To evaluate the exergy efficiencies of the processes the exergy model given by T. J. Kotas is used [120]. At first a definition of a thermodynamic system and process need to be established. “A system is an identifiable collection of matter whose behaviour is the subject of study. For identification, the system is enclosed by a system boundary, which may be purely imaginary or may coincide with a real boundary. The term closed system is sometimes used to emphasize that there is no flow of matter across the system boundary. [...] When motions are involved, the system definition must include a reference frame to which velocities and displacements are related. The most commonly used reference frame is the inertial reference frame in which a free particle moves at constant velocity4.” A process is defined by changing the state of a
system [120]. Since a system can enclose areas of different sizes, this definition of process is
applicable both for the hydrogen processes described in section 4 as well as thermodynamic state changes such as e.g. an isentropic compression.
Exergy is defined as the maximum energy of a system capable to perform work in respect to the environment as a universal reference system. Work can only be performed when two systems are not in the same state, meaning the systems are not in equilibrium. From this definition it follows that states of equilibrium with the environment with no exergy need to be defined. The first state is the environmental state, where the considered system is in thermal and mechanical equilibrium with the environment, thus, both temperature and pressure of the system are the same as the environment’s reference temperature Tref and pressure pref. The
second state is the dead state, in which additionally to the environmental state a chemical equilibrium is reached. Thus, the chemical potentials of the considered substances in the system and the reference substances in the environment are in equilibrium.
To calculate the exergy flows of a process the state points have to be determined as dis- cussed in the simulation model descriptions. The respective exergy flows ˙Ei at each state
point i are the sum of the single types of exergy ˙
Ei = ˙EW + ˙EQ+ ˙Ekin+ ˙Epot+ ˙Eph+ ˙Ech (5.58)
consisting of exergy of work transfer ˙EW, heat transfer ˙EQ, kinetic exergy ˙Ekin, potential exergy
˙
Epot, physical exergy ˙Eph and chemical exergy ˙Ech at this specific state point. The kinetic,
potential, physical and chemical exergy are always bound to a stream of matter and so can be combined into the exergy of a steady stream of matter ˙ES.
WORK TRANSFER
Work transfer ˙W as well as electrical power Pel are both considered pure exergy of work
transfer ˙EW by definition of exergy, thus:
˙
EW = ˙W (5.59)
˙
EW = Pel (5.60)
HEAT TRANSFER
The exergy of heat transfer is defined by considering a closed system with a heat source, the environment and a control surface in between both. The exergy of the heat transferred over the control surface is defined as the work that could ideally be utilized using the environment as a heat sink. Thus a heat transfer rate ˙Q over a surface with temperature Tsurf acemay create a maximum work ˙Wmaxof
˙ EQ = ˙Wmax = ˙Q· 1 − Tref Tsurf ace (5.61)
with Tref the reference temperature of the environment.
STEADY STREAM OF MATTER
The exergy ˙ES of a steady stream of matter consists of the sum of its four components: the
kinetic exergy ˙Ek, the potential exergy ˙Epot, the physical exergy ˙Eph and the chemical exergy
˙
KINETIC AND POTENTIAL EXERGY
Kinetic and potential energy are both ordered forms of energy and thus fully convertible to work. When velocity and height are given in relation to the environment the exergy then is given by ˙ Ek = ˙m· c2 2 (5.62) ˙ Epot = ˙m· g · z (5.63)
with ˙m the mass flow, c the speed relative to the environment, g the gravitational acceleration
and z the altitude above sea level.
PHYSICAL EXERGY
Physical exergy is the maximum amount of work obtainable when the stream of matter is brought from its initial state to the environmental state using processes with only thermal interaction with the environment. The physical exergy can be calculated by
˙
Eph = ˙m· hinit− href+ Tref ·(sinit− sref)
(5.64) with h being the specific enthalpy, s the specific entropy and the subscripts init and ref being initial and reference state, respectively.
CHEMICAL EXERGY
Chemical exergy is the maximum amount of work obtainable when the stream of matter is brought from the environmental state to the dead state using processes with heat transfer and substance exchange with the environment. To evaluate the exergy based on this definition it is necessary to define a general scheme of standard reference substances in the environment (e.g. oxygen, nitrogen, carbondioxide, ...). Their molar chemical exergy eǫ0is defined by
eǫ0= eRTrefln
pref patm
(5.65)
where eR is the universal gas constant and patm is the partial pressure of this substance in
the atmosphere. The exergy of a non-reference substance is the sum of its molar composing reference substances and its molar Gibbs function of reaction. Resulting molar exergies for different substances are given in the literature [120].
For a mixture of several substances the chemical exergy is calculated by accounting for each individual substances molar fraction in the mixture:
˙ Ech = ˙ m M · X i e χieǫ0i+ eRTref X i e χiln eχi ! (5.66)
with M the molar mass of the mixture and xi the molar fractions of components i.
EXERGY EFFICIENCY
Once the exergy of each state point around a process is determined the rational exergy effi- ciency ηex can be calculated with
ηex =
P ˙Eout
where P ˙Ein and P ˙Eout are the sums of input and output exergy streams of the process,
respectively.
If the exergy of a single thermodynamic state change such as compression is calculated the exergy efficiency is instead determined by
ηex =
P ˙Eout−PE˙in− ˙Ework,in ˙
Ework,in
(5.68)
with Ework,inas the exergy associated with the work needed for the state change.