Summer Course on Exergy and Its Applications

EXERGY ANALYSIS of

FUEL CELLS

C. Ozgur Colpan

July 2-4, 2012Osmaniye Korkut Ata Üniversitesi

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

2

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

3

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

4

Introduction (Cont’d)

Source: www.fuelcelltechnology.com

5

Introduction (Cont’d)

Source: Larminie and Dicks (2002)

6

Thermodynamics of Fuel Cells

V=Cell Voltage (V)I=Current Density (A/cm2)

Work is obtained from the transport of electrons across a potential difference and not from mechanical means.

7

Thermodynamics of Fuel Cells (Cont’d)Reversible Process1st Law:

Faraday constant=96485 CElectromotive force (EMF) or Reversible open circuit voltage (OCV)

Number of electrons transferred

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

8

How to find n?Example: PEMFC

Example: DMFC

Example: SOFC

Thermodynamics of Fuel Cells (Cont’d)

eHCOOHOHCH 66223

OHeHO 22 3665.1

OHCOOOHCH 2223 25.1

e2H2H 2

OHe2H2O5.0 22

OHOH 222 5.0

e2OHOH 22

2

22 Oe2O5.0

OHOH 222 5.0

Anode

Anode

Anode

Cathode

Cathode

Cathode

Overall

Overall

Overall

9

How to calculate ∆g?• Gibbs free energy depends on temperature, pressure,

and concentration

Thermodynamics of Fuel Cells (Cont’d)

Change in the molar specific Gibbs free energy of the reaction

Where

Chemical potential

Chemical potential in the standard state

ActivityFor ideal gases

For pure liquid

For example:

WhereChange in the molar specific Gibbs free energy of the reaction in the standard state

10

• 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

Thermodynamics of Fuel Cells (Cont’d)

Combine and

Nernst Voltage

11

Thermodynamics of Fuel Cells (Cont’d)

If all the pressures are given in bar, then

Example: Derivation of Nernst Voltage for SOFC

)(222 5.0 vOHOH

12

• 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:

Thermodynamics of Fuel Cells (Cont’d)

Nernst voltage becomes (Colpan et al., 2009):

13

Thermodynamics of Fuel Cells (Cont’d)

14

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.

15

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

16

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.

17

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)

18

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

Resistivity of the materials (determined by experiments)

Length of the electron and ion paths (generally taken as the thickness of the conducting layer)

Area Specific ohmic Resistance

19

Ohmic Losses (Cont’d)Example: The electrolyte of the SOFC (YSZ)

Source: Colpan et al. (2009)

20

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

Tafel slope (Higher for a slower reaction)

Exchange current density (Higher for a faster reaction)

Charge transfer coefficient 21

Activation Losses (Cont’d)

Source: Larminie and Dicks (2002)

Tafel Plots for slow and fast electrochemical reactions

22

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

23

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 24

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)

25

Mass Transport or Concentration LossesExample: For SOFC

Where

26

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.

Where Crossover current density

27

Case StudyPolarizations and specific exergy destruction for a SOFC

28

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.

29

Efficiency of Fuel Cells (Cont’d)

Source: Larminie and Dicks (2002)

Note: Fuel cell efficiency shown is relative to HHV.30

Exergy Analysis of Integrated Fuel Cell SystemsAPPROACH• Draw the control volumes enclosing a component or several

components of the system • Calculate the 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

31

Exergy Analysis of Integrated Fuel Cell Systems (Cont’d)Case Study: Integrated SOFC and Biomass Gasification

System

Source: Colpan et al. (2010) 32

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:

De

eei

iicvj

jj

o xEexnexnWQTT

10

)s(sT)h(hex oooPH

kkoCHkk

CH xxTRxexex ln

)(,15, 2 lOHchOHCch

processnet

enxE

xEW

zyx

fgCH hmLHVex 1

CO

CNCHCOCH/4124.01

/0493.0/0531.01/3493.0/016.0044.1

(for all substances)

(for ideal gas mixtures)

(for CxHyOz)

(for O/C<2)(Szargut, 2005)

33

Exergy Analysis of Integrated Fuel Cell Systems (Cont’d)

Exergy loss ratios

Performance assessment parametersFUE PHR

Case1: Air 18.5% 63.9% 0.409 30.9%Case2: Enriched O2 19.9% 60.9% 0.487 30.7%Case3: Steam 41.8% 50.8% 4.649 39.1%

Exergy destruction ratios

34

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.35