The method of exergy can be used to specify and quantify exergy destruction of process owing to the exergy losses and irreversibility. Therefore, it is alternating and informative tool in terms of evaluating and comparing systems and processes. In comparison to energy analysis, exergy analysis presents more meaningful efficiencies and identifies the thermodynamic losses more clearly.

The Exergy Concept

The compounds of specified reference surroundings and system do a maximal shaft work that is defined as the exergy of a system. Also, exergy can be described as some words such as available energy, useable energy and availability. Exergy has meaning beyond a thermodynamic property; it has the characteristics of both the reference surrounding and a system. When a system provides a condition of equilibrium with its environment, there is not exergy for system. If exergy diverge from the environment, the exergy of system rises.

To understand the different forms of exergy, some state definitions should be explained:

Process state: The beginning state of the system under a work is indicated by the process state (T, P).

Environmental state: The balance of mechanics and heat between the surroundings and the system is defined as the state of restricted equilibrium. System and ambient conditions such as pressures and temperatures are equal in the restricted equilibrium. Environmental state is described as a condition that satisfies the restricted equilibrium with the surroundings (T0, P0).

Dead State: Chemical potentials of the matters are required within the unrestricted equilibrium, including temperature and pressure of the system and surroundings to equal for providing thermodynamic balance totally between the surroundings and the system. Under these circumstances, the system exergy amount is equal to zero since the system cannot be exposed to any state changes during interaction with surroundings. This system state names as the dead state.

The exergy concept presents a global standard of energy quality in a specific environment. Exergy forming from the energy component may be converted to work for the reversible process but the energy quality reduces every time for real processes. Therefore, the exergy output is lower than its exergy input. This exergy equilibrium informs about the amount of exergy lost to the process. In other words, these exergy losses also named as irreversibility rate that are equal to degradation measure of the energy quality.

While analyzing the thermodynamic of the system, three valid equations are used generally. These equations are the conservation of both energy and mass as well as the nonconservation of entropy equation. Some assumptions for deriving these equations are made as follows:

1. There is a system in steady flow states.
2. Reference state conditions are defined as P0 = 101 kPa and T0 = 298.15 K.
3. Changes in the potential and kinetic energies are ignored.

These simplifications are applied for three equations. They are the mass, energy, as well as exergy balance equations shown in equations 3.1, 3.2 and 3.3 respectively:

exergy balance equations

For the streams in equations 3.1, 3.2 and 3.3, ṁ indicates the rate of mass flow, ̇ indicates the energy rate and Ė x indicates the exergy rate. Q̇ cv is the rate of heat into a control volume, ̇ cv is the work done on the part of a control volume, İcv is irreversible exergy loss of a control volume as well as inlet and exit of the stream are stated by the subscripts i and e in equations 3.1, 3.2 and 3.3. Also, the exergy losses from the control volume can be expressed as equation 3.4:

the exergy losses from the control volume

The Exergy of Closed Systems

A closed system of mass exergy is stated as nonflow exergy. Equation 3.5 shows the nonflow exergy that is consisted of physical, chemical, kinetic, and potential exergy configurations.

nonflow exergy

nonflow exergy 1

Terms of system in equations 3.6-3.9 correspond to velocity ν, gravity acceleration g, elevation z, chemical potential μi and moles number Ni, pressure P, temperature T, internal energy U, volume V, entropy S with equilibrium state of T0, P0 and μi00. Also, μi0 is equal to the value of μ where the environmental state. The subscript i denotes the species.

The maximum acquired work from the system is known as physical nonflow exergy while it comes to the ambient state. For instance, it is a condition of thermal and mechanical balance with the surroundings.

A maximum acquired work from the system is known as chemical nonflow exergy while it comes from an ambient condition to a dead condition. To illustrate, it is a condition of overall balance with the environment. Equation 3.10 calculates a mixture chemical exergy.

mixture chemical exergy

Where xi, exich, γi and R indicate the mole fraction, chemical exergy, the ith component activity coefficient as well as molar gas constant, respectively.

The first term of the equation 3.10 that is shown exich is used for specified components. This term can not be used directly for the mixture of petroleum components. Standard chemical exergy for the light petroleum components in reference temperature and pressure can take part in literature. Therefore, they can be substitute for chemical exergy exich. Since the mixture of heavy petroleum fraction can not be known exactly, it is separated into pseudo-components that need to be calculated depending on the lower heating value with equation 3.11

pseudo components

βi is described as the correction factor of the i-th component chemical exergy as well as equation 3.12 shows the β that is related to mass fractions of C, H2, O2, S, and N2

i

Where zC, zH2, zO2, zS, and zN2 correspond to mass fractions of C, H2, O2, S, and N2 respectively. LHV is also calculated by equation 3.13

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