Fuel Cells:Performance

Prof. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova

Laurea Magistrale in Scienza dei Materiali

Materiali Inorganici Funzionali

FC performance

Gibbs free energy and Nerst potentialIdeal performanceCell efficiencyActual performanceFC Performance variables

Rendimento Termodinamico

Massimo rendimento:(Ciclo di Carnot)

ηCarnot = (T2-T1)/T2

Massimo lavoro ottenibile: LMAX = ηCarnot Q

Termodinamica delle FC

Per una reazione l’energia scambiata: ∆U = Q - LMAX

(q = nF F = eN = 1.602 10-19 C 6.023e23 = 96488 C)

E = differenza di potenziale

∆U = Q - (Lmecc+ Lel)

Lel = nFE

∆U = Q – (P∆V + V∆P) - nFE

H = U + PV ∆H = Q - nFE

Ma: ∆G = ∆H - T∆ST∆S = Q

∆G = - nFE

∆H - ∆G = T∆S(calore ceduto all’ambiente, calore perso)

(energia disponibile dalla reazione)

Cell EfficiencyThermal efficiency of a fuel conversion device = amount of useful energy produced relative to the change in enthalpy, ∆H, between the product and feed streams.

Ideal efficiency of a FC, operating reversibly:

ηTherm =∆H - T∆S

∆HηTherm =

∆G

∆HPer la reazione: H2 + ½ O2 = H2O

ηTherm =- 228.61

-241.84= 0.945

ηTherm =- 237.19

-285.85= 0.83

Gas a fine reazione

Liquido a fine reazione

H2 fuelled cells

H2 + ½ O2 H2O

Efficiency often expressed in terms of the ratio of the operating cell voltage (< Vid for losses) to the ideal cell voltage.

Thermal efficiency of a H2/O2 FC in terms of the actual cell voltage (considering the complete fuel reaction):

ηηηη =Useful energy

∆H

Useful power

∆G/0.83=

Vactual Corrent

Videal Corrent/0.83=

0.83 Vactual

Eideal=

0.83 Vcelll

1.229= =0.675 x Vcell

EFFICIENZA NETTA DI CELLA =

EFFICIENZA DI VOLTAGGIO X

% USO DEL COMBUSTIBILE

= 0.675 x Vcellηηηη EFFICIENZA DI VOLTAGGIO

Gibbs Free Energy and Nerst PotentialPer la reazione generica:

α A + β B → γ C+ δ D Indicando con G°A, G°B, G°C, G°D le energie libere molari standard delle specie A,B,C,D :

∆G° = γγγγ G°C + δ G°D - α G°A - β G°B

G°I = energia libera molare per la specie e alla temperatura T.

All’equilibrio ∆G = 0

Poiché ∆G = -nFE

Ideal PerformanceThe Nerst potential gives the ideal open circuit cell potential (= upper limit achievable)

Electrochemical reactions in fuel cells

Ideal Performance

Fuel Cell Reactions and the Corresponding Nernst Equations

E° (298K) for a H2/O2 fuel cell = 1.18 V with gaseous water product.

Influenza della TemperaturaH2/O2 Potenziale ideale di cella in funzione della temperatura

0.910.991.031.141.161.171.18Ideal voltage

TSOFCITSOFCMCFCPAFCAFCPEFCCell type

1100°C

(1373 K)

800°C

(1073 K)

650°C

(923 K)

205°C

(478 K)

100°C

(373 K)

80°C

(353 K)

25°C

(298 K)

Temperature

Influenza della Temperatura

Consideriamo l’equazione di Kirchoff:

Aumento totale della capacità termica:

Costanti sperimentali validenel campo di temperature

273-1500Kespresse in cal/mole K

Nel nostro caso:

Integrando tratemperaturaambiente e 343 K:

∆∆∆∆H343 = - 242.296 J/mol K gas a fine reazione∆∆∆∆H343 = - 286.306 J/mol K liquido a fine reazione

Influenza della Temperatura

Calcoliamo ∆∆∆∆S°298:

∆∆∆∆S343 = - 45.76 J/mol K gas a fine reazione∆∆∆∆S343 = - 164.54 J/mol K liquido a fine reazione

Influenza dellatemperatura sullavariabile entropia:

Influenza della TemperaturaInfluenza della temperatura sul rendimento:

∆∆∆∆G343 = ∆∆∆∆H343 - T∆∆∆∆S343

∆∆∆∆G343 = -242.296 – (343 (-0.04576)) = - 226.6 kJ/mol Kgas a fine reazione

∆∆∆∆G343 = -286.306 – (343 (-0.164)) = - 229.8 kJ/mol Kliquido a fine reazione

η343 =- 229.8

- 286.306η343 =

- 226.6

- 242.296= 0.935= 0.802

liquido a fine reazionegas a fine reazione

l’influenza della temperatura sul rendimento è di pochi percento, ilcalcolo poteva essere svolto considerando i calori specifici costantisenza commettere errori significativilo stato dei prodotti di reazione influenza significativamente ilrendimento termodinamico.

