Fuel composition and diluent effect on gas transport and performance of anode-supported SOFCs

Article abstract of DOI:10.1149/1.1579480

Anode-supported solid oxide fuel cells (SOFCs) with Ni+yttria-stabilized zirconia (YSZ) anode, YSZ-samaria-doped ceria (SDC) bilayer electrolyte, and Sr-doped LaCoO₃ (LSC)+SDC cathode were fabricated. Fuel used consisted of H₂ diluted with He, N₂, H₂O, or CO₂, mixtures of H₂ and CO, and mixtures of CO and CO₂. Cell performance was measured at 800°C with the above-mentioned fuel gas mixtures and air as oxidant. For a given concentration of the diluent, cell performance was higher with He as the diluent than with N₂ as the diluent. Mass transport through porous Ni-YSZ anode for H₂-H₂O, CO-CO₂ binary systems, and H₂-H₂O-diluent gas ternary systems was analyzed using multicomponent gas diffusion theory. At high concentrations of diluent, the maximum achievable current density was limited by the anodic concentration polarization. From this measured limiting current density, the corresponding effective gas diffusivity was estimated. Highest effective diffusivity was estimated for fuel gas mixtures containing H₂-H₂O-He mixtures (～0.55 cm²/s), and the lowest for CO-CO₂ mixtures (～0.07 cm²/s). The lowest performance was observed with CO-CO₂ mixture as a fuel, which in part was attributed to the lowest effective diffusivity of the fuels tested and higher activation polarization.

Full text of DOI:10.1149/1.1579480

A942
Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
0013-4651/2003/150͑7͒/A942/10/$7.00 © The Electrochemical Society, Inc.
Fuel Composition and Diluent Effect on Gas Transport
and Performance of Anode-Supported SOFCs
,z
*
*
Yi Jiang and Anil V. Virkar
Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
Anode-supported solid oxide fuel cells ͑SOFCs͒ with Niϩyttria-stabilized zirconia ͑YSZ͒ anode, YSZ-samaria-doped ceria ͑SDC͒
bilayer electrolyte, and Sr-doped LaCoO3 ͑LSC͒ϩSDC cathode were fabricated. Fuel used consisted of H2 diluted with He, N2 ,
H2O, or CO2 , mixtures of H2 and CO, and mixtures of CO and CO2 . Cell performance was measured at 800°C with the
above-mentioned fuel gas mixtures and air as oxidant. For a given concentration of the diluent, cell performance was higher with
He as the diluent than with N2 as the diluent. Mass transport through porous Ni-YSZ anode for H2-H2O, CO-CO2 binary systems,
and H2-H2O-diluent gas ternary systems was analyzed using multicomponent gas diffusion theory. At high concentrations of
diluent, the maximum achievable current density was limited by the anodic concentration polarization. From this measured
limiting current density, the corresponding effective gas diffusivity was estimated. Highest effective diffusivity was estimated for
fuel gas mixtures containing H2-H2O-He mixtures ͑ϳ0.55 cm2/s͒, and the lowest for CO-CO2 mixtures ͑ϳ0.07 cm2/s͒. The lowest
performance was observed with CO-CO2 mixture as a fuel, which in part was attributed to the lowest effective diffusivity of the
fuels tested and higher activation polarization.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1579480͔ All rights reserved.
Manuscript submitted April 21, 2002; revised manuscript received January 20, 2003. Available electronically May 30, 2003.
Recent work has demonstrated that anode-supported solid oxide
reforming and gas shift reactions in a Ni-YSZ porous anode using a
single-channel model. The study showed that the anode structural
parameter, defined as the ratio of porosity, Vv , to tortuosity, ␶, had a
significant effect on methane conversion rate. A reduction of the
structural parameter by 26% lowered the methane conversion by
12%. No electrochemical overpotential or performance measure-
ments, however, were correlated with gas transport in this study.
Yakabe et al.12 studied gas transport in H2-H2O and CO-CO2 binary
systems through porous anodes. Under a constant current density,
the concentration distributions of reactants H2 and CO along the
direction normal and parallel to the electrode/electrolyte interface
were evaluated. The results showed that the calculated concentration
polarization was much higher for CO-CO2 than for H2-H2O due to
the much lower diffusivity of CO-CO2 . These computational results
were also compared with experimental measurements. The results
on steam-reformed methane as fuel indicated that the gas shift reac-
tion in porous anodes effectively reduces concentration polarization.
In the present paper, we address mass transport in porous anode
support of an SOFC. Studies were conducted on a variety of fuel
mixtures, such as as-received H2 ; mixtures of H2 with inert gases
such as He, and N2 ; H2-H2O, H2-CO, and H2-CO2 mixtures; and
CO-CO2 mixtures. All tests were conducted on one cell to ensure
that possible differences due to cell-to-cell variations are eliminated.
Mass transport in these binary and ternary systems was analyzed.
This included the estimation of effective diffusivities of gaseous
species through porous anodes, the effect of diluents on transport,
and the associated concentration polarization. In the case of mix-
tures of CO and H2 , the effect of in situ gas shift reaction was
examined.
fuel cells ͑SOFCs͒ exhibit high performance at intermediate tem-
peratures. Maximum power densities as high as 1.8-1.9 W/cm2 have
been reported at 800°C for anode-supported single cells.1-4 In a typi-
cal anode-supported SOFC, the anode support is a Ni-yttria-
stabilized zirconia ͑YSZ͒ cermet between ϳ0.5 and 2 mm thick. The
electrolyte is a thin ͑ϳ10 ␮m͒, dense YSZ film supported on a
porous anode substrate. The cathode is usually a porous mixture of
strontium-doped manganite, La1ϪxSrxMnO3Ϫ␦ ͑LSM͒, and YSZ,1-3
or a porous mixture of strontium-doped cobaltite, La1ϪxSrxCoO3Ϫ␦
͑LSC͒, and Sm-doped CeO2 ͑SDC͒.4 In addition, single-phase,
mixed ionic-electronic conductors ͑MIEC͒ materials have also been
used in high-performance fuel cells. The use of thin electrolyte film
results in a relatively low ohmic contribution to the total cell resis-
tance, which makes it possible to operate anode-supported SOFCs at
800°C or lower and thereby realize the benefits of a lower tempera-
ture operation, such as the use of inexpensive metallic interconnect.
