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Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Dynamic modeling and simulation of a proton exchange
membrane electrolyzer for hydrogen production
A. Awasthi a, Keith Scott b, S. Basu a,*
a
b
Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
School of Chemical Engineering and Advanced Materials, Newcastle University upon Tyne, Newcastle NE1 7RU, UK
article info
abstract
Article history:
Computational modeling of proton exchange membrane (PEM) water electrolyzers is
Received 3 September 2010
carried out to investigate the effect of operating conditions and on its performance by
Received in revised form
expending less time and effort than experimental investigations. The work presents
20 February 2011
a dynamic model of a PEM electrolyzer system based on MATLAB/Simulink software. The
Accepted 7 March 2011
model consists mainly of four blocks e anode, cathode, membrane and voltage. Mole
Available online xxx
balances on the anode and cathode blocks form the basis of the model along with Nernst
and ButlereVolmer equations. The model calculates the cell voltage by taking into account
Keywords:
the open circuit voltage and various over-potentials. The model developed predicted well
Water electrolyzer
the experimental data on PEM water electrolyzer available in the literature. The dynamic
PEM
behavior of the electrolyzer system is analyzed and the effects of varying electrolyzer
Hydrogen
temperature and pressure on electrolyzer performance and over-potentials are presented.
Modeling and simulation
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
1.
Introduction
In recent years, global energy shortages and ecological problems caused due to excessive use of fossil fuels have
strengthened the position of hydrogen as a future energy
carrier. Clean energy production devices such as fuel cells
which use hydrogen and oxygen as reactants emphasize the
role of hydrogen in future energy infrastructure. A major
hurdle in development of such technologies is the production
of pure hydrogen gas. Electrolysis of water to break it into
hydrogen and oxygen is a promising option for clean fuel
production. A method used in many commercial applications
is water electrolysis using alkaline electrolyte and nickel electrodes [1]. An electrolyzer system based on proton exchange
membrane presents several advantages over conventional
alkaline electrolyzers, such as higher efficiency [2], compact
mass volume characteristics and mainly a high purity of
hydrogen gas that is required for several applications [3].
However, these systems require more special components,
including expensive polymer membrane and porous electrodes, and current collectors.
A schematic of PEM electrolyzer operation is shown in Fig. 1.
Water is fed at anode where it breaks into protons and oxygen.
Protons travel through the membrane and combine with electrons from the outer circuit at cathode to form hydrogen.
Hydrogen production can be carried out both at low and high
pressures. Several authors have compared these options in
terms of cost effectiveness as well as the total power required in
production of hydrogen [4]. The advantages of high-pressure
electrolysis include elimination of hydrogen compression unit
which contributes significantly to cost and power savings. Onda
et al. [5] reported that the power required to produce highpressure hydrogen by high-pressure water electrolysis is about
5% less than that required for atmospheric water electrolysis.
There have been very few attempts made at the modeling
of PEM water electrolyzer systems. On the other hand several
* Corresponding author. Tel.: þ91 11 26591035; fax: þ91 11 26581120.
E-mail address: sbasu@chemical.iitd.ac.in (S. Basu).
0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2011.03.045
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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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 x x x ( 2 0 1 1 ) 1 e8
subsections of the model namely anode, cathode, PEM and
voltage calculation section. The model is developed using
MATLAB/Simulink as shown in Fig. 2. The model takes into
account various overvoltages and the open circuit voltage in
the calculation of cell polarization. Open circuit voltage (E ) is
calculated using Nernst equation, which takes into account
the effect of temperature and species concentration on the
cell emf (E ):
1=2
E ¼ E0rev þ
PH2 $PO2
RT
ln
nF
PH2 O
!
(1)
Many authors use a value of 1.23 V for E0rev , which is only
true at standard temperature and pressure. In this work we
have used a temperature dependent value of reversible cell
voltage [13] given by:
Fig. 1 e Schematic of a PEM water electrolyzer.
models are available for PEM fuel cell systems. A detailed
review of PEM fuel cell models can be found elsewhere [6].
They share a lot of characteristics with electrolyzer systems.
Yalcinoz et al. [7] have dynamically modeled an air
breathing PEM fuel cell with a feedback control system.
