1. Fuel Cell Thermodynamics

2. Fuel Cells Basics
Fuel cells convert chemical energy directly into electrical energy.
Difference with batteries: fuel cells require a fuel to flow in order to produce electricity.
Heat is produced from chemical reaction and not from combustion.
Types of fuel cells:
Proton exchange membrane (PEMFC)
Direct Methanol fuel cell (DMFC)
Alkaline fuel cell (AFC)
Phosphoric acid fuel cell (PAFC) (*)
Molten-carbonate fuel cell (MCFC) (*)
Solid-oxide fuel cell (SOFC) (*)
(*) Suitable for microgrids.

3. Fuel cells operation dc current Heat Oxygen Hydrogen Water
Example: PEMFC
The hydrogen atom’s electron and proton are separated at the anode.
Only the protons can go through the membrane (thus, the name proton exchange membrane fuel cell).
dc current
Heat
Oxygen
Hydrogen
Water
Catalyst (Pt)
Anode (-)
Membrane
(Nafion)
Catalyst (Pt)
Cathode (+)

4. Fuel cell thermodynamics
The first law of thermodynamics:
The energy of a system is conserved
In conservational fields, potential functions change depend only on initial and final values. Hence,
For a closed system (control mass system), such as a piston
(The total energy change equals the sum of the change in internal energy, the change in kinetic energy, and the change in potential energy)
Change of system’s total energy
Change of heat provided to the system
Change of work provided by the system

5. Fuel cell thermodynamics
For an open system with mass flow across its boundaries (control volume), such as a steam turbine
pV represents the work to keep the fluid flowing (p is pressure and V is volume). Hence, if a magnitude called enthalpy H is defined as
Then,
If we use the 1st law of thermodynamics for a stationary control volume (i.e. the kinetic and potential energies are constant in time, then
Thus, the enthalpy is the difference between the heat and the work involved in a system such as the one defined immediately above.

6. Fuel cell thermodynamics
If the change in enthalpy is negative, heat is liberated and the reaction occurs spontaneously (contrary to endothermic reactions that requires to apply heat in order for the reaction to occur).
In the anode:
In the cathode:
Hence, in a PEMFC, 285 kJ/mol are converted into heat (Q) and electricity (W).
Entropy: it is a property that indicates the disorder of a system or how much reversible is a process. This last definition relates entropy to energy “quality”.
In a reversible isothermal process involving a heat transfer Qrev at a temperature T0, the entropy is defined as

7. Fuel cell thermodynamics
In all processes involving energy conversion or interactions ΔS is non-negative. ΔS is zero only in reversible processes..
For any process then
The “=“ in the above relationship will give us the minimum amount of heat Qmin required in a process.
From the enthalpy definition a fuel cell can be considered as a system like the following one Q W Q ΔH

8. Fuel cell thermodynamics
The maximum possible efficiency for a fuel cell is, then
An alternative derivation involves using “Gibbs Free Energy”
The definition of entropy is relates with the 2nd Law of Thermodynamics. One of its interpretations is that it is impossible to convert all the energy related with irreversible processes, such as heat or chemical energy, into work.
Hence, it is possible to define a magnitude with units of energy called Gibbs Free Energy that represents the reversible part of the energy involved in the process.
Hence, for fuel cells, the electrical work represents the Gibbs Free Energy and the maximum possible energy conversion efficiency is

9. Fuel cell thermodynamics
From tables:
In the anode:
In the cathode:
And from slide #6 ΔH equals 285 kJ/mol. Thus,
The Gibbs Free Energy can also be used to calculate the output voltage of an ideal fuel cell. Since the Gibbs Free Energy equals the electrical work, and the electrical work equals the product of the charge and voltage, then
where F is the Faraday constant (charge on one mole of electrons) the factor of two represents the fact that two electrons per mole are involved in the chemical reaction.

