Numerical analysis of indirect internal reforming with self-sustained electrochemical promotion catalysts

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 6 4 8 2 e6 4 8 9

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Numerical analysis of indirect internal reforming with self-sustained electrochemical promotion catalysts Anchasa Pramuanjaroenkij a, Xiang Yang Zhou b,*, Sadik Kakac¸ c a

Department of Mechanical and Manufacturing Engineering, Kasetsart University, Chalermphrakiat Sakon Nakhon Province Campus, 47000, Thailand b Department of Mechanical and Aerospace Engineering, University of Miami, PO Box 248294, Coral Gables, FL 33124, USA c
u¨zo¨zu¨,
u¨zo¨zu¨ Cad. No.43 06560 So¨g Department of Mechanical Engineering, TOBB University of Economics and Technology, So¨g Ankara, Turkey

article info

abstract

Article history:

In this paper, we establish a numerical model for simulating an indirect internal reforming

Received 25 November 2009

section in a solid oxide fuel cell to demonstrate the effect of the electrochemical promotion

Received in revised form

and coupling between selective anode catalysts and selective cathode catalysts in the

15 March 2010

catalyst pack. The model employs a simplified geometrical model of an indirect internal

Accepted 25 March 2010

reforming section in the anode chamber of a solid oxide fuel cell. However, the model

Available online 5 May 2010

includes very complicated combination of conventional reforming processes, electrochemical promotion and coupling. The results predict that the electrochemical promotion

Keywords:

and coupling in a microscopic scale can enable a significant reforming and production of

Indirect internal reforming

hydrogen at a relatively low temperature (500
C).

Electrochemical promotion

ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

Electrochemical coupling

1.

Introduction

Hydrocarbon fuelled solid oxide fuel cells (SOFCs), in particular, low temperature SOFCs that operate at 500e650
C, require reforming of the hydrocarbon fuels [1e3]. The low operating temperature permits a larger range of choices for materials, higher durability, and less volume and mass of a SOFC system. However, the low operating temperature poses a difficulty for the reforming of the hydrocarbon fuel. Two reforming schemes are been implemented in the SOFC systems: external reforming and internal reforming (IR) [4e7]. In the case of internal reforming, the reformation of the hydrocarbon fuels takes place in the same chamber of the SOFC anode. The scheme of internal reforming is further categorized into indirect internal reforming (IIR) when the reforming reactions are separated spatially from the electrochemical reactions and direct internal

reforming (DIR) when the reforming reactions take place on SOFC anode. Use of IR schemes eliminates the external reformer as a subsystem, reduces the total size and mass, facilitates heat transfer, and enhances the thermal efficiency. Enhancement of intrinsic catalytic activity requires improvement of the catalyst material itself. Most catalysts contain active phases, promoters, and a support. Precious metals or alloys are commonly used as active phases [7e14]. Ni and Ni alloys are commonly used as non-precious metal active phases but require higher operating temperature and minor precious metal phases to mitigate sever coking problem [13e15]. Common catalyst supports such as alumina provide a catalyst carrier that prevents sintering or ripening of the active phases to ensure a stable high active surface area. Use of oxygen ion conducting materials including ceria and zirconia as catalyst supports has been a focus of research because these supports

* Corresponding author. Tel.: þ1 305 284 3287; fax: þ1 305 284 2580. E-mail addresses: [email protected] (A. Pramuanjaroenkij), [email protected] (X.Y. Zhou), [email protected] (S. Kakac¸). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.03.110

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can enable so called metal-support interaction [15e20]. Catalysts on non-stoichiometric ceria exhibit oxidation catalytic activity much higher than that for catalysts on other supports. The reason is that the ceria support provides surface oxygen species for the oxidation reaction and the consumed oxygen in the lattice is replaced via transfer of oxygen from oxidizing molecules to the lattice. However, for all these catalyst systems, the reforming reaction that involves at least two reactant molecules take place at close active sites with a distance of a few nanometers. This conventional concept of catalyst design at nanometer level has certain successes but in reality it has not satisfied the requirements for reforming technology that is specifically for low temperature SOFCs. Thus, most of previous experimental studies were conducted at high temperatures (>700
C) and with the aid of a large amount of oxygen or steam. Only a few papers reported reforming of heavy hydrocarbon fuels at low temperatures [21e24] from 500 to 650
C. In most of these studies, precious metals (Pt or Rh) were used as the major active phases in the catalysts. Electrochemical promotion of catalysis in the solid-state electrochemical systems with an external power source can accelerate reaction kinetics remarkably [25e27] at temperatures as low as 350
C. Electrochemical promotion is functionally identical to classical promotion; i.e., it is catalysed in the presence of a controllable electric double layer at the metal/gas interface. The electrochemical promotion is mainly due to electrochemical production of the short-lived sacrificial 2  2 promoters, such as O 2 , O2 , O , or most likely O , which are continuously supplied to the catalyst/gas interface via electrochemically controlled transport including surface diffusion from the solid electrolyte support. It is also called non-Faradaic electrochemical modification of catalytic activity or NEMCA effect. The rate enhancement ratio is defined by [25e27] r¼