One of the potential benefits of SOFCs over low-temperature fuel
cells, such as proton exchange membranes ͑PEMs͒ is fuel flexibility,
because SOFCs can potentially operate on various fuels including
hydrogen, carbon monoxide, methane, and other hydrocarbon fuels
without the problem of CO poisoning. Recent work has also shown
that it may be possible to operate SOFCs directly on a number of
hydrocarbon fuels, without the necessity of reforming.5-8 However,
in anode-supported SOFCs, significant losses may occur due to the
resistance to the transport of fuel gas through a relatively thick an-
ode, and especially at high fuel utilizations. The losses at the anode
are expected to become even more severe when the fuel used con-
tains gaseous species of molecular weights much greater than that of
hydrogen (H2), such as CO, CH4 , or other hydrocarbons. It is thus
imperative that a thorough investigation of the transport character-
istics of various gaseous species through porous anodes be con-
ducted to fully assess anodic concentration polarization losses in
anode-supported SOFCs. Gas transport through porous bodies, and
the effects of parameters such as volume fraction porosity, morphol-
ogy of pores, and pore size, have been studied in great detail.9,10
However, there is limited information available in the literature per-
taining to SOFCs.
Experimental
Cell fabrication.—While only measurements on one cell are re-
ported, a number of cells were fabricated. Single cells consisted of a
NiϩYSZ anode substrate, a NiϩYSZ anode interlayer, a YSZ-SDC
bilayer thin-film electrolyte, a LSCϩSDC cathode interlayer, and a
LSC cathode current collector layer. The procedure for preparing an
anode substrate and an anode interlayer was described elsewhere in
detail13 and is briefly described here. NiO and YSZ powders from
commercial sources were mixed in requisite proportions and ball-
milled in alcohol, dried, and screened through a 150 mesh sieve. A
circular disk ϳ1.2 mm thick and ϳ3 cm diam was uniaxially die-
pressed and presintered at 1000°C for 1 h. The disk was then coated
with a slurry of NiOϩYSZ anode interlayer and fired again at the
same temperature for 1 h to form a NiOϩYSZ interlayer ϳ20 ␮m
thick. YSZ and SDC layers were applied on the anode interlayer
Insofar as SOFCs are concerned, there are only a couple of pa-
pers in the literature examining gas-transport phenomena in porous
anodes with emphasis on hydrocarbon fuels. Lehnert et al.11 con-
ducted a simulation study of gas transport coupled with steam-
* Electrochemical Society Active Member.
z E-mail: anil.virkar@m.cc.utah.edu
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Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
surface sequentially using YSZ and SDC suspensions made from
A943
YSZ and 20 mol% samarium-doped CeO2 powders, dispersed ultra-
sonically in appropriate amounts of suitable liquids. Then the bilayer
electrolyte-anode substrate assembly was sintered in air at a tem-
perature between 1400 and 1500°C to form a dense, well-bonded
YSZ-SDC bilayer electrolyte-anode structure. The thickness of the
SDC layer was around 3 ␮m and the total thickness of the YSZ-
SDC bilayer electrolyte thin film was ϳ10 ␮m. The thin SDC layer,
as part of the electrolyte, served as a barrier, which prevented a
direct contact between YSZ and LSC. In this manner, the possible
chemical reaction between YSZ and LSC, which can form insulating
La2Zr2O7 during a high-temperature firing step, could be prevented.
The porous cathode interlayer was a composite of 50 wt %
strontium-doped lanthanum cobaltite La1ϪxSrxCoO3Ϫ␦ ͑LSC͒, x
͓
ϭ 0.3-0.7] and 50 wt % SDC. The cathode interlayer was applied
by screen-printing, followed by firing at a temperature between 1050
and 1300°C for 2 h to form a good bond between the SDC layer and
the cathode interlayer. The thickness of the interlayer after firing was
ϳ20 ␮m. On top of the interlayer, a porous layer of LSC was ap-
plied, followed by firing at a temperature between 1050 and 1300°C
for 1 h in air. The final anode thickness and the disk diameter were
1.1 and 27.7 mm, respectively. The cathode area was 1.1 cm2.
Figure 1. An SEM micrograph of a polished section of the NiϩYSZ anode
͑after impregnating with an epoxy͒.
The measurement of cell performance.—The cell was mounted in
a test fixture, which consisted of an alumina tube and an alumina
ring. The cell was secured between the alumina tube and the alu-
mina ring and spring-loaded to ensure good sealing between the cell
and the alumina tube using a flexible gasket. A silver mesh and a Ni
mesh, used as current collectors at the cathode and the anode, re-
spectively, were spring-loaded against, respectively, the cathode and
the anode. Measurements were carried out at 800°C, at 1 atm total
pressure ͑both fuel and air͒, and at predetermined, constant total
flow rates of fuel or fuel mixture and of air. The cell was reduced in
situ at 800°C in a 10% H2 ϩ 90% N2 mixture for several hours
prior to measurements. The fuel flow rate was maintained at 140
mL/min and the air flow rate was maintained at 550 mL/min in all
experiments. Open-circuit potentials ͑OCPs͒ were measured under
constant fuel flow over the anode and the airflow over the cathode.
Cell performance was measured using various fuel gas mixtures,
which included as-received H2 ͑straight from the as-received cylin-
ders, 99.99% pure H2), as-received CO ͑straight from the as-
received cylinders, 99.99% pure CO͒, H2 ϩ CO mixtures, H2 di-
luted with He, N2 , CO2 , H2O, and CO diluted with CO2 . Current-
voltage ͑I-V͒ curves were measured at various diluent
concentrations, i.e., at various partial pressures of the diluent, while
the total flow rate of fuel mixture was kept constant. Current densi-
ties were calculated based on the cathode area. The fact that cathode
area is different from the anode surface exposed to fuel introduces a
small error ͑typically Ͻ10%͒ in the power density. This issue has
been addressed in detail elsewhere.13 Cell tests with as-received
hydrogen were conducted without bubbling through a water bubbler.
Results
An SEM micrograph of a polished section of the Ni-YSZ anode
is shown in Fig. 1. Figures 2-4 show cell voltage vs. current density,
and power density vs. current density traces with as-received H2 ,
and H2 diluted with various concentrations of He, N2 , and CO2 . For
as-received H2 as the fuel, the OCP was around 1.05 V, the maxi-
mum power density was about 1.7 W/cm2, and there was no obvious
limiting current density, even at the highest current density of 4.5
A/cm2 at which measurements were made. When H2 was diluted
with various diluents, the general trend was similar for each diluent,
namely: ͑i͒ with increasing dilution the open-circuit voltage ͑OCV͒
decreased, and (ii) the maximum power density as well as the maxi-
mum current density decreased. At high diluent concentrations, sub-
stantial concentration polarization was present as evidenced by the
observation of a limiting current density. Since the cathode condi-
tions were kept the same, the observed changes in performance with
different diluents and their concentrations could be solely attributed
to changes made in anodic conditions.
