Uf H

H2,in H2,in where H2,in and H2,out are the mass flow rates of H2 at the inlet and outlet of the fuel cell, respectively. However, hydrogen can be consumed by various other pathways, such as by chemical reaction (i.e., with O2 and cell components) and loss via leakage out of the cell. These pathways increase the apparent utilization of hydrogen without contributing to the electrical energy produced by the fuel cell. A similar type of calculation is used to determine the oxidant utilization. For the cathode in MCFCs, two reactant gases, O2 and CO2, are utilized in the electrochemical reaction. The oxidant utilization should be based on the limiting reactant. Frequently O2, which is readily available from make-up air, is present in excess, and CO2 is the limiting reactant.

A significant advantage of high-temperature fuel cells such as MCFCs is their ability to use CO as a fuel. The anodic oxidation of CO in an operating MCFC is slow compared to the anodic oxidation of H2; thus, the direct oxidation of CO is not favored. However, the water gas shift reaction

reaches equilibrium rapidly in MCFCs at temperatures as low as 650°C (1200°F) to produce H2. As H2 is consumed, the reaction is driven to the right because both H2O and CO2 are produced in equal quantities in the anodic reaction. Because of the shift reaction, fuel utilization in MCFCs can exceed the value for H2 utilization, based on the inlet H2 concentration. For example, for an anode gas composition of 34% H/22% H2O/13% CO/18% CO2/12% N2, a fuel utilization of 80% (i.e., equivalent to 110% H2 utilization) can be achieved even though this would require 10% more H2 (total of 37.6%) than is available in the original fuel. The high fuel utilization is possible because the shift reaction provides the necessary additional H2 that is oxidized at the anode. In this case, the fuel utilization is defined by

7. Assumes no gas cross-over or leakage out of the cell.

8. Example 10-5 in Section 10 illustrates how to determine the amount of H2 produced by the shift reaction.

where the H2 consumed originates from the H2 present at the fuel cell inlet (H2,in) and any H2 produced in the cell by the water gas shift reaction (COin).

Gas composition changes between the inlet and outlet of a fuel cell, caused by the electrochemical reaction, lead to reduced cell voltages. This voltage reduction arises because the cell voltage adjusts to the lowest electrode potential given by the Nernst equation for the various gas compositions at the exit of the anode and cathode chambers. Because electrodes are usually good electronic conductors and isopotential surfaces, the cell voltage can not exceed the minimum (local) value of the Nernst potential. In the case of a fuel cell with the flow of fuel and oxidant in the same direction (i.e., coflow), the minimum Nernst potential occurs at the cell outlet. When the gas flows are counterflow or crossflow, determining the location of the minimum potential is not straightforward.

The MCFC provides a good example to illustrate the influence of the extent of reactant utilization on the electrode potential. An analysis of the gas composition at the fuel cell outlet as a function of utilization at the anode and cathode is presented in Example 10-5. The Nernst equation can be expressed in terms of the mole fraction of the gases (Xi) at the fuel cell outlet:

RT 1 Xh2 Xo2Xco2,cathode P

where P is the cell gas pressure. The second term on the right side of Equation (2-17), the so-called Nernst term, reflects the change in the reversible potential as a function of reactant utilization, gas composition, and pressure. Figure 2-7 illustrates the change in reversible cell potential calculated as a function of utilization using Equation (2-17).

Utilization (%)

Figure 2-7 The Variation in the Reversible Cell Voltage as a Function of Reactant Utilization

Utilization (%)

Figure 2-7 The Variation in the Reversible Cell Voltage as a Function of Reactant Utilization

(Fuel and oxidant utilizations equal) in a MCFC at 650oC and 1 atm. Fuel gas: 80% H2/20% CO2 saturated with H2O at 25°C; oxidant gas: 60% C02/30% O2/10% inert)

The reversible potential at 650°C (1200°F) and 1 atmosphere pressure is plotted as a function of reactant utilization (fuel and oxidant utilizations are equal) for inlet gas compositions of 80% H2/20% CO2 saturated with H2O at 25°C (77°F) (fuel gas9) and 60% C02/30% 02/10% inerts (oxidant gas); gas compositions and utilizations are listed in Table 2-4. Note that the oxidant composition is based on a gas of 2/1 CO2 to O2. The gas is not representative of the cathode inlet gas of a modern system, but is used for illustrative purposes only. The mole fractions of H2 and CO in the fuel gas decrease as the utilization increases and the mole fractions of H2O and CO2 show the opposite trend. At the cathode, the mole fractions of O2 and CO2 decrease with an increase in utilization because they are both consumed in the electrochemical reaction. The reversible cell potential plotted in Figure 2-7 is calculated from the equilibrium compositions for the water gas shift reaction at the cell outlet. An analysis of the data in the figure indicates that a change in the utilization from 20 to 80% will cause a decrease in the reversible potential of about 0.158 V, or roughly 0.0026 V/% utilization. These results show that MCFCs operating at high utilization will suffer a large voltage loss because of the magnitude of the Nernst term.

An analysis by Cairns and Liebhafsky (3) for a H2/air fuel cell shows that a change in the gas composition that produces a 60 mV change in the reversible cell potential near room temperature corresponds to a 300 mV change at 1200°C (2192°F). Thus, gas composition changes are more significant in high temperature fuel cells.

9. Anode inlet composition is 64.5% H2/6.4% CO2/13% CO/16.1% H2O after equilibration by water gas shift reaction.

Current Density: Figure 2-4 depicts the impact of current density on the voltage (performance) of a fuel cell. The effects on performance of increasing current density were addressed in Section 2.1.2. That section described how activation, ohmic, and concentration losses occur as the current is changed. Figure 2-2 is a simplified depiction of how these losses affect the shape of the cell voltage-current characteristic. As current is initially drawn, sluggish kinetics (activation losses) causes a decrease in cell voltage. At high current densities, there is an inability to diffuse enough reactants to the reaction sites (concentration losses) so the cell experiences a sharp performance decrease through reactant starvation. There also may be an associated problem of diffusing the reaction products from the cell.

Table 2-4 Outlet Gas Composition as a Function of Utilization in MCFC at 650°C

Gas

Utilizationa (%)

0

25

50

75

90

Anodeb

X H2

0.645

0.410

0.216

0.089

0.033

XQO2

0.064

0.139

0.262

0.375

0.436

XCO

0.130

0.078

0.063

0.033

0.013

XH2O

0.161

0.378

0.458

0.502

0.519

Cathode0

X CO2

0.600

0.581

0.545

0.461

0.316

Xo2

0.300

0.290

0.273

0.231

0.158

a - Same utilization for fuel and oxidant. Gas compositions are given in mole fractions. b - 80% H2/20% CO2 saturated with H2O at 25°C. Fuel gas compositions are based on compositions for water-gas shift equilibrium. c - 30% O2/60% CO2/10% inert gas. Gas is not representative of a modern system cathode inlet gas, but used for illustrative purposes only.

Ohmic losses predominate in the range of normal fuel cell operation. These losses can be expressed as iR losses where i is the current and R is the summation of internal resistances within the cell, Equation (2-2). As is readily evident from the equation, the ohmic loss and hence voltage change is a direct function of current (current density multiplied by cell area).

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