r r0

difference of the electrochemical potentials of the selective 2  2 cathode and anode, the oxygen ion species (O 2 , O2 , O , O , in general, Od) that are produced at the cathode will be driven to the anode through the oxygen ion conductor and participate in the oxidation of the hydrocarbon while the electrons produced from the oxidation reaction are driven to the cathode through the electronic conductor and participate in the reduction of oxygen. Thus, the electrochemical promotion does not need an external power supply or it is self-sustained. In addition to the NEMCA effect, the coupling between the anode and cathode phases at short or long distances will increase the effective reaction cross-section that is much greater than that for Al2O3 (an insulator) supported catalysts. This coupling is equivalent to increasing the probability with which the reacting molecules meet at the active sites. In the case where a small area of anode is coupled with a large area of cathode, the oxidation on the anode area can be further accelerated. The intimate contact between the functional phases (anode, cathode, electronic conductor, and ionic conductor) in the nano-scale could enable additional enhancement via concerted interfacial effects. Overall, this new concept of catalysts has potential to enable catalyst systems with unprecedented high intrinsic activities. In this paper, we present an integrated numerical model for simulating normal reforming reactions and electrochemical promotion effects. The objective is to demonstrate that the coupling between the microscopic anodes and cathodes and self-sustained electrochemical promotion resulting from the coupling can significantly promote the reforming of methane in an IIR section in a SOFC at a relatively low temperature and benefit low temperature SOFC.

2.

The numerical model

2.1.

Anode channel

(1)

and the enhancement factor (electrochemical promotion efficiency) by l¼

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r  r0 I 2F

(2)

It has been demonstrated that the electrochemical promotion of catalytic reforming can be more than 2 orders of magnitude or the promotion efficiency, l>>1, even at very low current density (w1 mA). Such a remarkable increase in reaction rate can provide a great potential for catalytic reforming. Yet, the electrochemical promotion can only be enabled via an external power source or via short-circuiting the anode and cathode of an electrochemical cell, which is equivalent to a single-chamber solid oxide fuel cell (SC-SOFC) [25]. This is neither realistic nor easy to realize. Here we propose a new concept of self-sustained electrochemical promotion (SSEP) catalysis that can take advantage of the promotion potential and can be readily synthesized. The SSEP catalysts consist of four main components: selective anodic catalysts, selective cathodic catalysts, O2 ions conductor, and electronic conductor. Unlike the normal electrochemical promotion devices with separated anode and cathode, the catalysts contain tiny anodes and cathodes in the form of fine particles, typically 20 nme0.5 mm. Because of the

Fig. 1 illustrates a 2-D geometrical model simulating an IIR section in a SOFC. In the case of a real fuel cell Wall A may be the anode of the SOFC. Because this paper is purported to reveal the effect of electrochemical promotion on the IIR, the complexity relating to the SOFC anode is not in the consideration. Both Wall A and Wall B assume a non-reactive and isothermal boundary condition. The master equations used in the two domains are as follows [28,29] vu vv þ ¼ Sm vx vy

(3)

where Sm ¼ 0; no accumulated mass in the channel.

u


vu vu vP 1 v2 u v2 u þv ¼ þ þ 2 þ Sdi;x 2 vx vy vx Re vx vy

(4)

where Sdi;x ¼ 0; no x-momentum source term in the channel. u


vv vv vP 1 v2 v v2 v þ Sdi;y þv ¼ þ þ vx vy vy Re vx2 vy2

(5)

where Sdi;y ¼ 0; no y-momentum source term in the channel.

