Download Modeling a Filter Press Electrolyzer for the Westinghouse

15th International Conference on Nuclear Engineering
Nagoya, Japan, April 22-26, 2007
ICONE15-10639
MODELING A FILTER PRESS ELECTROLYZER FOR THE
WESTINGHOUSE HYBRID CYCLE USING TWO COUPLED CODES
DRAFT
Florent Jomard
Commissariat à l’Énergie Atomique
DEN/DTEC/STCF/LGCI
Site de Marcoule BP 17171
30207 Bagnols sur Cèze, France
e-mail: [email protected]
Jean-Pierre Feraud
Commissariat à l’Énergie Atomique
DEN/DTEC/STCF/LGCI
Site de Marcoule BP 17171
30207 Bagnols sur Cèze, France
e-mail: [email protected]
Jacques Morandini
Astek Rhone-Alpes
1 place du Verseau
38130 Echirolles, France
e-mail: [email protected]
Yves Du Terrail Couvat
Laboratoire EPM, Madylam
1340 Rue de la Piscine
Domaine Universitaire
38400 Saint Martin d’Hères, France
e-mail: [email protected]
Jean-Pierre Caire
LEPMI, ENSEEG
1130 Rue de la Piscine
38402 Saint Martin d’Hères, France
e-mail: [email protected]
Keywords: model, Westinghouse cycle, coupling, electrolyzer
compartments separated by a membrane. Hydrogen is
reduced at the cathode and SO2 is oxidized at the
anode. In a complex reactor of this type the main
coupled physical phenomena involved are forced
convection of the electrolyte flows, a plume of
hydrogen bubbles that modifies the local electrolyte
conductivity, and irreversible processes (Joule effect,
overpotentials, etc.) that contribute to local
overheating. The secondary current distribution was
modeled with a commercial FEM code, Flux Expert®,
which was customized with specific finite interfacial
elements capable of describing the potential discontinuity associated with the electrochemical overpotential.
Since the finite-element method is not capable of
properly describing the complex two-phase flows in the
cathode compartment, the Fluent® CFD code was used
for thermohydraulic computations. In this way each
physical phenomenon was modeled using the best
numerical method. The coupling implements an
ABSTRACT
Mass production of hydrogen is a major issue for
the coming decades particularly to decrease greenhouse
gas production. The development of fourth-generation
high-temperature nuclear reactors has led to renewed
interest for hydrogen production. In France, the CEA is
investigating new processes using nuclear reactors such
as the Westinghouse hybrid cycle [Brecher, 1977]. A
recent study was devoted to electrical modeling of the
hydrogen electrolyzer, which is the key unit of this
process. An extensive literature review led to the
choice of electrolyte and electrode materials, and the
preliminary design of a new cell for production of
hydrogen was evaluated. This paper describes an
improved model coupling the electrical and thermal
phenomena with hydrodynamics in the electrolyzer.
The hydrogen electrolyzer chosen here is a filter press
design comprising a stack of cathode and anode
1
Copyright © 2007 by JSME
iterative process in which each code computes the
physical data it has to transmit to the other one: the
two-phase thermohydraulic problem is solved by
Fluent® using the Flux Expert® current density and heat
sources; the secondary distribution and heat losses are
solved by Flux Expert® using Fluent® temperature field
and flow velocities. The computations use two different
meshes and interpolations from of one mesh to the
other require a 3D algorithm to localize the calculation
points. A set of dedicated library routines was developed for process initiation, message passing, and
synchronization of the two codes. The first results
obtained with the two coupled commercial codes give
realistic distributions for electrical current density, gas
fraction and velocity in the electrolyzer. A design
optimization phase is in progress before proceeding to
the final design and manufacturing of a pilot
electrolyzer.
out to model a filter press electrolyzer for producing
hydrogen via the Westinghouse hybrid cycle. In view
of the complexity of the strongly coupled phenomena
that occur in this type of electrolyzer, no numerical
method is currently capable of satisfactorily describing
both the thermohydraulic and electrochemical aspects
of the electrolyzer. The idea behind this work was
to account for the coupled physical phenomena by
coupling two software packages that together are
perfectly suitable for describing the physical problems
encountered.
Flux Expert® and Fluent® were coupled to solve a
highly nonlinear steady-state problem involving the
coupling of equations from electrokinetics, fluid
mechanics, and thermal analysis. The following
solution was adopted for this purpose:
– Solve the electrokinetic equation using the Flux
Expert® finite-element code. One feature of this model
is the use of specific “interfacial finite elements”
developed to handle the overpotential at the
electrode/electrolyte interfaces.
– Solve the fluid mechanics equations of two-phase
turbulent flow in the electrolytes where gas bubbles are
generated by electrolysis. This step is performed using
the Fluent® code, which includes recently developed
effective models for modeling compressible and
incompressible two-phase fluid flows. In Fluent®, the
energy equation in terms of temperature can be
associated with the fluid equations and solved at the
same time.
The coupling is handled and each calculation is
initiated through the following steps:
– Create the models.
– Load the models in their respective codes.
– Start the coupled simulation: first Fluent® then Flux
Expert® or vice-versa.
NOMENCLATURE