A comparison of Fig. 2 (H2-He), 3 (H2-N2), 4 (H2-CO2), and 5
(H2-H2O) shows that the maximum power density achieved at the
highest concentration of the diluent ͑ϳ78-81%͒ was the highest for
H2-He mixtures ͑ϳ0.75 W/cm2͒ and the lowest for H2-CO2 mix-
tures ͑ϳ0.3 W/cm2͒. Also, the corresponding short-circuit current
Cell characterization.—Porosity of the Ni-YSZ anode was mea-
sured using the Archimedes method. The tested cell was broken into
several small pieces. Dry weight, Wdry , wet weight, Wwet , and
weight in water, Wwater , were measured using a high-accuracy bal-
ance. Wet weight was measured ͑in air͒ soon after the surface of the
sample was wiped dry, after boiling in water for 2 h. Porosity was
calculated according to the equation
Wwet Ϫ Wdry
Porosity ϭ
͓1͔
Wwet Ϫ Wwater
One of the fractured pieces was evacuated ͑to remove air from the
pores͒ and impregnated with an epoxy. After hardening the epoxy,
the sample was polished down to 1 ␮m finish. The microstructure of
the cell was examined using scanning electron microscopy ͑SEM͒
and the mean pore radius was determined by quantitative
stereology.14
Figure 2. Voltage and power density vs. current density at 800°C with as-
received H2 and H2 diluted with He as fuel.
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A944
Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
Figure 5. Voltage and power density vs. current density at 800°C for
Figure 3. Voltage and power density vs. current density at 800°C with as-
H2-H2O binary system with various concentrations of H2O.
received H2 and H2 diluted with N2 as fuel.
density was the highest for H2-He mixture ͑ϳ1.55 A/cm2͒ and the
lowest for H2-CO2 mixture ͑ϳ0.7 A/cm2͒. The highest power den-
sity measured was ϳ1.7 W/cm2 for this cell with as-received H2 as
the fuel. A comparison of H2-He and H2-N2 mixtures, wherein the
diluent is inert, shows that the maximum power density at the high-
est diluent concentration is ϳ0.75 W/cm2 for H2-He and ϳ0.5
W/cm2 for H2-N2 mixtures. Also, the corresponding anode-limiting
current densities were ϳ1.55 A/cm2 for H2-He mixture and ϳ0.85
A/cm2 for H2-N2 mixture of similar diluent concentrations.
As seen in Fig. 4 and 5, the OCV exhibited a stronger depen-
dence on the diluent concentration when the diluent was either CO2
or H2O, consistent with expectations as the diluents in these cases
are not inert, and enter into chemical reactions of the following type
In H2-H2O mixtures
considerably lower than that with as-received H2 as the fuel ͑Fig.
2-5͒. For the gas mixture containing 18% COϩ82% CO2 , the maxi-
mum power density was only ϳ0.1 W/cm2, and the corresponding
limiting current density was only ϳ0.2 A/cm2. An examination of
Fig. 2-6 shows that a limiting current behavior is observed in all
cases at higher diluent concentrations. The limiting current density,
i
as , for each case is plotted vs. the partial pressure of the fuel gas
͑either H2 or CO͒ in Fig. 7. It is seen that the dependence of ias on
the respective partial pressure (pH or pCO) is close to linear, with
2
H2-He fuel ͑or H2-H2O-He mixtures͒ exhibiting the highest ias and
the highest slope, and the CO-CO2 mixtures exhibiting the lowest ias
and the lowest slope.
Figure 8 shows the performance curves with H2 ϩ CO gas mix-
tures as the fuel, where the composition was varied between ϳ100%
͑as-received͒ H2 and ϳ100% ͑as-received͒ CO. The OCV is essen-
tially independent of the relative proportions of H2 and CO. The
maximum power density varied between ϳ1.7 W/cm2 for 100% H2
to ϳ0.7 W/cm2 for 100% CO. Note that the maximum power den-
sity for CO concentrations less than ϳ55% ranges between ϳ1.5
and ϳ1.7 W/cm2; and for CO concentrations between 68 and 100%,
the maximum power density ranges between ϳ1.2 and ϳ0.7 W/cm2.
H2 ϩ 12 O2⇔H2O
and in H2-CO2 mixtures
H2 ϩ CO2⇔H2O ϩ CO
until the respective reaction equilibria are established.
Discussion
Figure 6 shows cell performance curves for gas mixtures con-
taining CO and CO2 as the fuel. The maximum power density mea-
sured with as-received CO as the fuel was ϳ0.7 W/cm2, which is
Thermodynamic calculation of OCVs.—The thermodynamic
OCV of a fuel cell, which is the Nernst potential, is given by
Figure 4. Voltage and power density vs. current density at 800°C with as-
Figure 6. Voltage and power density vs. current density at 800°C for
received H2 and H2 diluted with CO2 as fuel.
CO-CO2 binary system with various concentrations of CO2 .
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Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
A945
Figure 9. Partial pressure of oxygen at the anode and OCV as a function of
pH for H2-H2O at 800°C.
O
2
Figure 7. Anode limiting current density vs. partial pressure of H2 or CO at
800°C.
H2 , whose water content was not known͒, the calculated OCV, and
the experimentally measured OCV as a function of pH O . The par-
pO
RT
2
2͑cathode͒
E ϭ
ln
͓2͔
ͩ
ͪ
tial pressure of oxygen at the anode increases from 10Ϫ20 atm to
4F
pO
2͑anode͒
10Ϫ17 atm, and the calculated OCV decreases from 1.021 to 0.877 V,
when the pH O increases from 0.15 to 0.8 atm. The measured OCV,
2
where pO
is the partial pressure of oxygen at the cathode
͑under open-circuit conditions͒, which is 0.21 atm when air is used
as the oxidant; pO is the partial pressure of oxygen in fuel at
2(cathode)
in general, exhibits the same trend as the calculated one, although it
is about 50 mV lower than the calculated OCV. For the reaction
2(anode)
CO ϩ 12 O2⇔CO2
͓5͔
the anode ͑under open-circuit conditions͒. For example, when H2 is
the fuel
the standard free energy, ⌬Go5 , is Ϫ189.65 kJ/mol.15 At pCO lower
than 0.8 atm, the disproportionation reaction
1
H2 ϩ O2⇔H2O
͓3͔
2
2CO⇔CO2 ϩ C
͓6͔
at equilibrium, the partial pressure of oxygen at the anode, pO
2(anode)
for which the standard free energy change is ⌬Gؠ6 ϭ 17.63
kJ/mol,15 should not occur at 800°C and 1 atm pressure, based on a
thermodynamic calculation. For values of pCO less than 0.8 atm, the
partial pressures of CO and CO2 in the initial gas mixture were used
to estimate the equilibrium partial pressure of oxygen at the anode,
is given as
2⌬Go3
pH O
2
ln pO
ϭ
ϩ 2 ln
͓4͔
ͩ ͪ
2͑anode͒
RT
pH
2
namely, pO
, using the following equation
where ⌬Go3 is the standard free energy of Reaction 3. The ⌬Go3 is
Ϫ188.165 kJ/mol at 800°C.15 At various partial pressures of H2 and
2(anode)
2⌬Go5
pCO
2
ͩ ͪ
pCO
ln pO
ϭ
ϩ 2 ln
͓7͔
H2O, pO
can be calculated from Eq. 4 and the OCV can be
2͑anode͒
2(anode)
RT
determined using Eq. 2.
