Losses effect on solid oxide fuel cell stack performance
**
*
**
**
**
H. Mahcene , H. Ben Moussa , H. Bouguetaia , B. Bouchekima , D. Bechki
*
Département de Mécanique, Faculté des Sciences de l'Ingénieur, Université de Batna- ALGERIE
**
Laboratory of Renewable Energy Ouargla University- ALGERIA
B.P N° 511 Ouargla- ALGERIE
Tel//Fax: 213 29 71 70 81
H2SOFC@gmail.com
hmohcin@yahoo.fr
ABSTRACT
This paper presents an investigation of electric performance and maintenance of fuel cells. These cells
(SOFC) have many characteristics that make them favorable as energy conversion devices, which rely on
transport reactants (oxygen and hydrogen) and produces (water and heat) with the possibility of use in
co-generation systems, because of its relatively high efficiency and very low environmental destruction.
Thus fuel cell power plants can be configured in the range of electrical output, ranging from watts to
megawatts. This investigation does not stop to the construction of the cells, but goes to maintenance
requirement, and that by following the potential out put of the cell with the current during the use period.
The actual performance is decreased from its equilibrium value because of irreversible losses. Many
phenomena contribute to irreversible losses in actual fuel cells. These losses originate primarily from
three sources: Activation polarization, Ohmic polarization, Concentration polarization
Key-words: Fuel Cells, Losses, SOFC, Electric Performance, Renewable Energy, Polarization.
I. INTRODUCTION
The fuel cell is an electrochemical device that converts chemical energy of its reactants directly to
electricity and heat without combustion. Fuel cells are commonly classified according to the electrolyte
used and operating temperature. This investigation addresses the development of the solid oxide fuel cell
(SOFC), which is a high- temperature fuel cell employing a solid ion conducting membrane as the
electrolyte. The fuel cell is an old innovation, but for along time it was hardly than a curiosity in the field
of energy technology. Fundamental technical breakthroughs, however, have been achieved during the past
decades, and fuel cells are now rapidly approaching commercialization in several applications. This
development is catalyzed by the fact that the global energy use is increasing steadily and environmental
problems related to energy production and transportation are growing. Solid oxide fuel cells (SOFCs)
hold the promise of playing a major role in future power grids either as gas turbine (GTs) or as stand
alone power units because of relatively high efficiency and very low environmental distraction (virtually
no acid gas or solid emissions). The efficiency of fuel cells is not limited by the Carnot limitations of heat
engines. High efficiency makes fuel cells attractive for a large variety of applications, included road
vehicles; decentralized power production, residential energy systems and possibly even smaller
applications, compact size and the lack of local emissions also increase the attractiveness of fuel cells.
The aim was to create a solid foundation for scientific work on (SOFC) technology. In the simulation part
of this work, basic characterization methods were established and basic problems of SOFC design were
addressed with emphasis on the control of operating conditions, the separation of over-potentials, and
flow field plate design. The work also included an extensive literature study on the subject. SOFCs
operate at temperature from 600°C to 1000°C. To avoid thermal shock during heat-up as well as
operation, inlet flow(fuel and air) temperatures and speeds must be carefully controlled to maintain the
temperature gradient within the SOFC stack. Furthermore, increased fuel flow tends to decrease the fuel
utilization but it can cause local fuel depletion and cold spots that exacerbate temperature non uniform
II. FUEL CELLS SOFCs THEORY
In fuel cells the reduction of oxidation at the cathode and the oxidation of hydrogen at the anode produces
water and heat according at the following reaction:
When using hydrogen fuel, the electrochemical reactions of the SOFC:
At the anode of SOFC
2H2 +2 O 2− → 2H2O +4 e − .
The reduction of oxygen in cathode is given by:
O2 + 4 e − → 2 O − −
The overall cell reaction is
4H + O2 → 2H2O + Heat
II.1 Fuel Cell Thermodynamics
II.1.1 Conversion of Gibbs Free Energy into Electrical Energy
Electrochemical energy conversion is the conversion of the free-energy change associated with a
chemical reaction directly into electrical energy. For a fuel cell, the maximum work available is related to
the free energy of reaction, whereas the enthalpy (heat) of reaction is the pertinent quantity in the case of
thermal conversion (such as a heat engine). For the state function
ΔG= ΔH – TΔS
Where ΔG, ΔH, T, ΔS are Gibbs energy free, enthalpy, temperature and entropy respectively.
