For any fuel cell system at steady operation, water must be balanced; that is, the amount of water entering the fuel-cell system plus the water produced by the reactions must equal the amount of water in the exhaust. Similarly, water must be in balance around each component of the system. Just as a water balance must be achieved in the system, thermal balance is a condition of steady operation. Although high, the efficiency of a fuel cell is well below 100%; this means that heat must be removed from the cell. The approach for heat rejection depends, as we have come to expect, on the electrolyte and temperature of the system. We’ll start by examining a SOFC system integrated with a reformer, and then examine a PEMFC operating on hydrogen. As we’ll see, thermal challenges and water balance issues are coupled.

Integration of SOFC Fuel Cell and Steam Reformer

Let’s again examine the fuel-cell system with a reformer. For simplicity, we assume that methane is reformed according to

(10.33)

Furthermore, we will assume the reaction goes to completion, in contrast to the assumption made earlier. Reforming reactions are endothermic. For instance, the change in enthalpy for reformation of methane (10.33) is 206 kJ·mol⁻¹-methane. Thus, energy must be added to drive the reaction. This feature will have important implications for systems that use hydrocarbon fuels.

There are several reactions that can lead to the formation of elemental carbon in the reactor during the reforming process. Formation of carbon in a reactor is called coking and must be avoided. An example of a coke-forming reaction is shown below:

(10.34)

where solid carbon is formed. Note that the carbon formation reaction is not favored in the presence of excess water. As a result, water in excess of that required for the reformation reaction (10.33) is added. The amount of water is described by the steam to carbon ratio, SC. The steam to carbon ratio may be as high as five in an industrial reformer. Where does this water come from? The clear source is the fuel cell. For the SOFC examined here, water is produced at the anode where hydrogen and carbon monoxide are oxidized,

(10.35)

and

(10.36)

For each mole of methane reformed, there is one mole of water consumed in the reformer and three moles of water produced in the fuel cell. So, in principle, we are in good shape since we produce more water than we consume. As shown in Figure 10.15, water can be recovered from the exhaust of the stack and recycled back to the reformer. However, it turns out that this is not a good approach. To understand why, we need to consider the thermal balance. A solid oxide fuel cell operates at 700–1000 °C. Therefore, the exhaust contains a large amount of energy that must be removed prior to separation of the water by condensation. Subsequently, heat needs to be added back to the water after separation to vaporize it (raise steam) before feeding it to the reformer. The reforming process is highly endothermic and additional heat is required to drive the reaction. Recall that the fuel-cell stack generates excess heat. An improved method of system integration would be to use excess heat from the fuel-cell stack in the reformer as shown with the lower image of Figure 10.15. Rather than trying to separate out the water, we simply recycle the hot exhaust gas from the outlet of the fuel-cell back to the reformer. Enough of the exhaust is recycled so that the desired SC ratio is achieved; what’s more, we have now transferred thermal energy from the fuel cell to the reformer where it is needed. Are there any disadvantages with this approach? First, a high temperature compressor is needed to recycle the hot gas. Second, as a result of the recycle, the concentrations of hydrogen and carbon monoxide are lower in the fuel-cell stack. This situation is explored in Illustration 10.7.

Proper integration with the fuel processing system reduces the cooling load substantially. In addition, heat can be removed with the air stream. Because water is not produced at the cathode in a SOFC and water does not play a key role in electrolyte conductivity, the water balance and the conductivity of the electrolyte are not linked to oxygen utilization, as they are for PEM fuel cells as described below. Therefore, the air flow rate and utilization can be used to control the temperature. Also, the high temperature of the SOFC permits much more heat to be removed with the air compared to that possible with low temperature fuel cells. Controlling the temperature of a SOFC with air utilization is explored in Problem 10.18.

ILLUSTRATION 10.7

Determine the amount of recycle needed to achieve a steam to carbon ratio (SC) of 2 in the reformer. Compare the composition of the anode gas for each of the two configurations shown in Figure 10.15.

In the first case, water is condensed and recycled to provide the correct SC; therefore, the amount of water that is recycled is known. The feed gas is assumed to be pure methane, and the reaction in the reformer is assumed to be complete (see Equation 10.33). Water is the only component recycled, and other components in the anode gas are exhausted from the system. For  [mols⁻¹] of methane in the feed, the molar flow rates of species exiting the stack can be determined from the reaction stoichiometry and the definition for utilization. To simplify the problem, we have assumed that the utilization of the CO and the H₂ is the same. The recycle stream is 100% water at a flow rate of SC.

