56. Wilke, C.R., 1950. Diffusional properties of multicomponent gases. Chem. Eng. Prog. 46, 95e104. Xiong, R., Ida, J., Lin, Y., 2003. Kinetics of carbon dioxide sorption on potassiumdoped lithium zirconate. Chem. Eng. Sci. 58, 4377e4385. Xiu, G., Rodrigues, A.R., 2002. Sorption-enhanced reaction process with reactive regeneration. Chem. Eng. Sci. 57, 3893e3908. Xu, J., Froment, G.F., 1989. Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AIChE J. 35, 88e96. Yi, K.B., Harrison, D.P., 2005. Low pressure sorption enhanced hydrogen production. Ind. Eng. Chem. Res. 44, 1665e1669.