Fuel Cells: Performance

Transcription

1 Laurea Magistrale in Scienza dei Materiali Materiali Inorganici Funzionali Fuel Cells: Performance Prof. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova

2 FC performance Gibbs free energy and Nerst potential Ideal performance Cell efficiency Actual performance FC Performance variables

3 Rendimento Termodinamico Massimo rendimento: (Ciclo di Carnot) η Carnot = (T 2 -T 1 )/T 2 Massimo lavoro ottenibile: L MAX = η Carnot Q

4 Termodinamica delle FC Per una reazione l energia scambiata: U = Q - L MAX U = Q - (L mecc + L el ) (q = nf F = en = C 6.023e 23 = C) E = differenza di potenziale L el = nfe U = Q (P V + V P) - nfe H = U + PV H = Q - nfe (energia disponibile dalla reazione) Ma: G = H - T S T S = Q H - G = T S (calore ceduto all ambiente, calore perso) G = - nfe

5 Cell Efficiency Thermal 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: H - T S G η Therm = η Therm = H H Per la reazione: H 2 + ½ O 2 = H 2 O η Therm = = Gas a fine reazione η Therm = = Liquido a fine reazione

6 H 2 fuelled cells H 2 + ½ O 2 H 2 O Efficiency often expressed in terms of the ratio of the operating cell voltage (< V id for losses) to the ideal cell voltage. Thermal efficiency of a H 2 /O 2 FC in terms of the actual cell voltage (considering the complete fuel reaction): η = Useful energy H = Useful power G/0.83 = V actual Corrent V ideal Corrent/0.83 = 0.83 V actual E ideal 0.83 V celll = =0.675 x V cell 1.229

7 η = x V cell EFFICIENZA DI VOLTAGGIO EFFICIENZA NETTA DI CELLA = EFFICIENZA DI VOLTAGGIO X % USO DEL COMBUSTIBILE

8 Gibbs Free Energy and Nerst Potential Per 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 = γ 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

9 Ideal Performance The Nerst potential gives the ideal open circuit cell potential (= upper limit achievable) Electrochemical reactions in fuel cells

10 Ideal Performance Fuel Cell Reactions and the Corresponding Nernst Equations E (298K) for a H 2 /O 2 fuel cell = 1.18 V with gaseous water product.

11 Influenza della Temperatura H 2 /O 2 Potenziale ideale di cella in funzione della temperatura Temperature 25 C 80 C 100 C 205 C 650 C 800 C 1100 C (298 K) (353 K) (373 K) (478 K) (923 K) (1073 K) (1373 K) Cell type PEFC AFC PAFC MCFC ITSOFC TSOFC Ideal voltage

12 Influenza della Temperatura Consideriamo l equazione di Kirchoff: Aumento totale della capacità termica: Costanti sperimentali valide nel campo di temperature K espresse in cal/mole K Nel nostro caso: Integrando tra temperatura ambiente e 343 K: H 343 = J/mol K gas a fine reazione H 343 = J/mol K liquido a fine reazione

13 Influenza della Temperatura Calcoliamo S 298 : Influenza della temperatura sulla variabile entropia: S 343 = J/mol K gas a fine reazione S 343 = J/mol K liquido a fine reazione

14 Influenza della Temperatura Influenza della temperatura sul rendimento: G 343 = H T S 343 G 343 = (343 ( )) = kj/mol K gas a fine reazione G 343 = (343 (-0.164)) = kj/mol K liquido a fine reazione η 343 = = gas a fine reazione η 343 = = liquido a fine reazione l influenza della temperatura sul rendimento è di pochi percento, il calcolo poteva essere svolto considerando i calori specifici costanti senza commettere errori significativi lo stato dei prodotti di reazione influenza significativamente il rendimento termodinamico.

15 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: H 2 + ½ O 2 H 2 O CO + ½ O 2 CO 2 CH O 2 2H 2 O + CO 2 Direct oxidation on CO and CH 4 = minor reactions CO + H 2 O H 2 + CO 2 CH H 2 O 4H 2 + CO 2 The driving force for anodic oxidation of CO and CH 4 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 CH 4 oxidation. Surface area and active surface sites available. Mass-transfer.