u
Velocity vector (m·s-1)

Density (kg/m-3)
g Gas concentration
σ;= Viscous stress tensor (Pa)

g Acceleration of gravity (m·s-2)
T
Temperature (K)
Cp Heat capacity (J·K-1·kg-1)
k
Thermal conductivity (W·m-1·K-1)
QV Volume heat sources (W·m-3)
QS Surface heat sources (W·m-3)
S Dirac surface distribution

J Current density (A·m-2)
jn
Current density normal to the interface (A·m-2)

Electrical conductivity (-1·m-1)
V
Electrical scalar potential (V)
V Electrical potential jump (V)
t
Time (s)

n Normal vector
S Dirac surface distribution

 Nabla vector differential operator
( x ,  y ,  z )
1.
2.
COUPLING PHENOMENA AND
ELECTROLYZER MODELING
The physics of the electrolyzer can be broken down
here into a two-phase thermohydraulic problem and an
electrokinetic problem with activation overpotentials.
These physical phenomena are schematically described
in the following paragraphs.
INTRODUCTION
2.1
Coupling of Physical Phenomena
The thermohydraulic phenomena are described by
the Navier-Stokes continuity and heat transfer
equations:
u

  (u  )u       g
t

   ( u)  0
t
T
 cp (
 u  T )    ( k T )  QV  QS  S
t
The hydraulic aspect consists of a two-phase
problem involving a continuous liquid phase, sulfuric
Within the framework of the Generation IV International Forum the Commissariat à l’Énergie Atomique
(CEA) is investigating the possibility of producing
hydrogen in industrial quantities. One of the main
objectives is to take advantage of the very hightemperature heat source (> 1100 K) made available at
low cost by new nuclear reactors such as the VHTR.
Large-scale hydrogen production is also being
considered using thermochemical or hybrid cycles such
as the Westinghouse cycle, which is based on sulfur
chemistry and electrochemical reduction of protons to
form hydrogen. This paper describes the work carried
2
Copyright © 2007 by JSME
acid, and a dispersed gas phase, the bubbles generated
at the cathode/catholyte interface.
The electrokinetic phenomena with activation
overpotentials are described by the current conservation
equation and by overpotential laws at the electrode/bath
interfaces:
  (V )  0
The electrokinetic problem with overpotentials is
solved using Flux Expert®, which gives the electrical
potential and current density fields and the losses due
to Joule effect over the finite-element mesh. Flux
Expert® requires the following inputs:
– T over the full calculation domain
– g in the fluid.
The following results are provided by Flux Expert®:
– J and V at the electrode boundary
– QS at the electrode interfaces
– QV in the electrically conductive zones.
Communication between the two codes is based on
the use of a simple and robust message-passing library
developed to allow two calculation codes to communicate without requiring them to be merged into a single
executable. The codes can thus be installed on one or
even two different UNIX machines. The two programs
can share the same physical inputs and results. The
message-passing function calls in this library were
developed as subroutines in Fluent® and Flux Expert®
specially designed for coupling.
The shared data include:
– Initial coupling definition data: the two programs
initially exchange the coordinates of the points for
which the expected physical quantities will be
computed.
– Coupling data, which are exchanged throughout the
resolution process. Before each iteration, the two
programs exchange the values of the physical quantities
computed during the preceding step, for those required
in the next iteration.
– Solution strategy data, i.e. the data that must be
exchanged between the programs to reach the same
solution: number of iterations, calculated precision,
etc., or events such as the end of the solution.
The algorithms developed are mainly location and
interpolation algorithms. Each of the calculation points
for the volume and surface heat sources of the Fluent®
mesh must be localized on the Flux Expert® mesh. At
the beginning of the iterations the heat sources are
interpolated over these points and supplied to Fluent®,
while the gas volume fraction and temperature must be
calculated by Fluent® for the Flux Expert® mesh points
and transmitted to Flux Expert®.
The combined operating procedure for the two
codes is shown schematically in Figure 1. “UDF” in
the Fluent® portion refers to User-Defined Functions in
Fluent®: the coupling routines are shown in green in the
flowchart.
V  f ( J  n )
where V represents the overpotential, the electrical
potential discontinuity V at the electrode/electrolyte
interface. This constitutes a system of nonlinear partial
differential equations with the following unknowns:

{ u , P, αg, T, V}. The nonlinearities are due to the
differential operators (the velocity transport term, for
example) but also to the physical properties (overpotentials in particular) and the coupling quantities,
which depend on one of the unknowns:
– Gas production at the electrode interfaces contributes to the electrolyte motion; the production is
proportional to the current density (Faraday’s law).
– The presence of a bubble plume modifies the local
electrical conductivity of the electrolyte.
– Losses by Joule effect result in a heat release.
– The physical properties, such as the electrical and
thermal conductivity of the bath, depend on the
temperature and on the local bubble production.
2.2
Software Coupling
The two types of physical phenomena described
above are solved using Fluent® and Flux Expert® with
different meshes (which may be structured or unstructured) and in some cases even in different calculation
domains. Although the hydraulic problem is generally
solved under transient conditions and the electrokinetic
problem under steady-state conditions, the coupling
implemented can deal with both steady-state and
transient problems.
The two-phase thermohydraulic problem is solved
using Fluent®, which gives the velocity, pressure, and
temperature fields and gas volume fraction (bubble
concentration) on the finite-volume mesh. Fluent®
requires the following inputs:
– Jn at the electrode boundary; the current density can
be used to compute the gas production term at the
interface.
– QS at the electrode/electrolyte interfaces; this is the
source term per unit area in the heat transfer equation
corresponding to the heat release related to the
overpotential irreversibility.
– QV in the electrically conductive zones, i.e. the
power density irreversibly generated by Joule effect;
this is the volume source term in the heat transfer
equation.
The following results are provided by Fluent ®:
– T over the full calculation domain
– g in the fluid.
3.
PILOT ELECTROLYZER GEOMETRY
AND CALCULATION HYPOTHESES
The filter press electrolyzer investigated here is a
laboratory prototype. The electrolyzer was modeled to
partially optimize the design of a small-scale pilot
before fabrication. The device operating principle is
shown in Figure 2.
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Copyright © 2007 by JSME
Main
memory
Main
memory
UDF
Swap
functions
FEcoupling.c UDF
FEcoupling.c
FLUENT®
where an additional hydrogen release zone ( in light
blue in Figure 2) had to be defined for Fluent® to
simulate hydrogen release at the electrode. Within the
adjustable thickness of zone  the gas release is
calculated according to the local current density.
3.1
Calculation Hypotheses
The electrolyzer measures 0.04 × 0.013 × 0.16 m.
The code is a 3D model. The study was carried out
under steady-state conditions. The physical properties
of all the electrolyzer components (, , k, Cp) are
temperature-dependent.
The anolyte consists only of a single-phase fluid, in
this case a sulfuric acid solution. The catholyte consists
of a two-phase fluid formed by a sulfuric acid solution
with small-diameter (about 100 µm) hydrogen bubbles
produced by an electrochemical reaction at the cathode.
All the outer walls of the electrolyzer are thermally
insulated. The two fluids with different sulfuric acid
concentrations pass through the vertical countercurrent
electrolyzer at equivalent rates.
The Flux Expert® input data are representative of
the operating conditions frequently described in the
literature [Goosen, 2003; Lu, 1980], i.e. a fluid inlet
temperature of 323 K and a pressure of 1 bar. The
sulfuric acid mass concentrations are 30% in the
catholyte and 50% in the anolyte. The overpotential
values at current densities of 2000 A·m-2 are about
0.6 V at the anode and 0.05 V at the cathode, which is
very low compared with other types of electrolysis
[Struck, 1980; Roustan, 1998].
Data
files
FLUX
EXPERT
®
Property
operators :
prxxxx.F
Swap
functions
Main
memory
Main
memory
Figure 1. Fluent®–Flux Expert® coupling flowchart
H2SO4
H2SO4
+ SO2
H2
  