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Fig. 1 e A simplified geometrical model of an IIR section in a SOFC.

u


2 vCi vCi 1 v Ci v2 Ci þ Ss;i þv ¼ þ vx vy ReSc vx2 vy2

(6)

where Ss;i ¼ 0; no species source term (no reaction in the channel).  vT vT 1 v T v T þ Sh;species þ Sh;reactions ¼ u þv þ vx vy RePr vx2 vy2


2

! 
vqy vqy v2 qy v2 qy 1 vP 1 þ Sdi;y ;qy ¼ 3v þ qy ¼ 3 þ rð2Þ qx þ vx vy 3 vy Re vx2 vy2

u

2


2  vv vv vP 1 v v v2 v þ v ¼  þ rð2Þ þ 2 þ Sdi;y 2 vx vy vy Re vx vy

(7)

where

where Sh;species ¼ 0; no heat source term from any species (no reaction in the channel) and Sh;reactions ¼ 0; no heat source term from any reactions (no reaction in the channel).

Sdi;y ¼

2.2.

The section is a porous material containing micro-particles or nano-particles of four types: (1) selective anode phase (Ni or NiO), (2) selective cathode phase (La0.8Sr0.2MnO3 or LSM), (3) solid oxide electrolyte or oxygen ion conductor (yttria stabilized zirconia or YSZ), and (4) electronic conducting phase (Cu). Thus, the catalysts actually are composed of numerous microelectrochemical cells in which anode phases and cathode phase are coupled via the solid oxide electrolyte (YSZ) and Cu. The coupling of the anode and cathode phases enables electrochemical promotion of the reforming reactions as has been demonstrated in Veyenas’s previous studies on the macroscopic solid-state electrochemical cells. Thus, the reforming processes are combination of the conventional reforming reactions and electrochemical promotion processes. The master equations in this IIR section are as follows. The conservation of mass: 
vqy vu vv vq þ ¼ xþ ¼ Sm (8) 3 vx vy vx vy where 
I I Aactive Sm ¼  MH2 þ MH2 O reff c 2F 2F The conservation of momentum:
2  
1 vq vq vP 1 v qx v2 qx þ Sdi;x ;qx ¼ 3u qx x þ qy x ¼ 3 þ rð2Þ þ vx vy 3 vx Re vx2 vy2

(9)

and

(16)

The species balance equation can be written as  

2 1 vCi vCi 3 v Ci v2 Ci þ qy ¼ qx þ 2 þ Ss;i 2 vx vy 3 ReSc vx vy

u

(17)


2 vCi vCi 3 v Ci v2 Ci þv ¼ þ 2 þ Ss;i 2 vx vy ReSc vx vy

(18)

where Ss;i ¼

Dh Ss;i ct Ui reff

(19)

The energy conservation equation can be written as follows:  

2 1 vT vT 1 v T v2 T þ Sh;species þ Sh;reactions ¼ qx þ qy þ 3 vx vy RePr vx2 vy2

u


2 vT vT 1 v T v2 T þv ¼ þ 2 þ Sh;species þ Sh;reactions 2 vx vy RePr vx vy

Sh;species ¼


2 n n X X Mi hi §eff 1 v Ci v2 Ci i þ 2 ;M ¼ Ci Mi 2 M cp;eff Ui Ti Dh i¼1 vx vy i¼1

Sh;reactions ¼

(20)

(21)

Dh Dh m3u Dh mu Sdi;x ¼ ¼3 reff Ui reff Ui k reff Ui k

(12)

Dh reff cp;eff Ui Ti

Sh;reactions ¼

Dh

2 X

reff cp;eff Ui Ti

i¼1

Ri Dhreaction;i

(22)

(23)

2

The porosity of the catalysts can be used to describe thermal properties of the anode by the following equations

where Sdi;x ¼

(15)

and

(10)

(11)

2

Dh Dh m3v Dh mv Sdi;y ¼ ¼3 reff Ui reff Ui k reff Ui k

where

 v u v u þ 2 þ Sdi;x 2 vx vy

vu vu vP 1 u þ v ¼  þ rð2Þ vx vy vx Re




(14)

ð1  3Þ2 rð2Þ ¼ 2:25 32

IIR section in anode chamber

(13)

keff ¼ 3kfluid þ ð1  3Þksolid

(24)

cp;eff ¼ 3cp;fluid þ ð1  3Þcp;solid

(25)

