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Citation: Witte, F.; Hofmann, M.;
Meier, J.; Tuschy, I.; Tsatsaronis, G.
Generic and Open-Source Exergy
Analysis—Extending the Simulation
Framework TESPy. Energies 2022,15,
4087. https://doi.org/10.3390/
en15114087
Academic Editor: Muhammad Aziz
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Accepted: 23 May 2022
Published: 1 June 2022
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energies
Article
Generic and Open-Source Exergy Analysis—Extending the
Simulation Framework TESPy
Francesco Witte 1,2,* , Mathias Hofmann 3, Julius Meier 3, Ilja Tuschy 1,2 and George Tsatsaronis 3
1Department of Energy and Biotechnology, Flensburg University of Applied Sciences, Kanzleistraße 91-93,
24943 Flensburg, Germany; ilja.tuschy@hs-flensburg.de
2Center for Sustainable Energy Systems (ZNES), 24943 Flensburg, Germany
3Institute for Energy Engineering, Technische Universität Berlin, Marchstraße 18, 10587 Berlin, Germany;
hofmann@iet.tu-berlin.de (M.H.); julius.meier@gmx.de (J.M.); georgios.tsatsaronis@tu-berlin.de (G.T.)
*Correspondence: info@witte.sh
Abstract:
Exergy-based methods support the identification of thermodynamic inefficiencies and the
discovery of optimization potentials in thermal engineering applications. Although a large variety
of simulation software is available in this field, most do not offer an integrated solution for exergy
analysis. While there are commercial products on the market with such capabilities, their access
for research and educational purposes is limited. The presented open-source software offers an
integrated and fully automated exergy analysis tool for thermal conversion processes. In a first step,
physical exergy is implemented, and the tool is then applied to three different example plants to
highlight its capabilities and validate the implementation: A solar thermal power plant, a supercritical
CO2
power cycle, and an air refrigeration cycle. The respective models and the results of the analyses
are presented briefly. By providing the results in modern data structures, they are easily accessible
and postprocessible. Future work will include chemical exergy to enable analyses of applications
with conversion of matter. Additionally, the implementation of the exergoeconomic analysis and
optimization is envisaged.
Keywords:
exergy analysis;simulation; free and open-source software; thermal conversion processes;
Python; generic topologies; Grassmann diagram; solar thermal power plant; supercritical carbon
dioxide power cycle; air refrigeration cycle
1. Introduction
1.1. Simulation-Based Thermodynamic Analysis
Systems with thermal conversion processes are often complex and require extensive
computational efforts to simulate. With the emerging usage of computers in mathematical
problem solving, simulation became a powerful and widespread tool in process engineer-
ing [
1
–
3
]. Its goal is the representation of a process by a mathematical model and its
(computer-aided) solution in order to obtain information about the process design and
the process performance, cp. [
4
–
6
]. While such models can, of course, be solved manually,
simulation shows clear advantages, including the following:
•
A validated model can be used to answer what-if questions (e.g., in parameter and
sensitivity analyses and process design studies) about the behavior of a real-world
system [7] and thus to improve understanding of its operation.
•
Computers accelerate the speed, increase the quantity, and can improve the quality of
calculations [8].
•
An extensive, disruptive, or expensive operation of a real-world system can be avoided.
Furthermore, scale-ups or novel concepts or components can be examined before they
are realized.
•
During the cost- and time-limited design cycle of a product, virtual prototypes based
on modeling and simulation can be used [9].
Energies 2022,15, 4087. https://doi.org/10.3390/en15114087 https://www.mdpi.com/journal/energies
Energies 2022,15, 4087 2 of 27
Consequently, many authors focused on engineering, technology, and processes simu-
lation and presented comprehensive modeling and simulation methodologies, e.g., [
10
–
12
].
Using generalized simulation software instead of specific tools for single instances only,
it is possible to solve generic models and enable time-efficient work [
13
]. For exam-
ple, Stamatelopoulos [
14
] presents some fundamentals of calculation and optimization of
power plants.
In addition to the engineering and planning of thermal engineering applications,
simulation, thermodynamic analysis, and optimization are powerful tools enabled by
specialized software. While a large variety of software focusing on steady-state simulation
of thermal conversion processes is available, see Table 1, most are proprietary. As stated
in a previous publication [
15
], the financial obligations arising from licensing agreements
are significant, despite the discounts that are commonly offered to academic institutions.
From our point of view, free and open-source software is therefore particularly suitable for
higher education and research.
Although the advantages and disadvantages of usage and development of free and
open-source software have already been discussed, e.g., [
16
–
18
], we would like to em-
phasize two benefits of free and open-source software in research. First, collaborative
source code development connects international research groups working on similar issues
or using similar methods. Their work is available via corresponding repositories and
therefore also other scientists are able to contribute and give suggestions (transdisciplinary
approach). Second, an increasing number of public funding agencies expect open-access re-
search. The use of proprietary software is not consistent with the requirement of traceability
of research results.
Finally, it is necessary to mention that a simple thermodynamic analysis based on
energy balances fails to identify the real thermodynamic inefficiencies within a system (see
Section 2.2). In consequence, the effective use of energy sources can not be guaranteed.
Examples given in [
19
] reveal the weaknesses of a first-law analysis based on energy
balances only (see
Equation (1)).
An exergy-based analysis should therefore be integrated
in a simulation-based thermodynamic analysis.
1.2. Motivation of the Approach
Steady-state (Thermal conversion processes are operated most of the time at steady-
state conditions at different loads. Therefore, it is sufficient for most applications to perform
a steady-state simulation for system operation at the design and some part-load conditions.)
thermal conversion process simulation [
6
,
14
,
20
,
21
] can be performed in proprietary or
open-source frameworks. Specialized software tools use predefined components, property
databases, simulation, and optimization subroutines to solve nonlinear equation systems, a
programming interface for mathematical-physical relationships, and mostly a graphical
user interface [
13
]. Table 1gives an overview of available tools. It is limited to software that
is still maintained and developed further. Also not considered is any software that requires
user-formulated equations to model standard components of thermal engineering systems.
The number of available predefined components varies depending on the orientation
and, especially in proprietary software, on the clientele requirements. Usually, it is possible
to integrate user-defined components and property functions via an application program-
ming interface (API). The user should be able to model and simulate standardized thermal
conversion processes, such as a Rankine cycle (vapor turbine), a Brayton cycle (gas turbine),
heat pump or refrigeration machines, or combinations and variants thereof.
Energies 2022,15, 4087 3 of 27
The majority of available tools do not offer an out-of-the-box exergy analysis [
22
],
although it could easily be integrated [
23
]. A handful of tools provide values for the specific
physical exergy, calculated from enthalpy, entropy, and a user-defined ambient temperature.
A comprehensive calculation of specific chemical exergies is usually not implemented.
One obstacle is the lack of an internationally accepted standard reference environment to
calculate standard chemical exergies. Approaches have been published among others by
Szargut et al. [
24
–
28
], Ahrents [
29
,
30
], Kameyama [
31
], van Gool [
32
], Diederichsen [
33
],
Shieh [
34
], Stepanov [
35
,
36
], etc. A discussion of some of these approaches can be found
in [
37
]. Some tools or routines developed in the past to perform exergy-based analyses
are closed-source, no longer available, distributed, or further developed, e.g., routines for
Aspen Plus [
38
–
44
], Aspen Hysys [
45
], ProSimPlus [
46
], Sim42 [
47
], or not assigned to a
specific software [
48
,
49
]. The computer program THESIS [
50
] was the first simulation tool
with an integrated exergy analysis for chemical and energy engineering. Parts of THESIS
are still used for the exergetic and exergoeconomic evaluation of thermal designs in courses
offered by the Institute for Energy Engineering at Technische Universität Berlin.
An integrated framework for the simulation and thermodynamic analysis based on
exergy destruction, exergy losses, and exergy efficiencies for thermal conversion processes
operating above and below the ambient temperature
T0
is unavailable. In case values for
specific physical or chemical exergies are completely calculated, users still have to provide
exergy balances or definitions for the exergies of product
˙
EP
and fuel
˙
EF
. Definitions of
these might vary, and they usually are specific to the individual application.