Gorgun et al. [8] presented a dynamic model of PEM electrolyzer system. The model was based on mole balance equations on anode and cathode. The calculation of partial
pressure of liquid water on anode side is done based on ideal
gas equation. However, no comparison with experimental
data has been made to validate the model. Dale et al. [9]
developed a semi-empirical model of PEM electrolyzer
system taking into account temperature dependent reversible
cell voltage. Curve fitting methods are used to fit the experimental data to determine various model parameters. Biaku
et al. [10] studied the temperature dependence of charge
transfer coefficient at the anode using a semi-empirical
model. Santarelli et al. [11] analyzed the effects of temperature, pressure and water feed rate on the electrolyzer operation with the help of a regression model. In another work,
Marangio et al. [12] present a detailed theoretical model of
electrolyzer system. The model presented includes activation,
ohmic and diffusion overvoltages. It also takes into account
the resistances of electrodes and plates along with resistance
of membrane. The model is fitted to experimental data and
a detailed analysis of operating parameters on electrolyzer
performance is presented. However, most models discussed
above are semi-empirical in nature. In the present investigation a model is developed based on analytical expressions,
which can dynamically model an electrolyzer system under
a wide range of operating conditions, e.g., temperature and
pressure.
2.
Model
The developed model aims at determining the relationship
between the cell current and cell voltage. This is done by
taking into account the interactions between various
E0rev ¼ 1:229 0:9 103 ðTel 298Þ
(2)
The activation overpotential is based on electrode kinetics
at the reaction site. This overpotential can be described in
terms of current density using ButlereVolmer (BeV) equation
for both anode and cathode as [14]:
hact ¼
RT
i
RT
i
arc sinh
arc sinh
þ
aan F
2io;an
acat F
2io;cat
(3)
Here, a is the charge transfer coefficient at the respective
electrodes and io is the exchange current density at the electrodes. The electrode kinetic model or ButlereVolmer equation
assumes symmetry of the reactions, i.e. the transfer coefficient
is numerically same for the oxidation and reduction parts of the
BeV equation. The charge transfer coefficient in the range of
0.18e0.42 is used in the model as determined by Baiku et al. [10].
The exchange current density in the range of 1013 and 106 A/
cm2 is reported in the literature [12]. It was decided to choose
a value for which experimental data on IeV characteristics of
PEM water electrolyzer is well predicted by the model.
Ohmic overvoltages are due to electrical resistances
present in the electrolyzer cell. The resistance of the electrodes and plates are very low as compared to the resistance
of the PEM [15]. Hence, we only considered the resistance of
the PEM in calculating the ohmic overvoltage:
hohm ¼
dm I
Asm
(4)
The conductivity of the PEM is given as [16]:
1
1
sm ¼ ð0:005139l 0:00326Þexp 1268
303 Tel
(5)
where, l is the degree of humidification of the membrane
expressed as molH2 O =molSO3 . In case of PEM water electrolyzers, the whole membrane can be considered to be fully
hydrated [12], since water is fed to the anode section in large
quantities. Usually in such cases l is taken to be in the range
14e21 and we have assumed it to be equal to 20. It should be
noted that while for single electrolyzer cell resistances of the
plates and electrodes are negligible; when considering a stack
of 10e15 cells these resistances may be more significant.
To calculate partial pressure of species which are required in
the Nernst equation, mass balance around various subsections
of the electrolyzer is performed. The anode section has a water
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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Fig. 2 e Simulink model of PEM water electrolyzer showing various interconnecting subsections.
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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Fig. 3 e Comparison of experimental data and model prediction of performance (VeI chr) of PEM water electrolyzer.
feed and it is consumed at the anode with the generation of
oxygen and protons. At the cathode, hydrogen is produced by
reduction of protons. The species generation and consumption
rates are given by Faraday’s law:
Nspecies ¼
I
nF
(6)
The transport of water is important to understand as it
passes through the membrane. The bulk of the water goes
through oxygen evolution reaction to generate proton and
oxygen. However, a small amount of water is transported
through PEM due to diffusion, caused by a difference in
concentration of water at both the ends of membrane. The
rate of water transport due to diffusion is calculated by integrating Fick’s law of diffusion between the two membrane
interfaces:
NH2 O;diff ¼
ADw CH2 O;me;cat CH2 O;me;an
dm
(7)
where, Dw is the diffusion coefficient and its value is dependent on value of l. The value for Dw from literature for high
values of l [7] is 1.25 1010 m2/s.
The water is also transported from the cathode section to
anode due to a large pressure difference between the two
sections. This mechanism is governed by Darcy’s law, which
takes into account the permeability of membrane:
NH2 O;pressure
Kdarcy $A$rH2 O $DP
dm $mH2 O $MH2 O
(8)
where, Kdarcy is the membrane permeability to water, m is the
viscosity of water and r is the density of water.
The most important mechanism of water transport is by
electro-osmotic drag which arises since the Hþ ions transferring through the membrane drag water molecules with
them. The molar flow rate is expressed as:
NH2 O;eod ¼
nd I
F
(9)
This transport mechanism mainly depends on the value of
the dimensionless parameter nd. The values of nd reported in
the literature are of wide range, some being low (0.2e0.3) [7]
and other high with large amount of water transport
through the membrane. So, the value of nd is chosen as
a fitting parameter in this model.