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Source terms in Eq. (19) for evolution and distribution of species are as follows: Ss;CH4 ¼ Rr MCH4 ¼ ðr0;r þ rr ÞMCH4

(26)

Ss;H2 ¼ ð3Rr þ Rs ÞMH2 ¼ ½3ðr0;r þ rr Þ þ ðr0;s þ rs ÞMH2

(27)

Ss;H2 O ¼ ðRr  Rs ÞMH2 O ¼ ½  ðr0;r þ rr Þ  ðr0;s þ rs ÞMH2 O

(28)

Ss;CO ¼ ðRr  Rs ÞMCO ¼ ½ðr0;r þ rr Þ  ðr0;s þ rs ÞMCO

(29)

Rr ¼ r0;r þ rp;r

(30)

Rs ¼ r0;s þ rp;s

(31)

Parameters

The reaction rates of non-electrochemical catalytic reaction of steam reforming (r0,r) and water gas shift (ro,s) reactions are calculated by using parameters from Fernandes and Soares [30] and Halabi et al. [31], the reactions and the calculations are as follows: CH4 þ H2 O4CO þ 3H2

(32)

CO þ H2 O4CO2 þ H2

(33)

r0;r ¼ r0;steam reforming reactkion ¼ R1 ¼

r0;s ¼ r0;water gas shift reactkion ¼ R2 ¼

k1 P2:5 H

k2 PH2

2

  P3 PCO PCH4 PH2 O  H2K1 DEN2

h

PCO PH2 O 

DEN ¼ 1 þ KCO PCO þ KH2 PH2 þ KCH4 PCH4

PH2 PCO2 K2

DEN2 KH O PH2 O þ 2 PH2 O

i

4.2248  1015 mol atm0.5/g h 1.955  106 mol/g h 6.65  104 atm1 1.77  105 6.12  109 atm1 8.23  105 atm1 7.846  1012 atm2 1.412  102

k1 k2 KCH4 KH2O KH2 KCO K1 K2

A general form of A þ D / products, where A is electron acceptor or oxidizing reactant and D is the electron donor or reducing reactant, the catalytic reaction rate of electrochemical promotion is [25e27]: rp ¼ kR qA qD

(41)

where kR is a constant due to reactions and the coverage ratios of the electron donor and acceptor, qD and qA, are given by: qD ¼

kD pD expðlD PÞ 1 þ kD pD expðlD PÞ þ kA pA ðlA PÞ

(42)

qA ¼

kA pA expðlA PÞ 1 þ kA pA expðlA PÞ þ kD pD ðlD PÞ

(43)

(35)

(36)

kR kA kD pA pD expðlD PÞexpðlA PÞ rpro ¼  2 1 þ kD pD expðlD PÞ þ kA pA ðlA PÞ

(44)

In the equations, P ¼ eFM =kb T, li is defined by a reduction or oxidation reaction, Sj denotes reactants (electron donor or acceptor), and pi is the partial pressure of species j. þlj

Sj ðgÞ/Sj

þ lj e

(45)

Table 2 e Important constants to calculate the electrochemical coupling [25e27].

Description of electrochemical promotion

Parameters

On anode particles:

CH4 þ O2 4 CO þ 2H2 þ 2e

(37)

CO þ O2 4 CO2 þ 4e

(38)

H2 þ O2 4 H2O þ 2e

(39)

On cathode particles:

O2 þ 4e 4 2O2

Values

(34)

where parameters are given in Table 1 according to literature data [30]. From Eqs. (34) and (35), r0 is in mol/gcath then I multiply r0 ðmol=gcat hÞ  rcat ðgcat =m3 Þ  1=3600 h=s, finally r0 is in mol/m3s . Since r0,r and r0,s vary with the pressure and, in the simulation, a local pressure of each node is different, so r0,r and r0,s are not constant throughout the domain. By using the reaction rates for non-electrochemical promotion reactions, the reforming processes can be modeled.

2.3.

Table 1 e Important constants to calculate the reaction rates of non-electrochemical catalytic reaction of steam reforming (r0,r) and water gas shift (ro,s) reactions [30].