III. ELECTROCHEMICAL MODEL
The excel spreadsheet based SOFC stack model, which was mentioned earlier, is included in the aspenbased system model. It predicts stack voltage responses to changes in fuel composition, fuel flow rate,
stack temperature and current demand, with response characteristics that are adjustable to changes in
stack component materials, and geometric well as to electrode porosity.
According to the discretization shown in Fig.1. An electrochemical analysis based on deviation from ideal
performance is proposed at each slice. Considering the electrodes to be equilibrium surfaces [r] the Nernst
voltage is defined by
1
⎛
2
⎜
p
p
RT
H2 O2
0
E Nernst = E T , P +
ln ⎜
nF ⎜ p H 2O
⎝
⎞
⎟
⎟
⎟
⎠
Where E 0T , P is the equilibrium potential for a given temperature and pressure,
E 0T , P =
ΔG r (T )
nF
ΔG r (T ) = ΔH r (T ) -T. ΔS 0r +
∫
Δc p r (T )
T
dT
ΔH r (T ) = ΔH 0r + ∫ Δc p r (T ).dT
Δc p r (T ) = c p H 2O (T ) - c p H 2 (T ) Such as
So
pH 2 O = p . X H 2 O ,
1
c p H 2O (T )
2
pH 2 = p . X H 2 , pO2 = p . X O 2
⎛ p 12. X . X 12 ⎞
RT
H2
O2 ⎟
E Nernst = E 0T , P +
ln ⎜⎜
⎟⎟
nF ⎜
X H 2O
⎝
⎠
Where p, X are gas pressure and molar fraction respectively.
In the models described here, however, we retain Butler-Volmer formalism for the charge transfer steps;
this approach provides quantities information about important functional dependencies such as the
reaction orders in the exchange current density. Irreversibility, also know polarizations arise that cause
voltage losses from the ideal voltage value and have a negative impact on fuel performance. These are
three types of losses:
- Activation polarization (ηAct)
-Ohmic polarization (ηohm)
- Concentration polarization (ηCon)
III.1 Activation Polarization (ηAct)
The activation polarization of electrolyte-supported SOFC occurs in both electrodes. The activation
polarization of the anode is obviously lower than of the cathode due to its lower exchange current density.
The activation overvoltage depends principally on current density. This parameter can be considered as
the forward and reverse electrode reaction rate at the equilibrium potential. High exchange current density
means high electrochemical reaction rate; in this case, good fuel cell performance expected. The value of
the exchange current density can be improved by increasing the fuel cell operating temperature or using
catalytic materials with lower activation energies. But in low and medium-temperature fuel cells, the
activation polarization plays the most important role on total losses causing voltage drop from ideal
voltage. Where the first term represents the reversible cell potential at standard temperature and pressure
and the second term corrects for changes in gas pressures. Under high activation over-potential, the
second term, the Butler-Volmer can be neglected and the formula can be rearranged.
ηact=
RT
nαF
ln(
i
)
i0
Where i, i0, R, F, n, α are the net current density, the exchange current density or the current densities for
forward and reverse reaction at equilibrium, the molar gas constant, faraday’s constant, the electron
number, and the charge transfer coefficient respectively. The charge transfer coefficient α value depends
on the reactions involved and on the materials. Its typical anode value is 0.5 and the cathode value often
varies between 0.1 and 0.5. Generally, the anode activation over-potential is smaller than that of cathode
because it is usually verified that (i0,C >> i0,A
). However, it is possible to summarize the anode and
cathode activation losses using the following formula:
⎛
i
⎜
ηact= (S A + S C ) ln ⎜
S
SA
⎜ (i )SA +SC + (i )SA +CSC
0,C
⎝ 0,A
⎞
⎟
⎟
⎟
⎠
Where i0,A , i0,C , SA, SC are the anode and the cathode exchange current density respectively, and the
anode and the cathode cell active surfaces respectively.