  
3.2
Boundary Conditions
To simplify the fluid mechanics computations, fluid
inlet and outlets at right angles in the cell were not
taken into account. A uniform velocity profile of
0.07 m·s-1 is therefore applied at the inlets to the
cathode and anode compartments. The boundary
conditions for the two codes are shown in Figure 3.
0.16m
+
-
Overpotential Area
160
0V
2000
-2
A.m
z
x
-1
V = 0.07 m·s , 323K
0.04m
Figure 2. Electrolyzer operating principle
( cathode;  hydrogen release zone;  catholyte;
 membrane;  anolyte;  anode
ANODE
CATHOLYTE
membran
CATHODE
CATHOLYTE
ANODE
Hydrogen
area
Z
-3
(10 m)
The electrolyzer mesh was prepared in Gambit®.
The electrolyzer geometric definitions for Fluent® and
Flux Expert® are practically identical except for the gas
release zone at the cathode /catholyte  interface
CATHOLYTE
0.013m
membran
CATHODE
H+ +H2SO4
H2SO4
+ SO2
CATHOLYTE
y
-3
Y (10 m)
0
1.5 6.5 6.6 11.2
V =13.1
0.07 m·s , 323K
-1
Figure 3. Boundary conditions
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Copyright © 2007 by JSME
4.
nates of the integration points, after which the physical
values are exchanged. A sudden increase in the
residuals is observed after 40 iterations in Fluent, i.e. at
the second iteration for Flux Expert®, corresponding to
the transmission of fresh data between the two codes.
For example, a data exchange concerning the mean
temperature in the electrolyzer for each iteration in
Fluent® is shown in Figure 5.
1
2 3 FE  Fluent data swap
T (K)
MODELING RESULTS FOR A FILTER
PRESS ELECTROLYZER PRODUCING
5 NL·h-1
4.1
Code Coupling Behavior
The interaction between the two codes is
demonstrated by the convergence of the computational
residuals with successive iterations. This data is
available in Fluent®. The residual is computed as
follows:
 A  A1 
Résidual   i 1

Ai


2
where Ai+1 is the value of the variable at iteration i+1
and Ai its value at iteration i.
As fluid mechanics models are more complex to
solve than electrokinetic models, exchanges between
the two codes are performed at each iteration for Flux
Expert® and only every twenty iterations for Fluent®.
The ratio between the number of iterations in the two
codes is user-adjustable. Figure 4 shows the variation
of the residuals in Fluent® from iteration 1 to iteration
180 (data transfers from Flux Expert® to Fluent®
corresponding to iterations 1 to 9 in Flux Expert®).
1
2
Figure 5. Mean temperature at each iteration
3 FE  Fluent data swap
Figure 5 reveals a temperature rise in steps of
decreasing amplitude with each successive iteration,
and confirms the convergence of the temperature
parameter.
4.2
Results of Heat Transfer and Fluid
Mechanics Computations with Fluent®
The initial results concerning the thermohydraulic
behavior of the filter press electrolyzer are shown here
under operating and modeling conditions that are
subject to optimization and improvement in subsequent
work. The thermal behavior of the electrolyzer is
shown in graded color in Figure 6:
Catholyte
Residuals continuity
u residual sulphuric acid
u residual hydrogen
v residual sulphuric acid
v residual hydrogen
w residual sulphuric acid
w residual hydrogen
T1 residual sulphuric acid
T2 residual hydrogen
K residual sulphuric acid
 residual sulphuric acid
(1–K) residual hydrogen
Anolyte












