Fuel Cell Systems Explained - from and for SET students

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2.5 The effect of pressure and gas concentration2.5.1 The Nernst equationAs mentioned in 2.1 is the Gibbs free energy change dependant on the temperature and in a morecomplex relation on the reactant pressure and concentration.In a chemical reaction every reactant and product have their own 'activity'. In case of an ideal gas,the 'activity' is definded asa = P / P 0withP: partial pressure of the gasP 0 : standard pressure, 0.1MPaThe activity of a gas is proportional to its partial pressure. The produced water in a fuel cell caneither be a liquid or steam. In case of liquid water, it is a reasonable approximation to assumea H2O =1.The activities of the reactants and products of a chemical reactionjJ + kK → mMmodify the Gibbs free energy change, given by the equationwith Δg̅ f 0 : molar Gibbs free energy change at standard pressure (from gas tables)R = 8.314 j/Kmol molar gas constantT: temperatureIt can be seen, that when the activities of the reactants increase, Δg̅ f becomes more negative, somore energy is released. On the other side, if the activity of the product increase, Δg̅ f becomes lessnegative, so less energy is released.Substitute this equation in the equation of the EMF gives the Nernst equation.with E 0 : EMF at standard pressureThe Nernst equation gives the EMF dependant on the product and reactant activities. The derivedEMF, also called Nernst voltage, is the reversible cell voltage that would exist at a giventemperature and pressure.Using the rules of logarithmic functions an the definition of activity, the equation can be simplified.In nearly all cases will be the pressures partial pressures, that is, the gases will be part of a mixture.It often appears that the pressures at cathode and anode are the same, to simplify the design.Note:In a mixture of gases, the total pressure is the sum of all the partial pressures of the components.From the gas law equation it can be shown, that the volume fraction, molar fraction and pressurefraction of a gas mixture are all equal.Example: CH 4 + H 2 O → 3H 2 + CO 2
The products are three parts of H 2 and one part of CO 2 by moles and volume. If thereaction takes place at 0.1MPa the partial pressures can be derivedP H2 = ¾ x 0.1MPa = 0.075MPaP CO2 = ¼ x 0.1MPa = 0.025MPa2.5.3 Fuel and oxidant utilisationAs air passes through a fuel cell, the oxygen is used, and so the partial pressure will reduce.Similarly, the fuel partial pressure will often decline, as the proportion of fuel reduces abd reactionproducts increase. That makes the logarithmic term in the Nernst equation smaller, and so the EMFwill fall. This circumstance will vary over the cell and will be worst at the fuel outlet as the fuel isused. Due to the conducting material of the bipolar plate the voltage is constant over the cell, thatmeans that the current will vary. The current density will be lower nearer the exit where the fuelconcentration is lower. The RT term indicates that the voltage drop due to fuel utilisation will begreater for high temperature fuel cells.A high system efficiency normally requires a high fuel utilisation. That counteracts the abovedescribed behaviour. The cell voltage, hence the cell efficiency will fall with higher fuel utilisation.Therefore, fuel and oxygen utilisation is an important aspect in the system design and thus needscareful optimisation.2.5.4 System pressureWhen the system pressure is known, the Nernst equation can be rewritten, usingP H2 = αP with α constant depending on the molar masses and concentration of H 2P O2 = βP with α constant of O 2P H2O = δP with α constant of H 2 OasIt can be seen, thet the EMF of the fuel cell is depending on the system pressure P. A hihgherpressure leads to a higher voltage. For high temperature fuel cells, for example SOFC at 1000°C,the predictions of the Nernst equation correlate with practise. For lower temperatures, as in a PAFCat 200°C, the voltage change is even bigger. This occurs due to increasing pressure also reduces thelosses at the electrodes, especially at the cathode. A similar effect occurs from switching from air tooxygen (β). The voltage losses at the cathode decline for pure oxygen.
Page 1 and 2: -Fuel Cell Systems Explained-(Summa
Page 3 and 4: 1.5 Fuel cell typesBesides the prac
Page 5 and 6: Fuel cells can be used successfully
Page 7: to the HHV or LHV. If the informati
Page 11 and 12: Figure 3.2 shows the performance of
Page 13 and 14: In order to get the current instead
Page 15 and 16: Assumption:Introduction a limiting
Page 17 and 18: To summarize the irreversibilities
Page 19 and 20: 4.4 Water management in the PEMFCWt
Page 21 and 22: With Pe: electrical Power of the st
Page 23 and 24: 4.4.5 External humidification - pri
Page 25 and 26: 4.6 PEMFC connection - the bipolare
Page 27 and 28: with T 1 : entry temperatureη c :
Page 29 and 30: thus leads to higher efficiency. He
Page 32 and 33: minimum difference. This so-called
Page 34: converted into hydrogen at operatin

Fuel Cell Systems Explained - from and for SET students

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