84 CHAPTER 3 MODELING OF SOLID OXIDE FUEL CELL – GAS TURBINE HYBRID SYSTEM “A model is neither true nor false – it is more or less useful” - (Stafford Beer, 1985) 3.1 Solid Oxide Fuel Cell Solid oxide fuel cells consists of a solid electrolyte (zirconia), which is a ceramic and a good conductor of oxygen ions. This property of zirconia was first discovered by Nernst in late 1890’s. Though the technology has evolved in these hundred years and production methods have improved, zirconia is still considered to be the best electrolyte for solid oxide fuel cells. Zirconia starts conducting oxygen ions when its temperature is above 700°C and thus solid oxide fuel cells are best suited for co-generation. Waste heat from the fuel cell can be utilized in a bottoming cycle and power generation efficiencies of more that 60% are achievable. Also, within the SOFC operating temperature range, emissions of NOx are likely to be very small resulting in a cleaner environment [19]. 3.1.1 Thermodynamics and Electrode kinetics of SOFCs A solid oxide fuel cell is an electro chemical reactor which converts hydrogen and oxygen into electricity. Figure 3.1 shows the schematic diagram of taking place in a solid oxide fuel cell. It basically consists of two porous electrodes (anode and cathode) separated by a ceramic
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MODELING OF SOLID OXIDE FUEL CELL GAS TURBINE HYBRID SYSTEM
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84
CHAPTER 3
MODELING OF SOLID OXIDE FUEL CELL – GAS
TURBINE HYBRID SYSTEM
“A model is neither true nor false – it is more or less useful”
- (Stafford Beer, 1985)
3.1 Solid Oxide Fuel Cell
Solid oxide fuel cells consists of a solid electrolyte (zirconia), which is a
ceramic and a good conductor of oxygen ions. This property of zirconia
was first discovered by Nernst in late 1890’s. Though the technology
has evolved in these hundred years and production methods have
improved, zirconia is still considered to be the best electrolyte for solid
oxide fuel cells. Zirconia starts conducting oxygen ions when its
temperature is above 700°C and thus solid oxide fuel cells are best
suited for co-generation. Waste heat from the fuel cell can be utilized
in a bottoming cycle and power generation efficiencies of more that
60% are achievable. Also, within the SOFC operating temperature
range, emissions of NOx are likely to be very small resulting in a
cleaner environment [19].
3.1.1 Thermodynamics and Electrode kinetics of SOFCs
A solid oxide fuel cell is an electro chemical reactor which converts
hydrogen and oxygen into electricity. Figure 3.1 shows the schematic
diagram of taking place in a solid oxide fuel cell. It basically consists
of two porous electrodes (anode and cathode) separated by a ceramic
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electrolyte, and flow channels for air delivery & collection and fuel.
Figure 3.1 Schematic of a Solid Oxide Fuel Cell[8]
H2 or a hydrocarbon like methane is supplied on the anode and
air or O2 on the cathode side of the fuel cell. H2 and CO (if H2 is not
pure) diffuse through the porous anode to the three phase boundary
formed by the electrolyte, the gaseous H2 and anode Similarly, O2
diffuses through cathode to three phase boundary of the cathode side
where it accepts electrons from the cathode and gives oxygen ions.
These oxygen ions travel through the porous electrolyte and react with
H2 to produce electrons and water at the anode and thus voltage is
generated between two electrodes. The two electrodes can be
connected via an external circuit and an electrical current can be
generated [19].
The general reactions in Fuel Cell are:
At the cathode : 2 4 2O e O (3.1)
At the anode : 2 22 2 4 4H O H O e (3.2)
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Water gas shift at anode : 2 2 2CO H O CO H (3.3)
If CO is present in the H2 stream, the CO reacts with H2O via a water
gas shift reaction that produces H2 and CO2.