Figure 4. Variation of residuals
over 180 iterations in Fluent, where:
Figure 4 illustrates the quality of the system
convergence. Data transfers between the coupled codes
occur at each iteration or every 20 iterations, depending
on the direction. During the first exchange after 20
iterations of Fluent®, the codes exchange the coordi-
Catholyte
Anolyte
Figure 6. Graded color temperature map
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Copyright © 2007 by JSME
The temperature depends on the volume heat
sources due to losses by Joule effect, on convective
transport in the countercurrent liquid flows, and on heat
exchange by conduction in the solids and liquids.
Countercurrent flow was selected here because it
allows greater control over the heat transfer properties
of the electrolyzer operating as a filter press plate-type
heat exchanger.
A cross-sectional view of the electrolyzer through
the middle of each compartment provides a better
indication of the temperature rise versus height.
0 .1 6
0 .1 4
0 .1 2
T e m p e r a tur e (K )
H e ig h t (m )
Catholyte
flow. Fluent allows the use of a quantity of substance
term that represents the electrochemically produced
hydrogen. The gas released at the cathode in bubbles
100 µm in diameter is transported by the bath and exits
at the top of the electrolyzer. Figure 8 shows the
variation of the gas volume fraction.
Cathode H2 catholyte
0 .1
A n o ly te
C a th o ly te
0 .0 8
3 mm
0 .0 6
0 .0 4
Figure 8. Graded color representation
of the gas volume fraction
0 .0 2
0
322
324
Figure 8 illustrates the hydrogen production along
the interface between cathode and the sulfuric acid
solution (catholyte); the gas volume fraction increases
along the cathode wall. It is interesting to note that the
bubble plume proposed by the first model appears too
localized at the cathode/catholyte interface. The local
maximum gas volume fraction (which reaches 97%)
appears overestimated. This problem is probably
attributable to the definition of zone 2 in Figure 1
being too narrow. If spherical hydrogen bubbles are
assumed to be stacked in a hexagonal close-packed or
face-centered cubic structure at the electrode, the
hydrogen volume fraction should not exceed 74%
[Arnaud, 1988].
The velocity vector plot in Figure 9 shows the
influence of the gas volume fraction on the electrolyte
flow velocity, notably the following aspects:
– The velocity in the anode compartment varies only
slightly and tends toward two parabolic profiles.
– The velocity in the cathode compartment varies
significantly with the gas volume fraction: the greater
the quantity of gas, the higher the velocity along the
electrode. At a constant feed rate, this observation is
directly related to the apparent restriction of the free
flow cross section. The maximum velocity reached is
0.825 m·s-1, which represents an acceleration by a
factor of 12 between the inlet and outlet velocity along
the cathode.
326
Anolyte
Figure 7. Temperature versus height
in the anolyte and catholyte
Figure 7 shows a temperature variation in both
electrolyzer compartments comparable to that observed
between the heat sink and source in a plate-type heat
exchanger [Roure, 2007]. Figures 5 and 6 show a
temperature rise limited to 4 K between the coldest
point (liquid inlets) and the hottest (anolyte outlet). The
temperature rise inside the electrolyzer reaches a
maximum where the electrical conductivity of the cell
is the lowest, and where the liquid flow velocity is also
the lowest.
For lack of experimental data, the results shown
here do not yet take into account the surface heat
sources generated by overpotentials, although their
effect on the temperature can be estimated at about 6 to
8 K given the overpotentials obtained (see paragraph
4.4). Similarly, it would be of interest in future
calculations to take into account the heat produced by
exothermic reactions such as dissolution in the anolyte
of the H2SO4 formed by oxidation of SO2.
4.3
Results of Two-Phase Flow
Calculations with Fluent®
Fluent® was selected for modeling the hydrodynamic characteristics in order to allow for two-phase
6
Copyright © 2007 by JSME
Although this initial numeric result must still be
confirmed by experimental tests, it highlights the
importance of optimizing the anode overpotential to
