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INL/EXT-05-00398
PREPRINT
Comparison Of A One-
Dimensional Model Of A
High-Temperature Solid-
Oxide Electrolysis Stack
With CFD And
Experimental Results
2005 ASME International Mechanical
Engineering Congress And Exposition
J. E. OBrien
C. M. Stoots
G. L. Hawkes
November 2005 1
Proceedings of IMECE2005
2005 ASME International Mechanical Engineering Congress and Exposition
November 5-11, 2005, Orlando, Florida USA
IMECE2005-81921
Comparison of a One-Dimensional Model of a High-Temperature Solid-Oxide
Electrolysis Stack with CFD and Experimental Results
J. E. OBrien, C. M. Stoots, and G. L. Hawkes
Idaho National Laboratory
Idaho Falls, ID 83415, USA;
james.obrien@inl.gov
ABSTRACT
A one-dimensional model has been developed to predict
the thermal and electrochemical behavior of a high-temperature
steam electrolysis stack. This electrolyzer model allows for the
determination of the average Nernst potential, cell operating
voltage, gas outlet temperatures, and electrolyzer efficiency for
any specified inlet gas flow rates, current density, cell active
area, and external heat loss or gain. The model includes a
temperature-dependent area-specific resistance (ASR) that
accounts for the significant increase in electrolyte ionic
conductivity that occurs with increasing temperature. Model
predictions are shown to compare favorably with results
obtained from a fully 3-D computational fluid dynamics model.
The one-dimensional model was also employed to demonstrate
the expected trends in electrolyzer performance over a range of
operating conditions including isothermal, adiabatic, constant
steam utilization, constant flow rate, and the effects of
operating temperature.
INTRODUCTION
A research program is under way at the Idaho National
Laboratory to assess the performance of solid-oxide cells
operating in the steam electrolysis mode for hydrogen
production over a temperature range of 800 to 900ºC. The
research program includes both experimental and modeling
activities. Experimental activities, including both single
button-cell testing and stack testing have been documented in
several recent publications [e.g., 1-3]. The modeling activities
include detailed computational fluid dynamics (CFD)
simulations [4] and system-level modeling.
In order to evaluate the potential hydrogen-production
performance of large-scale high-temperature electrolysis (HTE)
operations, we have developed an engineering process model at
INL using the commercial system-analysis code HYSYS.
Using this code, several detailed process flow sheets have been
defined that include all of the components that would be
present in an actual HTE plant such as pumps, compressors,
heat exchangers, turbines, and the electrolyzer. Since the
electrolyzer is not a standard HYSYS component, a custom
one-dimensional electrolyzer model was developed for
incorporation into the overall process flow sheet. This
electrolyzer model allows for the determination of the average
Nernst potential, cell operating voltage, gas outlet temperatures,
and electrolyzer efficiency for any specified inlet steam,
hydrogen, and sweep-gas flow rates, current density, cell active
area, and external heat loss or gain. The one-dimensional
electrolyzer model was validated by comparison with results
obtained from a fully 3-D computational fluid dynamics model
and by comparison with experimental results. This paper
provides details on the one-dimensional electrolyzer model,
comparisons to CFD and experimental results, and electrolyzer
performance predictions based on the one-dimensional model
over a range of operating conditions.
NOMENCLATURE
A
cell
per-cell active area, cm
2
ASR
area-specific resistance, Ohm cm
2
F
Faraday number, 96487 J/V mol
)
(T
G
R

Gibbs energy of reaction, J/mol
o
i
i
H
T
H
)
(
sensible enthalpy, J/mol
i
o
f
H
enthalpy of formation, J/mol
i current
density,
A/cm
2
current, A
LHV
low heating value of hydrogen, J/mol
i
N

