*2.3. Exergy Content of a Single Process Stream*

Referring to the observations formulated at the end of Section 2.1.3, the values of EXA and EXL can be estimated for any stream in the considered system. Each process stream is modelled as having two exergy sets: EXA is assigned positive values, and EXL is assigned negative values. Summing the assets and the liabilities for the stream produces the net balance, resulting in the potential exergy profit (positive balance) or loss (negative balance).

The model development starts with the identification of the potential components of the exergy content in a stream. According to the theory presented in [7], the following components can be distinguished in the exergy content of a thermodynamic system, including a process stream [7]:

(1) Thermo-mechanical/physical exergy: This is based on the thermal and pressure conditions of the system and can be expressed as in Equation (4) when no pressurised gas is present:

$$\rm{Ex}\_{\rm{phy}} = (H - H\_0) - T\_0 \times (S - S\_0) \tag{4}$$

where Exphy (MW) is the thermo-mechanical exergy flow rate, H and H0 are the enthalpy flow rates of the stream (MW) at the current conditions and at the reference conditions, respectively, T0 ( ◦C) is the temperature at the reference conditions, and S and S0 are the entropy flow rates (kW/ ◦C). The typical reference conditions are 25 ◦C and 1 atm. It has to be noted that the temperature-related quantities are given in ◦C. While the definitions of the thermodynamic properties are based on the Kelvin scale, the usual temperature specifications are in ◦C, which is the much more commonly used scale in engineering calculations.

(2) Chemical exergy: This is the retrievable exergy from the system by applying potential chemical and physical conversions or the exergy input required for cleaning/separation. This component can be expressed in different ways, depending on the particular processes (chemical and/or biochemical). For chemical reactions, the chemical exergy can be evaluated as

$$\text{Ex}\_{\text{chem}} = \sum\_{\text{i}} (\mu\_{\text{i}} - \mu\_{\text{i},0}) \times \text{N}\_{\text{i}} \tag{5}$$

where Exchem (kW) is the chemical exergy flow rate, μ<sup>i</sup> and μi,0 (kJ/kmol) are the chemical potentials at current, and reference conditions, respectively, and Ni (kmol/s) is the molar flow rate of the flow. In this work, the reference state of the materials is evaluated based on the Szargut method [76]. The detailed calculation steps of the chemical exergy are shown in [6]. For simplicity, an open-source online tool [77] is used to estimate the chemical exergy of materials in this paper.

(3) Gravitational exergy: This expresses the potential energy (directly convertible to exergy; see [7]) resulting from the elevation of the system above a certain base point:

$$\mathbf{Ex\_G = m \times g \times \Delta h} \tag{6}$$

where ExG (kW) is the gravitational (potential) exergy, m (kg/s) is the mass flow rate, g (m/s2) is the acceleration due to gravity, and Δh (m) is the elevation difference between the current location of the stream and the location of the environmental reservoir selected for the reference point.

(4) Kinetic exergy: This expresses the kinetic energy (directly convertible to exergy).

$$\mathbf{Ex\_{K}} = \frac{1}{2} \times \mathbf{m} \times \mathbf{v}^{2} \tag{7}$$

where Exk (kW) is the kinetic exergy, m (kg/s) is the mass flow rate, and v (m/s) is the velocity of the stream.

(5) Electromagnetic exergy: The component (ExEM) can also be defined for electrochemical systems and problems, expressing the potential of the system within an electromagnetic field. This can be calculated as equivalent to the energy delivered by the electric current [7].

For each modelling context, the significance and the relevance of each of the components have to be evaluated, and only the significant ones should be retained in the model. In the current work, only the thermo-mechanical and the chemical exergy components are evaluated. The other components are relevant to specific applications: the gravitational component is applicable to accounting for process layout, and the electromagnetic component is relevant to the electrochemistry and electromagnetism domains.