lower the cost of hydrogen production.
Electrical potential (V)
Anolyte
Catholyte
Cathode
Anode
0,73 V
0.6
Cathodique
Potential
jump
0.03 V
0.3
Anodique
potential
jump
0.47 V
0
0
0.00655
0.0131
Lenght (m)
-1
Figure 9. Vector plot of electrolyte velocity (m.s )
at the top of the cell
Figure 11. Potential variation
between the cathode and anode
4.4
Results of Electrokinetic Simulations
with Flux Expert®
The data supplied to Flux Expert® by Fluent® are
used to calculate the electrical potential of the cell
taking into account the gas volume fraction and the
local temperature. The potential gradient in the
electrolyzer is shown in graded color in Figure 10.
Cathode
5.
CONCLUSIONS AND OUTLOOK
The model described here was designed to simulate
the operation of the electrolyzer that is the fundamental
component in the Westinghouse process for producing
hydrogen by a hybrid electrochemical-thermochemical
cycle at high temperature (VHT reactor). The filter
press electrolyzer selected for its compact size was
modeled by coupling the Fluent® and Flux Expert®
codes. This approach allowed us to take into account
under optimum conditions both the electrochemical
phenomena (overpotentials in particular) and the
complex two-phase flow due to hydrogen production at
the cathode. The calculations showed the significant
influence of fluid mechanics and gas production on the
reactor heat transfer properties. The fluid flow velocity
along the cathode increased by a factor of 12 in the
reactor due to the release of hydrogen bubbles. This
finding of particular importance for the preliminary
design of a future fully optimized electrolyzer was one
of the principal results obtained by coupling the Flux
Expert® and Fluent® codes.
The overpotentials and highly exothermic chemical
reactions were not taken into account with sufficient
accuracy for lack of experimental measurement data,
but the coupled model is capable of doing so without
difficulty. The initial calculations showed that the
plume of hydrogen bubbles was apparently slightly too
narrow. Population balance models allowing for bubble
coalescence and breakage should also be taken into
account through the development of specific physical
operators. Finally, the two-phase flow model will have
to be calibrated by bubble concentration measurements
along the cathode in the laboratory pilot device
specified from the model.
Anode
Potential (V)
Figure 10. Electrical potential variation in the cell
Observing the secondary current distribution
reveals the positive overpotential (yellow) due to the
irreversibility of electrochemical oxidation of SO2 into
H2SO4. This phenomenon is detailed in the cross
section below by plotting the potential variation at the
center of the electrolyzer along a horizontal path.
Figure 11 shows the individual contributions to the
overall potential of the electrolysis cell. Here the anode
overpotential accounts for 70% of the cell potential.
Hydrogen production results in a potential drop of
30 mV, or only 4% of the cell potential.
7
Copyright © 2007 by JSME
of Electrochemical Society, 127/12, 2610–2616,
1980.
Roure A., Caire J.P., ICONE 15, 10493
Roustan, H., Caire, J.P., Nicolas, F., Morandini, J.,
Improving the numerical stability of advection
equations in a fluid: example of an electrolyzer,
CHISA’98, 12th International Congress of
Chemical and Process Engineering, Prague, Czech
Republic, 23–28 August 1998.
Struck, B.D., Junginger, R., Boltersdorf, D. and
Gehrmann, J., The anodic oxidation of sulfur
dioxide in the sulfuric acid hybrid cycle,
International Journal of Hydrogen Energy, 5, 487–
497, 1980.
REFERENCES
Arnaud, P., Cours de chimie physique, Dunod, 1988
Brecher, L.E., Spewock, S. and Warde, C.J., Westinghouse sulfur cycle for the thermochemical decomposition of water, International Journal of
Hydrogen Energy, 2, 7–15, Pergamon Press, 1977.
Goosen, J.E., Lahoda, E.J., Matzie, R.A. and
Mazzoccoli, J.P., Improvements in Westinghouse
process for hydrogen production, pp.1509–1513,
New Orleans, LA, USA, November 16-20, 2003.
Lu, P.W.T. and Ammon, R.L., An investigation of
electrode materials for the anodic oxidation of
sulfur dioxide in concentrated sulfuric acid, Journal
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