Study of an Alkaline Electrolyzer Powered by Renewable

Study of an Alkaline Electrolyzer
Powered by Renewable Energy
E. Amores Vera(*),(1), J. Rodríguez Ruiz(*),(2), C. Merino Rodríguez(*), P. García Escribano(*)
(*) Centro Nacional del Hidrógeno. Prolongación Fernando El Santo s/n. 13500 Puertollano (Ciudad Real) - SPAIN
(1) [email protected], (2) [email protected]. Tel: +34 926 420 682
INTRODUCTION
RESULTS AND DISCUSSIONS
1000
3
800
5
600
400
200
6
2
01
8:00
10:00
6
5
3
4
5
3
2
2
1
0 1
8:00
12:00 14:00 16:00 18:00 20:00
Hour (hh:mm)
4
6
10:00
a
12:00 14:00 16:00 18:00 20:00
b
Hour (hh:mm)
Fig 4. Irradiation solar and current density profile
0.06
Hydrogen void fraction (1)
3
2.5
E (V)
This work reports the model of an alkaline
electrolysis cell powered by the profile of
a PV-module (Fig 1). Special attention was
paid to variations in generation of gas due
to changes in the power supply.
Energy that powered the alkaline electrolysis cell
7
4
Current Density (kA m-2)
The alkaline electrolysis is a highly developed technology in the industry and the main way of
obtaining hydrogen by electrolysis. Nowadays, commercial alkaline electrolyzers are designed
for a constant power supply. However, renewable energies are very fluctuating because of
their strong dependence on weather conditions. These fluctuations in power supplies to the
electrolyzer can cause problems such as generation of explosive mixtures, corrosion of
materials, reduced efficiency, pressure drops, changes of temperature, etc. The design of
alkaline electrolyzers powered by renewable energy is a critical issue to avoid these problems.
For these reasons, the model is presented as an important design tool.
SOLAR ENERGY
PV-MODULE
2
1.5
1
ELECTROLYZER
Hydrogen Overpotential
Oxygen Overpotential
Ohmic Loss
Erev
0.5
Fig 1. Electrolyzer powered by a PV module
0
5
1. Cathode
2. Cathodic
Compartment
3. Membrane
4. Anodic
Compartment
5. Anode
2
4
b
a
500
1000 1500
2000
2500
3000
3500
4000
4500
I (A/m2)
MODEL SET-UP
3
5000
0.04
0.03
0.02
0.01
0
0.05
0.15
0.1
0.2
x-Coordinate (cm)
T = 348K
Fig 5. Polarization curve
Taking as reference a commercial
electrolysis cell, the geometry of
the model was built following
fluid dynamic requirements (Fig
2). In this way, simplifications
were made in order to reduce
the model complexity. As result,
a good approximation can be
made just by 2D geometry,
which allows an optimal study of
the main involved variables.
1/7 H
3/7 H
5/7 H
H
electrode surface
0.05
0
0
1
Taking a real solar irradiation
profile as reference, current
density profile of PV-module
was implemented on COMSOL
(Fig 4). From the typical alkaline
electrolysis polarization curve
(Fig 5), it can be observed that
the effect of Ohmic losses
becomes important at high
current densities [4, 5].
Current density profile from a PV module
Solar irradiance profile
Puertollano, SPAIN (38° N, 4° W) - June 2011
1200
Solar Irradiance (W m-2)
The production of hydrogen from renewable energy surplus is seen as a key strategy for
energy storage. The Centro Nacional del Hidrógeno works actively in this direction by
considering a strategic line in order to achieve a sustainable energy future.
0.25
0.3
I = 6300 A/m2
Fig.6. H2 void fraction at 4 locations of the electrode
Next to the electrode surface, the volume fraction reaches the highest value, and
decreases towards the membrane (Fig 6), according with dynamic evolution of gas profiles
on cathode, when the cell is powered with PV module profile (Fig 7). In Fig 8, higher values
of current in the PV profile correspond with higher applied potential on the cell. Current
draws a particular distribution in the cell, being more intense in electrodes extremes [6].