The species concentration at the membraneeelectrode
interface needs to be calculated in order to evaluate the water
diffusion rate as well as partial pressures for the Nernst
equation evaluation. Marangio et al. [12] assumed that the
molar flux of species between the electrode surface and
membraneeelectrode interface is governed by diffusion
phenomena and it is given by:
nH2 O;an ¼ Deff;an
CH2 O;ch;an CH2 O;me;an
de;an
nH2 O;cat ¼ Deff;cat
CH2 O;ch;cat CH2 O;me;cat
de;cat
(10)
(11)
Deff is the effective binary diffusion coefficient and can be
determined by applying a porosity correction; given as [17]:
e ep a
Deff ¼ DAB e 1 ep
(12)
where, e is the electrode porosity and ep is the percolation
threshold. Here a is an empirical coefficient and its value is
taken to be 0.785 [16]. A detailed mathematical formulation for
the calculation of species concentration and mole fractions at
the membraneeelectrode interface can be found elsewhere
[12]. Once these concentrations are calculated partial pressures are calculated by multiplying the pressures in anode and
cathode section with mole fractions of respective species.
The various subsections of the model interconnected with
each other are shown in Fig. 2. The anode and cathode
sections are used to calculate concentrations of species in the
respective flow channels. These are then sent to the PEM
section, where the amount of water transported through the
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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Fig. 4 e Contribution of various overvoltages to cell polarization of PEM water electrolyzer.
Fig. 5 e Hydrogen outflow rate with varying power of PWM water electrolyzer.
membrane is calculated. This section also calculates partial
pressure of the species which are sent to the voltage calculation for the open circuit voltage using the Nernst equation.
The calculated water transport through the membrane is fed
back to the anode and cathode sections.
3.
Results and discussion
3.1.
Model validation
The model results are simulated and validated with experimental data available in the literature [3,12]. Fig 3 shows that
experimental data of voltageecurrent plot for an electrolyzer
are well predicted by the model. The lines represent model
predictions and the symbols are the experimental data. As
stated before, nd is used as a fitting parameter for the model.
The value of nd obtained through fitting is 5, which is quite high
as compared to that (0.2e0.3) used in literature. This indicates
that a large amount of water transports through the PEM due to
electro-osmotic drag. The model is further used to analyze the
performance of electrolyzer under wide range of operating
conditions. Some variation between the experimental data and
model prediction is seen for temperature value of 90 C. This is
due to the use of different catalyst in experimental analysis of
electrolysis cell [3]. The value of charge transfer coefficient was
adjusted for a better fit to experimental data. Fixed values of
anode and cathode exchange current densities are used in the
model, although they vary with different catalysts. Also, value
of charge transfer coefficient has been reported to vary with
Fig. 6 e Effect of temperature on PEM water electrolyzer
performance (VeI chr).
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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Fig. 7 e Effect of pressure on PEM water electrolyzer performance (VeI chr).
operating temperature [10], which is not taken into account in
the model.
A comparison of contribution of various overvoltages in
total cell polarization is shown in Fig. 4. It is seen that the
contribution of ohmic overvoltage increases significantly with
the increase in current density. On the other hand, the
percentage contribution of activation overvoltage (around 15
%) does not change significantly with the increase in current
density. This suggests that membrane material, which has
a lower electrical resistance can be advantageous at high
current density, indicating higher hydrogen production rate.
3.2.
Transient behavior
The present model is capable of capturing the transient
dynamic behavior of the electrolyzer. It should be noted that an
environmentally favorable operation of electrolyzers involve
their coupling with renewable energy sources like wind, solar
and tidal energies. These sources often involve current transients, so a model which can be used to combine these transient sources with the electrolyzer can be used in development
Fig. 8 e Combined effects of pressure and temperature on
PEM water electrolyzer polarization.
of sustainable clean energy systems. A variation of hydrogen
outflow rate with changing current is shown in Fig. 5. The
results show hydrogen outflow rate under transient power
conditions. Although there is no time lag shown in the results,
the model provides an option for inclusion of response time of
an electrolyzer cell for variations in load. The characteristic
response time of the cell will include time delay due to reaction
rates, diffusion across gas diffusion layers and water transport
across the membrane.
3.3.
Effect of operating conditions
The effect of temperature on cell polarization at various
current densities is shown in Fig. 6. The increase in cell
temperature results in enhancement of cell performance due
to decrease in cell polarization for a given value of cell current.