(40)

ioc ioa ba bc R F Ee,15 Ee,16 e kb kD kA kR lA lD

Values 2300 5300 0.5 0.5 8.314 J/mol/K 96485.3 0 1.048417181 V 1.6  1019 C 1.38  1023 J/K 0.01 100 6.19  106 mol/s 0.15 or 0.08 0.15 or 0.09

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where Ee,15 Ee,16 are the electrochemical equilibrium potentials for reactions (37) and (38), respectively, and a, b, and c are reaction orders. Integrate the Eq. (46) by substituting the Eqs. (47) and (48) FM ¼

0:25 3 i0;c PO2 dc bc Ee;16 þ ba Ee;15 RT ln þ bc þ ba Fðba þ bc Þ i0;c PO2 PH2 O d3a

(49)

Parameters are given in Table 2 according to literature data [25e27].

3.

Fig. 2 e CH4 mole fraction distribution in the anode domain without new electrochemical promotion calculation at 500
C.

2.4.

electrochemical coupling

Electrochemical coupling is given as ZZZ ðia ðFM Þ þ ic ðFM ÞÞdxdydz ¼ 0

(46)

where FM is the mixed electrochemical potential of the anode, cathode, and electronic conductor. Assuming that the electrochemical reactions of the anode and cathode are dominated by reaction (37) and (38), respectively (the subscripts follow the reactions) and the reactions are far from equilibrium.    a  b

b F exp a ðFa  Ee;15 Þ pH2 O ia ¼ ia;0 pH2 RT

(47)

   c

bF  exp  c ðFc  Ee;16 Þ ic ¼ ic;0 pO2 RT

(48)

Results and discussions

In the first set of computations, the reaction rates are given by Eqs. (30) and (31) but the rp,r and rp,s due to electrochemical promotion for the steam reforming and water gas shifting reactions respectively are set as zero. The results for an average temperature of 500
C are given in Figs. 2 and 3. The concentrations of CH4 in the catalyst pack and in the channel are almost the same or 0.5. At the outlet, the concentration reduces in a stepwise manner. This is due to the boundary condition that is established at the outlet. This result reveals that for conventional catalysts the reforming reaction rates are too low to enable significant consumption of CH4. As shown in Fig. 3, accordingly the production of hydrogen is very low in the level of 105. Figs. 4 and 5 illustrate the results for the case when rp,r and rp,s are added into Eqs. (30) and (31) for the description of the electrochemical promotion effect. The rates, rp,r and rp,s are evaluated using Eq. (41) in which the surface coverage ratios are evaluated using Eqs. (42) and (43). The electrochemical potential parameters in Eqs. (42) and (43) are evaluated using Eqs. (46)e(49). Thus, the concentrations, reaction rate, electrochemical potential, and the electrochemical promotion are inter-related in a self-consistent manner in the mathematical model. Figs. 4 and 5 clearly demonstrate that at a relatively low temperature (500
C) fast reforming of CH4 can be enabled with the electrochemical promotion. In the channel, the concentration of CH4 is 0.45 whereas in the catalyst pack, the concentration is less than 0.01. The hydrogen concentration in the channel is close to zero while in the catalyst pack the value is

Fig. 3 e H2 mole fraction distribution in the anode domain without new electrochemical promotion calculation for 500
C.

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Fig. 4 e CH4 mole fraction distribution in the anode domain with new electrochemical promotion calculation for 500
C.

0.06. The distributions of reaction rates in the chamber can also reveal the effect of electrochemical promotion. In the case that there is no electrochemical promotion, the rate is close to zero while if there is electrochemical promotion the rate is 3  106 mole/s. The overall conversion of methane is also a function of the ratio of channel size to pack size and a function of the inlet flow rate. The optimal parameters for design of an IIR may be obtained by varying these parameters in a realistic range. One of the present authors have conducted experimental work using a catalyst pack in a reforming reactor with a length of 22 cm and a high conversion (90%) of hydrocarbon fuels has been obtained at temperatures from 450 to 650
C. While the results are in the process of publication, experimental observations from two types of experiments support the simulation results. Firstly, in experimental work [32,33] on cogeneration SOFC where oxygen ions were supplied to the anode to promote syngas production high conversion rates were obtained at 700e800
C. In the SOFC, the internal resistance between the anode and cathode was much greater than that in a microscopic cell. If the internal resistance between the anode and cathode