Surface: H2 Volume Fraction (1)
Max. Void Fraction
4.88 %
5.88 %
3.81 %
Surface: Potencial Distribution (V)
Arrows: Current Density (proportional)
Vmax
0.0 V
1.93 %
2.0 V
3.1 V
3.4 V
2.7 V
2.0 V
0.05
3
0.04
2.5
0.03
2
1.5
0.02
control
volume
1
Gas and
electrolyte out
H
dy
H
1
0.5
4
2
dy
0.01
cell
5
δ
Electrolyte in
δ
c
4
5
6
11:00
14:00
17:00
18:30
0
1
2
3
4
8:00
8:30
11:00
14:00
Fig 7. Gas generation profiles
3
dz
W
3
e
d
Fig 2. Geometry of a commercial electrolysis cell implemented on COMSOL Multiphysics®
5
6
17:00
0
18:30
Fig 8. I-V distributions
Figure 9 shows a model of coalescence between two bubbles of hydrogen using COMSOL
Multiphysics®. During electrolysis of water, the bubbles rise by buoyancy and join in the
upper regions of the cell. The study of coalescence lets us know how the gas is
accumulated in the output channels of the electrolysis cell.
FORMULATION OF THE PROBLEM IN COMSOL®
MATHEMATICAL MODEL
ELECTRIC CURRENTS
(I-V distribution)
TWO PHASE FLOW, BUBBLY FLOW
(model gas generation)
TWO PHASE FLOW, PHASE FIELD
(motion of bubbles and coalescence)
r
r r
é
r 2 r r öù
r r
¶u
æ r
fl × rl × l + fl × rl × ul × Ñul = -Ñp + Ñ × êfl × (hl + hT )× ç Ñul + ÑulT - × (Ñul )× I ÷ú + fl × rl × g + F
¶t
3
è
øû
ë
r
r
¶
Ñ × J = -Ñ × d ((e oe r ÑV ) - Ñ × (s ÑV - J e ) = dQ j
¶t
¶
(fl × rl + fg × r g ) + Ñ × (fl × rl × url + fg × r g × urg ) = 0
¶t
¶fg × r g
¶t
DESCRIPTION
Faraday’s law of electrolysis
linking current supply (i) with
&H2)
hydrogen produced ( m
i ×M i
z×F
Bruggemann’s correlation linking
void fraction (f) with electrolyte
conductivity (σ)
s = s o × (1 - f )
1.5
)]
(
)
æ e 2 ö ¶f ext
÷
÷
è l ø ¶f
y = -Ñ × e 2Ñf + f 2 - 1 f + çç
SUBDOMAIN & BOUNDARY SETTINGS
æ i ö Tafel equation relates the rate of
R ·T
h = 2.3 ·
· logçç ÷÷ an electrochemical reaction (i) to
a ·F
è io ø the overpotential (η)
m& i =
[
(
r
+ Ñ(fg × r g × u g ) = -mgl
AUXILIARY EQUATIONS
EXPRESSION
r
r
r r r
r
¶u
r r
r r
r + r (u × Ñ )u = Ñ × - pI + m Ñu + Ñu T + Fg + Fst + Fext + F
¶t
r
Ñ×u = 0
¶f r
gl
+ u × Ñf = Ñ × 2 Ñy
¶t
e
SYMBOL
VALUE
p
1 bar
Pressure
DESCRIPTION
Temperature
T
348 K
io_cathode
0.02 A m-2
Exchange current density, cathode [1]
io_anode
0.016 A m-2
Exchange current density, anode [1]
s_membrane
67 S m -1
s_0
vo
130 S m
-1
0.1 m s-1
Membrane conductivity (PTFE) [2]
F Archim.
F Horizontal
F Friction
a
F Pump
b
Fig 3. Motion of bubbles in an electrolysis cell
0.0 s
0.2 s
0.4 s
0.6 s
0.8 s
1.0 s
1.4 s
1.8 s
2.0 s
2.5 s
Fig 9. Detail of coalescence phenomena between hydrogen bubbles
CONCLUSION
• COMSOL Multiphysics® 4.1 was used to model the behavior of a commercial electrolysis
cell for hydrogen production.
• It has obtained the distribution of O2 and H2 gas when the cell is powered by a PV module.
• Using the model developed in COMSOL Multiphysics® 4.1, we have determined the
current and potential distribution along the electrolysis cell.
• COMSOL Multiphysics® 4.1 can model phenomena of localized coalescence.
