Fuel Cell Basics – Introduction

Chapter 8

Basic overall reaction for hydrogen powering

• 2H2 + O2 ↔ 2H2O

Hydrogen produces electrons, protons, heat and water

PEMFC

• Anode reaction: H2 → 2H+ + 2e-

• Cathode reaction: (½)O2 + 2H+ + 2e- → H2O

• Overall: 2H2 + O2 ↔ 2H2O

Introduction❖ How do PEM fuel cells work?

http://www.intelligent-energy.com/technology/technology-faq/ (Animation)

SOFC

• Anode reaction: H2 + O2- → H2O + 2e

-

• Cathode reaction: (½)O2 + 2e- → O2-

• Overall: 2H2 + O2 ↔ 2H2O

A planar fuel cell layout

A fuel cell stack

A cylindrical fuel cell layout

Open Circuit Voltage (OCV)

Inputs and Outputs

Hydrogen Energy

Oxygen Energy

Electric Energy, V•I•t

Heat

Water

Enthalpy of formation

Enthalpy of formation of the product in a chemical reaction is the difference in enthalpy of the product and sum of enthalpy of all reactants

Enthalpy of formation Reference state is 25 C and 0.1 MPa. At this state the

enthalpy of the reactants is zero.

The enthalpy of the product at the reference state is then given by the net heat transfer and this is termed the

enthalpy of formation of the product

Enthalpy of formation

The enthalpy of formation can be determined by experiments but commonly statistical thermodynamics is

used to determine it for various compounds. Table is provided.

= Hp= QCV

Enthalpy of formation Enthalpy of formation of the components and compounds at any

other state than the reference base state is estimated by adding the change in enthalpy between the given state and the reference state

as

∆h25C, 0.1MPa → T,P → ∫ cp(T)dT

0

25 ,0.1 , ( , ) (25 ,0.1 )f C MPa T ph T p h C MPa h →= +

Gibbs free energy of formation

Gibbs free energy of formation

Fuel Cell BasicsChapter 8 in course book

Gibbs free energy of formation

Gibbs free energy of water at various temperatures and stateWater Product Temperature, C Δgf , kJ/mole Max EMF, V Efficiency limit %

liquid 25 -237.2 1.23 83

liquid 80 -228.2 1.18 80

gas 100 -225.3 1.17 79

gas 200 -220.4 1.14 77

gas 400 -210.3 1.09 74

gas 600 -199.6 1.04 70

gas 800 -188.6 0.98 66

gas 1000 -177.4 0.92 62

Estimation of open circuit voltage, OCV

Electrochemistry and Thermodynamics• The amount of work performed by the device on its surroundings is –W.

Integrated over a time period, it may be expressed as

-∆W = -∆Welectric + ∫pdV

where the last term is zero if the system is held at a fixed volume. The electric work -∆Welectric ,which the electrochemical system can deliver to a device (e.g., an electric motor) attached to an external circuit, may be expressed in terms of the electric potential difference between the positive and negative electrodes and the number of electrons travelling, i.e.,

-∆Welectric = ne•NA•e•∆Φext = ne•F •∆Φext

where the electron charge is e = 1.6•10-19 C (e•∆Φext, the energy difference for a single electron), ne is the number of moles of electrons, NA = 6.23•10

23

Avogadro’s constant (the number of particles-here electrons-per mole) and F = NA•e = 96 400 C/mol is the Faraday’s constant.

Cell voltage

• The potential difference between the electrodes determines the theoretical cell voltage, Ecell , also called the electrochemical force (emf). This is primarily expressed as Gibbs free energy of the charge of the cell, ∆Gcell

As reaction occurs, there is a decrease in the free energy of the cell according to:

∆Gcell = -nFEcell

where Ecell ,is related to the sum of the standard potential of each electrode as:

Ecell = Epositive - Enegative

Estimation of open circuit voltage, OCV

Efficiency

Efficiency

Influence of Pressure on Gibbs Energy and Reversible Voltage

• Gibbs energy or function is defined as

G = H-TS or g = h-Ts = u + pv –Ts

First law of thermodynamic states thatdu = q – pdv = Tds – pdv

By combining these it is possible to find

dg = vdp-sdT or dG = Vdp – SdT

Effect of gas concentration

Reaction Quotient See, battery section

Effect of gas concentration-continued

Effect of gas concentration-continued

Effect of gas concentration-continued

Nernst EquationSee battery section

Fuel Cell Reaction involving Hydrogen -Oxygen

EMF valuesDepends on temperature

Low temperature (40 C): EMF ≈ 1.2 V

High temperature (800 C): EMF ≈ 1 V

Gibbs free energy of water at various temperatures and stateWater Product Temperature, C Δgf , kJ/mole Max EMF, V Efficiency limit %

liquid 25 -237.2 1.23 83

liquid 80 -228.2 1.18 80

gas 100 -225.3 1.17 79

gas 200 -220.4 1.14 77

gas 400 -210.3 1.09 74

gas 600 -199.6 1.04 70

gas 800 -188.6 0.98 66

gas 1000 -177.4 0.92 62

EMF versus temperature

Operational losses

FC-Ireversibilities, Voltage losses

• Activation loss

• Ohmic loss

• Concentration loss

• Cross-over and short circuit losses

Fuel Cell Polarization CurveLosses: anode and cathode activation losses, ohmic losses, mass transfer losses,

losses due to short circuit, losses due to reactant crossover

The net fuel cell overpotential becomes:

Principle sketch of a polarization curve - Operational voltage versus current density

Voltage losses

• Activation losses ”over potential”

• Fuel crossover/internal current losses

• Ohmic losses

• Mass transport/concentration losses

Activation losses

• The activation losses are non-linear with current. Typically the activation losses introduce a sharp initial drop in the cell open circuit EMF with increasing current load. The losses are different at each electrode (the anode and cathode) because the double layer configuration is different. These losses are directly related to the energy barrier (resistances) for oxidation and reduction at the electrodes.

As a metal electrode is placed in an electrolyte, the charge of the metal will attract ions of opposite charge in the

electrolyte. Then a layer of charge is formed both in the electrolyte and the metal. This layer is called the

electrical double layer and a principle sketch is provided in the Figure below. The electrochemical reactions take

place in this layer.

Electrical Double Layer

All atoms or ions being reduced or oxidized have to pass through this layer. The kinetics of the electrode

reaction is controlled by the possibility for ions to pass across this layer. The energy barrier for the electrode

reaction, called the activation energy of the electrochemical reaction is situated in this electrical double layer

Principle of Activation Energy

The activation energy has to be supplied to jump over the hill. If the probability of a molecule is low

for having sufficient energy, the actual reaction will proceed slowly.

The slow reaction rates can be affected by a) using catalysts, b) increasing

the temperature and c) increasing the electrode area (porous with

microstructure).

The reaction area involving the fuel or oxidant with the electrolyte and the

electrode is sometimes called the three-phases contact or triple phase

boundary.

Activation losses

• The activation losses for the anode and cathode are given by the equations below:

• For a hydrogen-oxygen FC, the cathodic activation loss is dominating and hence the anodic one is neglected.

Activation loss

• For equal charge coefficients, i.e.,

αa = αc = α

It can be found based on Butler-Volmer equation

• ηact =

Exchange current density and charge transfer coefficient.

A large value of means low electrode losses.

n, F and R cannot be changed for a given reaction. Increase in T and increase of the reactant concentration C can lead to higher values of .

Minimizing activation losses

• High operational temperature, i0 goes up

• Catalytic presence

a) Rough catalysts mean more contact area, b) increase operational pressure, c) selection of catalytic material, Ni, Pt used commonly otherwise Pd better.

Ohmic losses

These occur due to resistance to the flow of electrons in the interconnect, anode and cathode

Directly proportional to the current

Major loss in both low and high temperature fuel cells

Ohmic losses

Mass transport/concentration losses

For low and high temperature fuel cells

Particularly at high current densities

Loss of high concentration of either fuel (at anode) or oxygen (at cathode)

Fuel or oxygen is used faster than supplied

Mass transport loss

• The balance between the rate of transport of species and the rate of consumption at the interface determines the maximum current.The key transport processes are convection, diffusion and migration.

