Direct Energy Conversion: Fuel Cells

Transcription

1 Direct Energy Conversion: Fuel Cells References and Sources: Direct Energy Conversion by Stanley W. Angrist, Allyn and Beacon, Fuel Cell Systems, Explained by James Larminie and Andrew Dicks, Wiley, Fuel Cell Technology Hand Book, Edited by Gregor Hoogers, CRC Press, 2002 Fuel Cell Hand Book, US DOE - available on the web.

2 Fuel Cell Design Calculation Performance of a single cell operating on hydrogen as the fuel and oxygen in air as the oxidizer. The porous electrodes of either carbon or nickel employed are separated by a 30% solution of KOH (potassium hydroxide). The cell operates at a temperature of 298K and the fuel and air are supplied at one atmosphere. The faradic efficiency (the fraction of the reaction which is occurring electrochemically to give a current is called faradic or current efficiency, η F = 1/(nFN fu ); where N fu is the total number of moles of fuel reacted electrochemically per second) for the cell is estimated to be 95% 20% of the fuel supplied to the cell will escape through the electrolyte unreacted. Separation between electrodes, w= 0.25cm w =0.25cm l =12cm Height of the cell, l = 12 cm Depth of the cell, d = 6cm Average electrolyte velocity, u = 5cm/s (Supplied by an external pump)

3 Electrolyte Properties The physical properties of the electrolyte at 298K area as follows: Concentration: 30% KOH (wt) or c b = 6.9 x 10-3 mole/cm 3 Density: ρ = gm/cm 3 Dynamic Viscosity: μ = 2.43 x 10-2 poise Kinematic Viscosity: ν = x 10-2 cm 2 /s Conductivity: σ = (ohm-cm) -1 Diffusion Coefficient for OH - ions: D = 1.5 x 10-7 cm 2 /s

4 Open Circuit Voltage We now calculate the open circuit voltage. We assume that each electrode reaction follows the half-cell reactions H 2 (g) 2H + + 2e 0.5O 2 (g) + 2H + + 2e H 2 O(l) Yielding a cell reaction of H 2 (g) + 0.5O 2 (g) H 2 O(l) Anode E o = 0 Cathode E o = 1.23v We may now apply the Nernst equation to our cell potential E = E o RT n e F ln P i = n i n t P t P H 2O 1/2 P H 2 P O2 where P t is the total pressure of the mixture and n i /n t is the mole fraction of the i th constituent.

5 The partial pressures in the Nernst equation are often eliminated in favor of a function that is derived from general equation of state, generally denoted by f, the fugacity, which is a measure of the tendency of a component to escape from a solution. It is equal to partial pressure only when the vapor behaves like an ideal gas. We also define a quantity called the activity a A = f A /f Ao. We can then write the Nernst equation as E = E o RT n e F ln a H 2O a H 2 a O2 The activity of H 2 O to be used in this equation should be that of water in 30% KOH solution. This value is somewhat less than one, but we may take it as one to make our answer conservative. The hydrogen is supplied at one atm (has an activity of one since the activity is equal to the partial pressure of an ideal gas), the activity of oxygen is Then we have E = V = () /2 ( )( 298) ( ) ln () 1 () ( ) 0.5 E = V = ln(2.18) =1.22volts Open Circuit Voltage

6 Chemical Polarization We initially assume an operating current density for our fuel cell of 0.5 amp/cm 2 Use Tafel equation to calculate looses due to chemical polarization. ΔV chem = a + b lnj a = RT αnf ln( j ) o b = RT αnf ΔV chem(a) = lnJ ΔV chem(c) = lnJ Where the current density is expressed in milliamperes per square centimeter. ΔV chem(a) = ln(500) = 0.17volt ΔV chem(c) = ln(500) = 0.24volt

7 We now calculate the polarization due to concentration gradients in the electrolyte near the electrodes. ΔV conc(c) = RT nf ln J L J L J ΔV conc(a) = RT nf ln J L + J J L Calculation of the limiting current density: J L = nfd δ Velocity of the electrolyte = 5 cm/s; For a fully established flow between the electrodes, we have J L,av =1.62nFc b u( Re w ) 2/3 ( Sc) 2/3 ( w /l) 1/3 Re w = uw ν = 66.2 Concentration Polarization c b Sc = ν D =1.26x105 w l = J L,av = 0.956amp/cm 2

8 Concentration Polarization ΔV conc(c) = RT nf ln J L 0.01volt J L J ΔV conc(a) = RT nf ln J L + J 0.01volt J L The gas side concentration polarization at the anode is ignored. We will calculate the gas side polarization at the air electrode using the partial pressure of oxygen in the air for p g. ΔV conc(g ) = RT nf ln P r P = 0.013ln 1 = 0.02volts g 0.21 Where P r is the gas pressure in the pores of the electrode

9 Resistance Polarization IR = Jw σ = = 0.2volts We now compute the actual operating voltage of the fuel cell by subtracting from the open circuit voltage 1.22 volts, the various polarization losses and IR drop across the cell: V ac = = 0.57Volt The power out put of the cell: P o = V ac I = V ac JA = = 20.5watts

10 The thermal efficiency is given by Efficiency η ac = nfv ac 2(mole elec /mole) 23.06(kcal /volt mole) 0.57Volt = 1 ΔH 68.32kcal 10 /mole ΔH = 68.32kcal /mole = 38.5% F = kcal/volt-mole The efficiency based on the actual voltage is η v = V ac V = = 46.7% Assuming that the product of the reaction is liquid water, the faradaic efficiency is given by. η F = JA = = 0.95 nfn fu N fu F = 96,500 (amp-sec)/(mole-sec) N fu = moleh 2 /s

11 Heat Transfer Q Ý rev = η F N fu ( ΔH ΔG)= 0.95 N fu ( ( 56.69))= 9.1watts ΔH = 68.32kcal /mole ΔG = 56.69kcal /mole Q Ý chem(irr) = ( 1 η F )N fu ( ΔH)= 2.8watts 11 Q Ý ΔV = IV ( ac V)= 23.4watts Total heat that must be removed from the cell for it to stay steady state is 35.3 watts, 50% larger than net power output of the cell.