Following a consequent object-oriented program structure, it is possible to implement
the tools required for generic exergy analysis by defining exergy balance equations for
all classes of components. These balance equations use the physical and chemical exergy
values of all mass flows in a system (representing the connections between the components)
and the exergy values associated with heat and work.
Consequently, our research aims to consolidate the knowledge of the last decades in the
methodology of exergy analysis and to provide this information in the form of a software
tool as part of the object-oriented and open-source thermal conversion process simulation
software TESPy (Thermal Engineering Systems in Python). In particular, all definitions of
exergy efficiencies for the most essential components of thermal conversion systems are
compiled. By providing this information not only on written documentation but also within
the framework of functional software, these additional valuable functions may support
researchers and engineers in using the tool in process development and improvement.
First, the fundamentals of thermal conversion process simulation and exergy analysis
are described, followed by the specific implementation of exergy balance equations in the
component classes. Subsequently, the structure and procedure of the exergy analysis tool
in TESPy are presented. The approach is then applied and validated in three different
example applications highlighting the tool’s flexibility. The next section summarizes some
aspects of the methodologies used. The thermodynamic models, exergy analysis, and
their implementation in TESPy are presented. Section 4contains the example application,
including the description of the simulation, the validation, and the results of the exergy
analysis. All simulations carried out are given as supplementary material to the present
publication. The conclusions are summarized in the last section.
Energies 2022,15, 4087 4 of 27
Table 1. Frameworks for the simulation of steady-state processes in thermal conversion systems.
Solver Features Exergy Analysis
NameSource eq.-Orient. †seq.-mod. Part-Load Properties Flowsheeting ePH eCH ˙
EDand ˙
ELεkfor Tj>T0εkfor Tj<T0Notes, Remarks
Proprietary, closed-source (with license fee or free of charge)
Aspen Plus aX X X X X focus on chemical engineering
ExerCom bX X exergy routine [51] for ASPEN
Chemcad cX X X X focus on chemical engineering
Cycle Tempo dX X X X X X X exergy analysis, for systems with Tj>T0
Ebsilon eX X X X X focus on power plants
EES fX X heat transfer and property library
TAESS gXhExcel exergy cost [52] calc., EES exampl.
IPSEpro iX X X X conceived for thermal power plants
KPRO jX X X X closed-loop calc., no iteration control req.
Modelon kX X X X steady-state and transient simulation
PEPSE ln/a n/a X X X steady-state energy balance software
PPSD mX X X X focus on steam generators/boilers
ProSimPlus nX X X X steady-state simulation
Thermoflow oXstand-alone mod. for spec. plant categ.
TRNSYS pn/a n/a X X X focus on transient simulation
ValiEnergy qn/a n/a X X X Energy performance monitoring sys.
Free and open-source (free of charge)
COCO rX X X CAPE-OPEN compliant chem. flowsh.
DWSIM sX X X CAPE-OPEN compliant chem. flowsh.
ThermoCycle tX X X thermal systems library for Modelica
†
also known as simultaneous or simultaneous-modular approach;
a
Aspen Plus, AspenTech, aspentech.com/en/products/engineering/aspen-plus;
b
ExerCom, CCS Energie-adies,
ccsenergieadvies.nl/en/exercom;
c
Chemcad, Chemstations, chemstations.com/CHEMCAD;
d
Cycle Tempo, Asimptote, asimptote.nl/software/cycle-tempo;
e
Ebsilon Professional,
Steag Energy Services, steag-systemtechnologies.com/en/products/ebsilon-professional;
f
Engineering Equation Solver, F-Chart Software, fchartsoftware.com/ees;
g
Thermoeconomic
Analysis of Energy Systems Software, UNIZAR-CIRCE, exergoecology.com/taess/download-taess;
h˙
EP
and
˙
EF
must be defined, values
˙
Ej
must be given from outside;
i
IPSEpro, SimTech,
simtechnology.com/CMS/index.php/ipsepro;
j
KPRO Kreisprozessrechnung, Fichtner, kpro-fichtner.de/index.php?id=70&L=1;
k
Modelon, Modelon, modelon.com/industries/energy-
power-system-simulation-optimization-software;
l
PEPSE, Scientech, Curtiss-Wright, cwnuclear.com/brands/scientech/information-technologies/pepse/;
m
Power Plant Simulator
& Designer, KED, powerplantsimulator.com;
n
ProSimPlus, ProSim, prosim.net/en/product/prosimplus-steady-state-simulation-and-optimization-of-processes;
o
Thermoflow,
Thermoflow, thermoflow.com;
p
TRNSYS, Thermal Energy System Spec., trnsys.com/;
q
Vali Energy, Belsim, belsim.com/business/solution/vali-energy/;
r
COCO, AmsterCHEM,
cocosimulator.org;sDWSIM, DWSIM, dwsim.inforside.com.br;tThermoCycle, ThermoCycle, thermocycle.net (all accessed on accessed on 8 April 2022).
Energies 2022,15, 4087 5 of 27
2. Methodology
This section shows the general modeling approach for thermal conversion processes
introducing different solver concepts. Subsequently, the exergy analysis theory is discussed.
The most important equations of the components required for modeling the applications in
Section 4as well as the respective exergy balance equations are presented. Based on these,
the implementation of the generic exergy analysis in TESPy is described in Section 3.
2.1. Simulation of Thermal Conversion Processes
Simulation of thermal conversion processes can be performed with different method-
ological approaches. In general, the behavior of the plant is represented with equations
modeling the physical processes in the plant’s components. For each component, mass
and energy balance equations must be fulfilled. Different approaches to the simulation
of such systems, i.e., sequential-modular (SM) approach and equation-oriented (EO) ap-
proach, have been developed since the 1970s, and the basic concepts have been extensively
discussed [
53
–
55
]. They are covered in a variety of textbooks as well, for instance, [
6
,
56
,
57
].
A short overview of these two basic approaches is provided. On top of that, the choice of
variables in the EO approach for thermal engineering applications is discussed.
The sequential-modular approach (SM) used, for example, by Aspen Plus or Chemcad
(see Table 1), starts at a specific point of the plant and solves the equations of the components
one after the other. After determining the change of the fluid’s state within a component
based on the parameters specified, the result is carried to the next one. While this approach
is easy to use and performs quickly for simple and linear plants, generic solutions are
more challenging to implement; the calculation routines differ depending on the state
at the inlet of a specific component and the parameters specified by the user. Therefore,
the order of specifications is restricted or requires iterative solution control. Especially
more complex plants with (multiple) recirculations require more solver iterations. Last, the
implementation of new components or additional parameters for existing components to
an existing software requires the physics applied and an individual solution procedure.
In contrast to the SM strategy, the plant is represented by a full system of equations in
the EO approach. It is built from the topology of the plant and the parameters applied and
is subsequently solved by an appropriate algorithm, e.g., Newton’s method. As the system
of equations represents both, the structure and the parameters specified, all equations
can be solved simultaneously without additional iterations or slowing down convergence
in case of recirculations. Furthermore, the user is free in the specification of topology
and parameters as long as the system of equations is well determined with respect to its
variables. The main disadvantage is that troubleshooting requires more experience as
the solver cannot point out a specific reason for failure. In addition, the solver requires
starting values for all variables. An initial guess for generic topologies and generic fluids is
challenging to implement and thus might require user inputs. However, running additional
simulations based on a converged solution leads to faster convergence.
The EO approach should be favored when modeling generic plants. A combination
of both approaches, e.g., by separating mass and energy balance equations from solving
equations regarding conversion of matter depending on the convergence state of the system
of equations, might improve the convergence stability of EO. However, such additions will
not be further investigated since the focus of this publication is on the implementation of a
generic exergy analysis.
Last, the variables of the system of equations for the EO approach are an essential
factor in determining the formulation of each equation. This approach often requires a
numerical calculation of derivatives, e.g., to determine the Jacobian matrix in the Newton
algorithm. Thus, the amount of numerically determined derivatives should be minimized
for performance reasons. The component parameters of a plant can be calculated once
the state of the fluid is fully determined for all inlets and outlets of all components. The
state of the pure fluid (or mixture) can be obtained by combining several parameters,
Energies 2022,15, 4087 6 of 27
for example, pressure and density, pressure and enthalpy, temperature and entropy, or
enthalpy and entropy. The combination of pressure and temperature is unfavorable as
additional information is required if a pure fluid is in the two-phase region. Additionally,
information on mass flow is required to solve energy balance equations. On top of that, the
fluid composition, e.g., mass fraction or mole fraction of the different chemical components,
is a crucial variable in case conversion of matter or mixing of different fluids occurs. The
changes in kinetic and potential energy can usually be neglected in thermal engineering.