The composition of hydrogen at the stack exit is plotted as a function of system utilization. For a utilization of 0.85, the mole fraction is 0.09 for H₂ and 0.71 for H₂O.

The analysis of second case, where the anode exhaust gas is recycled, still just requires material balances; however, the balances are significantly more complex and the details are left to Problem 10.25. As before, SC, the overall utilization, and the inlet flow rate of methane are specified. The recycle ratio, R_r, defined as the moles being recycled divided by the moles in the feed, , changes to keep the SC ratio constant. Since SC is based on the feed rate of methane to the reformer, the mole fraction of water decreases as the recycle ratio is increased, as shown in the figure. The relationship between overall utilization and the fuel utilization in the stack is shown in the inset. For an overall utilization of 0.85, the stack utilization is 0.71, and the gas mole fraction exiting the stack is 0.15 for H₂ and 0.52 for H₂O. From the Nernst equation, the change in potential can be determined.

Thus, as the mole fraction of hydrogen increases and that of water decreases, the potential of the cell increases. Using the composition at the exit for the two cases, we determine the change in potential. The equilibrium potential is reduced 26 mV for the water-only recycle and 16 mV for the anode gas recycle.

The principal advantage with anode gas recycle though is in heat integration. Assuming the reformer is at 550 °C and the cell stack at 850 °C, the sensible heat in the recycle stream can be transferred back to the reformer. As shown in the third figure, a significant fraction of the energy needed to drive the reformer can be obtained from the anode gas recycle.

PEM Water Balance

We now turn our attention to PEM fuel cells, which operate at much lower temperatures, use hydrogen as the fuel, and incorporate an ion-exchange membrane as the electrolyte. Utilization of the fuel in these fuel cells is typically quite high. Balancing of the water represents a key challenge for PEM fuel cells. Recall from Chapter 9 that, in contrast to most electrolytes, the conductivity of the proton exchange membrane depends strongly on its water content. Too little water and the membrane conductivity drops; too much water, however, and the electrode floods. The ideal situation is for the gas in contact with the membrane to be saturated with water vapor.

To examine the situation further, let’s perform a water balance for the fuel-cell stack. Referring to Figure 10.16, we assume that the inlet air has a water mole fraction of y_w,in, and that the mole fraction of oxygen in the air feed is known. We further assume that the mole fraction of water in the air exit stream, y_w,out, is at the saturation value. We neglect the water removed by the fuel stream since the utilization of hydrogen is near unity. We will use as a basis the moles of dry air supplied, even though the actual inlet stream also contains water. With  (mol·s⁻¹ of dry air supplied) and total cell area (A) we have,

(10.37)

(10.38)

(10.39)

The term in the parentheses is the molar flow rate of dry, vitiated (spent) air leaving, which is now depleted in oxygen due to reaction. If we assume that the spent air stream must be saturated with water to keep the membrane conductive, the mole fraction of water out is given simply as

(10.40)

where p_vap(T_cell) is the vapor pressure of water at the cell temperature. Next, the utilization of oxygen is used:

(10.18)

Substituting, a material balance on water yields

(10.41)

 cancels out, and now we see that the utilization and the outlet mole fraction of water are related. Since we assume that the outlet mole fraction is saturated, we can relate utilization and cell temperature. This connection is illustrated in Figure 10.17. Here it is assumed that the incoming air is near room temperature and as such cannot hold a lot of water vapor. For a given cell temperature there is only one value for utilization of air that perfectly balances water. A higher utilization of oxygen will result in cell flooding and lower u_O2 causes dry out of the ionomer.

The perfect balance just described is difficult to achieve. Consequently, it is impractical to avoid liquid water completely while simultaneously ensuring that the membrane is kept fully hydrated. Therefore, some means of dealing with liquid water is needed for PEMFCs. In practice, capillary forces are used to wick out the liquid or, alternatively, high velocities are used in the flow channel to physically expel the water droplets. Exploring these topics, however, is beyond the scope of this book.

Heat removal is important for PEMFCs, just like it was for SOFCs, although the waste heat is at a much cooler temperature. One important way to remove heat is to provide coolers between cells in the cell stack assembly. These coolers may be located between each cell or between groups of cells, such as every six or seven cells. For a bipolar stack, these coolers must allow for electronic current flow through them. Such coolers typically use a liquid as the cooling fluid. The heat is then rejected to the atmosphere in a separate heat exchanger.