Summer Course on Exergy and Its Applications EXERGY ANALYSIS of FUEL CELLS C. Ozgur Colpan

1. Summer Course on Exergy and Its Applications EXERGY ANALYSIS of FUEL CELLS C. Ozgur Colpan July 2-4, 2012 OsmaniyeKorkut Ata Üniversitesi

2. OUTLINE Introduction to fuel cells Thermodynamics of fuel cells Fuel cell irreversibilities and exergy destruction • Ohmic losses • Activation losses • Mass transport or concentration losses • Losses due to fuel crossover Efficiency of fuel cells Exergy analysis of integrated fuel cell systems Summary

3. Introduction • Fuel cell: An electrochemical device that converts the energy of fuel into electricity • High efficiency • Low environmental impact • Main components: • Anode • Cathode • Electrolyte • Electrochemical reactions occur at the electrodes • Production and consumption of ions • Ions are conducted from one electrode to the other through electrolyte • Electrons are cycled via an external load. Electrode

4. Introduction (Cont’d) A single cell can produce only a small amount of power Fuel cell stack: Combination of many single cells to produce the desired power output • Generally done by connecting single cells in series using bipolar plates • Bipolar plates forms air and fuel flow channels and conducts electrons

5. Introduction (Cont’d) Source: www.fuelcelltechnology.com

6. Introduction (Cont’d) Source: Larminie and Dicks (2002)

7. Thermodynamics of Fuel Cells Work is obtained from the transport of electrons across a potential difference and not from mechanical means. V=Cell Voltage (V) I=Current Density (A/cm2)

8. Thermodynamics of Fuel Cells (Cont’d) Reversible Process 1st Law: 2nd Law: Combining 1st and 2nd Laws: If we divide both sides with the number of moles of fuel utilized Molar specific Gibbs free energy change of the reaction Faraday constant=96485 C Electromotive force (EMF) or Reversible open circuit voltage (OCV) Number of electrons transferred

9. Thermodynamics of Fuel Cells (Cont’d) How to find n? Example: PEMFC Example: DMFC Example: SOFC Anode Cathode Overall Anode Cathode Overall Anode Cathode Overall

10. Thermodynamics of Fuel Cells (Cont’d) How to calculate ∆g? Gibbs free energy depends on temperature, pressure, and concentration Change in the molar specific Gibbs free energy of the reaction Where For ideal gases Activity Chemical potential Chemical potential in the standard state For pure liquid For example: Change in the molar specific Gibbs free energy of the reaction in the standard state Where

11. Thermodynamics of Fuel Cells (Cont’d) EMF in terms of product and/or reactant activity is called Nernst Voltage. • It is the reversible cell voltage that would exist at a given temperature and pressure Combine and Nernst Voltage

12. Thermodynamics of Fuel Cells (Cont’d) Example: Derivation of Nernst Voltage for SOFC If all the pressures are given in bar, then

13. Thermodynamics of Fuel Cells (Cont’d) We can also show Nernst voltage of the SOFC in terms of fuel utilization ratio and air utilization ratio. • Fuel utilization ratio: • Air utilization ratio: • Nernst voltage becomes (Colpan et al., 2009):

14. Thermodynamics of Fuel Cells (Cont’d)

15. Fuel Cell Irreversibilities and Exergy Destruction Entropy is generated due to irreversibilities in fuel cells. Entropy generation rate may be written as follows after combining first and second laws of thermodynamics. For a hydrogen fuel cell, entropy generation rate per molar flow rate of hydrogen utilized can be shown as (for 0D modeling): For 1 mol of H2 utilized, 2F current is produced.

16. Fuel Cell Irreversibilities and Exergy Destruction (Cont’d) The difference between Nernst voltage (reversible cell voltage) and operating cell voltage is known as polarization or overpotential or voltage loss or irreversibility. There are four major irreversibilities in fuel cells. • Ohmic losses • Activation losses • Mass transport and concentration losses • Losses due to fuel crossover (e.g. in DMFCs) If we neglect the fuel crossover losses

17. Fuel Cell Irreversibilities and Exergy Destruction (Cont’d) Using Guoy-Stodola theorem, specific exergy destruction in a process may be shown as Hence, combining equations For high temperature fuel cells (e.g. SOFC), the operating cell voltage is generally higher than low temperature fuel cells (e.g. PEMFC), because the irreversibilities are smaller.