Thus, given the general energy balance of a thermodynamic open system in steady-state
(Equation
(1)
), the choice of parameters to describe the state of the fluid falls to enthalpy
and pressure.
˙
W+˙
Q=∑
out
(˙
m·h)out −∑
in
(˙
m·h)in (1)
2.2. Exergy Analysis
Exergy is an extensive property giving information about the quantity and the thermo-
dynamic quality of any energy carrier within an thermal conversion process. Consequently,
only the exergy-based analysis enables comparability in evaluating material and energy
flows of an overall plant or specific components [58].
The total exergy rate is the product of mass flow rate and specific exergy, which
consists of the sum of physical
ePH
, chemical
eCH
, kinetic energy
eKN
, and potential exergy
ePT
. Effects associated with nuclear, magnetic, or electric processes are not considered [
59
].
˙
E=˙
mePH +eCH +eKN +ePT(2)
In the first step of implementing an exergy analysis in TESPy, only physical exergy
will be considered.
ePH =(h−h0)−T0(s−s0)=eT+eM(3)
Furthermore, it is possible to split physical exergy into thermal and mechanical parts
using the following Equations
(4)
and
(5)
[
60
]. In the first step, the fluid’s temperature is
changed isobarically to the ambient temperature to obtain the thermal exergy. In the second
step, the mechanical exergy is obtained by changing the fluid’s pressure isothermally to the
ambient pressure.
eT=(h−h(p,T0)) −T0(s−s(p,T0)) (4)
eM=(h(p,T0)−h(p0,T0)) −T0·(s(p,T0)−s(p0,T0)) (5)
Thermal conversion processes are mainly open systems (see Figure 1). In addition
to the energy flows of heat and work, there is also an exchange of material flows across
the system boundary. The time-related change in the exergy within the overall system
corresponds to the difference between all exergy flows entering and leaving the system,
minus the exergy destruction caused by irreversibilities.
dEtot
dt=∑
j
˙
Eq,j+∑
i
˙
Ew,i+∑
in
˙
Ein −∑
out
˙
Eout −˙
ED(6)
In the steady-state operation of a thermal conversion process, Equation
(6)
can be
simplified.
0=∑
j
˙
Eq,j+∑
i
˙
Ew,i+∑
in
˙
Ein −∑
out
˙
Eout −˙
ED(7)
The exergy destruction quantifies the thermodynamic inefficiencies associated with a
process. These can be caused by chemical reaction, heat transfer, mixing, and friction and
occur in every real system. The approach can thus be used to determine the components
with the highest exergy destruction and the processes causing them [61].
Energies 2022,15, 4087 7 of 27
total system boundary, tot
Figure 1. Exergy balance of an open system.
For a single component
k
within the considered system, each term in Equation
(7)
can
be assigned to the exergetic product or to the exergetic fuel [
62
]. The exergy destruction
within the component is the difference of both terms.
˙
ED,k=˙
EF,k−˙
EP,k(8)
The exergy efficiency of a component kis the ratio [63]:
εk=˙
EP,k
˙
EF,k
(9)
The sum of the exergy destruction in all components is equal to the exergy destruction
of the total system. In addition, unused flows across the system boundary can be taken
into account as exergy loss of the overall system.
˙
EF,tot =˙
EP,tot +˙
ED,tot +˙
EL,tot (10)
Finally, the exergy efficiency of the overall system is defined as:
εtot =˙
EP,tot
˙
EF,tot
=1−˙
ED,tot +˙
EL,tot
˙
EF,tot
(11)
Based on the information from the overall system, the exergy destruction ratios for a
component can be determined.
yD,k=˙
ED,k
˙
EF,tot
(12)
y∗
D,k=˙
ED,k
˙
ED,tot
(13)
Especially for larger systems with many components, it might be reasonable to aggre-
gate several components into functional groups for improved readability of the analysis
results. A functional group
G
consists of one or more components of the system, e.g., a
steam generator, which composes of an economizer, a steam drum, an evaporator, and a
superheater. In contrast to individual components, fuel and product exergy definitions
cannot be made for generic functional groups. Therefore, instead of
˙
EF
and
˙
EP
, the sum
of exergy carried into a functional group
˙
Ein,G
and the sum of exergy carried out of a
functional group
˙
Eout,G
are used. The difference between these two values must then be
the total exergy destruction of the functional group
˙
ED,G
. This value must also be equal
to the sum of exergy destruction values of all components
g
within that functional group
(Equation
(14)
). Therefore, the exergy destruction ratios of a functional group
yD,G
and
y∗
D,Gcan be calculated analogously as shown in Equations (12) and (13).
˙
ED,G=∑
g
˙
ED,g(14)
Energies 2022,15, 4087 8 of 27
2.3. Component-Based Thermodynamic Model
This section will formulate the equations used to model selected components of ther-
mal conversion processes and the corresponding exergy balances. The full set of equations
available for each component, as well as other components available in the software with
their respective exergy balance equations, are documented in the API documentation [
64
].
2.3.1. Turbomachinery
All turbomachinery components, i.e., turbines, pumps, fans, and compressors, are con-
sidered to be adiabatic components. Therefore, the power transferred
˙
W
can be calculated
as the product of mass flow
˙
m
and the change of enthalpy
h
between inlet (index in) and
outlet (index out) of the component.
0=˙
W−˙
m·(hout −hin)(15)
The isentropic efficiency is a key figure of adiabatic turbomachinery. For a turbine,
it describes the ratio of actual change in enthalpy to the theoretical maximum change in
enthalpy of the isentropic process for a given change of pressure. The enthalpy at the outlet
of the isentropic process
hout,s
is calculated from the outlet pressure and inlet entropy of
that process (Equation (17)).
0=ηs,t ·(hout,s −hin)−(hout −hin )(16)
hout,s =h(pout,s(pin ,hin)) (17)
The exergy balance of adiabatic expansion, therefore, is defined as follows. Three
different cases are distinguished, depending on the ambient temperature in the exergy
analysis [65].
˙
EP=
|˙
W|Tin,Tout ≥T0
|˙
W|+˙
ET
out Tin >T0≥Tout
|˙
W|+˙
ET
out −˙
ET
in T0≥Tin ,Tout
(18)
˙
EF=
˙
EPH
in −˙
EPH
out Tin,Tout ≥T0
˙
ET
in +˙
EM
in −˙
EM
out Tin >T0≥Tout
˙
EM
in −˙
EM
out T0≥Tin ,Tout
(19)
Similar concepts apply to compression machines, e.g., pumps and compressors. How-
ever, in contrast to expansion, the isentropic efficiency is defined reciprocally.
0=ηs,c ·(hout −hin)−(hout,s −hin )(20)
The exergy balance equations are similar to expansion processes as well. The compres-
sion machine draws power instead of supplying it.
˙
EP=
˙
EPH
out −˙
EPH
in Tin,Tout ≥T0
˙
ET
out +˙
EM
out −˙
EM
in Tout >T0≤Tin
˙
EM
out −˙
EM
in T0≥Tin ,Tout
(21)
˙
EF=
|˙
W|Tin,Tout ≥T0
|˙
W|+˙
ET
in Tout >T0≤Tin
|˙
W|+˙
ET
in −˙
ET
out T0≥Tin ,Tout
(22)
An essential component of thermal processes is a multistage steam turbine with
intermediate steam extraction for feedwater preheating. Such components can be modeled
using multiple turbine parts connected to each other with splitters between one part and
Energies 2022,15, 4087 9 of 27
the next. Therefore, it is assumed that the entire mass flow of steam leaves a turbine part
before entering the next one.
2.3.2. Heat Exchangers
Heat exchangers do only transfer heat. Heat losses to the ambient are neglected. The
heat provided by the hot side (index 1) of a heat exchanger is therefore fully transferred
to the fluid on the cold side (index 2) (Equation
(23)
). The heat transferred
˙
Q
is calculated
using Equation (24).
