Efficiency fuel cell

The efficiency of any energy conversion device is defined as the ratio between useful energy output and energy input. The efficiency limit for heat engines, such as steam and gas turbines, is known as the Carnot limit. If the maximum temperature of the heat engine is Tj, and flie heated fluid is released at temperature T2, which is never likely to be smaller flian room temperature (about 290 K), then the Carnot limit of the efficiency can be calculated by 

Basically, there must be some heat energy, proportional to the lower temperature T2 that is always thrown away or wasted. Thus, the practical efficiency is always lower than the efficiency limit 

If both AG and EH are divided by nF, the fuel cell efficiency may be expressed as a ratio of two potentials  

The actual efficiency of the cell is defined as the actual voltage divided by the thermoneutral potential, that is, 

In practice, a fuel cell is normally operated under conditions such that not all the fuel that is fed to flie cell is consumed. Some fuel has to pass through unreacted. Therefore, fliere is another parameter that needs to be taken into account to calculate the cell effieieney, the fuel utili2ation eoefficient, whieh is defined as 

A fuel cell performance may be expressed by considering different quantities such as thermod5mamic efficiency based on energy forms voltage efficiency based on operating voltage and all irreversible losses, and current efficiency based on excess fuel supplied. 

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Fuel Cell Efficiency The theoretical energy conversion efficiency of a fuel cell ° is given by the ratio of the free energy (Gibbs function) of the cell reaction at the cell s operating temperature AG to the enthalpv of reaction at the standara state AH°, both quantities being based on a mole of fuel ... 

Reactant Utilization and Gas Composition Reactant utilization and gas composition have major impacts on fuel cell efficiency. It is apparent from the Nemst equations in Table 2-2 that fuel and oxidant gases containing higher partial pressures of electrochemical reactants produce a higher cell voltage. 

Two additional aspects of efficiency are of interest 1) the effects of integrating a fuel cell into a complete system that accepts readily available fuels like natural gas and produces grid quality ac power (see Section 9), and 2) issues arising when comparing fuel cell efficiency with heat engine efficiency (see below). 

An intrinsic, exothermic water-gas shift reaction occurs in the steam reformer reactor. The combined reaction, steam reforming and water gas shift, is endothermic. As such, an indirect high temperature heat source is needed to operate the reactor. This heat source usually takes the shape of an immediately adjacent high temperature furnace that combusts a small portion of the raw fuel or the fuel effluent from the fuel cell. Efficiency improves by using rejected heat from other parts of the system. Note that the intrinsic water-gas shift in the reactor may not lower the... 

The reactor was tested using a range of methanol and water concentrations, and researchers found the best results using a water and methanol mixture with a steam-to-carbon ratio (S C) of 1.1 1. They were able to achieve 90% conversion at 260 °C with a reactant liquid flow rate of 12 cmYh. Assuming a fuel cell efficiency of 60% and 80% hydrogen utilization, they estimated the output power to be 15 W. Eventually the complete system will include a cata-... 

The complete system with fuel cell is under development. Its projected cost will be 400—500 (U.S. dollars) for a 130 Wg output. The system efficiency is estimated to be 9%. This efficiency includes parasitic losses and an assumed fuel cell efficiency of 50%. The parasitic power requirements by the BOP components are about 70 Wg, mostly from the eight magnetic valves, which is one cause for the low system efficiency. The researchers are looking for lower-power magnetic valves and other solutions to decrease the parasitic power requirements. 

To understand the peak recuperated case efficiency, note that as the pressure ratio decreases, the turbine is taking less energy from the air, increasing the temperature going to the recuperator. Thus, ultimately less auxiliary fuel is needed at the postcombustor to keep the temperature at the cathode inlet fixed at 973 K. At a pressure ratio between 3 and 4, fuel to the auxiliary fuel is no longer necessary to preheat the air to the cathode inlet. This is the point of maximum efficiency for this system. The decrease in fuel cell efficiency with pressure is not enough to offset the improved recuperated GT efficiency, which is incidentally near its peak efficiency... 

Single-cycle fuel cell efficiencies range from 47 to 50%. The efficiency of combined-cycle fuel cells is about 60%, and if the generated heat is also recovered (in the form of hot water), the total efficiency can be around 80%. In comparison, the efficiency of gasoline engines is around 25%, of nuclear power plants about 35%, and of subcritical fossil fuel power plants, 37%. 

The combustion of a mol of hydrogen produces 286 kj (1.0 kj = 0.948 Btu = 0.278 Wh) of energy. If the combustion of hydrogen takes place in a fuel cell, only 237.3 kj of this energy can be recovered in the form of electric energy, whereas 48.7 kj will be lost in the form of heat to the environment. Therefore, in an ideal (theoretically perfect) fuel cell, efficiency could reach 237/286 = 83%. 

Fig. 13.31. Fuel cell efficiency vs. power (International Fuel Cells 50-kWe PEM fuel cell system). (Reprinted from Fuel Cells for Transportation, U.S. Dept, of Energy, 1996.)...

Suppose that this energy is to be supplied to cars in the form of hydrogen in a fuel cell from re-formed methanol, (c) How many moles of C02 andH2 would be required to form the methanol (d) Calculate the cubic meters of air per day that would have to be collected at a given gas station to allow extraction of the necessary C02 (0.3% in air), (e) Then calculate the number of moles per day of H2 needed to form the corresponding methanol (fuel cell efficiency is 60%). (f) Calculate the area of solar panels (number of square meters for a 10-kW sunny day) required to produce this H2 at 20% efficiency for the conversion of solar... 

Since a fuel cell can be operated at different current densities, the related cell voltage controls the fuel cell efficiency, that is, diminishing the current density increases the cell voltage thus the fuel cell efficiency increases. 

Figure 1.21. Comparison of fuel cell efficiency with Carnot efficiency, assuming the coolant temperature is 50°C [3], (From Larminie J, Dicks A. Fuel cell systems explained. 2003 John Wiley Sons Limited. Reproduced with permission from the publisher and the...

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