When the activation over-potential is low, it is possible to expand the Butler-Volmer equation as a Taylor
series; neglecting the higher terms, the result is
ηact=
i
RT
ln(
)
nαF
i0
III.2 Ohmic Losses(ηohm)
The Ohmic over-potential ηohm, due primarily to resistance of ion transport in the cathode, anode,
electrolyte and mostly interconnections. Since these resistances obey Ohm’s law, the overall Ohmic overpotential can be written as:
ηohm=
i
le
σeff
Where i, σeff , le are nominal current density of the cell, the electric conductivity of the diffusion layer and
thickness respectively.
3.3 Concentration Losses (ηConc)
To avoid a heavily reliance on correlation to determine the limiting current density. The concentration
loss is evaluated using the Fick law formula.
ηconc=
RT ⎛
i⎞
1⎞ ⎛
⎜⎜ 1 + ⎟⎟ ln ⎜⎜ 1 − ⎟⎟
nF ⎝ α i ⎠ ⎝
il ⎠
Where il is the limiting current density (corresponding to a surface concentration value of zero), i
represents each in the reactions. Concentration over-potential becomes significant when large amount of
current drawn the fuel-cell. The partial pressures of the gases at the reaction sites, which correspond to the
volume concentration of the gases, will be less than in the bulk of the gas stream when a large amount of
current is drawn. If such partial pressures or concentration of gases are unsustainable, concentration
losses will cause excessive voltage losses and the fuel-cell will cease to operate. The global effect is a
reduction in hydrogen partial pressure. A similar phenomenon also occurs at air electrode.
III.4 Electrical Power and Heat Transfer Losses
The cell potential Ecell is being calculated by subtracting these over-potential from the Nernst potential:
Ecell = E T0 , P - ηAct - ηOhm- ηConc
The electrical power produced by the fuel-cell is calculated by:
W = Ecell.i
VI.4. SOFC MODEL
VI.1. Governing Equations
The governing equations for the steady state and one dimension heat and mass transfer are:
Continuity:
∇ (ρu) = 0
Momentum equations:
∇ (ρuu) = ∇ p + ∇ .(μ ∇ u)
Energy equation:
∇ (ρuCpT) = ∇ p + ∇ .(k ∇ T) + q
Concentration equation:
∇ (ρuYi) = ∇ p + ∇ .(ρDi,j ∇ Yi) + Sm
.
.
Where ρ, u , p, Cp , Sm , μ , k, q , Di,j , Yi are density, velocity, pressure , calorific capacity, thermal
conductivity, viscosity , heat source or flux and
binary diffusion coefficient and
mass fraction
respectively.
VI.2. Discretization Method
The equations are solved in their differential form. Instead, the finite volume method is applied, which
uses the integral form conservation equations as a starting point. The integration of the transport
equations results in linearized equations. In order to solve these, the solution domain is subdivided into a
finite number of contiguous control volumes (CV’s), and the conservation equations are applied to each
CV. At the centered of each CV lies a computational node at which the variable values are calculated,
Fig.2. Interpolation is used to express variable value at the CV surface in terms of the nodal (CV-center)
values. The complete set of equations is not solved simultaneously (in other words by a direct method).
Quite apart from the excessive computational effort which would entail, this approach ignores the nonlinearity of the underlying differential equations.
V. RESULTAS AND DISCUSSIONS
Details of different losses as a function of current density in a fuel-cell operated at 1023K are shown in
Fig.3. The activation overvoltage depends principally on current density at this operating temperature,
which is 5300 A/m2 for anode and 2000 A/m2 for cathode. This parameter can be considered as the
forward and reverse electrode reaction rate at the equilibrium potential. Results show that Ohmic and
activation losses in the cathode are responsible for the major over- potentials in the fuel-cell
The cathode
concentration over-potential becomes significant when the fuel-cell operates near to the
limiting current density. Compared with the anode, the cathode exhibits higher activation over-potential,
which is due to the poor ‘apparent’ exchange current density at the cathode/electrolyte or
anode/electrolyte (LSM-YSZ/YSZ) interface, as will be seen in Fig.3. Since the cathode exchange current
density directly affects the electrochemical reaction rate in the cathode leads to high cathode activation
losses in the fuel-cell.