0=˙
min,1 ·(hout,1 −hin,1)−˙
min,2 ·(hout,2 −hin,2)(23)
0=˙
Q−˙
min,1 ·(hout,1 −hin,1)(24)
Regarding the exergy balance of heat exchangers, it is necessary to distinguish six cases.
Five cases are illustrated in Figure 2. The sixth variant is denoted as a purely “dissipative”
heat exchanger regarding exergy, as the hot side of the heat exchanger is cooled toward
T0
while the cold side is heated towards
T0
, but
T0
is not crossed. While this type of heat
exchanger has no exergetic product, it might be necessary to implement such a component
for economic or technical reasons.
˙
EP=
˙
ET
out,2 −˙
ET
in,2 (a) Tin,1,Tin,2,Tout,1,Tout,2 >T0
˙
ET
out,2 (b) Tin,1,Tout,1,Tout,2 ≥T0>Tin,2
˙
ET
out,1 +˙
ET
out,2 (c) Tin,1,Tout,2 >T0≥Tin,2,Tout,1
˙
ET
out,1 (d) Tin,1 >T0≥Tin,2,Tout,1,Tout,2
˙
ET
out,1 −˙
ET
in,1 (e) T0≥Tin,1 ,Tin,2,Tout,1,Tout,2
not defined (f) Tin,1,Tout,1 >T0≥Tin,2,Tout,2
(25)
˙
EF=
˙
EPH
in,1 −˙
EPH
out,1 +˙
EM
in,2 −˙
EM
out,2 (a) Tin,1,Tin,2,Tout,1,Tout,2 >T0
˙
EPH
in,1 −˙
EPH
out,1 +˙
EPH
in,2 −˙
EM
out,2 (b) Tin,1,Tout,1,Tout,2 ≥T0>Tin,2
˙
EPH
in,1 +˙
EPH
in,2 −˙
EM
out,1 −˙
EM
out,2 (c) Tin,1,Tout,2 >T0≥Tin,2,Tout,1
˙
EPH
in,1 +˙
EPH
in,2 −˙
EPH
out,2 −˙
EM
out,1 (d) Tin,1 >T0≥Tin,2,Tout,1,Tout,2
˙
EPH
in,2 −˙
EPH
out,2 +˙
EM
in,1 −˙
EM
out,1 (e) T0≥Tin,1 ,Tin,2,Tout,1,Tout,2
˙
EPH
in,1 −˙
EPH
out,1 +˙
EPH
in,2 −˙
EPH
out,2 (f) Tin,1,Tout,1 >T0≥Tin,2,Tout,2
(26)
Temperature
Heat transferred
Hot side fluid
Cold side fluid
(a)
(b)
(c)
(d)
(e)
Figure 2. Illustration of use cases for heat exchangers. Not illustrated: variant f.
In addition to the energy and exergy balances, essential parameters for the design of
heat exchangers are the terminal temperature difference values defining the temperature
Energies 2022,15, 4087 10 of 27
difference between the fluid on the hot side and the fluid on the cold side when entering and
leaving the component. In TESPy, all heat exchangers implemented are countercurrent heat
exchangers. The hot side inlet temperature difference
∆Tin
describes the temperature differ-
ence of the fluid entering the hot side to the fluid leaving on the cold side
(Equation (27))
.
Similarly, the hot side outlet temperature difference
∆Tout
is the temperature difference of
the fluid leaving the component on the hot side to the fluid entering on the cold side in
Equation (28).
0=∆Tin −T(pin,1,hin,1)+T(pout,2 ,hout,2)(27)
0=∆Tout −T(pout,1,hout,1)+T(pin,2 ,hin,2)(28)
For condensers, i.e., heat exchangers with the purpose of condensing a fluid, there
are two modifications applied. The condensing fluid on the hot side of the heat exchanger
leaves the component as saturated liquid, i.e., the vapor mass fraction
x
equals zero
(Equation
(29)
). The hot side inlet temperature difference is often referred to as terminal
temperature difference, which uses the saturation temperature at the hot side inlet instead
of the actual temperature in case the fluid enters the component as superheated vapor
(Equation
(30)
). This is done because the enthalpy difference during desuperheating is
much lower than during condensation. This also ensures that the cold side temperature
can never be higher than the temperature of the condensing fluid in the model.
0=hout,1 −h(pout,1,x=0)(29)
0=∆Tin −Tsat (pin,1 )+Tout,2 (30)
Last, the approach point temperature difference (Equation
(31)
) is an essential pa-
rameter. It describes the temperature difference to the boiling point
∆Tap
of the working
fluid for some heat exchangers, e.g., feedwater preheaters. In the economizer, it describes
the temperature difference between vaporization temperature in the steam drum and the
final preheating temperature and is thus crucial in the design to avoid evaporation in
the economizer.
0=Tsat(p)−∆Tap −Tap (31)
2.3.3. Energy Balance Closing Components
In many applications, it might be useful to have a component closing the energy
balance for the overall system, e.g., the solar field of a solar thermal power plant, as it effec-
tively serves as energy input without necessarily needing information about the secondary
side of the component. Therefore, the energy balance (Equation
(32)
) is applied. Other
examples for this component might be heat losses in pipelines or solar-thermal collectors.
0=˙
Q−˙
m·(hout −hin)(32)
The exergy balance is related to the exergy balance of the heat exchanger but needs to
distinguish between heat input and heat output:
˙
EP=
(not defined if dissipative
˙
ET
in −˙
ET
out else Tin,Tout ≥T0
˙
ET
out Tin ≥T0>Tout
˙
ET
out −˙
ET
in T0≥Tin ,Tout
˙
Q<0
˙
EPH
out −˙
EPH
in Tin,Tout ≥T0
˙
ET
in +˙
ET
out Tout >T0≥Tin
˙
ET
in −˙
ET
out +˙
EM
out −˙
EM
in T0≥Tin ,Tout
˙
Q>0
(33)
Energies 2022,15, 4087 11 of 27
˙
EF=
˙
EPH
in −˙
EPH
out Tin,Tout ≥T0
˙
ET
in +˙
EM
in +˙
ET
out −˙
EM
out Tin ≥T0>Tout
˙
ET
out −˙
ET
in +˙
EM
in −˙
EM
out T0≥Tin ,Tout
˙
Q<0
˙
ET
out −˙
ET
in Tin,Tout ≥T0
˙
ET
in +˙
EM
in −˙
EM
out Tout >T0≥Tin
˙
ET
in −˙
ET
out T0≥Tin ,Tout
˙
Q>0
(34)
2.3.4. Merge Points
Another important component is the merge in which two or more different incoming
streams (indexed
i
) are mixed with no transport of heat or power to the surroundings.
Therefore, the energy balance equation can be deducted.
0=∑
i
(˙
min,i·hin,i)−˙
mout ·hout ∀i∈inlets (35)
The exergy balance equations are defined with the analogous approach of the heat
exchanger exergy balance equations. For a mixing temperature
Tout
higher than the am-
bient temperature, the product is heating the colder fluids. For a mixing temperature
below the ambient temperature level, the product is cooling the hotter fluids. In addi-
tion, a distinction must be made in case an incoming stream is heated starting below the
ambient temperature or cooled starting above the ambient temperature. In these cases,
only change of exergy starting at the ambient temperature is accounted for in the product
exergy
(Equation (36))
. The fuel exergy is then defined analogously (Equation
(37)
). If the
temperature of the mixed stream is at ambient temperature, the component is considered
a dissipative one. In the current version of the software TESPy, it is assumed that all
mixed streams have the same chemical composition. Therefore, chemical exergies are not
considered.
Equations (36) and (37)
cover all possible cases. It should be noted, however,
that some of them are thermodynamically not meaningful.
˙
EP=
(∑i˙
mi·ePH
out −ePH
in,iTin,i<Tout &Tin,i≥T0
∑i˙
mi·ePH
out Tin,i<Tout &Tin,i<T0
Tout >T0
not defined Tout =T0
(∑i˙
mi·ePH
out Tin,i>Tout &Tin,i≥T0
∑i˙
mi·ePH
out −ePH
in,iTin,i>Tout &Tin,i<T0
Tout <T0
(36)
˙
EF=
(∑i˙
mi·ePH
in,i−ePH
outTin,i>Tout
∑i˙
EPH
in,iTin,i<Tout &Tin,i<T0
Tout >T0
∑i˙
EPH
in,iTout =T0
(∑i˙
EPH
in,iTin,i>Tout &Tin,i≥T0
∑i˙
mi·ePH
in,i−ePH
outTin,i<Tout
Tout <T0
(37)
2.3.5. Steam Drum
A drum is implemented to separate saturated liquid from saturated vapor in the
evaporation process. The drum’s energy balance is similar to that of a merge point with
two streams leaving the device. Additional constraints are applied, i.e., the saturated liquid
state at the first outlet stream and the saturated vapor state at the second outlet stream.