18. Fuel Cell Irreversibilities and Exergy Destruction (Cont’d) A typical low temperature fuel cell A typical high temperature fuel cell Source: Larminie and Dicks (2002)

19. Ohmic Losses Caused by the resistance to the flow of ions through the electrolyte and resistance to the flow of electrons. Ohm’s law describes that there is a linear relationship between voltage drop and current density. Where Area Specific ohmic Resistance Length of the electron and ion paths (generally taken as the thickness of the conducting layer) Resistivity of the materials (determined by experiments)

20. Ohmic Losses (Cont’d) Example: The electrolyte of the SOFC (YSZ) Source: Colpan et al. (2009)

21. Activation Losses Caused by the slowness of the reactions taking place on the surface of the electrodes. Different equations in literature • From the most simple to the complex: a linear equation with constant coefficients, Tafel equation, and Butler-Volmer equation. Tafel Equation For a hydrogen fuel cell with two electrons transferred per mole Exchange current density (Higher for a faster reaction) Tafel slope (Higher for a slower reaction) Charge transfer coefficient

22. Activation Losses (Cont’d) Tafel Plots for slow and fast electrochemical reactions Source: Larminie and Dicks (2002)

23. Activation Losses (Cont’d) Exchange Current Density There is a continual backwards and forwards flow of electrons from and to the electrolyte At exchange current density, there is an equilibrium between forward and backward reactions Higher the exchange current density, better the performance Example: Cathode reaction of PEMFC

24. Activation Losses (Cont’d) For a low temperature, hydrogen fed fuel cell, a typical value for exchange current density is 0.1 mA cm-2 at the cathode and about 200 mA cm-2 at the anode. For SOFC • Butler-Volmer Equation • Assuming charge transfer coefficient for anode and cathode as 0.5 e.g. Exchange current density of anode: ~650 mA cm-2 Exchange current density of cathode: ~250 mA cm-2

25. Mass Transport or Concentration Losses When gases at the channels diffuse through the porous electrodes, the gas partial pressure at the electrochemically reactive sites becomes less than that in the bulk of the gas stream. • Hence, a voltage drop occurs which is called concentration polarization. • Limiting current density • The current density at which the fuel is used up at a rate equal to its maximum supply. • Can be found solving diffusion equations (e.g. Fick’s law)

26. Mass Transport or Concentration Losses Example: For SOFC Where

27. Losses due to Fuel Crossover Fuel crossover occurs when some fuel diffuses from the anode through the electrolyte to the cathode. This fuel reacts directly with the oxygen, producing no current. The term ‘mixed potential’ is often used to describe the situation that arises with fuel crossover. For example, for DMFC, it affects the cathodic activation polarization. Crossover current density Where

28. Case Study Polarizations and specific exergy destruction for a SOFC

29. Efficiency of Fuel Cells Electrical efficiency of a fuel cell Exergetic efficiency of a fuel cell Maximum electrical efficiency of a fuel cell Fuel cells are not subject to Carnot efficiency.

30. Efficiency of Fuel Cells (Cont’d) Source: Larminie and Dicks (2002) Note: Fuel cell efficiency shown is relative to HHV.

31. Exergy Analysis of Integrated Fuel Cell Systems APPROACH Draw the control volumes enclosing a component or several components of the system Calculatethe flow exergies of each state (Physical+Chemical exergies if other exergy components are negligible) Apply exergy balances around the control volumes to find the exergy destruction in those control volumes Compare the exergy destruction in a control volume to the total exergy destructions within the overall system Compare the exergy destructions and losses to the chemical exergy of the fuel Calculate the exergy efficiency of the integrated system

32. Exergy Analysis of Integrated Fuel Cell Systems (Cont’d) Case Study: Integrated SOFC and Biomass Gasification System Source: Colpan et al. (2010)

33. Exergy Analysis of Integrated Fuel Cell Systems (Cont’d) • The physical and chemical exergy flow rates: • The exergy balance: • The exergetic efficiency of the system: (for all substances) (for ideal gas mixtures) (for CxHyOz) (for O/C<2) (Szargut, 2005)

34. Exergy Analysis of Integrated Fuel Cell Systems (Cont’d) Performance assessment parameters Exergy destruction ratios Exergy loss ratios

35. Summary • Reversible open circuit voltage (OCV) or Electromotive force (EMF) depends on the change in the Gibbs free energy of the overall reaction and the number of electrons transferred. • Nernst voltage is the EMF written in terms of product and/or reactant activity. • The difference between the reversible OCV and operating cell voltage is known as polarization or overpotential or voltage loss or irreversibility. • Four major irreversibilities in fuel cells are: ohmic losses, activation losses, mass transport or concentration losses, and fuel crossover losses. • For high temperature fuel cells, the maximum theoretical efficiency can be lower than the Carnot efficiency. • Exergy analysis is an useful tool to find the exergy destructions and losses, and exergetic efficiency of integrated fuel cell systems.