Che2009 Tawil

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]

Electricity e- e-

1. Introduction process in which the energy stored in a fuel is converted

e

-

Cathode

Electrolyte

Anode

Fuel cells generate electricity through an electrochemical

-

e e

-

H 2O

H+

e-

directly into DC electricity Figure 1.

e

-

H2O

H+ H+ H+

H2

H+

H2

O2

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 .

Figure 1. Fuel Cell Electrochemical

Thermodynamics and Electrochemical Analysis of Fuel Cells. 2 The source of energy is fuel, in which the energy is bound in

Electricity CV

chemical form.

O2 / Air input

H2 input

2.1. Cell Energy Balance

Fuel Cell

The energy balance around the fuel cell is based on the energy absorbing/releasing processes (e.g., power produced,

QFC =Heat out at TFC

Chemical products at TFC

Surrounding at To = 298 K

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:

H 2+ ½ O 142 43 2 Reactants (R)

→ H 2O {

Product (P)

Figure 2. Energy balance around the fuel cell

2.1.2. Energy Balance for Chemical Reaction: The chemical processes within the CV are governed by the First law of thermodynamics.

Assumptions:k e = Pe = 0thus

1.Neglect effects of kinetic and potential energies , dE cv = 0. 2.For steady state processes dt 3.The hydrogen and oxygen behave as ideal gas.

eT =. h

After applying assumptions, we obtain the relation:

(

q j − w = h H 2O

) − (h P

H2

+ ½h O 2

)

R

= h RP

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

w FC,elec = q FC − h RP 2.1.3. Entropy Balance: Entropy balance for chemical reaction for a generic rate of heat transfer crossing the system boundary at Tj :

qj Tj

( ) −(s

+ s gen = sH2

P

H2

+ sO2

)

R

= s RP

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

q FC as: = TFC .sRP crosses the system boundary at temperature TFC, qFC can be calculated

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”.

∆gf = ∆h f − T.∆ s The value of ∆h f is the difference between h f of the products and h f of the reactants. So for hydrogen fuel reaction, we have the ‘product’ is one mole of H2O and the ‘reactants’ are one mole of H2. and half a mole of O2. Thus:

∆h f = h H2 O − h H2 +½h O2 Similarly, ∆ s is the difference between entropy of the products and reactants so that:

∆ sf = sH 2O − sH 2 + ½sO2 the enthalpy is a function of the temperature only, and can found by use of an equation of cp as:

h T,P = h + ∫ ° f

T

298

cp dT

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

cp

298

T

° sT = s298 +∫

Where:

dT

cp = M.Cp = M. a + bT + cT 2 + dT 3 kJ/kmol.K 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 mole becomes:

∆gf = (g f ) H 2O − (g f ) H 2 − ½(g f ) O2

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

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.

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

w rev = wΔg max =

When rearranged, gives:

E =

nFE f = − Δgf 2F

This fundamental equation gives the electromotive force (EMF) or reversible open circuit voltage of the hydrogen fuel cell . The reversible efficiency ηrev of the fuel cell is the ratio of the Gibbs enthalpy Δgf and the reaction enthalpy Δh f at the thermodynamic state of the fuel cell. We can express maximum possible efficiency as:

Δgf ηrev =×100% Δh f

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.

 a H2 .a O2 1/2  Δg = Δg − RTln   a H O   2  o

Where Δgº, is the Gibbs free energy of reaction at operating temperature and standard pressure of fuel cell. For ideal gases the activities of the reactants,

ai =

Pi Po .

where Pi is the partial pressure of the gas and Po is standard pressure, 1bar. Then 1/2   P .P H O Δg = Δg o − RTln  2 2   PH O   2 

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

2.4. Electrochemical Process Fuel cell’s reversible voltage is a function of temperature and partial pressures of reactants and product as Nernst Equation: 1/2 RT  PH2 .PO2 E=E + ln  nF  PH2O o

  

℃T > 100

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

E

o

-∆g o = nF

Then the Nernst equation for liquid case of water becomes:

E = Eo +

RT ln PH2 .PO2 1/2 nF

(

)

T≤100 ℃

3. TCHMFC Program TCHMFC computer program (C language) is developed to simulate and calculate all thermo-chemical and electrochemical 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:

y y y y C x H y +α(x+ )(O 2 +3.76N 2) → xCO 2+ H 2O+(α-1)(x+ )O 2+3.76α(x+ )N 4 2 4 4

2

Where α corresponds to the stoichiometric amount of air (a percent theoretical air α ≥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.

Results 1.

Reversible efficiency

Figure 3. Variation of reversible efficiency with operating temperature

2.

Enthalpy of Reaction

Figure 4. Variation of enthalpy of reaction with operating temperature

3. Reversible potential

Figure 5. Variation of reversible potential with operating temperature

4.Electrical work

Figure 6. Variation of maximum work with operating temperature

5.

Heat Transfer

Figure 7. variation of heat out fuel cell with operating temperature

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.