10. Fuel cell thermodynamics
Thus,
and since F = 96,485 C/mole and ΔG = kJ/mole, then
E0 is also denoted by Er, the reversible voltage.
This is the voltage that can be obtained in a single ideal PEMFC when the thermodynamic reaction limitations are taken into account. I.e., this is the output voltage of a single ideal PEMFC when it behaves as an ideal voltage source. However, additional energy loosing mechanisms further reduce this voltage.

11. PEMFC output: Tafel equation
The Tafel equation yields the cell’s output voltage Ec considering additional loosing mechanisms:
The first term is the reversible cell voltage (1.23V in PEMFCs)
The last term represents the ohmic losses, where i is the cell’s current density, and r is the area specific ohmic resistance.
The second term represent the losses associated with the chemical kinetic performance of the anode reaction (activation losses). This term is obtained from the Butler-Volmer equation and its derivation is out of the scope of this course.
In the second term, i0 is the exchange current density for oxygen reaction and b is the Tafel slope:

12. PEMFC output: Tafel equation
In the last equation R is the universal gas constant (8.314 Jmol-1K-1), F is the Faraday constant, T is the temperature in Kelvins, n is the number of electrons per mole (2 for PEMFC), and β is the transfer coefficient (usually around 0.5). Hence, b is usually between 40 mV and 80 mV.
The Tafel equation assumes that the reversible voltage at the cathode is 0 V, which is only true when using pure hydrogen and no additional limitations, such as poisoning, occur.
The Tafel equation do not include additional loosing mechanisms that are more evident when the current density increases. These additional mechanisms are:
Fuel crossover: fuel passing through the electrolyte without reacting
Mass transport: hydrogen and oxygen molecules have troubles reaching the electrodes.
Tafel equation also assumes that the reaction occurs at a continuous rate.

13. PEMFC electrical characteristics
Er = 1.23 V
Maximum power operating point
Er =1.23V
b=60mV,
i0=10-6.7Acm-2
r=0.2Ωcm2
Activation loss region
Mass transport loss region
Ohmic loss region
(linear voltage to current relationship)
Actual PEMFCs efficiency vary between 35% and 60%

14. PEMFC electrical characteristics
This past curve represent the steady state output of a fuel cell.
The steady state output depends on the fuel flow:
Amrhein and Krein “Dynamic Simulation for Analysis of Hybrid Electric Vehicle System and Subsystem Interactions, Including Power Electronics”

15. Hydrogen production
Hydrogen needs to be produced, and sometimes it also needs to be transported and/or stored. Hydrogen is not a renewable source of energy. Hence, FC are alternative sources of energy.
Methods for hydrogen production:
Methane Steam Reforming (MSR)
It uses natural gas
Two-step process: 1)
endothermic reaction (needs heat) 2)
exothermic reaction (provides heat)
75 % to 80 % efficient.
Partial oxidation (POX)
It also uses natural gas or other hydrocarbon
and/or
POX is compact and has faster dynamic response than MSR, but MSR provides higher hydrogen concentration.

16. Hydrogen production More methods for hydrogen production:
Electrolysis of water
Water molecules can be separated using electricity. But we use electricity to produce hydrogen to produce electricity again.
Pure water is in many places an scarce resource.
The electricity for the electrolysis needs to be produced and the water needs to be purified (soft de-ionized water is needed).
Reaction:
Electricity can be obtained at a large scale from nuclear reactors but the hydrogen needs to be stored and transported, and nuclear fuel is not a renewable source of energy.
At a VERY small scale wind or solar power can be used, but this energy is available only when there is wind or sunlight.
Gasification of Biomass, Coal or Wastes
These methods are still a long way into the future.

17. Hydrogen Storage
Hydrogen atoms are the lightest and smallest of all elements. For this reason, it is very difficult to keep hydrogen from escaping confined environments such as tanks or pipes.
Since an “effort” (i.e. work) needs to be done to keep hydrogen stored, storing hydrogen implies loosing efficiency.
Some storage methods:
Pressure Cylinders: Some efficiency is lost in the compressing process
Liquid Hydrogen: it requires lowering the hydrogen temperature to K. This process already reduces 1/3 of the efficiency.
Metal Hydrides: These are compounds of hydrogen and Magnesium, titanium and other metals. Efficiency is low to medium and lot of heat is generated when the hydrogen is released, but these compounds are very easy to store in the form of soils.
Carbon nano-fibers: New technology.