Figure 9 shows the calculated pO
͑except for as-received
For values of pCO greater than 0.8 atm, first the partial pressures of
2(anode)
CO and CO2 according to the disproportionation reaction, Reaction
6, were estimated. Then pO
was estimated using the corre-
2(anode)
sponding values of the partial pressures of CO and CO2 and Eq. 7.
Finally, the OCV was calculated as a function of the partial pressure
of CO2 in the initial mixture, poCO . The calculated pO
, the
2(anode)
2
calculated OCV, and the measured OCV are plotted as a function of
poCO in Fig. 10. The trends in the measured OCV and the calculated
2
OCV are similar, although the measured OCV is between 50 and 75
mV lower than the theoretical values.
For calculating pO
and OCV for H2 ϩ CO2 gas mixtures as
2(anode)
the fuel, the reverse gas shift reaction, namely
H2 ϩ CO2⇔H2O ϩ CO
͓8͔
for which the standard free energy is ⌬Go8 ϭ 0.385 kJ/mol at 800°C
was considered. The corresponding equilibrium pCO , pCO , pH
,
2
2
and pH O were calculated. Then the corresponding pO
was cal-
2
2(anode)
culated using either the H2-H2O equilibrium or the CO-CO2 equi-
librium. Using the calculated pO , the OCV was estimated by
Figure 8. Voltage and power density vs. current density at 800°C for H2-CO
mixtures as fuel with various concentrations of CO.
2(anode)
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A946
Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
cant uncertainties may exist in such calculations, no corrections for
leakage were made, and the data reported are as measured.
Gas transport in porous anodes.—Gas transport through porous
electrodes and correlation with electrochemical performance for bi-
nary gases, H2-H2O in the anode and O2-N2 in the cathode, have
been addressed in detail.2 There are two main fluxes contributing to
mass transport in a porous electrode: a diffusive and a viscous flux.
In general, the viscous flow, which is driven by a pressure gradient,
is negligible compared to the diffusive flow in porous electrodes.
Therefore, gas transport in porous electrodes is mainly due to diffu-
sion, which includes free molecular or Knudsen flow, and a con-
tinuum flow.
The general diffusion process for a multicomponent gas system
is described by the Stefan-Maxwell equation
Ni
XjNi Ϫ XiNj
P dXi
RT dx
ϩ
ϭ Ϫ
͓9͔
͚
DK,i
Dij
jϭ1
jÞi
Figure 10. Partial pressure of oxygen at the anode and OCV as a function of
pCO for CO-CO2 at 800°C.
2
where Ni and Nj are molar fluxes of components i and j ͑no.
mol/cm2 s͒, respectively, DK,i and Dij are the Knudsen diffusion
coefficient for component i and the binary diffusion coefficient for
components i and j, respectively, Xi and Xj are the mole fractions of
components i and j, respectively, P is the total pressure, R is the gas
constant, T is the absolute temperature, and x is the coordinate along
the diffusion direction. Knudsen diffusion is due to molecule-to-wall
collision, which predominates over molecule-to-molecule collision
when the pore size is smaller than the mean free path.10 The Knud-
sen diffusion coefficient can be computed according to the kinetic
theory of gases, using the following formula
Eq. 2. The calculated pO
, the calculated OCV, and the mea-
2(anode)
sured OCV are plotted as a function of the partial pressure of CO2 in
the initial gas mixture, poCO , in Fig. 11. As seen in the figure, the
2
calculated and the measured OCV are in good agreement, especially
for higher values of pCo O
.
2
The thermodynamic calculations and comparison with experi-
mental results show generally reasonable agreement between the
calculated and experimental OCV values, insofar as the trends are
concerned. However, the experimental values of the OCV are typi-
cally about 50 mV lower, and in some cases as much as 100 mV
lower. There are a couple of possibilities for this discrepancy. ͑i͒
There may have been a few pinholes in the YSZ film. (ii) The
sealing may not have been perfect. A lower OCV thus would imply
a higher H2O or CO2 pressure and a correspondingly higher partial
1/2
2
3
8RT
␲Mi
¯
DK,i
ϭ
r
͓10͔
ͩ
ͪ
¯
where r is the mean pore radius and Mi is the molecular weight of
the diffusing gas. The binary diffusion coefficient, Dij , is generally
experimentally measured or calculated using the Chapman-Enskog
equation,16 if it is not available experimentally. According to the
Chapman-Enskog model, the binary diffusion coefficient in cm2/s is
given by16
pressure of oxygen at the anode, pO
. Leakage is also the pos-
2(anode)
sible reason that OCV in H2-He and H2-N2 mixtures is dependent
upon the relative proportions of H2 and inert gas. If there had been
no leakage, ideally, it would be expected that the OCV would be
essentially independent of the concentration of inert diluent, He or
1/2
1
1
1.86 ϫ 10Ϫ3T3/2
ϩ
ͩ
ͪ
Mi
2
ij
Mj
Dij ϭ
͓11͔
N2 . In principle, using the measured OCV, this pO
can be
2(anode)
p⍀␴
calculated and thus the relative amount of water ͑or CO2) present in
the fuel can be estimated. However, as the general trend in measured
OCV is consistent with calculations ͑and expectations͒ and signifi-
where ⍀ is the collision integral ͑dimensionless͒, ␴ is the average
ij
collision diameter ͑in angstroms͒, Mi and Mj are molecular weights
of component i and j, respectively, and P is the total pressure ͑in
atm͒. Using ⍀ and ␴ data from Cussler,16 the calculated Dij for
ij
various gaseous species and at several temperatures are listed in
Table I, along with some experimental values from the literature for
comparison.15,17,18 Slight difference, usually less than 10%, is often
observed between the calculated values and the experimental values
over a range of temperatures between room temperature and 473 K.
