Page 103 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

80 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

5 The electric efficiency of an IN'EX design with two turbines is about 70%
[19], similar to the EXCO design. The exhaust temperature in the INEX
design is about 200°C and that of the EXCO design is about 500-600°C
depending on the individual parameters.

The EXCO design has thus the potential for a combination with a steam
turbine cycle (ST) that could be, for example, a Cheng cycle. This leads to an
electric efficiency of about 75% [20]. The first studies [20] of the EXCO design
included a reheat cycle with an additional heat exchanger within the SOFC
module. This design seemed to be too complicated. But a comparison of both
designs shows that the benefit of the EXCO design to reduce the excess air in one
process step at one pressure level with small HEXs can be combined with the
benefit of the INEX design to allow a simple cascading of GT cycles as needed for a
reheat GT cycle. This led to the proposal of the reheat SOFC-GT cycle combined
with a steam turbine (ST) cycle which reaches slightly more than 80% as the
calculated efficiency [2 11.

3.7 Summary
Thermodynamic considerations are used to understand the processes of energy
conversion in SOFCs. Such theoretical studies of the behaviour of the reversible
processes have a high practical value in helping to understand complex systems.
The reversible work of a fuel cell is defined by the free or Gibbs enthalpy of
the reaction. If we use the assumption of the ideal gas we immediately get the
equation of the Nernst voltage from the Gibbs enthalpy of the reaction. The
consideration of the electrical effects shows that the molar flow of the spent fuel
is proportional to the electric current and the reversible work is proportional to
the reversible voltage. A coupling between the thermodynamic data and the
electrical data is only possible using the quantities power or heat flow and not by
using work and heat. This is caused by the fact that we use a mass or substance
transport as the basis for thermodynamic considerations and we use a charge
transport to describe electrical phenomena.
Irreversible losses cause a difference in the efficiency of reversible and real
processes. These losses can be described and quantified by their irreversible
entropy production. The consideration of the ohmic losses shows that
the irreversible entropy production in a SOPC is smaller than in another
Iow-temperature fuel cell. This is caused by the lower irreversible entropy
production of the heat dissipated at a higher temperature. The effects of the
irreversible mixing of reactants and products lead to an irreversible entropy
production as well that reduce the cell voltage. The changes in the Nernst
voltage can be understood by the analysis of the fuel utilisation.
Because all the fuel cannot be fully reacted in practice within the fuel cell,
the SOFC stack can be treated like a power generating burner so as to integrate
it easily into a system model. The stack cooling depends on the amount of
excess air.