Note that blowdown is not be considered in this modeling approach.
0=∑
i
(˙
min,i·hin,i)−∑
j˙
mout,j·hout,j(38)
Energies 2022,15, 4087 12 of 27
0=hout,1 −h0(pout,1)
0=hout,2 −h00(pout,2)(39)
It is usually not meaningful to define an exergy efficiency just for a steam drum alone,
since this component is part of an evaporator.
2.3.6. Motors and Generators
The turbines of the plant power a generator, whereas pumps and fans require an
electrical motor to be powered. Assuming an efficiency for the generator
ηel,m
, its elec-
trical power output of a generator
˙
Wel,gen
is calculated according to Equation
(40)
. The
turbine power
˙
W
(Equation
(15)
) is multiplied with the efficiency factor
ηel,m
considering
mechanical and electrical losses.
˙
Wel,gen =˙
W·ηel,m (40)
Analogously, in Equation
(41)
, the electrical power input for a motor
˙
Wel,mot is determined
.
˙
Wel,mot =˙
W
ηel,m
(41)
3. Implementation of the Exergy Analysis in TESPy
Here, the implementation of a generic exergy analysis is presented. The software
TESPy is designed to simulate the steady-state operation of thermal conversion processes,
such as thermal power plants, heat pumps, or pipeline networks at the component level.
The software models typical units (e.g., turbines, pumps, heat exchangers), thus allowing
the user to build generic plant models [
66
]. An introduction to Python fundamentals is
given in [67].
Figure 3shows an overview of the structure of TESPy. Each simulation model is based
inside the network class. The class automatically builds a system of nonlinear equations
representing the plant’s topology and the boundary conditions specified, for instance,
cooling water temperature or turbine isentropic efficiency. The topology is derived from the
connections between the system’s components. Therefore, the connection class holds the
topological information by connecting a source component with a target component and
the fluid property data, i.e., mass flow, pressure, enthalpy, and mass fraction. In addition, it
is possible to connect pure energy streams, e.g., the power of a turbine or the power of a
pump, by the use of energy busses (class bus). Conversion losses can be considered with
constant efficiency values.
The system of equations is solved numerically with the multidimensional Newton-
Raphson algorithm for the system’s variables, which are mass flow, pressure, enthalpy, and
fluid mass fraction on every connection. As mass flow and fluid property data are available
for all connections after a converged simulation is obtained, all remaining variables of a
stream, e.g., pressure or temperature, and all component parameters, can be determined
with the fluid property module. The module holds all functions to calculate required fluid
properties, including calculation of physical exergy using CoolProp [
68
]. The online docu-
mentation provides extensive information on the component models and fluid property
calculations applied in the software.
Figure 4illustrates the procedure of the exergy analysis implemented in TESPy. The
user defines the busses of the TESPy network, which hold information on fuel and product
exergy and exergy loss. These are passed together with the network to create an instance of
the class ExergyAnalysis (see also Figure 3). Subsequently, the exergy analysis is carried
out using data of the ambient state, i.e., pressure and temperature. In the first step, physical
exergy, including thermal and mechanical exergy (see Equations
(5)
and
(4)
) of all fluid
streams, is calculated for the connection objects of the network. In the second step, the
exergy balance of all components (see Section 2.3) is evaluated.
Energies 2022,15, 4087 13 of 27
Based on the exergy balances of the components, the exergy balances of the busses
corresponding to the plant’s total fuel and product exergy and exergy loss are evaluated.
Furthermore, the balance equations for internal massless exergy transfer, e.g., a feed pump
that is directly driven by a respective turbine, are calculated. The individual conversion
factor of each component as part of a bus object is applied to the exergy flow, analogously
to the definition of generator and motor power in Equations
(40)
and
(41)
. The exergy
destruction within each component and their corresponding bus (if any) is summed to
calculate the network’s total exergy destruction
˙
ED,tot
. As all elements of the overall
network exergy balance are now known (Equation
(10)
), a consistency check can be carried
out, where the deviation
∆E
of total fuel exergy
˙
EF,tot
from the sum of total product exergy
˙
EP,tot
, exergy loss
˙
EL,tot
, and exergy destruction
˙
ED,tot
must be equal to zero. To account
for rounding errors, the absolute value of
∆˙
E
should be smaller than a threshold value
of
0.001 W
. When running the exergy analysis on a converged simulation, this condition
must be true. If it is not, some exergy streams in the overall system have not correctly been
accounted for in the exergy analysis setup.
Network
connections
components
busses
results
…
Connection
label
source: Component
source_id: 'in1', 'in2', …
target: Component
target_id: 'out1', 'out2', …
fluid property data
Component
label
parameters
…
Bus
label
components
conversion factors
…
ExergyAnalysis
network
E_F, E_P, E_L, internal_busses
results
…
…
exergy_balance()
…
get_physical_exergy()
analyse(pamb, Tamb)
generate_plotly_sankey_input()
…
…
solve()
fluid_properties module
T(p,h), s(p,h), v(p,h), µ(p,h)
inverse functions: h(p,T), …
-> CoolProp API calls
…
calc_physical_exergy():
exM = f(p,Tamb,pamb)
exT=f(p,h,Tamb)
exPH=exM + exT
Figure 3. Simplified structure of the TESPy package and the embedding of the exergy analysis.
Energies 2022,15, 4087 14 of 27
Component group
information (optional)
converged TESPy
Network instance
select Bus instances:
fuel, product, loss &
internal conversion
analyse Network
instance
define ambient state:
pamb, Tamb
calculate (physical)
exergy of Connections
calculate exergy
balance of Components
input data
output data
calculate exergy
balance of Components
on respective Busses
build DataFrame
for Network exergy
fuel, product and loss
build DataFrame
for Component exergy
balance results
build DataFrame
for Bus exergy
balance results
False
build component
group structure
from topology data
build DataFrame
for Component group
exergy balance result
provide sankey
input data
end
instanciate object of
class ExergyAnalysis
start
error message output
True
Figure 4. Simplified flowchart of the exergy analysis in TESPy.
Finally, all exergy balance data of the components and their respective busses, includ-
ing exergy efficiency as well as exergy destruction and exergy loss ratio, are provided to
the user as pandas DataFrames [
69
], which can easily be exported to any tabular format.
Furthermore, the physical exergy values of all connections are accessible in a DataFrame.
In addition, during the setup of the system’s components, the user can assign each
component to a functional group, as described in Section 2.2. A DataFrame is then provided
for all functional groups, including their information on the inflow
˙
Ein,G
and outflow
of exergy
˙
Eout,G
, the total exergy destruction as well as the exergy destruction ratios
according to their definitions in Equations
(7)
and
(12)
–
(14)
. If a component is not assigned
to any functional group, it will form a functional group by itself. With these data, a
graphical representation of exergy flows between the different functional groups of the
system in a Grassmann diagram [
70
] is enabled. For this purpose, the data is provided
as expected by the Python library plotly for its Sankey class [
71
]. The functional groups,
including individual components, that form their own functional group, are the nodes of
the Grassmann diagram. The edges represent the exergy flows. The values are shown in
a true-to-scale manner by the width of the edges. The exergy flows of the overall system
across the system boundary (see Equation
(10)
) are each represented by their respective
color. Exergy flows associated with a mass flow of a fluid, a heat rate, or work rate within
the system boundary are marked with a unique color. The software provides default color
codes; however, the user can specify the colors as desired. For more information, please
visit the respective section of the online documentation [
64
]. The diagram is provided in an
interactive format, showing additional information when hovering over nodes and edges.
The displayed data can be modified according to the user’s requirements following the API
of plotly.
Given the exergy streams crossing the system’s boundaries are well defined by the user,
changing any values in the process’s specifications or even modifying the plant’s topology
Energies 2022,15, 4087 15 of 27
does not require any changes regarding the exergy analysis setup. The analysis can be
performed again easily. The online documentation of TESPy provides several examples on
the usage and implementation of the exergy analysis as well.