Migration means transport of ionic species toward or away from the electrode due to the effect of an electric field. A high electric field gives high migration rate.

Diffusion means transport of reactant or product species because of a concentration gradient.

Convection means transport of reactant or product species by bulk fluid motion driven by natural or applied mechanical forces.

Mass transport loss

Concentration lossesFor reaction kinetics and based on the Butler-Volmer

equation it can be derived

ηconc,k =

Concentration losses

• Concentration effects can be found by using the Nernst equation

• ηconc,N =

Concentration losses

• ηconc = ηconc,k + ηconc,N = (1 + 1/α)

Reactant crossover and internal currents

• The electrolyte of a fuel cell mainly conducts ions but it is not completely insulated from electrons. It will be able to support a small amount of electron conduction. This electron conduction in the electrolyte or internal current creates a net loss of current to external load. Also some reactants will diffuse from one electrode to another through the electrolyte where reactions occur without external electron transfer.

Fuel cross-over/internal current loss

Losses throughout the electrolyte

a) Fuel is leaking through the electrode

b) Electrons are leaking through the electrode

Fuel leakage most severe but has a significant effect only at low temperature

jL

• jL is the maximum current density or limiting current density. At this all reactant gas has been consumed and the output cell voltage is zero.

PEMFCC

ell

voltage,

volt

Current density, mA cm-2

“No loss” voltage of 1.2 volts

00 400200 800600 1000

0.2

0.6

0.4

0.8

1.0

1.2

Even the open circuit voltage is less than the

theoretical no loss value

Rapid fall at

higher currents

Rapid initial fall in voltage

Region where voltage falls slowly

and graph is fairly linear

SOFCC

ell

voltage,

volt

Current density, mA cm-2

“No loss” voltage of 1.0 volts

00 400200 800600 1000

0.2

0.6

0.4

0.8

1.0

1.2

Very small initial fall on voltage, OCV

almost equals to the theoretical value

Rapid fall at higher

currents, as with

low temp. cells

Graph mostly linear

Butler Volmer equation

• A key issue in the physical understanding, modeling and simulation of fuel cells is to determine the current generated by a cell. The most common method is to apply the so-called Butler-Volmer equation which relates the current density to the activation overpotential at each electrode/electrolyte interface. It reads:

Butler-Volmer equation

Typical parameters for PEMFC and SOFC

Parameters PEMFC SOFC

Open-circuit voltage (V) 1.22 1.06

1 x 10-4 0.1

1.5 1.5

0.002 0.002

0.03 0.09

A (V) 0.05 0.03

B(V) 0.06 0.08

Oxygen-Hydrogen-Water Flow Rates

Direct oxygen consumption

• The total charge current I is given by

where is the number of electrons per mole of oxygen, F the Faraday constant and is the number of mol/s of oxygen.

Direct oxygen consumption

• For a stack of Nc number of cells the oxygen consumption is given by

• In terms of mass flow rate (kg/s) we have

Direct oxygen consumption

• The power consumption in a single cell and in a stack can be expressed as

Pc = I•VcPt = Nc•Pc = Nc• I•Vc

Then the mass flow rates can be expressed as:

Direct oxygen consumption

• For stack:

• For cell:

Oxygen consumption as air

• Let the mol fraction of oxygen in air be

The the number of moles of oxygen per kilogram air is:

The consumption of air for a cathodic reaction is then

Oxygen consumption as air

• Commonly an excess amount of oxygen is supplied and the excess air supply is defined in terms of a stochiometric factor ξair

• Then the supply air mass flow rate (stack) is given by

Oxygen consumption as air

• The exit air flow rate is then simply

Hydrogen consumption and supply rates

• Similarly it is possible to estimate the hydrogen mole consumption in an anodic reaction as (cell):

• For a stack:

Hydrogen consumption and supply rates

• Mass flow rates of hydrogen:

Stack

cell

Water production rate

• Consider a hydrogen-oxygen FC and then 1 mol of water is produced for every two electron charges. The water production rate is given by:

Water production rate

• Mass flow rate

Heat Generation Rate