Little data are available at higher temperatures. Hence, Dij at 800°C
were estimated using the Chapman-Enskog model.
In the present experiments, the mean pore radius of the Ni-YSZ
electrode was estimated from SEM micrographs ͑Fig. 1͒ to be ϳ0.5
␮m. The calculated Knudsen diffusion coefficients at 800°C for H2
and CO through the Ni-YSZ porous electrode are 11.3 and 3 cm2/s,
respectively. These values are comparable to the respective binary
diffusion coefficient of H2-He, which is 13.3 cm2/s, and CO-CO2 ,
which is 1.41 cm2/s at the same temperature ͑Table I͒. This indicates
that Knudsen diffusion is an important process in the present porous
anodes with 0.5 ␮m mean pore radius and should be taken into
account.
For a ternary system such as H2-He-H2O, the H2 molar flux
from Eq. 9 is given by
Figure 11. Partial pressure of oxygen at the anode and OCV as a function of
pH for H2-CO2 at 800°C.
2
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Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
A947
cients or diffusivities are termed effective diffusion coefficients or
effective diffusivities. For H2 and CO, the corresponding effective
diffusivities are given by16
Table I. Calculated binary diffusion coefficients from the
Chapman-Enskog equation and comparison with some experi-
mental data from the literature.
Vv
Dij
͑cm2/s͒ H2-He H2-N2 H2-CO2 H2-H2O H2-CO CO-CO2
DH ,eff ϭ
DH
͓18͔
2
2
␶
293K
1.535 0.722
0.604
0.738
0.726
0.735a
0.772c
0.149
1.53a
1.49c
0.728a
0.772c
0.651b
0.834b
0.162c
and
Vv
D
CO,eff ϭ
DCO
͓19͔
473K
3.417 1.626
1.395
1.513b
1.473c
1.819
1.642
1.651a
1.743c
0.349
␶
3.45a
3.39c
1.631a
1.743c
1.996b
0.384c
where DH and DCO are given, respectively, by Eq. 15 or 16 and 17.
2
1073K
13.29
6.303
5.56
7.704
6.373
1.408
As shown on the right side of Eq. 15, for a ternary system DH is
2
a From Ref. 17.
b From Ref. 18.
c From Ref. 15.
not only a function of diffusion coefficients, DK,H , DH ,He , and
2
2
DH ,H O , but is also a function of the mole fraction of the diluent
2
2
gas, XHe . If XHe varies from position to position along the diffusion
direction, DH will be a function of position. The variation of XHe as
2
a function of the position, x, can be determined by solving Eq. 9 for
the He flux, NHe , given by
NH
XHeNH Ϫ XH NHe
X
H ONH Ϫ XH NH O
2
2
2
2
2
2
2
ϩ
ϩ
DK,H
DH
DH
,He
,H O
2
2
2
2
XH NHe Ϫ XHeNH
XH ONHe Ϫ XHeNH O
2 2
NHe
2
2
dXH
P
ϩ
ϩ
2
DK,He
DHe,H
DHe,H O
2
ϭ Ϫ
͓12͔
2
RT dx
P dXHe
RT dx
ϭ Ϫ
͓20͔
Under steady-state conditions, NH O ϭ ϪNH and NHe ϭ 0. Thus
2
2
dXH
P
1
XHe
DH
1 Ϫ XHe
2
Because the net flow of He, NHe , is zero and NH ϭ ϪNH O in
steady state, Eq. 20 becomes
NH
ϩ
ϩ
ϭ Ϫ
͓13͔
ͩ
ͪ
2
2
2
DK,H
DH
RT dx
,He
,H O
2
2
2
2
From Eq. 13, H2 flux can be written in a similar form as Fick’s
equation by
1
1
P dXHe
RT dx
NH
Ϫ
XHe ϭ Ϫ
͓21͔
ͩ
ͪ
2
DHe,H O
DHe,H
2
2
PDH dXH
2
2
NH ϭ Ϫ
͓14͔
Integration of Eq. 21 gives
2
RT dx
RTNH la
1
1
2
XlHae ϭ XoHe exp
Ϫ
͓22͔
where DH is defined as the H2 diffusion coefficient in the
2
ͫ
ͬ
ͩ
ͪ
P
DHe,H
DHe,H O
2
2
H2-H2O-He ternary system, and is given by
Ϫ1
where la is the anode thickness, XؠHe is the mole fraction of He at
1
XHe
DH
1 Ϫ XHe
DH
ϭ
ϩ
ϩ
͓15͔
ͩ
ͪ
x ϭ 0, and XlHae is the mole fraction of He at x ϭ la . The case of
interest is that of a porous anode. Thus, the diffusivities must be
those corrected for porosity and tortuosity factor. Thus, the appli-
cable equation is actually
2
DK,H
DH
,He
,H O
2
2
2
2
When XHe ϭ 0, i.e., for H2-H2O binary system, the H2 diffusion
coefficient becomes
Ϫ1
1
1
RTNH la
1
1
2
XlHae ϭ XoHe exp
Ϫ
͓23͔
DH
ϭ
ϩ
͓16͔
ͩ
ͪ
2
DK,H
DH
,H O
2
ͫ
ͬ
ͩ
ͪ
2
2
P
DHe,H
DHe,H O,eff
,eff
2
2
Similarly, for the CO-CO2 binary system, the CO diffusion coeffi-
cient is given by
Equation 22 and 23 show that XHe varies exponentially as a function
of position. For the case of transport through space, in the absence
of a porous body, the calculated variation of XHe along the electrode
is very small. Using the estimated diffusion coefficients from the
Chapman-Enskog model, DHe,H ϭ 13.29 cm2/s and DHe,H O
Ϫ1
1
1
D
CO ϭ
ϩ
͓17͔
ͩ
ͪ
DK,CO
DCO,CO
2
2
2
ϭ 4.07 cm2/s, the XHe at the electrode/electrolyte interface (la
ϭ 0.1 cm͒ is about 0.8% lower than the bulk molar value of He,
XؠHe , at a current density of 1 A/cm2, i.e., for a molar flux of 5.18
ϫ 10Ϫ6 mol/cm2s. Even at a current density close to the anode
where DK,CO and DCO,CO are the Knudsen diffusion coefficient of
2
CO and the binary diffusion coefficient of CO-CO2 , respectively.