were decreased to level for a microscopic cell, the temperature at which the production rate of syngas is significant might be even lower than 700
C. Secondly, oxidation of ethylene into carbon dioxide was significantly accelerated at 425
C on a YSZ supported film containing Au and dispersed Pt when there was no externally imposed current [34]. Fernades et al. [30] and Halabi et al. [31] modeled reforming of CH4 in a conventional (powder bed) and membrane reactors. The values of the equilibrium and kinetic parameters are evaluated on the basis of experimental results. According to the modeling results, the conversion of CH4 in a reactor consists of conventional power bed Ni/MgAl2O4 as long as 20 m is less than 40% at 520
C and 29 atm. If the length is only 22 cm, the conversion is a few percent. The present results that are obtained using the same values of the parameters for the conventional catalysts without promotion also indicate a conversion of a few percent for 500
C and 1 atm and a length of 22 cm (Figs. 2 and 3). Thus, the previous and present modeling results are consistent at the point that at around 500
C and for a short reactor with a length of only 22 cm, the conversion of

Fig. 5 e H2 mole fraction distribution in the anode domain with new electrochemical promotion calculation for 500
C.

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CH4 is insignificant. However, if there is electrochemical promotion or the catalysts consist of four components, anode, cathode, electrolyte, and electron conductor in the form of microscopic particles, the conversion of methane can be as high as 90% at this relatively low temperature.

4.

Conclusions

Following conclusions can be drawn from the present simulation work. (1) The electrochemical promotion effect has been simulated using a 2-D numerical model of a indirect internal reforming section in a solid oxide fuel cell. (2) This 2-D model includes both the electrochemical promotion and coupling using mainly the equations observed by Veyenas and electrochemical ButlereVolmer equations. (3) The simulation results demonstrate that at a relatively low temperature (500
C) at which conventional catalysts are difficult to enable a significant reforming and production of hydrogen from CH4, the electrochemical promotion via coupling of the selective anode catalysts and selective cathode catalysts can result in a considerable reforming and production of hydrogen.

Acknowledgements This work is supported by US National Science Foundation under NSF CBET-0828379.

Nomenclature Aactive, actual reaction surface area per unit volume, m1 cp,eff, effective specific heat, kJ/kg K ct, total mole Ci, mole fraction of species i Dh, hydraulic diameter, m F,Faraday’s constant, 96,487 coulombs/mol hreactions,i, enthalpy of each reaction, kJ/kg i, current density, A/m2 i0, exchange current density, A/m2 I, current, Amp k, thermal conductivity, W/m K kb, Boltzmann constant kj the reaction rate constant Mi, molecular weight of species i, kg/mol pi, partial pressure of the species i P, dimensionless pressure term Pr, Prandtl number r, the catalytic rate of promotion at current I that is provided by the external power sources r0, the open-circuit catalytic rate r0,r, the reaction rates of non-electrochemical catalytic reaction of steam reforming reaction r0,s, the reaction rates of non-electrochemical catalytic reaction of water gas shift reaction rp,r, the reaction rates due to electrochemical promotion for the steam reforming reaction

rp,s, the reaction rates due to electrochemical promotion for the water gas shift reaction Re, Reynolds number Ri, reaction rate of reaction i Rr, the steam reforming reaction rate Rs, the water gas shifting reaction rate Sc, Schmidt number Ss,i, species source term of species i Sdi;x , dimensionless x-momentum source term Sdi;y , dimensionless y-momentum source term Sh;reactions , dimensionless energy source term due to each reaction Sh;species , dimensionless energy source term due to each species Sm , dimensionless mass sources term Ss;i , dimensionless species source term T, dimensionless temperature term Ti, inlet temperature, K Tw, wall temperature, K u, dimensionless velocity vector in x direction Ui, inlet velocity, m/s v, dimensionless velocity vector in y direction c, electrode volume, m3 Greek symbols b, symmetry factor l, the enhancement factor (electrochemical promotion efficiency) §, diffusion coefficient r, the rate enhancement ratio reff, effective density, kg/m3 m, fluid dynamic viscosity, Pa s or kg/(ms) e, porosity k, permeability, m2 F, the electrochemical potential of the catalysts Fm, the mixed electrochemical potential of the anode, cathode, and electronic conductor Subscripts a, anodic c, cathodic eff, effective fluid, fluid properties inside the electrode CH4, methane CO, carbon monoxide H2, hydrogen H2O, water i, species i in the electrode reaction solid, solid properties of electrodes t, total Superscripts eff, effective transport coefficients

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 6 4 8 2 e6 4 8 9

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