Electrolyte conductivity (30% KOH)
REFERENCES
Inlet velocity
COALESCENCE PHENOMENA IN MOTION OF BUBBLES
H2 bubble
cell
To determine the motion of a bubble, it is necessary
to establish the forces acting on it and put a
balance on the amount of movement as in Fig 3b
[3]. In commercial electrolyzers, the residence time
of bubbles is small due to the forces of Archimedes
and the void fraction is small.
During the rise of gas inside the electrolyzer the
coalescence of bubbles happen frequently. These
phenomena can be modeled in COMSOL® by
laminar two-phase flow, phase field.
[1] Roy A., Watson S., Infield D., Int. J. Hydrogen Energy 31 (2006) 164-179
[2] Rosa V.M., Santos B.F., Da Silva E.P., Int. J. Hydrogen Energy 20 (1995) 697-700
[3] Mandin Ph, Ait A, Roustan H, Hamburger J, Picard G, Chem Eng Process 47 (2008) 1926-1932
[4] Djafour A. et alt., Int. J. Hydrogen Energy 36 (2011) 4117-4124
[5] Nagai N., Takeuchi M., Kimura T., Oka T., Int. J. Hydrogen Energy 28 (2003) 35-41
[6] Katukota S.P., Nie J., Chen Y., Boehm R. F., Numerical investigation for hydrogen production
using exchange water electroysis cell, COMSOL Users Conference 2006, Las Vegas
PSE-120000-2009-3
This project was financed by:
Study of an Alkaline Electrolyzer Powered by Renewable
Energy
E. Amores Vera1,*, J. Rodríguez Ruiz 1, C. Merino Rodríguez1, P. García Escribano1
1
Centro Nacional del Hidrógeno. Prolongación Fernando el Santo, s/n - 13500 Puertollano (SPAIN)
*Corresponding author: [email protected]. Tel: +34 926 420 682
Abstract: Modeling of water electrolyzers can
be considered a fundamental optimization tool
for production of hydrogen by renewable
energy. This work reports the model developed
in COMSOL of an alkaline water electrolysis
cell powered by a PV-module. The geometry
model was created taking as reference a
commercial electrolysis cell. The model
involves transport equations for both liquid
and gas phases, charge conservation and forces
balances for the study of coalescence
phenomena. Results showed changes on gas
profiles with the evolution of solar irradiation
during the day, as well as changes on void
fraction and potential distribution.
Keywords: Water electrolysis, renewable
energy, hydrogen, void fraction, coalescence
1. Introduction
The production of H2 from renewable energy
surplus is seen as a key strategy for energy
storage. Centro acional del Hidrógeno
(CNH2) works actively in this direction, which
is considered a strategic line in order to
achieve a sustainable future energy.
Alkaline electrolysis is a highly developed
technology in the industry and the main way to
obtain sustainable hydrogen. Nowadays,
commercial
alkaline
electrolyzers
are
designed for a constant power supply.
However, renewable energies are nondispatchable because of their strong
dependence on weather conditions. The
fluctuations in power supplies to the
electrolyzer could cause problems such as
generation of explosive mixtures, corrosion of
materials, lower efficiency, pressure drops,
changes of temperature, etc. The design of
alkaline electrolyzers powered by renewable
energy is a critical issue to avoid these
problems. For these reasons, the CFD
simulation is an important design tool.
a
Solar irradiance profile
Puertollano, SPAIN - June 2009
SOLAR EERGY
b
Current density profile normalized from a
PV module
PV-MODULE
ELECTROLYZER
Figure 1: Electrolyzer powered by a PV-module: a) irradiation profile; b) current density profile.
This work reports the model of an alkaline
electrolysis cell powered by a PV-module (Fig
1). Fig 1a is a typical solar irradiance profile
for a sunny day in Southern Spain. Fig. 1b
shows a current density profile implemented in
COMSOL® from a PV-module that powered
the electrolyzer. To this aim, Interpolation
Function tool was used. Maximum value of
solar radiation occurs at 14:00.
2. Model Set-Up
2.1. Alkaline electrolysis water
During alkaline water electrolysis
following reactions take place:
-
the
On cathode, the evolution of H2 gas take
place:
4 H 2 O + 4e − → 2 H 2 ( gas ) + 4OH −
-
On anode, O2 gas is generated according
with:
4OH − → O2 ( gas ) + 2 H 2 O + 4e −
the bottom inlets. Over the active surface of
electrodes, water splits following the
electrochemical reactions described above,
evolving oxygen and hydrogen, respectively
for anode and cathode. The mixture of
generated gases and electrolyte leaves the
compartment through the upper outlets (Fig 2).