The preceding equations for diffusion coefficients are for trans-
port in a multicomponent gas system and do not account for the
volume fraction of porosity and the tortuous nature of path through
porous bodies. When the transport occurs through a porous body, the
interaction of gaseous species with the porous matrix must be in-
cluded. The simplest approach for taking this into account is to
modify the diffusion coefficients by the volume fraction porosity,
Vv , and the tortuous nature of the actual transport, characterized by
the so-called tortuosity factor, ␶.16 The resulting diffusion coeffi-
limiting current density, 3 A/cm2, XHe is only 3% lower than XHؠ e
.
Such, however, is not the case for a porous body. For transport
through porous anodes, Eq. 23 must be used. The corresponding
variation in XHe is ϳ10% at a current density of 1 A/cm2 and ϳ20%
at a current density of 3 A/cm2. Though this variation is not insig-
nificant, for simplicity we neglect this aspect and assume that the
diffusion coefficient of H2 is independent of position.
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A948
Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
2FDH ,effpoH
If the electrode microstructure is not a function of position, i.e.,
2
2
Vv and ␶ are constant, integration of Eq. 14, using effective diffu-
sivities, gives a simple equation for H2 flux in a ternary system,
similar to that for a binary system, namely
RTla
i
as ϭ
͓31͔
DH
,eff
AP
2
1 ϩ
RTla mT
PDH
,eff
2
NH ϭ Ϫ
X
Ϫ XHЈ ͒
2
͓24͔
͑
H
2
2
RTla
In all experiments, when the mole percent of the diluent was
more than 40%, a limiting current density was observed. From the
experimentally measured anode limiting current density, one can
estimate the effective diffusion coefficients for H2 for several dilu-
ents and at various concentrations by rearranging Eq. 31 as follows
where XHЈ and XH are the mole fractions of H2 over the anode
2
2
surface (x ϭ 0) and at the anode/electrolyte interface (x ϭ la), and
DH ,eff is the effective ternary diffusion coefficient as defined by Eq.
2
15 and 18. Replacing mole fractions with partial pressures, Eq. 24
becomes
ias
DH ,eff ϭ
͓32͔
2FpoH
2
ias AP
2
DH
,eff
2
Ϫ
RTla
RTla mT
NH ϭ Ϫ
p
Ϫ pHЈ ͒
2
͓25͔
͑
H
2
2
RTla
Also, for CO-CO2 mixtures, Eq. 32 can be used with poH replaced
2
where pHЈ and pH are the partial pressure of H2 over the anode
2
2
by poCO , and DH ,eff replaced by DCO,eff . Table II lists the calculated
2
surface (x ϭ 0) and the partial pressure of H2 at the anode/
electrolyte interface (x ϭ la), respectively. Assuming gases are well
mixed above the anode, similar to the situation in a continuously
diffusion coefficients from Equation 15-17, the estimated effective
H2 ͑and CO͒ diffusion coefficients from Eq. 32, and the experimen-
tally measured ias values from the voltage-current density polariza-
tion curves.
stirred tank reactor ͑CSTR͒, pЈH is given by
2
From Table II, it is seen that the H2 diffusion coefficient, DH
,
2
NH
A
2
pHЈ ϭ poH
Ϫ
2
P
͓26͔
for H2-H2O is about five times larger than that for CO-CO2 , DCO
.
2
mT
For H2-H2O, the effective diffusion coefficient estimated using Eq.
32, ranges from 0.470 to 0.506 cm2/s, almost independent of gas
composition, consistent with Eq. 16. For CO-CO2 mixtures, it varies
from 0.063 to 0.090 cm2/s over the range of pCO investigated. This
suggests that mass transport of H2 in H2-H2O mixtures should be
about five to six times faster than that of CO in CO-CO2 mixtures. If
CO is used as a fuel, the cell performance is expected to be lower
than with H2 as a fuel due to slow diffusion rate, regardless of other
effects, such as the intrinsically low electrochemical activity of CO.
Prior work has shown that anodic concentration polarization for
H2-H2O gas mixtures is given by2
where poH is the initial ͑incoming fuel͒ partial pressure of H2 , A is
the electrode area ͑1.1 cm2͒, mT the total molar flow rate of fuel and
2
diluent, and P is total pressure. Substituting for pЈH from Eq. 26 into
2
Eq. 25 gives
DH
NH A
2
,eff
2
NH ϭ Ϫ
p
Ϫ poH
2
ϩ
P
͓27͔
͓28͔
ͩ
ͪ
H
2
2
RTla
mT
Rearranging Eq. 27, H2 molar flux is given by
pHo
i
RT
i
RT
2
DH
p
Ϫ poH
H
2
͒
͑
,eff
␩
ϭ Ϫ
ln 1 Ϫ
ϩ
ln 1 ϩ
͓33͔
2
2
ͩ
ͪ
conc
ͩ
ͪ
poH Oias
2F
ias
2F
RTla
2
NH ϭ Ϫ
2
DH
,eff
AP
2
It is readily seen that the corresponding equation for CO-CO2 gas
mixtures as a fuel is given by
1 ϩ
RTla mT
poCOi
RT
i
RT
A maximum in H2 flux occurs when pH at the interface approaches
zero. This maximum flux is given by
2
␩
ϭ Ϫ
ln 1 Ϫ
ϩ
ln 1 ϩ
͓34͔
ͩ
ͪ
conc
ͩ
ͪ
poCO ias
2F
ias
2F
2
DH ,effpoH
2
2
Using Eq. 33 and 34,a ␩
was calculated as a function of current
conc
RTla
density for a H2-H2O mixture of composition 34% H2 Ϫ 66%
H2O, and for a CO-CO2 mixture of composition 32% COϪ68%
CO2 , for which the corresponding anode limiting current densities
were ϳ2 and ϳ0.5 A/cm2, respectively. The calculated concentra-
tion polarization is compared with the measured total polarization
͑by subtracting the ohmic contribution͒ in Fig. 12. It is readily seen
that anodic concentration polarization is much greater in CO-CO2
mixtures as compared to H2-H2O mixtures. The difference between
the measured total ͑excluding the ohmic͒ and the calculated anodic
concentration polarization is attributed to anodic and cathodic acti-
NH ,max ϭ
͓29͔
2
DH
,eff
AP
2
1 ϩ
RTla mT
The net current density passing through the cell is related to the net
hydrogen flux arriving at the anode/electrolyte interface, and is
given by
2FDH
p
Ϫ poH
͒
2
͑
,eff
H
2
2
RTla
DH
i ϭ 2FNH ϭ Ϫ
͓30͔
2
,eff
AP
2
1 ϩ
a Since the partial pressure of H2 or CO at the anode/fuel interface is a function of
RTla mT
the current density ͑using Eq. 26͒, one must strictly use pH instead of poH ͑or pCO
2
2
instead of pؠCO) in estimating the concentration polarization and attribute the re-
mainder of the terms to polarization associated with the depletion of fuel. Here, the
two terms are combined into a single equation describing concentration polariza-
tion, namely, Eq. 33 for H2 as a fuel ͑or Eq. 34 for CO as a fuel͒.