The effect of temperature of the interconnector, electrolyte, cathode and anode is presented in Fig. 4a-d,
respectively. The resistances of this fuel-cell component are determined by the conductivity of the
materials used and their respective thickness according to the formulae below. The results show that the
resistances of the interconnector, electrolyte, cathode and anode.
Fuel utilization
93%
Air pressure
7%
Electrical (Ω-1m-1) and thermal λ (Wm-1K-1) conductivities
Interconnect
σ
9.3 10 6
1100
exp−
T
T
λ
2
Electrolyte
3.3 4104 exp−
10300
T
Cathode
Anode
9.5 107
1150
exp−
T
T
4.2 107
1200
exp−
T
T
2
2
DO2
DO2
2
Diffusion coefficient
Values (cm2s-1)
⎛ T ⎞
0.181 * ⎜
⎟
⎝ 273 ⎠
1.5
⎛ T ⎞
0.753 * ⎜
⎟
⎝ 273 ⎠
1.5
Tab.1. The Cell Parameters
The performance of fuel-cell as a function of temperature is presented in Fig.5. In the form of fuel-cell
voltage versus current density. Results shown that the higher the temperature, despite the lower Nernst
potential. As more current is drawn from the fuel-cell, however, a higher cell voltage can be maintained
under higher temperature operating at the same current density. There is significant reduction of both
Ohmic and activation over-potential at higher temperature operating.
IV. CONCLUSIONS
The performance model was calculated from semi- empirical correlations based on kinetic data, which are
very sensitive to temperature variations. The model allowed determination of temperature, flow and
current distributions for different geometries. The model predicted temperature, mass and electrical
distribution for the entire stack which consisted of an array of unit cells. The finite-volume method was
used for solving the governing equations
REFERCENCES
[1] H. Mohcene, H. Ben Moussa, H.Bouguettaia, D.Bechki. Power Make Up Conference in
Countries 27-28 November, 2006, Beirut-Lebanon.
Arab
[2] H .Ben moussa, D. Haddad, K.oulmi, International Chemical Engineering Conference V (JICEC05),
from the 12th to14th of September (2005), Amman (Jordan.)
[3] K.Oulmi, H. Ben moussa, D. Haddad, Electrochemical energy conversion and storage (fuel cells), the
56th International society of electrochemistry, Sept 25–30, (2005) Bexco, Busan, Korea.
[4] High Temperature Solid Oxide Fuel Cell. Fundamentals, Design and Applications. Sub
Singhal Kevin Kendall, ELSEVIER, 2004
hash C
[5] Sadik Kakaç, Anchsa Pramuanjaroenkij, Xiang Yang Zhou, Areview of numerical of solid oxide fuel
cells, International Journal of Hydrogen Energy, 18, (2006), 1-26.
[6] Dayadeep S. Monder, K.Nandakumar, Karl T.Chuang, Journal of Power Sources 162
414
[7] Huayang Zhu, Robert J.Kee, Vinod M. Janardhanan and Al, Journal of Electroche152 (12) A2427-A2440 (2005).
(2006) 400micalSociety,
[8] Pei-Wen Li, Minking K. Chyu, Simulation of the chemical/ electrochemical reactions and
transfer for a tubular SOFC in a stack, Journal of Power Sources 124 (2003) 487-498
[9] GrayDavid.Govmore, Analyses and Technology Transfer for Fuel Cell Systems.,
ENERGY COMMISSION, June 2000.
heat/mass
CALIFIRONIA
[10] Heuveln, Fredrik Hendrik van Characterisation of Porous Cathodes for Application in
Fuel Cells, 24 January 1997.
Solid Oxide
[11] SOFC mathematic model for systems simulations. Part one: from a micro-detailed to macro-blackbox model, International Journal of Hydrogen Energy, 30, (2005) 181-187.
[12] E. Riensche, E. Achenbach, D. Froning, M. R. Haines, W. K. Heidug, A, Clean combined-cycle
SOFC power plant-cell modelling and processanalysis Journal of Power Sources, 86 March (2000)
404-410
[12] S.C. Singhal, Advances in solid oxide fuel cell technology, Solid State Ionics 135
313
(2000) 305–