2.2. Model Geometry
Taking as reference a modified commercial
electrolysis cell (Fig 2a), the geometry of the
model was built following fluid dynamic
requirements. In this way, simplifications were
made in order to reduce the model complexity
(Fig 2c). As result, a good approximation can
be made just by 2D geometry, which allows an
optimal study of the main involved variables
(Fig 2e).
3. Formulation of the problem in
COMSOL Multiphysics®
Depending of studied phenomena, the model
can be divided into:
-
Water electrolysis by renewable
energies, with Electric Currents and
Two phase-flow bubbly flow modules.
In a typical operation, electrolyte (KOH) enters
in the anodic and cathodic compartments by
1.
Cathode
2.
Cathodic compartment (hydrogen
generation)
3.
Membrane
4.
Anodic compartment (oxygen
generation)
5.
Anode
Figure 2: Geometry of a commercial electrolysis cell implemented on COMSOL Multiphysics®.
-
Motion of bubbles next to electrode
surface with Two phase-flow phase
field module of COMSOL®.
Table 1 shows the boundary settings and initial
conditions used in the model (see Appendix).
3.1 H2 generation by Renewable Energy
Charge transport was studied using Electric
Currents module of COMSOL®, which solves
a current conservation problem for the scalar
electric potential V [1]. For time dependent
studies, the continuity equation takes the form
(1):
r
∂
∇ ⋅ J = −∇ ⋅ d ((ε oε r ∇V )
∂t
r
− ∇ ⋅ (σ ∇ V − J e ) = dQ j
(1)
In this case, electric transport charges on
electrodes is not considered, and only ionic
transport is studied inside the electrolysis cell.
On the other hand, movement of gases and
liquid was modeled applying Laminar Bubbly
Flow module of COMSOL®. This application
mode describes the two-phase flow using a
Euler-Euler model. The module solves for the
volume fraction occupied by each of two
phases, without defining each bubble in detail.
It is a macroscopic model for two-phase fluid
flow. It treats the two phases as
interpenetrating media, tracking the averaged
concentration of the phases. One velocity field
is associated with each phase, and the
dynamics of each of the phases are described
by a momentum balance equation and a
continuity equation. Following simplifications
are considered when this module is used [2]:
-
The gas density is negligible
compared to the liquid density.
-
The motion of the gas bubbles
relative to the liquid is determined by
a balance between viscous drag and
pressure forces.
-
The two phases share the same
pressure field.
For this simulation, high level of bubble
definition was not required, and this approach
allows reducing the computational cost doing a
good approximation to our system.
For Laminar Bubbly Flow, sum of the
momentum equations for the two phases gives:
a momentum equation for liquid (2):
r
∂u l
r
r
+ φ l ⋅ ρ l ⋅ u l ⋅ ∇ u l = −∇ p +
∂t
2
r
r
r r 

∇ ⋅ φ l ⋅ (η l + η T ) ⋅  ∇ u l + ∇ u lT − ⋅ (∇ u l ) ⋅ I  
3



r r
+ φl ⋅ ρ l ⋅ g + F
(2)
φl ⋅ ρ l ⋅
A continuity equation (3),
∂
(φl ⋅ ρl + φg ⋅ ρ g ) +
∂t
r
r
∇ ⋅ (φl ⋅ ρl ⋅ ul + φ g ⋅ ρ g ⋅ u g ) = 0
(3)
And a transport equation (4) for the volume
fraction of gas,
∂φ g ⋅ ρ g
∂t
r
+ ∇(φ g ⋅ ρ g ⋅ u g ) = −mgl
(4)
Where (mgl) is the mass transfer rate from gas
to liquid.
In order to complete the system, auxiliary
equations were used:
-
Activation overpotentials (η) were
defined for cathode and anode by ButlerVolmer equations form (Tafel equation):
η = 2.3 ·
-
R ·T
α ·F
i
· log  
 io 
Bruggeman equation (6) relates the
variation of conductivity of electrolyte
(σ) with the volume fraction of gases (f),
for each section.
σ = σ o ⋅ (1 − f )1.5
-
(5)
(6)
Gases generated fluxes on active surfaces
of electrodes are defined by Faraday
equation, for H2 (7) and O2 (8):
m& H2 =
i ⋅M H2
2⋅F
(7)
m& O2 =
i ⋅M O2
4⋅F
(8)
3.2. Motion of bubbles
4. Mesh
During the rise of gas inside the electrolyzer
the coalescence of bubbles happens frequently.