For the maximum possible hydrogen flux given by Eq. 29, there will
be a corresponding maximum in current density, which is the anode
limiting current density given by
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Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
A949
Table II. Partial pressure of dilute gas, anode limiting current density, H2 and CO diffusion coefficient, porosity, and tortuosity.
H2-H2O Binary System
DH ͑cm2/s͒
DH
͑cm2/s͒
͑exp.͒
Porosity ͑%͒
͑exp.͒
,eff
2
2
pH
ias ͑A/cm2͒
͑cal.͒
Tortuosity
2
0.2
0.34
0.5
1.3
2.1
3.25
4.58
4.58
4.58
0.506
0.470
0.506
54
54
54
4.89
5.26
4.89
CO-CO2 Binary System
DCO ͑cm2/s͒
͑cal.͒
DCO,eff ͑cm2/s͒
͑exp.͒
Porosity ͑%͒
͑exp.͒
pCO
ias ͑A/cm2͒
Tortuosity
0.18
0.23
0.32
0.44
0.21
0.31
0.49
0.73
0.958
0.958
0.958
0.958
0.063
0.073
0.084
0.091
54
54
54
54
8.27
7.08
6.17
5.65
H2-He-H2O Ternary System
DH ͑cm2/s͒
DH
DH
DH
͑cm2/s͒
,eff
͑exp.͒
Porosity ͑%͒
͑exp.͒
2
2
2
2
pHe
ias ͑A/cm2͒
͑cal.͒
Tortuosity
0.78
0.65
0.53
0.42
1.5
2.4
3.25
4
5.677
5.458
5.269
5.108
0.545
0.550
0.558
0.556
54
54
54
54
5.62
5.35
5.10
4.96
H2-N2-H2O Ternary System
DH ͑cm2/s͒
͑cm2/s͒
Porosity ͑%͒
͑exp.͒
,eff
2
pN
ias ͑A/cm2͒
͑cal.͒
͑exp.͒
Tortuosity
2
0.8
0.67
0.57
0.5
0.89
1.56
2.3
4.135
4.2
4.252
4.289
0.295
0.320
0.379
0.375
54
54
54
54
7.56
7.09
6.05
6.18
2.65
H2-CO2-H2O Ternary System
DH ͑cm2/s͒
͑cm2/s͒
Porosity ͑%͒
͑exp.͒
,eff
2
pCO
ias ͑A/cm2͒
͑cal.͒
͑exp.͒
Tortuosity
2
0.81
0.68
0.6
0.7
1.43
1.88
2.4
3.858
3.957
4.021
4.103
0.230
0.296
0.317
0.327
54
54
54
54
9.00
7.20
6.84
6.77
0.5
vation polarizations and cathodic concentration polarization. The ca-
thodic polarization ͑activationϩconcentration͒ is the same for the
two curves. For the test with H2-H2O as the fuel, at 0.25 A/cm2 the
difference between the measured and the calculated polarization
͑Eq. 33͒ is ϳ0.017 V, which includes: ͑a͒ cathodic concentration
polarization, ͑b͒ cathodic activation polarization, and ͑c͒ anodic ac-
tivation polarization. At the same current density, the difference be-
tween the measured and calculated polarization ͑Eq. 34͒ is ϳ0.19 V
for CO-CO2 as the fuel. However, the cathodic polarizations for ͑a͒
and ͑b͒ are identical for the two tests. Clearly, greater polarization
with the CO-CO2 mixture, beyond what can be attributed to anodic
concentration polarization, is attributed to anodic activation polar-
ization. That is, anodic activation polarization with CO-CO2 gaseous
mixture of the chosen composition at 0.25 A/cm2 is ϳ0.173 V
higher than that with H2-H2O gaseous mixture. This also suggests
that NiϩYSZ is not a very good anode for CO as the fuel. Indeed, it
has been reported in the literature that the electrochemical reaction
rate of CO is slower than that of H2 by at least a factor of two.12
Comparison of performance curves for H2-H2O mixtures with
CO-CO2 mixtures from Fig. 5 and 6 shows that the lower perfor-
mance with CO-CO2 mixtures cannot be attributed entirely to con-
centration polarization. Thus, although CO does not poison SOFC
anodes unlike PEM fuel cells, its low electrochemical activity, at
least with nickel-based anodes, and high concentration polarization
suggests that it is not an ideal fuel for SOFCs if a high power
density is a requirement.
The estimated DH using the Chapman-Enskog model and the
2
analysis of multicomponent transport as a function of diluent type
and concentration is given in Table II. The experimentally deter-
Figure 12. Comparison of the measured total polarization ͑less the ohmic
contribution͒ as a function of current density vs. calculated concentration
polarization for: ͑a͒ ϳ34% H2 ϩ ϳ 66% H2O and ͑b͒ ϳ32% COϩϳ68%
CO2 .
mined DH
from the anode-limiting current behavior via Eq. 32,
,eff
2
which includes the effects of porosity and tortuosity, are also given
in Table II. Note that for He as a diluent, the estimated DH is higher
2
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A950
Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
the exception of a small difference related to differences in concen-
tration polarization͒. There is very little difference in performance
with fuels ranging in composition from ϳ100% H2 and ϳ45% H2
ϩ ϳ 55% CO, as seen in Fig. 8. For compositions of fuel contain-
ing substantially greater than 50% CO, the H2O produced by the
electrochemical oxidation of H2 is not sufficient to shift most of the
CO to CO2 . The remaining CO has to be oxidized electrochemically
to CO2 , for which polarization is observed to be much greater ͑Fig.