molar flow rate, mol/s
N
cells
total number of electrolysis cells
Q

heat transfer rate to electrolyzer, W
R
universal gas constant, J/mol K
T temperature,
K
V voltage,
V
W
electrical work performed on electrolyzer, W
y mole
fraction
H
overall thermal-to-hydrogen efficiency 2
ONE-DIMENSIONAL ELECTROLYZER MODEL
In general, for an operating electrolysis stack, there will be
a temperature change associated with the electrolysis process.
For these cases, the energy equation for electrolysis process can
be written as:
P
o
i
P
i
o
f
i
H
T
H
H
N
W
Q
i
]
)
(
[
R
o
i
R
i
o
f
i
H
T
H
H
N
i
]
)
(
[
(1)
where Q is the external heat transfer rate to or from the
electrolyzer,
W
is the rate of electrical work supplied to the
electrolyzer,
i
N
is the molar flow rate of each reactant or
product,
i
o
f
H is the standard-state enthalpy of formation of
each reactant or product and
o
i
i
H
T
H
)
(
is the sensible
enthalpy for each reactant or product. Applying the energy
equation in this form, all reacting and non-reacting species
included in the inlet and outlet streams can be accounted for,
including inert gases, inlet hydrogen (introduced to maintain
reducing conditions on the steam/hydrogen electrode), and any
excess unreacted steam. In general, determination of the outlet
temperature from Eqn. (1) is an iterative process. The heat
transferred during the process must first be specified (e.g., zero
for the adiabatic case). The temperature-dependent enthalpy
values of all species must be available from curve fits or some
other data base. The solution procedure begins with
specification of the cathode-side inlet flow rates of steam,
hydrogen, and any inert carrier gas such as nitrogen (if
applicable). The inlet flow rate of the sweep gas (e.g., air or
steam) on the anode side must also be specified. Specification
of the gas flow rates allows for the determination of the inlet
mole fractions of steam, hydrogen, and oxygen that appear in
the Nernst equation. The steam mole fraction is expressed in
terms of the hydrogen mole fraction as 1-y
H2
-y
N2
.
The current density and active cell area are then specified,
yielding the total operating current. Care must be taken to
insure that the specified inlet gas flow rates and total cell
current are compatible. The minimum required inlet steam
molar flow rate is the same as the steam consumption rate,
given by:
2
2
min
,
2
,
2
2
H
cells
cell
cells
O
H
O
H
i
N
N
F
A
i
N
F
I
N
N
(2)
which is of course also equal to the hydrogen production rate.
Once the total and per-cell hydrogen production rates are
known, the outlet flow rates of hydrogen and steam on the
cathode side and oxygen on the anode side can be determined.
The flow rates of any inert gases, the anode-side sweep gas, and
any excess steam or hydrogen are the same at the inlet and the
outlet. Once all these flow rates are known, the summations in
Eqn. (1) can be evaluated. The product summation must be
evaluated initially at a guessed value of the product
temperature, T
P
.
The operating voltage corresponding to the specified
current density is obtained from:
)
(T
ASR
i
V
V
Nernst
op
(3)
where the stack area-specific resistance, ASR(T), must be
estimated and specified as a function of temperature. The cell-
mean Nernst potential can then be obtained from an integrated
Nernst equation:
)
)(
)(
(
2
1
,
,
,
,
,
,
,
,
2
2
2
2
C
H
i
C
H
o
A
O
i
A
O
o
R
P
Nernst
y
y
y
y
T
T
F
V
P
R
A
O
o
A
O
i
C
H
o
C
H
i
T
T
y
y
y
y
O
H
O
H
N
H
R
dT
dy
dy
y
y
y
y
RT
T
G
,
2
,
,
2
,
,
2
,
,
2
,
2
2
2
2
2
2
2
/
1
1
ln
)
(
(4)
where y
i, O2, A
is the anode-side inlet mole fraction of oxygen,
etc. Note that the upper limit of integration on the temperature
integral, T
P
, is initially unknown. Once the ASR and the mean
Nernst potential are known, the operating voltage is obtained
from Eqn. (3) and the electrical work term in Eqn. (1) is
obtained from
I
V
W
op
. An algorithm then must be
developed to iteratively solve for the product temperature, T
P
,
in order to satisfy Eqn. (1). This algorithm can then be
imbedded in a loop so that a full numerical sweep can be
performed. We have implemented this procedure in MathCad.
The MathCad model provides accurate estimates of electrolyzer
operating voltage (and corresponding electrolyzer efficiency)
and outlet temperatures, for any specified electrolyzer heat loss
or gain, gas flow rates, current density, and per-cell ASR(T).
This electrolyzer model was developed for incorporation into
system-level electrolysis plant models being developed using
HYSYS system simulation software. With a realistic
electrolyzer model incorporated into the overall HYSYS plant
model, good estimates of overall hydrogen-production
efficiencies can be obtained over a wide range of prospective
operating conditions.
Predictions obtained from the 1-D integral model have
been compared to results obtained from a fully 3-D FLUENT
simulation. Complete details of the FLUENT electrolysis stack
model are provided in [4]. A condensed description