4. Example Applications
Exergy analyses are carried out for three different applications to demonstrate the
new feature in TESPy. The Python scripts, the result reports, and the model validation are
available via zenodo.
• The so-called “Solar Energy Generating System VI” (SEGS) [72] , see Section 4.1
• Supercritical CO2power cycle [73] , see Section 4.2
• Refrigeration machine using air as working fluid [74] , see Section 4.3
Subsequently, the examples are briefly presented with the respective results generated
by the exergy analysis tool. The SEGS model is validated using the proprietary software
Ebsilon. The other two examples have originally been published in [
75
,
76
]. These contain
all data necessary to set up and evaluate the TESPy simulation. Therefore, the respective
TESPy models are compared to results from these publications instead of using Ebsilon.
The versions used are TESPy v0.6.0 [77] and Ebsilon 14.03.01.
4.1. Solar Energy Generating System
The SEGS in Southern California, USA, has been chosen as a real application. A
complete set of parameters and performance data is available in References [
78
,
79
] for this
concentrating solar power (CSP) plant.
4.1.1. Process Simulation and Validation
SEGS consists of three major subsystems: the solar field, the power cycle, and the
cooling water system. The TESPy model corresponds to the layout shown in Figure 5.
HPT1 HPT2 LPT1 LPT2 LPT3 LPT4 LPT5 G
Solar
Field
FWT
CON
CP
FWP
EV
RH
FP
SH
ECO
DR
12
3
4
5
6
7
8
9
10
11
12
13
14
15
16
23
24
32
33
34
35
36
37
45 46
47 58
70 71
72
75
76
77
78
79
62
63
2
17
18
19
22
26
40
42 44
50 55 61
LPP1
LPP2
LPP3
HPP1
HPP2
134
5
1
7
1
2
34 5 6
5
CWP
M
M
M
M
234
60
20
21
25
64
65
CT
38
41
48
51
52
53
59
66
Fan
M
73
74
27
28
29
30
31
LPsub1
LPsub2
LPsub3
HPsub1
HPsub2
39
43
49 54
57
56
Figure 5. Flow chart of SEGS implemented in TESPy.
Energies 2022,15, 4087 16 of 27
In the first subsystem, a eutectic mixture of diphenyl oxide and biphenyl, commercially
known as Therminol VP-1 [
80
], circulates as the heat transferring fluid (HTF). The heat rate
from the solar field is transferred through the heat exchangers of the steam generator and
the reheater to the power cycle. In the steam generator, the HTF is split into two parallel
heat exchanger trains. Each consists of a superheater, evaporator, and economizer. The
division into two parallel streams also applies to the reheater. For simplicity, the two trains
are modeled as a single one in both cases. A field pump ensures the circulation of the HTF.
The solar field is modeled as simple heat input. The exact layout of the solar field does not
influence the overall analysis.
The steam turbine drives the generator to provide electricity. The steam turbine is
divided into a high-pressure and a low-pressure turbine. In between, reheating is used. The
turbine sections are split into two and five parts to extract steam for preheating, respectively.
The power plant has three low-pressure and two high-pressure preheaters and a feedwater
tank (deaerator).
An induced draft cooling tower is used for recooling. Therefore, a cooling water cycle
is modeled, transporting the heat rate from the power cycle via a heat exchanger to the
ambient air. A fan provides the necessary mass flow rate of air.
The example covers the design state in full-load steady-state conditions and pure solar
mode. Table 2summarizes selected process and component parameters. For a complete set
of input parameters, see model documentation in [72].
The isentropic efficiencies of the turbines are taken from [
81
], which are derived them
from the stated properties for every stream in [
78
]. Due to inconsistencies in the primary
data, a reasonable isentropic efficiency for the fourth low-pressure turbine stage of 88%
was assumed.
Regarding the preheaters, the pressure drop on the hot side is neglected. The pressure
drop on the cold side has been calculated by using the stated properties for every stream
in [
78
]. This procedure has also been applied to the steam generator and reheater. The
temperature difference for the approach point in the steam generator is assumed to be
2 K
, and the pinch point temperature difference is at
5 K
. Regarding the temperature
specifications of the preheaters and the steam generator, the assumptions listed in Table 2
have been applied.
Table 2. SEGS—Parameters of the overall process and components [78,82].
Parameter Symbol Unit Value
HTF temperature T70 °C 390
HTF mass flow ratio ˙
m76/˙
m70 - 0.13
Steam temperatures T1,T7°C 371, 371
Steam pressures p1,p7bar 100, 17.1
Steam mass flow ˙
m1kg/s 38.97
Condensation pressure p17 bar 0.08
Pumps, efficiencies ηis,ηel,m % 70.0, 95.0
Generator, efficiency ηel,m % 97.0
Air fan, efficiency ηis % 60.0
Preheaters, upper temperature difference ∆Tt,u K 5
Subcoolers, lower temperature difference ∆Tt,l K 10
Pressure losses during the condensation on the hot side of the condenser are neglected.
For the cooling system, the parasitic power requirement is at
0.91 MW
[
78
]. Therefore, an
air cooling tower is implemented to cool the water in an intermediate cycle for the main
condenser of the power plant. With the assumptions made in the simulation, the parasitic
power requirements for the cooling system add up to 0.92 MW.
In addition to the TESPy model, an identical model has been built with the industrial
standard software Ebsilon. As TESPy’s thermodynamic library for fluid property calcula-
Energies 2022,15, 4087 17 of 27
tion CoolProp [
68
] is available for Ebsilon as well, it is used in both models. The library
contains Therminol VP-1 as an incompressible liquid, the air is calculated as pseudopure
fluid with the Helmholtz equation of state (HEOS) back-end, and for water, the IAPWS-95
formulation is implemented. The results obtained from both models are identical.
4.1.2. Results of the Exergy Analysis
The exergy-based analysis is carried out for the specifications used in the model
validation. The ambient temperature T0is 25 °C; the ambient pressure p0is 1.013 bar.
Table 3shows the exergy balance of the overall process for SEGS. The product exergy
corresponds to net power output. If the energy rate absorbed by the parabolic trough
collectors is specified as the exergetic fuel, this results in an exergy efficiency
εtot
of 66.7%
for the overall process. The real thermodynamic losses at the solar field, i.e., the difference
between the exergy of the incident global radiation and the exergy associated with the
absorbed heat rate, are thus not taken into account. The overall exergy loss
˙
EL,tot
is the
release of the cooling air to the environment. Compared to the overall exergy destruction,
the overall exergy loss is significantly smaller since the temperature of the released air, and
thus the physical exergy of the material flow, is low.
Table 3. SEGS—Results of the exergy analysis, overall process. All values given in MW.
˙
EF,tot ˙
EP,tot ˙
ED,tot ˙
EL,tot
47.63 31.77 15.37 0.49
The power plant simulation model consists of a large number of individual compo-
nents. For a better understanding of the causes of exergy destruction, components were
accumulated into functional groups. Results are presented in Table 4. Based on these
results, the Grassmann diagram feature of TESPy can be used to create Figure 6, which
illustrates the flow of exergy through the functional groups.
It can be seen that the low-pressure turbine (LPT) and the cooling water system (CW)
account for almost 50% of the overall exergy destruction rate. Especially the low value of
isentropic efficiency of the low-pressure turbine causes a high share of exergy destruction.
For the cooling water system, only the condensate is reused within the plant, which is close
to the ambient state. Therefore, most of the exergy is destroyed or lost to the ambient state.
Other quantitatively relevant contributions to the overall exergy destruction rate occur in
the steam generator (SG) and the high-pressure turbine (HPT). All other functional groups
account for less than 10% each, summing up to approx 24% in total.
Table 4.
SEGS—Results of the exergy analysis, functional groups. If not given, dimension of data
is MW.