12 Heat Generation Area = 100 cm 2; Operating pressure = 1 atm; Operating Temperature = 80 o C; E = 0.7 V; Current generation = 0.6 A/cm 2. Power due to heat = Total power generated - electrical power P heat = P total -P electrical = (V ideal x I cell ) - (V cell x I cell ) = (1.2V -0.7V) x 60A = 0.5 V x 60A = 30 J/s = 108 KJ/hr = 30 W While generating about 42 W of electrical energy.

13 Operating Variables Pressure, Temperature, Gas composition, Reactant utilization and Current density

14 Operating Pressure T ΔV loss = P 2 η m η c P λ Stoichiometry (~ 2.0) ΔV gain = Cln P 2 P 1 C volts Motor and drive system efficiency~ 0.95 Compressor efficiency ~ 0.75

15 Operating Pressure Net voltage change resulting from operating at high pressure for two different PEM fuel cell models

16 Temperature Effect

17 Polarization Contribution

18 Effect of Oxygen Pressure

19 Polarization Curve Source:

20 Polymer Electrolyte Membrane Fuel Cell Load Fuel Cell stack

21 The Backing Layer Equivalent concentration profile Porous carbon cloth or carbon paper, typically μm thick. About 4-12 sheets are used. δ True concentration profile Diffusion layer Effective diffusion of each reactant gas to the catalyst on the Membrane Electrode Assembly (MEA). The diffusion takes place from a region of high concentration, outer side of the backing layer, to a region of low concentration, the inner side of the backing layer next to catalyst layer where the gas is consumed by the reaction. The gas is in contact with the entire surface area of the catalyzed membrane. 1 Assist in water management during the cell operation. Allows the right amount of water vapor to reach the MEA to keep the membrane humidified. It also allows the liquid water produced at the cathode to leave the cell.

22 The Bipolar Plate Main tasks: Current conduction; Heat conduction; control of gas flow and product water removal The first main task is to provide reactant gases evenly across the active area of the MEA. Current designs have channels to carry reactant gas from the point at which it enters the cell to the pint at which the gas exits. The flow field in the channels has a large impact on the distribution of gases. The design also effects water supply to the membrane and water removal from the cathode. The second main task is that of current collector. Usually made of graphite into which channels are machined. These plates have high electronic and good thermal conductivity and stable in the chemical environment inside the cell.

23 Water Management Use the water leaving the cell to do the humidification. Channels in bipolar plates

24 Some times referred to as Solid Polymer fuel cell (SPFC) The electrolyte: Ion conduction polymer (works at low temperatures, hence start quickly) Electrodes: Catalyzed porous electrodes The anode-electrolyte-cathode assembly (membrane electrode assemblies (MEA)) is one item and is very thin. The MEA s are connected in series using bipolar plates. No corrosive fluid hazards - suitable for use in portable applications and widely used in cars and buses The most commonly used polymer membrane: Nafion PEM Fuel Cells (PEMFC) Source: Fuel Cell systems Explained by James Larminie & Andrew Dicks, Wiley, 2003, Chapter 4.

25 Polymer Electrolyte Most commonly used: sulphonated fluoropolymers - fluoroethylene sulphonated fluoroethylene (PTFE) The strong bonds between the fluorine and the carbon make it durable and resistant to chemical attack and can be made into very thin films (~50μm). It is strongly hydrophobic, which helps to drive the product water out of the electrode.

26 Platinum is used generally as the catalyst (0.2 mg/cm 2 ) Electrodes Anode and cathode are essentially the same. The platinum is formed into very small particles on the surface of larger particles of finely divided carbon powders. The carbon-supported catalyst is fixed to a porous and conductive material such as carbon cloth or carbon paper. The carbon paper also diffuses the gas on to catalyst -the gas diffusion layer. Alternatively, the platinum on carbon catalyst is fixed directly to the electrolyte, thus manufacturing the electrode directly on to the membrane. Then a gas diffusion layer - carbon cloth or paper (200 to 500 μm thick) is added. It also forms an electrical connection between the carbon-supported catalyst and the bipolar plate.

27 Platinum Loading Effect

28 Water Management Proton conductivity is proportional to the water content. The H + ions moving from the anode to the cathode pull water Molecules with them (up to five H 2 O molecules are dragged for each proton - electro-osmotic drag). At high current densities, the anode side of the electrolyte can be dried out. At temperatures over 335K, the electrodes are typically dry. Solution: Air and hydrogen humidification before they enter the cell.

29 Heat Production 12 W fuel cell 2 kw fuel cell system

30 PEM Fuel Cell Stack Load

31 Multi-cell Stack Performance Simulation Results - PEMPC stack Hydrogen produced from gasoline Source: Simulation study of a PEM Fuel cell system fed by Hydrogen produced by partial oxidation by Ozdogan S., et al.

32 Multi-cell stack Performance 11

33 PEMFC System Hydrogen tank

34 Cooling Air Supply Ballard Nexa PEM Fuel cell.