To determine the motion of a bubble it is
necessary to determine the forces acting on it
and put a balance on the amount of movement
as in Fig 2d [3, 4]:
For electrolysis cell model, a triangular mesh
was generated (Fig 3a). Mesh elements were
coarse predefined on the electrolyte domain,
but normal on the membrane and electrodes
boundaries.
-
Archimedes’ principle to determine
the buoyancy. In commercial
electrolyzers, the residence time of
bubbles is small due to the forces of
Archimedes and the void fraction is
small.
-
Friction force according to the drag
coefficient
-
Horizontal force of the bubbleelectrode
and
bubble-bubble
interactions
-
Pump force.
These phenomena can be modeled in
COMSOL® by laminar two-phase flow, phase
field. This application mode describes the
two-phase flow dynamics using a CahnHilliard equation. The equation describes the
process of phase separation, by which the two
components of a binary fluid spontaneously
separate and form domains pure in each
component.
In the case of motion of bubbles, a physicscontrolled mesh was used (Fig 3b). The mesh
is finer on the bubble domain.
(a)
10 mm
(b)
2 mm
Figure 3: Mesh generation for the used geometry:
a) mesh for hydrogen generation model; b) mesh for
bubbles motion model.
COMSOL Multiphysics® solves the CahnHilliard equation by two equations (9), (10):
5. Results
∂φ r
γλ
+ u ⋅ ∇φ = ∇ ⋅ 2 ∇ψ
∂t
ε
In Fig 4, a typical polarization curve is shown
[6, 7]. According with other authors [8],
oxygen and hydrogen overpotentials are the
main source of reaction resistances, and at high
current densities, it is very significant the
effect of Ohmic losses.
(
(9)
)
 ε 2  ∂f ext


 λ  ∂φ
ψ = −∇ ⋅ ε 2∇φ + φ 2 − 1 ·φ + 
(10)
5.1. Polarization Curve
Where (u) is the fluid velocity, (γ) is the
mobility, (λ) is the mixing energy density, and
(ε) is the interface thickness parameter. The
(ψ) variable is referred to as the phase field
help variable [5].
The transport of mass (3) and momentum (11)
is governed by the incompressible NavierStokes equations including surface tension (st):
r
r
∂u
r
r
r
r
+ ρ (u ⋅ ∇ )u = ∇ ⋅ − pI + µ ∇u + ∇u T +
∂t
r
r
r
r
(11)
Fg + Fst + Fext + F
ρ
[
(
)]
Figure 4: Polarization curve, including overpotentials and ohmic losses contributions.
5.2. I-V Distributions
On Fig 5 it is possible to follow the dynamic
evolution of potential distribution over the
electrolysis cell during operation. Applied
potential increases with increasing of current
density. Attending current vector arrows, it can
be seen higher values of current next to
electrodes extremes, which is in agreement
with observed for electrochemical models by
other authors [9].
Figure 5: Potential distribution of electrolysis cell
when it is powered by a PV-module.
5.3. Gas generation profile
Evolution of hydrogen profile can be evaluated
from picture on Fig 6. Hydrogen void fraction
(occupied space by hydrogen bubbles) draws a
typical profile next to electrode surface [10,
11]: void fraction progressively increases on
vertical direction of electrode.
Figure 6: Hydrogen volume fraction evolution for
electrolysis cell during a day operation.
The predicted void fraction of hydrogen at 4
different points along the electrode surface is
reported on Fig 7. H is the height of the
electrode and point x=0 corresponds with the
surface of electrode. As can be seen, next to
the electrode surface volume fraction reaches
the highest value, and decreases towards the
membrane. Void fraction also increases from
bottom to top of electrode due to accumulated
generation of gas, and effect of forced
convection [12], as observed in Fig 6.
Figure 7: Void fraction distribution at four
locations.
Influence of current density on generated gas is
reported on Fig 8. As expected, hydrogen void
fraction increases at higher current density
values. From this plot it can be also deduced
that higher the current density, higher the gas
penetration at lateral direction, because of
increasing of lateral velocity of gas [13].
Figure 8: Void fraction of gas for different values
of current density.