16 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, H 2 and O 2 utilization, the expected power produced, and a percent heat loss.

17 Graph showing the voltage for a typical air pressure FC operating at about 800 C. Graph showing the voltage for a typical low temperature, air pressure, FC

18 Phenomena contributing to irreversible losses Activation-related 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. Ohmic 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. Mass-transport transport-related related 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.

19 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) La 2 Cu 0.2 Co 0.8 O 4 La 0.9 Sr 0.1 Ga 0.8 Mg 0.8 O 3

20 LA VELOCITA DI REAZIONE 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 +. Maggiore è k maggiore è la velocità La concentrazione dei reagenti può influenzare la velocità di reazione Dr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova

21 LA COSTANTE DI VELOCITA Fattore d urto k = A e - E a/rt Costante di velocità Energia di attivazione > Energia di attivazione > effetto della temperatura > T > k > A > k

22 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.

23 Tafel Plots Tafel 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 η act = 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.

24 A = Tafel slope: is higher for a slow electrochemical reaction The constant i 0 is higher if the reaction is faster. i 0 = current density at which the overvoltage begins to move from zero Tafel plots for slow and fast electrochemical reactions

25 V = RT α nf ln i i 0 α = electron transfer coefficient of the reaction at the electrode i 0 = exchange current density. For a FC which has no losses at all except for the activation overvoltage: V = E A a ln ( i i 0a ) A c ln ( i i 0c )

26 Exchange current density 2 O 2 + 4e - + 4H + 2H 2 O At zero current density the reaction is taking place all the time but the reverse reaction is also taking place 2O 2 + 4e - + 4H + 2H 2 O 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 i 0.

27 Activation Voltage Drop i 0 is much smaller for oxygen electrode (10-8 A/cm 2 ) the overvoltage at the anode is negligible compared to that of the cathode (for hydrogen FCs) i 0 cathode = 0.1 ma/cm 2 i 0 anode = 200 ma/cm 2 Raising the cell temperature Using more effective catalysts Increasing the roughness of the electrodes Increasing the reactant concentration Increasing the pressure Catalytic effect

28 Ohmic Polarization Ohmic losses = resistance to flow of ions in the electrolyte + resistance to flow of electrons through the electrode. < electrode separation, > electrolyte ionic conductivity = < Ohmic losses η ohm = i R i = current flowing through the cell, R = total cell resistance = R electronic + R ionic + R contact Any of these components can dominate the ohmic resistance, depending on the cell type: for SOFCs: the ionic resistance in planar electrolytesupported; electronic bulk resistance in tubular; contact resistances in planar thin-electrolyte Area Specific Resistance (ASR = ohmic resistance normalized by the active cell area Ωcm 2 ) 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.

29 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

30 Mass Transport Losses (i) A reactant is consumed at the electrode by electrochemical reaction, (ii) it is often diluted by the products, (iii) finite mass transport rates limit the supply of fresh reactant and the evacuation of 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 more limiting than the supply of fuel, given the difference between the diffusivities of hydrogen and water (vapor).

31 Mass Transport Losses The Nernst equation for the reactant species at equilibrium conditions, or when no current is flowing, is 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:

32 Mass Transport Losses: the Nerstian drop If this loss is the only one: V = E + B ln 1 - i i l E = 1.2 V B = V, V i l = 1000 ma B = Type of FC, operating state, operating conditions Hydrogen supplied from reformers Air cathode: air not well circulated Mass transport problems for nitrogen left behind

33 Summing Cell Voltage V = E A a ln ( i i 0a ) A c ln ( i i 0c ) (i+i n ) r + B ln 1 - i i l E = reversible open circuit voltage i n = internal and fuel crossover equivalent current density A = slope of the Tafel line i o = exchange current density at the cathode/anode B = constant in the mass transfer overvoltage equation i l = limiting current density at the electrode with the lowest limiting current density r = area specific resistance.

34 V cell 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 impurity concentration). Compromises with problems associated with the stability/durability of cell components, cost

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