6͒. Indeed, Fig. 8 shows that the performance is much worse with
fuels containing ϳ68% COϩϳ32% H2 and ϳ80% COϩϳ20% H2 .
than with N2 as the diluent. Table II also shows that estimated
DH ,eff is also similarly higher for He as a diluent compared to N2 as
2
a diluent. Similar trends are observed for CO2 as a diluent. Finally,
for CO-CO2 mixtures, the estimated DCO is much lower and so is
the DCO,eff . In the case of either N2 or CO2 as a diluent, it is also
seen that the trends in DH and DH
as a function of composition
,eff
2
2
are similar. That is, the results indicate that except for He, H2 diluted
with either N2 or CO2 not only lowers the partial pressure of H2 but
also reduces the effective H2 diffusion coefficient. Thus, the diluent
can lower cell performance in two ways, reduced pH and reduced
2
Conclusions
transport kinetics. From the experimental results ͑Fig. 3͒, at 32% N2
dilution the maximum power density was reduced by more than
30%. It was even worse for CO2 dilution with almost 40% reduction
of the maximum power density ͑Fig. 4͒ at the same diluent concen-
tration. This suggests when either partial oxidation or auto-thermal
reforming is used for processing fuel, nitrogen introduced into fuel
leads to a lowering of diffusive transport, in addition to fuel dilution.
The present work also shows that if in a reforming stage most of the
CO is converted to CO2 via a gas shift reaction, in addition to fuel
dilution there is also an adverse effect on diffusive transport.
Using DH , DH ,eff , DCO , and DCO,eff and the measured porosity
Based on the present work, the following conclusions are drawn:
1. Anode-supported SOFCs exhibit substantial effect of an inert
gas diluent in the fuel on concentration polarization, consistent with
expectations based on multicomponent gas diffusion in porous bod-
ies. Specifically, anodic concentration polarization is lower with an
inert gas diluent of low molecular weight ͑such as He͒ than an inert
gas diluent of higher molecular weight ͑such as N2).
2. For a sufficiently high concentration of the diluent, the volt-
age vs. current density traces exhibits anode limiting current density
behavior, characterizing a rapid drop of voltage at a critical current
density. This current density was used to estimate the corresponding
effective diffusivities.
3. Electrochemical performance with CO ϩ CO2 gas mixtures
is much worse than fuel gas mixtures containing H2 . This is ratio-
nalized in part on higher anodic concentration polarization and
slower electrochemical oxidation of CO. The results show that Ni
ϩYSZ is an excellent anode for H2-containing fuel, but not for CO.
4. Studies on cell performance with CO ϩ H2 gas mixtures as
fuel show that water gas shift reaction plays a major role. Effec-
tively, as long as the H2 content is greater than ϳ50%, high perfor-
mance is maintained by producing additional H2 through the shift
reaction. As a result, the cell performance with essentially pure H2 is
about the same as that with a H2 ϩ CO gaseous mixture as fuel, as
long as the CO concentration is not too high.
2
2
of 54% for the Ni-YSZ anode, the tortuosity factor of the anode, ␶,
was calculated from Eq. 18 and 19. All of the tortuosity factors fall
between 5.0 and 7.0 from H2-H2O and CO-CO2 binary system mea-
surements ͑with the exception of one value which is over 8.0͒ and
from H2-H2O with He, N2 and CO2 dilution ͑with the exception of
one value which is 9͒. The observation that tortuosity factor is on the
order of ϳ5 to ϳ7 justifies the use of effective diffusivities. At the
same time, the observation that the estimated tortuosity factor does
exhibit some variability suggests that it may include effects in addi-
tion to purely geometric factors ͑such as, possibly, adsorption and
surface diffusion͒. A value of five measured by a different method
for a Ni-YSZ anode has been reported in the literature.11 This sug-
gests that the possible effects of adsorption/desorption and surface
diffusion must be small in anodes of the present study.
Cell performance with H2 ϩ CO mixture as the fuel.—The cell
performance with as-received CO as fuel was poor because of slow
diffusion and slow electrochemical reaction rate, as discussed ear-
lier. However, the cell performance on H2 ϩ CO even when CO
concentration was as high as 55% was very high, close to that with
as-received H2 ͑Fig. 8͒ and quite high with CO content as high as
80%. The diffusion coefficient of H2 in H2-H2O-CO ternary mix-
tures ͑ignoring the effects of CO2) may be given by
Acknowledgments
This work was supported by the U.S. Department of Energy
͑NETL͒ under contract no. DE-AC26-99FT40713.
The University of Utah assisted in meeting the publication costs of this
article.
List of Symbols
A
cathode area, cm2
Ϫ1
Di diffusion coefficient of gaseous species i, cm2/s
1
XCO
DH
1 Ϫ XCO
DH
ϭ
ϩ
ϩ
͓35͔
DK,i knudsen diffusion coefficient of gaseous species i, cm2/s
Di,eff effective diffusion coefficient of gaseous species i, cm2/s
Dij binary diffusion coefficient of gaseous species i and j, cm2/s
Dij,eff binary effective diffusion coefficient of gaseous species i and j, cm2/s
ͩ
ͪ
2
DK,H
DH
,CO
,H O
2
2
2
2
The calculated DH ranges between 4.17 and 4.31 cm2/s for CO
E
F
nernst voltage, V
faraday constant, C/mol
2
mole fraction between 0.8 and 0.5, which is similar to that for
H2-H2O-N2 . However, the observed performance with H2-CO is
much superior to that with H2-H2O-N2 mixtures as the fuel. This is
consistent with expectations because a shift reaction is expected in
H2-CO gas mixtures during cell operation. At 800°C the standard
Gibbs free energy for the gas shift reaction
⌬G° standard free energy change, kJ/mol
i
current density, A/cm2
ias anode-limiting current density, A/cm2
la anode thickness, cm
Mi molecular weight of gaseous species i, g
mT total molar flow rate of fuel, mol/s
Ni molar flux of gaseous species i, mol/cm2
pi partial pressure of gaseous species i, atm
s
CO ϩ H2O⇔CO2 ϩ H2
R
T
ideal gas constant, J/mol K
temperature, K
Vv volume fraction porosity
is only Ϫ0.368 kJ/mol.15 However, the reaction rate constant is very
high as reported in the literature and thus it may be assumed that the
shift reaction at the anode/electrolyte interface is at equilibrium.11
Thus, for a fuel gas composition containing greater than 50% H2
͑and balance CO͒, it can be argued that H2O produced by the elec-
trochemical oxidation of H2 is more than sufficient to react with CO
present to form H2 and CO2 . In such a case, there should be little
difference in performance when compared to pure H2 as fuel ͑with
W
x
mass, g
coordinate along the diffusion direction, cm
Xi mole fraction of gaseous species i
Greek
␩
polarization, V
␴
average collision diameter of gaseous species i and j, A
tortuosity factor
ij
␶
⍀
collision integral
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Journal of The Electrochemical Society, 150 ͑7͒ A942-A951 ͑2003͒
A951
9. E. A. Mason and A. P. Malinauskas, Gas Transport in Porous Media: The Dusty
Gas Model, Elsevier, Amsterdam ͑1983͒.
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