Influence of reactant concentrations and type Less concentrated reagents = correction of the Nerst potential (as much as 250 mV in higher-temperature cells).

The ideal performance of a FC depends on the electrochemical reactions:

Direct oxidation on CO and CH4 = minor reactions

H2 + ½ O2 H2O CO + ½ O2 CO2 CH4 + 2 O2 2H2O + CO2

• The driving force for anodic oxidation of CO and CH4 is lower (higher open circuit voltage of the hydrogen oxidation).• The kinetics of hydrogen oxidation on the anode are significantly faster than that of CO or CH4 oxidation.• Surface area and active surface sites available.• Mass-transfer.

CO + H2O H2 + CO2 CH4 + 2 H2O 4H2 + CO2

Cell Energy Balance

The cell energy balance states that the enthalpy flow of the reactants entering the cell will equal the enthalpy flow of the products leaving the cell plus the sum of three terms:

(1) The net heat generated by physical and chemical processes within the cell(2) The dc power output from the cell(3) The heat loss from the cell to its surroundings

The energy balance varies for the different types of cells because of the differences in reactions that occur according to cell type.

A typical energy balance determines the cell exit temperature knowing the reactant composition, the feed stream temperatures, H2and O2 utilization, the expected power produced, and a percent heat loss.

Graph showing the voltage for a typical low temperature, air pressure, FC

Graph showing the voltage for a typical air pressure FC operating at about 800°C.

Phenomena contributing to irreversible losses ActivationActivation--related lossesrelated losses. Kinetic aspects. Activation energy of the electrochemical reactions at the electrodes; depend on the reactions, the electro-catalyst material and microstructure, reactant activities (and hence utilization), and weakly on current density.

OhmicOhmic losses.losses. Ionic resistance in the electrolyte and electrodes, electronic resistance in the electrodes, current collectors and interconnects, and contact resistances.Ohmic losses are proportional to the current density, depend on materials selection and stack geometry, and on temperature.

MassMass--transporttransport--related lossesrelated losses. Finite mass transport limitations rates of the reactants; depend strongly on the current density, reactant activity, and electrode structure.

Fuel crossover and internal currents. Energy loss resulting from waste of fuel passing through the electrolyte, electron conduction through the electrolyte.

La2Cu0.2Co0.8O4

La0.9Sr0.1Ga0.8Mg0.8O3

Activation related losses In low and medium temperature FCs activation overvoltage is the most important cause of irreversible voltage drop

It occurs mainly at the cathode (the activation overvoltage of both electrodes is important in cells using fuels other than hydrogen)

a A + b B …. → g G + h H ….

Velocità di reazione = k [A]m[B]n ….

Costante di velocità = k

Ordine globale di reazione = m + n + ….

LA VELOCITALA VELOCITA’’ DI REAZIONEDI REAZIONE

Dr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di PadovaDr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova

Maggiore è k maggiore è la velocità

La concentrazione dei reagenti può influenzare la velocità di reazione

k = A e- Ea/RT

Costante di velocità

Fattore d’urto

Energia di attivazione

> Energia di attivazione > effetto della temperatura > T > k > A > k

LA COSTANTE DI VELOCITALA COSTANTE DI VELOCITA’’

Phenomena contributing to irreversible losses: activation losses

Activation Losses: slow electrode kinetics; are the result of complex surface electrochemical reaction steps, each of which have their own reaction rate and activation energy.Usually, the rate parameters and activation energy of one or more rate-limiting reaction steps control the voltage drop. Heterogeneous reaction

It is possible to approximate the voltage drop due to activation polarization by a semi-empirical equation, called the Tafel equation.

Tafel PlotsTafel plots: a visual understanding of the activation polarization of a FC. They are used to measure the exchange current density, given by the extrapolated intercept at ηact = 0 and the transfer coefficient (from the slope).

This simplified description did not try to describe: absorption of reactant species, transfer of electrons, desorption of product species, and the nature of the electrode surface.