Before we begin to look at how the electromotive force (EMF) and thus
power is produced in a fuel cell, it is necessary to understand some
basic thermodynamic concepts [19]. Consider the following
thermodynamic relation for a reversible process when there is no shaft
work extracted and the system is restricted to do only expansion work:
dG = VdP – SdT (3.4)
if the process is isothermal, the above equation reduces to:
dG = VdP (3.5)
using the ideal gas relation, PV=nRT in Equation 4 where n is the
number of moles of the gas, we get
dG = nRTdP/P (3.6)
Integrating the above Equation from state 1 to state 2, we get,
G2-G1 = nRT ln(P2/P1) (3.7)
If the state 1 is replaced with some standard reference state, with
Gibbs free energy G° and standard pressure P°, the Gibbs free energy
per unit mole at any state ‘i’ is given by,
gi = g° + RTln(Pi/P°) (3.8)
Consider that the following chemical reaction takes place at constant
temperature and pressure,
aA + bB mM + nN (3.9)
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where a, b, m, and n are the stoichiometric coefficients of the
reactants A and B and the products
M and N, respectively. Now, Equation 8 takes the following form,
lnm n
M No a b
A B
P PG G RT
P P
(3.10)
where G0 is the standard Gibbs free energy change for the reaction,
o o o o
o M N A BG mg ng ag bg (3.11)
gi°, are the standard Gibbs free energies of the constituents.
Equation 10 gives the Gibbs free energy change for the reaction. To
find that relation, consider the following thermodynamic identity for a
reversible process, (dQ = TdS)
dG = -W + PdV + VdP – SdT (3.12)
At constant temperature and pressure, the above equation can be
written as,
dG = - W + PdV (3.13)
Since it is a non-expansion work, equation 13 takes the form,
dG = -We (3.14)
i.e. the change in Gibbs free energy of the reaction is equal to the
maximum electrochemical work, We , that can be extracted when
reactants A and B react to give products M and N under constant
temperature and pressure conditions through a reversible reaction.
The Electro Motive Force produced due to half-cell reactions
drives the electrons to move from anode to cathode. If ne mole of
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electrons move from anode to cathode per unit time and the Electro
Motive Force of the cell is E, the power produced is simply EMF
multiplied by the current,
We = ne FE (3.15)
where F is the total charge of 1 mole of electrons, known as Faraday’s
constant.
Therefore G = -ne FE (3.16)
Applying equation 16 to equation 10, we get what is known as Nernst
equation,
ln
m n
M No a b
e A B
P PRTE E
n F P P
(3.17)
where E° is related to G° by Equation 15.
For the reaction occurring in an SOFC,
2 2 2
1
2H O H O
(3.18)
the reversible potential can be written as,
2
2 2
1/2ln
2
H O
o
H O
PRTE E
F P P
(3.19)
This maximum theoretical voltage, E, is also known as “Open Circuit
Voltage” and can be measured when there is no current in the circuit.
Also, it can be observed, that to get the maximum Open Circuit
Voltage, a high concentration of reactants is required [19].
Equation 19 gives the maximum Open Circuit Voltage but this
is not the operating voltage of the fuel cell. The operating voltage is
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always less than the OCV due to the losses associated with the
current production. There are three major types of voltage losses as
shown in the Figure 3.2.
Figure 3.2 Current-Voltage Characteristics of a Fuel Cell Operating at
1073K [19]
Activation loss is associated with the energy intensive activities of
the forming and breaking of chemical bonds at the electrodes. At the
cathode, the oxygen enters a reaction site and draws electrons from
the catalyst to form oxygen ions. The produced ions form bonds with
the catalyst surface while electrons remain near the catalyst until
another oxygen molecule starts to react with the catalyst, thus
breaking the bond with the ion. The energy input to break the bond
with the ion finds whether the electron will bond again with the
catalyst, or will remain with the ion. The same procedure occurs at
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the anode also. The incoming hydrogen is broken up into it’s
components by the catalyst where it draws oxygen ions to form water
and electrons are released on the anode. The amount of energy needed
for these activities of breaking and forming of chemical bonds comes
from the fuel, and thus reduces the overall energy the cell can
produce. If the reaction rate increases (high current density), the fuel
flow rate must also increase, which increases the kinetics and thus
lowers the energy required to break bonds. Therefore when the
current requirement is low, the overall cell polarization is dominated
by the activation losses. Other factors, which lowers the activation
polarization, are increasing temperature, active area of the electrode,
and activity of electrodes by the use of suitable catalyst.