Functional Group G˙
Ein,G˙
Eout,G˙
ED,GyD,G(%) y∗
D,G(%)
Low-pressure turbine (LPT) 36.01 31.94 4.07 8.6 26.5
Cooling water system (CW) 4.09 0.59 3.50 7.3 22.8
Steam generator (SG) 107.46 104.94 2.52 5.3 16.4
High-pressure turbine (HPT) 46.66 45.06 1.60 3.4 10.4
Reheater (RH) 43.64 42.41 1.23 2.6 8.0
Solar field (SF) 114.09 112.89 1.20 2.5 7.8
Low-pressure preheater (LPP) 5.25 4.51 0.74 1.6 4.8
High-pressure preheater (HPP) 10.13 9.79 0.33 0.7 2.2
Feedwater pump (FWP) 5.26 5.07 0.18 0.4 1.2
Energies 2022,15, 4087 18 of 27
E_F
SG HPT RH LPT total output power
LPP FWP E_P
CW
SF
HPP
E_D
E_L
Figure 6.
Machine-generated Grassmann diagram based on functional groups of SEGS. The value of
the exergy flows are shown in a true-to-scale manner by the width of the edges.
4.2. Supercritical Carbon Dioxide Power Cycle
As a second example, the variant c) of the supercritical
CO2
(s
CO2
) power cycles
reported by Penkuhn and Tsatsaronis [
75
] has been implemented and analyzed using
TESPy as all necessary input data, and the results of the exergy-based analysis are available.
4.2.1. Process Simulation and Validation
The investigated cycle is the recompression, recuperated cycle, with two compressors
and one turbine. The working fluid is heated and routed to the turbine. After expansion,
two recuperators are used to preheat the compressed
CO2
. After exiting the recuperators,
one part of the fluid is cooled and compressed before entering the cold side of the recupera-
tor 1. The remaining
CO2
is compressed without entering the cooler and mixed into the
reheated
CO2
stream from the first compressor and then routed through the recuperator 2
before entering the heater. The model created in TESPy corresponds to the layout shown
in Figure 7.
0
G
M
4
511
3131221
615
10
14
0
Compressor 1
Compressor 2
Cooler
Heater
Recuperator 1 Recuperator 2
Turbine
Figure 7. Flow chart of sCO2power cycle implemented in TESPy.
In contrast to the original study, the exergy balances of the heater and the cooler
are modeled without knowledge of the temperature profile of the non-
CO2
side (see
Section 2.3.3). The cooler is considered a dissipative component. Thus, the plant will not
have exergy losses. Furthermore, the distribution of the mass flow through compressor 1
and compressor 2 is assumed to be a result of the temperature values observed at the merge
point between the recuperators. The compressor 2 and recuperator 1 outlet temperatures
T11
and
T12
are thus specified to be equal (but unknown prior to the calculation) values.
Table 5summarizes selected process and component parameters. For a complete set of
input parameters, see model documentation [73].
Energies 2022,15, 4087 19 of 27
Table 5. sCO2power cycle—Parameters of the overall process and components [75].
Parameter Symbol Unit Value
Turbine inlet temperature T5°C 600
Turbine inlet pressure p5bar 250
Compressor inlet pressures p1,p10 bar 75, 75
Compressors, efficiencies ηis,ηel,m % 85.0, 95.1
Turbine, efficiencies ηis,ηel,m % 90.0, 98.0
Recuperators, lower temperature difference ∆Tt,l K 5
In this example, HEOS back-end of CoolProp was used as well. Although the data
from the original source are based on the REFPROP database and calculation, the relative
deviation between both libraries is less than
10−9
for enthalpy values and
10−12
for entropy
values. Consequently, the results agree except for numerical deviations without impacting
real-life operation. The highest deviation in thermodynamic properties is observed in the
turbine outlet temperature
T5
with
0.2 K
. All other (nonspecified) temperature values are
within less than
0.1 K
compared to the original data. Therefore, a deviation can be observed
in the physical exergy of the streams. Considering the overall cycle efficiency
ηth
, a relative
deviation of about 0.1% occurs.
4.2.2. Results of the Exergy Analysis
The exergy-based analysis is carried out for an ambient temperature
T0
of
25 °C
and an ambient pressure
p0
of
1.013 bar
. The results of the analysis are summarized in
Tables 6and 7.
Since the number of components in this application is low, the component
results are reported instead of the functional group results. The net power generation of
the process is associated with the product exergy
˙
EP,tot
. If the exergy rate supplied to the
process associated with the heat rate is considered as fuel exergy
˙
EF,tot
, the overall exergy
efficiency εtot is 64.6%. Figure 8illustrates the exergy flow rates within the process.
Table 6.
s
CO2
power cycle—Results of the exergy analysis, overall process. All values given in
MW
.
˙
EF,tot ˙
EP,tot ˙
ED,tot ˙
EL,tot
154.93 100.00 54.93 0.00
Table 7.
s
CO2
power cycle—Results of the exergy analysis, components. If not given, dimension of
data is MW.
Component k˙
EF,k˙
EP,k˙
ED,kεk(%) yD,k(%) y∗
D,k(%)
Compressor 1 47.49 40.20 7.29 84.6 4.7 13.3
Compressor 2 37.58 32.81 4.76 87.3 3.1 8.7
Heater 154.93 154.09 0.84 99.5 0.5 1.5
Recuperator 1 73.81 69.93 3.87 94.8 2.5 7.1
Recuperator 2 139.19 135.43 3.76 97.3 2.4 6.8
Turbine 197.19 185.07 12.12 93.9 7.8 22.1
Water cooler 22.28 nan 22.28 nan 14.4 40.6
The highest share of the overall exergy destruction rate can be observed in the cooler.
The exergy destruction rate of the rotating equipment—compressors and turbine—amounts
to a cumulative
24 MW
. The heater has the smallest share in the total exergy destruction
rate, as per definition in Equations
(33)
and
(34)
only the pressure losses account for the
exergy destruction rate in this type of heat exchanger. Note that the difference in the
definition of the heater’s exergy balance is the reason why a high relative deviation in
Energies 2022,15, 4087 20 of 27
the exergy destruction values between the results of this paper and the original study
(approx. −70%) is observed.
E_D
E_F Heater Turbine total output power E_P
CMP REC Water cooler
Figure 8.
Machine-generated Grassmann diagram based on functional groups of s
CO2
power cycle.
The value of the exergy flows are shown in a true-to-scale manner by the width of the edges.
4.3. Air Refrigeration Cycle
The third example focuses on a refrigeration cycle using air as working fluid originally
presented by Morosuk and Tsatsaronis [76].
4.3.1. Process Simulation and Validation
The process consists of a four-component refrigeration cycle with compressor, heater,
cooler, and turbine. The compressor and turbine are on a single shaft, and an inverter is
included in the original analysis to account for conversion losses of the electrical power
input to mechanical power of the shaft driving the compressor, as seen in Figure 9. The
cycle is applied to cool air. The heat sink is water at ambient conditions.
Table 8summarizes selected process and component parameters. For a complete set
of input parameters, see model documentation [
74
]. The input data match the original data
from [
76
]. However, due to the architecture of the TESPy solver and the exergy analysis
feature, losses on a single shaft with respect to the residual power
˙
Wcmp +˙
Wtur
cannot be
accounted in the same way as in the original study. Therefore, the residual power is first
determined without accounting for losses.
˙
Wcmp +˙
Wtur
ηel,original
=˙
Wcmp
ηel,m
+˙
Wtur ·ηel,m (42)
In a second step, equal efficiencies
ηel,m
for both, the turbine’s generator and the
compressor’s motor, are applied to the power bus to match the efficiency specifications
of the original study
ηel,original =
0.9 (see Equation
(42)
). This results in an efficiency
ηel,m
of 96.2%.
M
G
Compressor
Turbine
Cooling heat exchanger
Heat sink heat exchanger
0
1
2
22
21
3
4
12 11
Figure 9. Flow chart of the air refrigeration cycle implemented in TESPy.
Energies 2022,15, 4087 21 of 27
Table 8. Air refrigeration cycle—Parameters of the overall process and components [76].
Parameter Symbol Unit Value
Compressor inlet temperature T1°C −30
Compressor inlet pressure p1bar 1
Turbine inlet temperature T3°C 35
Turbine inlet pressure p3bar 5
Ambient air temperatures T21,T22 °C 25, 40
Refrigeration temperatures T11,T12 °C −10, −20
Compressor/turbine efficiencies ηis,ηel,m % 80.0, 96.2
For the original analysis, the used fluid property back-end is not documented. In the
TESPy model, the HEOS for pseudopure dry air is applied using CoolProp. Deviations in
the outlet temperature of the compressor and the turbine of 0.04% and
−
0.18%, respectively,
can be observed. A relatively high deviation is found in the enthalpy difference at the
cooling side heat exchanger with about 2%. For the other components, the maximum
deviation is at the heat sink heat exchanger with about 0.6% and 0.55% on the secondary
stream of the cooling heat exchanger. Due to the 2% deviation, the cycle’s mass flows
calculated with the TESPy model deviate by the same value as the governing equation for
mass flow is the heat transferred at that heat exchanger (see Equation (23)).
