Page 96 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Thermodynamics 73

It is well known from heat engines that < is between about 0.7 and 0.8. All
types of real cells have efficiencies between 5 5 and 6 5% but there is no significant
difference caused by the cell temperature TFc as we would expect from the
thermodynamic considerations [2]. Thus it is obvious that real cells operating
at lower temperatures do not use their potential m70rk wtFCrev properly. Real
high-temperature fuel cells use their potential work reasonably well. The
exergetic efficiency of fuel cells is described in [5] for the H2 fuel. It can be shown
easily that the SOFC has the best exergetic efficiency here. The exergetic
efficiency ~,FC (Eq. (80)) can be related to the total fuel feed if we assume that
the non-utilised fuel can be burnt in an isothermal combustor. We can define the
fuel cell and the isothermal combustor as one unit in that case (see Figure 3.7).
The system efficiency qsyst of any real hydrogen-fuelled combined fuel
ceIl-heat cycle is plotted against the cell temperature Tpc in Figure 3.10 (right).
The exergetic efficiency of the fuel cell CFC is the parameter (0.7; 0.8; 0.9; 1.0)
and the exergetic efficiency of the heat engine CHE is kept constant at 0.7.
The system efficiency qsyst increases with an increasing cell temperature TFc
for all exergetic efficiencies CFC < 1 .O until a maximum is reached. The location
of the maximum of qsyst shifts with increasing exergetic efficiencies LFc to
decreasing TFc. But there are no big changes in the region of the maximum if we
change TFc at constant LPc, The influence of the Carnot cycle dominates at lower
temperatures and lower exergetic efficiencies <FC.
The main result of these considerations is the possibility of designing hybrid
fuel cell-heat cycles with efficiencies of about 80% [5]. This efficiency value is a
target of the US Department ofEnergy since 1999 [6]. It appears useful to operate
the cell at the lowest possible cell temperature TFc in the region of the maximum
of qsyst for reducing materia1 costs of the heat engine and the heat exchangers.
An increase in TFC leads to only a negligible increase in the system efficiency
Ysyst.
The use of natural gas or other hydrocarbons changes the system design
because of the processing of the fuel before its use in the SOFC. The following
investigations will be done for methane as the main component of natural gas to
keep the calculations simple. A very common fuel processing for hydrocarbons is
the endothermic steam reforming process as shown for methane in Eq. (81) with
the heat demand of Eq. (82)
CHq -t H20 4 3H2 + co, (81)

ArH( 75OoC),,= + 1406 5, lkJ/kgCH*. (82)

Heat is also needed to evaporate the feed water. It is useful to use the waste
heat of the cell for these purposes. A general model of a methane fired combined
SOFC cycle based on the reference cycle of Figure 3.9 is shown in Figure 3.1 1 to
describe the thermodynamic influences on the system’s behaviour as simply as
possible [2,7,8].
The SOFC can be modelled as one unit of two parallel operating SOFCs fuelled
with hydrogen and carbon monoxide. All irreversible effects including mixing is