CHE2009 Tawil

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Tawil I.H.

Renewable Energy Authority of Libya (Tripoli)

[email protected]

Bsebsu F.M.Renewable Energies and Water Desalination Research Center, REWDRC,

P. O. Box 30878, Tajoura (Tripoli) Libya,

[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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1. Introduction

Fuel cells generate electricity through an electrochemical

process in which the energy stored in a fuel is converted

directly into DC electricity Figure 1.

The input fuel passes over the anode (and oxygen over

the cathode) where it catalytically splits into ions and

electrons. The electrons go through an external circuit to

serve an electric load while the ions move through the

electrolyte toward the oppositely charged electrode. At

the electrode, ions combine to create by-products,

primarily water .

e-

e-

e-

e-

e-

e-

e-

Anode

Electrolyte

H2O

O2

Cathode

H2

H2

H2O

H+

H+

H+

H+

H+

Electricity

Figure 1. Fuel CellElectrochemical

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The source of energy is fuel, in which the energy is bound in

chemical form.

2.1. Cell Energy Balance

The energy balance around the fuel cell is based on the

energy absorbing/releasing processes (e.g., power produced,

reactions, heat loss) that occur in the cell.

2.1.1. Chemical Balance:

The chemical balances for the reactions occurring inside the

fuel cell are identical:

Chemical

products at

TFC

Fuel Cell

Electricity

H2 inp

ut

QFC =Heat out at

TFC

Surrounding

at To = 298 K

O2 / Air

input

CV

Figure 2. Energy balancearound the fuel cell

{2 2 2Product (P)Reactants (R)

H + O H O14243

2.1.2. Energy Balance for Chemical Reaction:

The chemical processes within the CV are governed by the First law of thermodynamics.

2.Thermodynamics and Electrochemical Analysis of Fuel Cells

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The electrical work produced by the fuel cell per unit molar flow rate of fuel yields:

( ) ( )2 2 2 j H O H O RPP R

q w h h h h = + =

2.1.3. Entropy Balance:

Entropy balance for chemical reaction for a generic rate of heat transfer crossing the system

boundary at Tj :

Assumptions:-

1.Neglect effects of kinetic and potential energies , thus .

2.For steady state processes .

3.The hydrogen and oxygen behave as ideal gas.

After applying assumptions, we obtain the relation:

FC,elec FC RPw q h=

( ) ( )2 2 2j

gen H H O RPP R

j

q

s s s sTs+ = + =

Noting that the reaction inside an ideal fuel cell is internally reversible and the heat transfer

crosses the system boundary at temperature TFC, qFC can be calculated as:FC FC RPq T .s=

Te h=e ek P 0= =cvdE 0

dt=

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To analyze the chemical energy changes throughout the chemical process involved in the operation of

a fuel cell, one must be aware of and understand Gibbs free energy.

f fg h T. s =

The value of is the difference between of the products and of the reactants. So for

hydrogen fuel reaction, we have the product is one mole of H2

O and the reactants are one mole of

H2. and half a mole of O2. Thus:

2 2 2f H O H Oh h h h = +

Similarly, is the difference between entropy of the products and reactants so that:s

2 2 2f H O H Os s s s = +

the enthalpy is a function of the temperature only, and can found by use of an equation of as:pc

T

T,P f p298

h h c dT= +

fh fhfh

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Similarly, the molar entropy, , at temperature T is given by:-

T p

T 298298

cs s dT

T= +

M is the molecular mass and a, b, c and d are empirical constants

the hydrogen fuel cell reaction the change in the Gibbs free energy of formation per molebecomes:

2 2 2f f H O f H f Og (g ) (g ) (g ) =

Where , a change for different molecular states of the materials in the fuel cell and at

different fuel cell temperatures.

fg

2.2. Reversible work and efficiency of fuel cell

The electrical work done by the fuel cell in moving two electrons around the circuit is given by:

Electrical work done = charge voltage = 2FE Joules

Where, E is the voltage of the fuel cell.

2 3

p pc M.C M. a bT cT dT = = + + + Where: kJ/kmol.K

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If the process is reversible for hydrogen reaction, then all this Gibbs free energy is converted into

electrical energy.

Then: rev max f w wg nFE= = =

When rearranged, gives: fg

E2F

=

This fundamental equation gives the electromotive force (EMF) or reversible open circuit voltage of

the hydrogen fuel cell .

The reversible efficiency rev of the fuel cell is the ratio of the Gibbs enthalpy and the reaction

enthalpy at the thermodynamic state of the fuel cell.

We can express maximum possible efficiency as:

fh

fg

frev

f

g =100%

h

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2.3. The Effect of Pressure and Gas Concentration

The following relates Gibbs free energy, partial pressure of reactants and products, and the

Nernst Equation.

Where g, is the Gibbs free energy of reaction at operating temperature and standard pressureof fuel cell.

For ideal gases the activities of the reactants, .

where Pi is the partial pressure of the gas and is standard pressure, 1bar.

Then

Where R is the gas constant (8.314 J/mol K)

2 2

2

1/2

H Oo

H O

a .ag g RTln

a

=

ii o

Pa

P=

oP

2 2

2

1/2

H Oo

H O

P .Pg g RTln

P

=

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2.4. Electrochemical Process

Fuel cells reversible voltage is a function of temperature and partial pressures of reactants and

product as Nernst Equation:

2 2

2

1/2

H Oo

H O

P .PRTE E lnnF P

= +

T > 100

and E is the reversible standard potential of an electrochemical reaction:

oo - g

EnF

=

Then the Nernst equation for liquid case of water becomes:

( )2 2

o 1/2

H O

RTE E ln P .P

nF= + T100

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3. TCHMFC Program

TCHMFC computer program (C language) is developed to simulate and calculate all thermo-chemical andelectrochemical equation and parameters for hydrogen fuel cells, and also it used for internal combustion

engines to calculate heat and energy of combustion.

The general reaction equation, which used in this program for 1mol CxHy as follows:

Where corresponds to the stoichiometric amount of air (a percent theoretical air 100%).

3.1 Fuel Cells Model Result

The model is based on thermochemical engineering fundamentals and has been developed on the following

assumptions:

1. Fuel and oxidant are perfect gases.

2. The model can be applied on any type of fuel cell.

3. The fuel is H2 and the oxidant is O2.

4. The conversion of energy occurs isothermally and constant volume.

5. The operating temperature range for all hydrogen fuel cell types.

x y 2 2 2 2 2 2

y y y yC H +(x+ )(O +3.76N ) xCO + H O+(-1)(x+ )O +3.76(x+ )N

4 2 4 4

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1. Reversible efficiency

Figure 3. Variation of reversible efficiency

with operating temperature

Results

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2. Enthalpy of Reaction

Figure 4. Variation of enthalpy of reaction


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3. Reversible potential

Figure 5. Variation of reversible potential


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4.Electrical work

Figure 6. Variation of maximum work


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5. Heat Transfer

Figure 7. variation of heat out fuel cell with

operating temperature

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Conclusions

From the results of TCHMFC Program, we conclude that the program is suitable

tools and model for hydrogen fuel cells calculation parameters as a function of

operating temperature such as:

1. The reversible efficiency of fuel cell.

2. Maximum work (Gibbs free energy).

3. Open circuit voltage of fuel cell (EMF)

4. Fuel cell heat output.

5. Other fuel cell parameters.Finally, the TCHMFC program is also used to simulate the thermo-chemical process

for internal combustion engine i.e. enthalpy of formation.

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CHE2009 Tawil

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