Tafel plots for slow and fast electrochemical reactions

A = Tafel slope: is higher for a slow electrochemical reaction

The constant i0 is higher if the reaction is faster.

i0 = current density at which the overvoltagebegins to move from zero

For a FC which hasno losses at all except for the activation

overvoltage:

V = E – Aa ln ( ii0a

) – Ac ln ( ii0c

)

V =RT

αααα nF

iln

i0

α = electron transfer coefficient of the reaction at the electrodei0 = exchange current density.

2 O2 + 4e- + 4H+ 2H2O

2O2 + 4e- + 4H+ 2H2O

At zero current density the reaction is taking place all the time but the reverse reaction is also taking place

There is a continual backwards and forwards flow of electrons from and to the electrolyte.This current density is the exchange current density

> Current density = the surface of the electrode is more “active”.

Graph of cell voltage against current density, assuming losses are due only to the activation overvoltage at one electrode, for three different values of exchange current density i0.

Exchange current density

Raising the cell temperature Using more effective catalysts Increasing the roughness of the electrodes Increasing the reactant concentration Increasing the pressure

i0 is much smaller for oxygen electrode (10-8 A/cm2) – the overvoltage at the anode is negligible compared to that of the cathode (for hydrogen FCs) i0 cathode = 0.1 mA/cm2

i0 anode = 200 mA/cm2

Activation Voltage Drop

Catalytic effect

Ohmic PolarizationOhmic losses = resistance to flow of ions in the electrolyte + resistance to flow of electrons through the electrode.

< electrode separation, > electrolyte ionic conductivity = < Ohmic losses

ηηηηohm = i R

Any of these components can dominate the Any of these components can dominate the ohmicohmic resistanceresistance, depending on the cell type: for SOFCs: the ionic resistance in planar electrolyte-supported; electronic bulk resistance in tubular; contact resistances in planar thin-electrolyte

Area Specific Resistance(ASR = ohmic resistance normalized by the active cell area Ωcm2)function of the cell design, material choice, manufacturing technique, and, because material properties change with temperature, operating conditions.ASR is a key performance parameter, especially in HTFC, where the ohmic losses often dominate the overall polarization of the cell.

i = current flowing through the cell, R = total cell resistance = Relectronic + Rionic+ Rcontact

Ohmic Polarization

Electrodes with the highest possible conductivity

Electrolyte with the highest possible conductivity

Electrolyte as thin as possible

Good design and use of appropriate materials for the bipolar plates or cell interconnects

Mass Transport Losses

(i) A reactant is consumedconsumed at the electrode by electrochemical reaction, (ii) it is often diluteddiluted by the products, (iii) finite mass transport rates limit the supplylimit the supply of fresh reactant and the evacuationevacuationof products. As a consequence, a concentration gradient is formed which drives the mass transport process.

With purely gas-phase reactants and products (such as an SOFC), gas diffusion processes control mass transfer.

In other cells, multi-phase flow in the porous electrodes can have a significant impact (e.g. in PEFC).

In hydrogen fuel cells, the evacuation of product is often morelimiting than the supply of fuel, given the difference between the diffusivities of hydrogen and water (vapor).

Mass Transport Losses

When current is flowing, the surface concentration becomes less than the bulk concentration, and the Nernst equation becomes

The potential difference (ΔE) produced by a concentration change at the electrode is called the concentration polarization:

The Nernst equation for the reactant species at equilibrium conditions, or when no current is flowing, is

V = E + B ln 1 -il

i

E = 1.2 VB = 0.016 V, 0.200 Vil = 1000 mA

Hydrogen supplied from reformers Air cathode: air not well circulated Mass transport problems for nitrogen left behind

Mass Transport Losses: the Nerstian dropIf this loss is the only one:

B = Type of FC, operating state, operating conditions …

E = reversible open circuit voltagein = internal and fuel crossover equivalent current densityA = slope of the Tafel lineio = exchange current density at the cathode/anode

Summing Cell Voltage

B = constant in the mass transfer overvoltage equationil = limiting current density at the electrode with the lowest limiting current densityr = area specific resistance.

1 -il

i V = E – Aa ln ( ii0a

) – Ac ln ( ii0c

) – (i+in) r + B ln

Vcell modifications to

Fuel cell design (electrode structures, electro-catalysts, more conductive electrolyte, thinner cell components, etc.).

System Design

Operating conditions (e.g., higher gas pressure, higher temperature, change in gas composition to lower the gas impurityconcentration).

Compromises with problems associated with the stability/durability of cell components, cost

Bibliography

J. Larminie, A. Dicks; Fuel Cell Systems Explained – Wiley 2000