Figure 9: Detail of coalescence phenomena between hydrogen bubbles
5.4. Coalescence phenomena
Fig 9 shows a model of coalescence between
two bubbles of hydrogen using COMSOL
Multiphysics®.
During electrolysis of water, the bubbles rise
by buoyancy and join in the upper regions of
the cell. The study of coalescence lets us know
the dynamic of the gas: generation,
distribution, evolution, etc.
6. Conclusions
•
•
•
•
COMSOL® was used to model the
behavior of an electrolysis cell for
hydrogen production.
The distribution of oxygen and hydrogen
gas when the cell is powered by a PV
module was obtained.
Using
the
model
developed
in
COMSOL®, we determined the current
and potential distribution along the
electrolysis cell.
COMSOL® can model phenomena of
localized coalescence.
7. References
[1] COMSOL Multiphysics - User’s Guide.
Electric Currents AC/DC Module. Burlington,
MA: COMSOL, Inc.; 2007
[2] COMSOL Multiphysics - User’s Guide.
Bubbly Flow Model, Chemical Engineering
Module. Burlington, MA: COMSOL, Inc; 2007
[3] Mandin Ph., Ait A., Roustan H.,
Hamburger J., Picard G. Two-phase
electrolysis process: From the bubble to the
electrochemical cell properties, Chem Eng
Process 47 (2008) 1926-1932.
[4] Mandin Ph., Hamburger J., Bessou S.,
Picard G. Modelling and calculation of the
current density distribution evolution at
vertical
gas-evolving
electrodes,
Electrochimica Acta 51 (2005) 1140-1156
[5] COMSOL. Multiphysics 3.5 - Chemical
Engineering
Module
Model
Library.
Burlington, MA: COMSOL, Inc.; 2008
[6] Djafour A., Matoug M., Bouras H,
Bouchekima B, Aida M.S., Azoui B.,
Photovoltaic-assisted
alkaline
water
electrolysis: Basic principles, Int. J. Hydrogen
Energy, 36, 4117-4124, 2011.
[7] Ðukic A., Firak M., Hydrogen production
using alkaline electrolyzer and photovoltaic
(PV) module, Int. J. Hydrogen Energy, 36,
7799-7806, 2011.
[8] Zeng K., Zhang D., Recent progress in
alkaline water electrolysis for hydrogen
production andapplications, Prog. Energ.
Combust., 36, 307-326 (2010)
[9] Katukota S.P., Nie J., Chen Y., Boehm R.
F. Numerical investigation for hydrogen
production using exchange water electroysis
cell, COMSOL Users Conference 2006 Las
Vegas
[10] Sasaki
T., Nagai
N., Murai Y.,
Yamamoto F., Particle Image Velocimetry
measurement of bubbly flow induced by
alkaline water electrolysis, Proceedings of
PSFVIP-4 , Chamonix, France, 2003.
[11] Aldas K., Pehlivanoglu N., Mat M.D.,
Numerical and experimental investigation of
two-phase flow in an electrochemical cell, Int.
J. Hydrogen Energy , 33, 3668–3675 (2008)
[12] Mat M.D., Aldas K., Olusegun J. I., A
two phase flow model for hydrogen evolution
in a electrochemical cell, Int. J. Hydrogen
Energy, 29 (2004) 1015-1023
[13] Aldas K. Application of a two phase flow
model for hydrogen evolution in a
electrochemical cell, Appl. Mathematics and
Computation, 154 (2004) 507-519
9. Acknowledgements
The authors acknowledge financial support
from Ministerio de Ciencia e Innovación
(MICINN, Spain), Junta de Comunidades
Castilla-La Mancha (JCCM) and Fondos
Europeos de Desarrollo Regional (FEDER).
Project PSE 120000-2009-3.
10. Appendix
Table 1: Constants, Sub-domain and Boundary
Settings
Symbol
Value
Description
p
1 bar
Pressure
operation
T
348 K
Temperature
operation
io,c
0.02 A/m2
Exchange current
density (cathode)
io,a
0.016 A/m2
Exchange current
density (anode)
σ0
130 S/m
Electrolyte (30%
KOH) conductivity
σ
67 S/m
Membrane (PTFE)
conductivity
v0
0.1 m/s
Inlet
velocity
R
8.31 J K-1
mol-1
Ideal gas
constant
F
96485 C
Faraday
constant
α
0.5
Charge transfer
coefficient