18. PEMFC Technology and issues
Expected life of PEMFC is very short (5,000 hours).
The most commonly used catalyst (Pt) is very expensive.
The most commonly used membrane (Nafion – a sulfonated tetrafluorethylene copolymer is also very expensive).
PEMFCs are very expensive.
CO poisoning diminishes the efficiency. Carbon monoxide (CO) tends to bind to Pt. Thus, if CO is mixed with hydrogen, then the CO will take out catalyst space for the hydrogen.
Hydrogen generation and storage is a significant problem.
Additional issues to be discussed when comparing other technologies: dynamic response and heat production.

19. Direct Methanol Fuel Cells (DMFC)
The main advantage is that they use a liquid fuel.
Reactions:
Anode
Cathode
Voltages: V at anode, 1.23 V at cathode, 1.18 V overall.
Methanol has high energy density so DMFC are good for small portable applications.
Issues:
Cost
Excessive fuel crossover (methanol crossing the membrane)
Low efficiency caused by methanol crossover
CO poisoning
Low temperature production
Considerable slow dynamic response

20. Phosphoric Acid Fuel Cells (PAFCs)
One of their main advantages is their long life in the order of 40,000 hours.
The phosphoric acid serves as the electrolyte.
The reactions are the same than in a PEMFC. Hence, the reversible voltage is 1.23 V
The most commercially successful FC: 200 kW units manufactured by UTC
They produce a reasonable amount of heat
They support CO poisoning better than PEMFC
They have a relatively slow dynamic response
Relative high cost is an important issue

21. Alkaline Fuel Cells (AFCs)
The main advantage is that their cost is relatively low (when considering the fuel cell stack only without “accessories”.
Reactions:
Anode
Cathode
Developed for the Apollo program.
Very sensitive to CO2 poisoning. So these FCs can use impure hydrogen but they require purifying air to utilize the oxygen.
Issues:
Cost (with purifier)
Short life (8000 hours)
Relatively low heat production

22. Molten Carbonate Fuel Cells (MCFCs)
One of the main advantages is the variety of fuels and catalyst than can be used.
Reactions:
Anode
Cathode
They operate at high temperature. On the plus side, this high temperature implies a high quality heat production. On the minus side, the high temperature creates reliability issues.
They are not sensitive to CO poisoning.
They have a relatively low cost.
Issues:
Extremely slow startup
Very slow dynamic response

23. Solid Oxide Fuel Cells (SOFCs)
One of the main advantages is the variety of fuels and catalyst than can be used.
Reactions:
Anode
Cathode
They operate at high temperature with the same plus and minus than in MCFCs.
They are not sensitive to CO poisoning.
They have a relatively low cost.
They have a relatively high efficiency.
They have a fast startup
The electrolyte has a relatively high resistance.

24. Fuel cell technologies
Comparison of the most common technologies
PEMFC
DMFC
AFC
PAFC
MCFC
SOFC
Fuel H2
CH3OH
H2, CO, CH4, hydrocarbons
Electrolyte
Solid polymer
(usually Nafion)
Potasium hydroxide (KOH)
Phosporic acid (H3PO4 solution)
Lithium and potassium carbonate
Solid oxide (yttria, zirconia)
Charge carried in electrolyte H+
OH-
O2-
Operational temperature (oC)
50 – 100
175 – 200
650
1000
Efficiency (%)
35 – 60
< 50
35 – 55
35 – 45
45 – 55
50 – 60
Unit Size (KW)
0.1 – 500
<< 1
< 5
5 – 2000
800 – 2000
> 2.5
Installed Cost ($/kW)
4000
> 5000
< 1000*
3000 – 3500
* Without purifier