4.3.2. Results of the Exergy Analysis
The ambient state is not explicitly reported in the original study but can be derived
from the exergy tables. The ambient temperature
T0
is
25 °C
; the ambient pressure is
1.0 bar
.
Overall, the specific thermal exergy data of the streams are consistent with the reported
data from literature. The mechanical exergy matches for all streams, as all pressure values
are identical. The deviations in the thermodynamic properties, including the exergy values
between the original paper and the calculations reported here, are lower than 2.1% and
are caused by the different fluid properties functions used in each calculation. Since the
inverter is treated separately in the original study, high deviations are observed in the
compressor and turbine exergy analysis results.
The results of the exergy analysis are presented in Tables 9and 10. The total product
exergy is associated with the exergy rate required to cool the air. The total fuel exergy
represents the power input. This results in an overall exergy efficiency of 3.5%.
The compressor, the turbine, and the heat sink heat exchanger have the highest shares
of the overall exergy destruction rate, with 92.5%. This includes the mechanical losses on
the shaft, which account for 10.7% of the overall exergy destruction rate. The heat sink heat
exchanger has the smallest share of the overall exergy destruction rate. Figure 10 illustrates
the exergy flow rates within the process.
Heat sink heat exchanger
E_P
E_D
power input Compressor
heat sink E_L
Turbine
Cooling heat exchanger
cooling
E_F
Figure 10.
Machine-generated Grassmann diagram for the refrigeration cycle. The value of the exergy
flows are shown in a true-to-scale manner by the width of the edges.
Energies 2022,15, 4087 22 of 27
Table 9.
Air refrigeration cycle—Results of the exergy analysis, overall process. All values given
in kW.
˙
EF,tot ˙
EP,tot ˙
ED,tot ˙
EL,tot
439.80 15.51 412.22 12.07
Table 10.
Air refrigeration cycle—Results of the exergy analysis, components. If not given, dimension
of data is kW.
Component k˙
EF,k˙
EP,k˙
ED,kεk(%) yD,k(%) y∗
D,k(%)
Compressor 815.29 674.08 141.21 82.7 32.1 34.3
Cooling heat exchanger 46.30 15.51 30.79 33.5 7.0 7.5
Heat sink heat exchanger 107.31 12.07 95.24 11.2 21.7 23.1
Turbine 549.60 404.62 144.98 73.6 33.0 35.2
5. Conclusions
Exergy-based analyses are powerful tools for the thermodynamic and thermoeconomic
investigation of thermal conversion processes. Available simulation and analysis software,
proprietary as well as free and open-source, do not provide a fully integrated solution
for such analyses. Considering that such analysis requires knowledge of the topological
structure of a process and the results from a respective simulation, it is evident that exergy-
based analyses should be integrated as automatic analyses following the solution of the
system of equations of the simulation.
For the first time, open-source software can perform a generic exergy analysis for
thermal conversion processes. The automated exergy analysis allows evaluation for pro-
cesses above, below, and with a transition at
T0
. The study provides exergy efficiencies for
all possible application cases for all basic unit operations of thermal process engineering
(for the heat exchanger, for example, see Equations
(25)
and
(26)
). Furthermore, Grassman
diagrams can be generated.
The paper discussed the approach, summarized the equations and definitions used,
and validated the results with three example applications. The contributions of our research
can be summarized as follows.
•
A complete set of exergy balance equations, including definitions of fuel and prod-
uct exergy, for the most important components in thermal conversion processes
is implemented.
•
The paper presents a generic and reproducible workflow. It allows researchers to perform
exergy analyses based on any thermodynamic application modeled by the software.
•
The thermodynamic models and the results of the exergy analysis have been validated
based on published research.
•
Due to the fully integrated solution, changes in topology or parameter specifications
of an existing model do not require changes in the exergy analysis setup.
•
Providing the results in modern data structures enables further investigation or in-
tegration of external algorithms, e.g., exergy-based optimization procedures. For
instance, refs. [
83
,
84
] published implementations of optimization procedures using
first law analysis with TESPy.
• Updating and evaluating exergy analyses of published research is possible.
While the exergy analysis in the presented research as well as the software implemen-
tation do cover a wide range of thermal engineering applications, two important use cases
for exergy analysis have not yet been considered, in addition to the inclusion of calculation
of chemical exergies. These are:
•
Analysis of processes with conversion of matter, such as gas turbine power plants or
power-to-gas facilities.
• Provision of exergoeconomical analysis tools.
Energies 2022,15, 4087 23 of 27
The next step in the further development of the software is the implementation of
chemical exergy. Due to the modular structure, this step means to integrate the methods of
chemical exergy calculation for every stream of matter and to update the exergy balance
equations of the components to account for the change in chemical exergy. For the imple-
mentation of the exergoeconomic analysis, additional functionalities have to be added to
the component classes to define cost balances and auxiliary equations.
Author Contributions:
Conceptualization, F.W., M.H. and I.T.; methodology, F.W. and M.H.; software,
F.W. and J.M.; validation, F.W. and I.T.; formal analysis, F.W. and J.M.; investigation, F.W., J.M. and
M.H.; resources, M.H. and I.T.; data curation, F.W.; writing—original draft preparation, F.W., J.M.
and M.H.; writing—review and editing, F.W., M.H., I.T. and G.T.; visualization, F.W., J.M. and M.H.;
supervision, I.T. and G.T. All authors have read and agreed to the published version of the manuscript.
Funding:
We acknowledge financial support by Land Schleswig-Holstein within the funding pro-
gramme Open Access-Publikationsfonds.
Data Availability Statement:
All models and data used are available (see [
72
–
74
]). If you want
to report bugs use the respective Github repositories (see [
85
–
87
]). The software presented can be
downloaded via [77]. An online documentation [64] is available too.
Acknowledgments:
During writing this paper, a long-time employee of our department passed away
suddenly and unexpectedly. Christine Gharz supported our scientific activities with great engagement
for more than 25 years. George Tsatsaronis and Mathias Hofmann dedicate this article to her memory.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
Abbreviations
API Application programming interface
CMP Compressors
CON Condenser
CSP Concentrating solar power
CP Condensate pump
CT Cooling tower
CW Cooling water
CWP Cooling water pump
ECO Economizer
EO Equation-oriented
EV Evaporator
DR Drum
FP Field pump
FWP Feed water pump
FWT Feed water tank
HEOS Helmholtz equation of state
HPP High-pressure preheater
HPT High-pressure turbine
HTF Heat-transfer fluid
IAPWS International Association for the Properties of Water and Steam
LPP Low-pressure preheater
LPT Low-pressure turbine
NIST National Institute of Standards and Technology
REC Recuperators
RH Reheater
sCO2supercritical CO2
SH Superheater
SEGS Solar Energy Generating System
SG Steam generator
SM Sequential-modular
sub Subcooler
TESPy Thermal Engineering Systems in Python
Energies 2022,15, 4087 24 of 27
Latin symbols
˙
mMass flow, kg/s
cFlow velocity, m/s
˙
EExergy flow, W
gGravity, m/s²
hSpecific enthalpy, J/kg
pPressure, bar
˙
QHeat flow, W
sSpecific Entropy, J/kgK
TTemperature, °C
˙
WPower, W
xSteam mass fraction, -
yExergy destruction ratio, -
zHeight, m
Greek symbols
ηEnergetic efficiency
∆Difference
εExergetic efficiency
Subscripts and superscripts
0 Reference state
ap Approach point
CH Chemical
cmp Compressor
D Destruction
el Electrical
F Fuel
g gth component of functional group
gen Generator
G Functional group
in Inlet
k kth component
KN Kinetic
L Loss
m Mechanical
M Mechanical
min Minimum
mot Motor
out Outlet
P Product
PH Physical
PT Potential
s Isentropic
sat At saturation
T Thermal
tot Total
tur Turbine
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