Exergy Analysis¶
Exergy analysis is a powerful tool for evaluating and optimizing thermodynamic systems. Unlike conventional energy analysis, which focuses on the quantity of energy, exergy analysis considers both the quantity and the quality of energy, providing deeper insights into system inefficiencies. This approach helps identify where and why irreversibilities occur, enabling engineers and researchers to develop strategies for improving efficiency, reducing costs, and supporting sustainable energy conversion.
The ExerPy library offers a flexible, Python-based solution for conducting exergy analysis on energy-conversion systems. It supports integration with simulation tools like Ebsilon Professional, Aspen Plus, and TESPy, allowing users to extract detailed data about components and connections.
The features described in this section are based on a paper published for TESPy. For more details, see [2].
Fundamentals of exergy analysis¶
Energy is a concept of the first law of thermodynamics. It cannot be destroyed. However, when it comes to the design and analysis of thermal systems, the idea that something can be destroyed becomes useful. According to the second law of thermodynamics, the conversion of heat and internal energy into work is limited. This constraint and the idea of destruction are applied to introduce a new concept: “Exergy”.
Exergy can be destroyed due to irreversibilities. It is also able to describe the quality of different energy forms. The difference in energy quality can be illustrated by the following example. 1 kJ of electrical energy is clearly more valuable than 1 kJ of energy in a glass of water at ambient temperature [3].
In literature, exergy is defined as follows:
“An opportunity for doing useful work exists whenever two systems at different states are placed in communication, for in principle work can be developed as the two are allowed to come into equilibrium. When one of the two systems is a suitably idealized system called an environment and the other is some system of interest, exergy is the maximum theoretical useful work (shaft work or electrical work) obtainable as the systems interact to equilibrium, heat transfer occurring with the environment only.” [3]
Physical exergy¶
In many energy conversion systems, chemical reactions are absent. In such cases, the consideration of chemical exergy is not necessary. Additionally, when the contributions of potential and kinetic exergy are negligible, the focus is exclusively on physical exergy. The specific physical exergy of stream \(i\) is defined as [3]:
where \(h_i\) and \(s_i\) are the specific enthalpy and entropy at state \(i\), and \(h_0\) and \(s_0\) are the specific enthalpy and entropy at the ambient conditions (\(T_0\), \(p_0\)).
Warning
For substances that are not fluid under ambient conditions, the physical exergy calculation requires a modified approach. In such cases, the specific physical exergy is calculated as:
where the subscript “min” refers to the modified state at the given pressure but at the minimum possible temperature at which the substance remains in its fluid state. For example, for a molten salt consisting of 60% NaNO₃ and 40% KNO₃, the minimum temperature is 200°C.
This formulation has been validated with Ebsilon Professional only.
Splitting of physical exergy¶
Since some thermal systems include states at ambient temperature, the splitting of physical exergy into thermal and mechanical parts enables a more comprehensive analysis of the system’s components [4]. These two parts represent the contribution of the temperature and pressure to the physical exergy. This separation is particularly valuable for defining more meaningful exergetic efficiencies for components operating below ambient temperature and components where distinguishing between thermal and mechanical exergy contributions provides more precise thermodynamic characterization. The separation is given by:
with the thermal exergy defined as:
and the mechanical exergy defined as:
In these expressions, state \(A\) is at ambient temperature \(T_0\) and pressure \(p_i\).
Component-level exergy balance¶
The exergy analysis at the component-level uses standardized balance equations, following the approach developed by [2]. The exergy balance equation of component \(k\) can be formulated as:
Each component \(k\) is evaluated by three metrics that quantify its performance and losses: the exergetic efficiency \(\varepsilon_k\), the exergy destruction ratio \(y_k\) measuring the share of the total exergy fuel destroyed by component \(k\), and the exergy destruction ratio \(y^*_k\) measuring the share of the total exergy destruction attributable to component \(k\):
System-level exergy balance¶
At the system level, the overall exergy balance is expressed as:
where the fuel, product, and loss streams of the overall system need to be defined according to the thermodynamic purpose of the system under consideration.
Terminology¶
The definitions and nomenclature used in the exergy analysis in ExerPy are based on [5]. The exergy destruction ratios are described in more detail in [3]. Changes in kinetic and potential exergy are neglected and therefore not considered.
Variable |
Name |
Symbol |
Description |
|---|---|---|---|
|
(specific) physical exergy |
\(e^\mathrm{PH}\), \(E^\mathrm{PH}\) |
due to the deviation of the temperature and pressure of the system from those of the environment |
|
(specific) thermal exergy |
\(e^\mathrm{T}\), \(E^\mathrm{T}\) |
associated with the system temperature |
|
(specific) mechanical exergy |
\(e^\mathrm{M}\), \(E^\mathrm{M}\) |
associated with the system pressure |
|
(specific) chemical exergy |
\(e^\mathrm{CH}\), \(E^\mathrm{CH}\) |
based on standard chemical exergy in ambient model, the exerpy.data module provides three different datasets for standard exergy based on various sources, i.e. Ahrendts [6, 7, 8], Szargut1988 [9] and Szargut2007 [10, 11]. |
|
product exergy |
\(\dot{E}_\mathrm{P}\) |
represents the desired result (expressed in terms of exergy) generated by the system being considered |
|
fuel exergy |
\(\dot{E}_\mathrm{F}\) |
represents the resources (expressed in terms of exergy) expended to provide the product exergy |
|
exergy destruction |
\(\dot{E}_\mathrm{D}\) |
thermodynamic inefficiencies associated with the irreversibility (entropy generation) within the system boundaries |
|
exergy loss |
\(\dot{E}_\mathrm{L}\) |
thermodynamic inefficiencies associated with the transfer of exergy through material and energy streams to the surroundings |
|
exergetic efficiency |
\(\varepsilon\) |
ratio between product exergy and fuel exergy |
|
exergy destruction ratio |
\(y_\mathrm{D,k}\) |
rate of exergy destruction in a component compared to the exergy rate of the fuel provided to the overall system |
|
exergy destruction ratio |
\(y^*_\mathrm{D,k}\) |
rate of exergy destruction in a component compared to the total exergy destruction rate within the system |
Note
The generic exergy analysis balance equations have been implemented and tested only for the most common components. A list of components that have been considered can be found in the API documentation.