This in turn results in consumption of less power for
a particular hydrogen production rate. At higher temperature,
the kinetics of the charge transfer reaction improves at the
electrodeemembrane interface. It should be noted that
conductivity of the proton exchange membrane increases
with the increase in temperature. This results in lower ohmic
overvoltage at higher temperatures.
The effect of changing pressure on cell polarization for
different values of current density is shown in Fig. 7. It is seen
that an increase in pressure causes a decrease in electrolyzer
performance, i.e. increases the cell polarization. Marangio et al.
[12] state that high counter pressure could reduce the kinetics
of the charge transfer thus causing an increase in cell polarization. In the model, an increase in cell pressure increases the
partial pressures of the species which in turn increase the open
circuit voltage calculated using Nernst equation. The effect of
pressure is more prominent at high current densities.
Although high-pressure operation seems to worsen the
electrolyzer performance it enables high temperature operation of the water electrolyzer even above 100 C. Also, a higher
pressure operation is beneficial in terms of hydrogen storage
[5]. The increase in temperature and pressure has opposite
effects on the electrolyzer performance and a set of values can
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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Fig. 9 e Effect of current density on water transport through the membrane of PEM water electrolyzer.
be reached for the optimum performance of electrolyzer
depending upon the pressure values required corresponding
to hydrogen storage unit. Fig. 8 shows the combined effect of
pressure and temperature on total cell polarization. It can be
seen that a high temperature and low pressure is the most
favorable operation.
Another important factor in determining the electrolyzer
performance is the water transport through the membrane.
Hydrogen outlet from the cathode is accompanied by water
that is transported from anode to cathode side. So, determination of water transport through the membrane is important. Fig 9 shows the effect of operating current density on
water transport through the membrane. It should be noted
that most of the water is transported by electro-osmotic drag
and the contribution by other mechanisms, i.e. diffusion and
pressure difference, is very less. A more detailed study of
water transport inside the electrolyzer is required.
A control system with thermal model, which may be used
to operate electrolyzer efficiently, can be added to the model
for further extension of this work. Finally, the electrolyzer
model can be coupled with renewable energy sources like,
solar and wind, and can be used for the optimization of such
integrated systems [18].
4.
Conclusion
The work presented here on model of PEM water electrolyzer
captures the dynamic behavior of electrolyzer to some extent.
It analyzes the performance of electrolyzer under different
operating conditions and the contributions of different overvoltages. It is noticed that ohmic overvoltage increases
sharply while activation overvoltage remains constant with
the increase in current density, indicating that improvement
in electrolyzer performance is possible by using low resistance
electrolyte. The experimental data on PEM water electrolyzer
performance at different temperatures is well predicted by the
model. The model is further used to study the effect of
pressure on PEM water electrolyzer performance. The results
from the model show that operating temperature and pressure have opposite effects on the performance. The electrolyzer must be operated at set values of temperature and
pressure such that cell performance and pressure required for
storage of evolved hydrogen from electrolyzer is optimized.
Acknowledgment
Authors would like to acknowledge the financial support of
UKIERI and Shell Hydrogen for the execution of the above
project.
List of symbols
Latin letters
A
contact area of membraneeelectrode assembly,
160 104 m2
C
concentration, mol/m3
D
diffusion coefficient, m2/s
E
reversible cell potential, V
F
faraday constant, 96,485 C/mol
membrane permeability to water, 1.58 1018 m2
Kdarcy
I
cell current, A
i
current density, A/m2
io
exchange current density, A/m2
M
molar mass, kg/mol
N
molar flow rate, mol/s
n
molar flux, mol/s m2
nd
electro-osmotic drag coefficient
P
pressure, Pa
R
universal gas constant, J/mol K
T
temperature, K
t
time, s
V
cell voltage, V
electrons transfer in redox reaction
ve
Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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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 x x x ( 2 0 1 1 ) 1 e8
Greek letters
sm
membrane conductivity, ohm1 m1
d
thickness, m
e
electrode porosity
h
over potential, V
a
charge transfer coefficient
b
empirical coefficient in porosity correction for
pressure
m
viscosity of water, 1.1 103 Pa s
r
density of water, 1000 kg/m3
Subscripts
hydrogen
H2
oxygen
O2
water
H2O
act
activation
ohm
ohmic
rev
reversible
m
membrane
me
membraneeelectrode interface
ch
in channel
e
electrode
eff
effective
an
anode side
cat
cathode side
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Please cite this article in press as: Awasthi A, et al., Dynamic modeling and simulation of a proton exchange membrane
electrolyzer for hydrogen production, International Journal of Hydrogen Energy (2011), doi:10.1016/j.ijhydene.2011.03.045
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