Page 94 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Thermodynamics 71

HPF has to be supplied reversibly with the work \i’tHpFrev that is equal to the
exergy eFFC of the fuel with the thermodynamic state of the fuel cell and the heat
qHpFrev from the environment

WtHPFrev eFFC = ~;FC - TO ’ S$FC = (hFFC - hF0) - TO ’ (SFFC - SFO) (73)

In the right-hand part of Eq. (73) the definition of the exergy of the fuel with
the thermodynamic state of the fuel cell is now worked out in more detail. Similar
processes are used for the reversible heating of the air and the reversible cooling
of the flue gas. The reversible air heating needs the work wtHPA

WfHPArev = PA ’ eAFC = PA ’ (h&C - TO . s2FC) (75)
and the reversible heat engine HEG for the cooling of the flue gas G delivers the
work WtHEGrev

WtHEGrev = --(PA f 1) ’ eGFC = --(PA f 1) ’ (h&c - TO . Sipc). (76)

The total work of the reversible fuel cell-heat engine system is defined by

Wtsystrev = WtFCrev f WtCCrcv f WtHPFrev f WtHPdrev f WtHEGrev (77)

UsingEqs. (S), (70), (73) and(75)-(77) weget

Wtsystrev = A‘HO - T~ . A‘SO = A‘GO (78)

The reversible work wtsystrev of any fuel cell-heat engine system is independent
of the state of the cell and is equal to the free enthalpy of the reaction A‘GO at the
ambient state [3]. The standard condition is assumed to be the ambient state to
keep the argument simple.
It is useful to define a simplified process for further analysis, because the three
reversible heat engines HPA, HPF and HEG do really nothing else than to heat
fuel and air by cooling the flue gas - their total reversible work is negligible. Thus
the simplified process uses a heat exchanger system for the heat recovery instead
of HPA, HPF and HEG, as shown in Figure 3.9. But this simplified reference cycle
is generally not reversible [5]. This is caused by the changes of the specific heat
capacities of the different substances with the reaction temperature T that
change the reaction enthalpy ArH(T,p). A (small) amount of the waste heat of FC
must be used to heat the reactants completely. We lose this amount of heat for
further reversible use in the Carnot cycle CC.
The simplified fuel cell-heat engine hybrid cycle as a reference cycle fits the
reversible system well; the deviation at 1000°C is -0.76% only for the hydrogen
oxidation. Figure 3.10 shows the applications of this cycle. The left-hand side of