Ohmic loss is caused by the electrical resistance the charge has to
overcome when traveling across the different materials or interfaces of
the cell. The resistances of the electrodes, current collectors and the
electrolyte are all factors which add to the energy loss. Resistance is
added by the electrodes because of the contact resistance through the
electrode material itself, with the current collectors and with the
electrolyte. The electrolyte can add to the ohmic polarization through
the resistance to ionic flow [19].
Concentration loss is also known as diffusion polarization. It results
from restrictions to the transport of gases to the chemical reaction
sites. This usually occurs at high current densities because the rate at
which the fuel (hydrogen) is consumed at reaction sites is higher than
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the rate of diffusion. The scarcity of hydrogen at the chemical reaction
sites effectively reduces the electrode activity leading to a
corresponding loss in output voltage. This polarization is also affected
by the physical restriction of the transfer of a large atom, oxygen, to
the chemical reaction sites on the cathode side of the fuel cell.
Concentration polarization can be reduced by increasing the fuel
concentration and gas pressure, using high surface area electrodes, or
using thinner electrodes which shortens the path of the gas to the
reaction sites [19].
The combination of all the three polarizations affects the overall
operating voltage. Each polarization dominates at a different current
density range. Figure 3.2 shows that when there is no current in the
circuit, the Open Circuit Voltage is reduced by the activation
polarization. As the current increases, the activation polarization
continues to decrease the operating voltage but the rate of reduction
decreases in a parabolic manner. For moderate current densities, the
ohmic polarization dominates and the polarization curve remains
more or less a straight line as shown in the figure 3.2. There is an
inflection point observed at a certain value of the current density and
afterwards the concentration polarization dominates.
As mentioned earlier, the efficiency of the fuel cell is not
restricted by the Carnot limit. Because of the isothermal nature, most
of the energy released in the chemical reaction is converted to
electrical energy, instead of being consumed to raise the products
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temperature. Hence, the electrochemical processes in the cell offer
high generation efficiencies. The first law efficiency of a SOFC based
upon the lower heating value, is written as,
,e
th cell
n FE
LHV
(3.20)
If fuel input energy is considered, the overall conversion efficiency of
the fuel cell system is given by
*/overall e fW m LHV (3.21)
Where, mf is the mass of fuel consumed
A term, called ideal efficiency, is defined for a fuel cell as :
/ideal G H (3.22)
Which is simply the ratio of available Gibb’s free energy to the total
enthalpy of reaction. For a hydrogen-oxygen cell, operating at
standard condition, the value of this ratio is about 83%. This value
shows the enormous potential of a fuel cell. To achieve a matching
efficiency a Carnot engine would be required to exchange heat with a
source of about 1773K, while rejecting heat to sink at 288K.
The second law efficiency or exergetic efficiency for the
electrochemical process is given by the following expression:
II
Wactual work ideal reversible work
e
G
(3.23)
Considering the fuel cell as steady flow device, the second law
efficiency can also be conveniently expressed as
II
exergy out + work output
exergy in
(3.24)
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where, the exergy values of the inlet and outlet streams are the values
obtained by adding the physical as well as chemical exergy terms of
the respective streams (by neglecting exergy associated with KE, PE
and other kind of energy).
3.2 Modeling of Solid Oxide Fuel Cell-Gas Turbine Combined
Cycle Power Plant For Different Fuels
A solid oxide fuel cell (SOFC) is an electrochemical conversion device
that produces electricity directly from oxidizing a fuel. Fuel cells are
characterized by their electrolyte material; the SOFC has a solid oxide
or ceramic, electrolyte. Advantages of this class of fuel cells include
high efficiency, long-term stability, fuel flexibility, low emissions, and
relatively of low cost. The largest disadvantage is the high operating
temperature which results in longer start-up times and mechanical
and chemical compatibility issues.
Solid oxide fuel cells are a class of fuel cell characterized by the
use of a solid oxide material as the electrolyte. In contrast to proton
exchange membrane fuel cells (PEMFCs), which conduct positive
hydrogen ions (protons) through a polymer electrolyte from the anode
to the cathode, the SOFC uses a solid oxide electrolyte to conduct
negative oxygen ions from the cathode to the anode. The
electrochemical oxidation of the oxygen ions with hydrogen or carbon
monoxide thus occurs on the anode side. They operate at a very high
temperature, typically between 500 and 1,000°C. At these
temperatures, SOFCs do not require an expensive platinum catalyst