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A Computer Program for the Exergoeconomic
Analysis of Energy Conversion Plants
vorgelegt von Pei Zhao
geb. in Jiangsu China
von der Fakultät III - Prozesswissenschaften der Technischen Universität Berlin
zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften
-Dr.-Ing.-genehmigte Dissertation
Promotionsausschuss: Vorsitzender: Prof. Dr. Georg Erdmann
Gutachter: Prof. Dr. –Ing. George Tsatsaronis Gutachter: Prof.Dr. Giampaolo Manfrida
Gutachter: Prof.Dr.Tetyana Morozyuk Tag der wissenschaftlichen Aussprache: 23.10.2015
Berlin 2015
i
Acknowledgements
This work has been conducted during my stay as a doctoral student at the Institute
for Energy Engineering and Protection of the Environmental of the Technische
Universität Berlin, which was supported by the Scholarship Council of China.
With this opportunity, I would like to express my sincere gratitude and
appreciation to my supervisor, Professor George Tsatsaronis. I appreciate his expert
guidance and mentorship, his patience and extremely valuable scientific advice. And
Prof Tatiana Morosuk was so kind and passionate, always willing to assist. I also
would like to thank Professor Giampaolo Manfrida for his recommendations and
detailed review. I still want to thank Professor Georg Erdmann for his willingness to
chair my thesis defense.
This work would not have been possible without the constant support of my
family, especially my dear wife Dr. Anyi Wang. I would like to express my honest and
eternal gratitude towards you and our son Max for having supported me through this
long journey. I shall never forget your encouragement and strong back at all levels.
Last but not least, I would like to thank to my colleagues, Dr. Fontina
Petrakopoulou and Dipl.‐Ing. Max Sorgenfrei, for providing me the reference cases of
power plant.
ii
Abstract
The exergoeconomic analysis is an important deep‐going evaluation method for
energy conversion systems. It is a continuation of the energetic and exergetic analysis
and a combination of the exergy and economic analysis. In this work, a computer
program was developed to facilitate the application of the exergoeconomic analysis
to the power plants. The initial data are input to the program, then the calculation of
enthalpy and entropy of each material flow is attained by an ideal gas model and the
steam table formulation IAPWS‐IF97. The values of physical and chemical exergy of
the streams are obtained by their definitions and the specific values of the reference
state. Finally, the fuel and product exergy, the exergy destruction and the cost rates
associated with these exergies of each component are calculated by the program
with the SPECO approach.
Three reference cases: a combined cycle power plant, an IGCC plant with CO2
capture and a compression refrigeration machine are introduced to test the program.
Compared to the reference values, the average relative errors of the enthalpy,
entropy, exergy and specific cost for each material flow, the fuel exergy, the product
exergy and the cost rates of fuel and product for the component, are all below 1.5%.
The exergy destruction and the cost rate associated with the exergy destruction can
correctly reflect the thermodynamic inefficiencies and the cost related to these
inefficiencies of the energy conversion systems.
The exergoeconomic analysis program affords a direct connection to the process
simulation software. When complex energy systems and separated exergy forms are
taken into consideration such as the IGCC power plant with CO2 capture, the program
is more effective. Although the degree of accuracy of the program can be further
improved in the future, it is still appropriate to evaluate an energy system in general
for now.
iii
TableofContents
List of Tables .......................................................................................................... vii
List of Figures ...........................................................................................................x
Nomenclature ......................................................................................................... xi
1. Introduction ........................................................................................................ 1
2. Simulation and evaluation software for energy conversion systems ................... 4
2.1 Process simulation software ................................................................................ 4
2.2 Advantages and disadvantages of existing simulation software ......................... 6
2.2.1 Ebsilon Professional ....................................................................................... 8
2.2.2 Aspen Plus ...................................................................................................... 9
2.3 The lack of exergoeconomic analysis in process simulation software ........... 11
3. Energy and exergy based analyses .................................................................... 12
3.1 State of the art ................................................................................................... 12
3.2 Exergy‐based analyses ........................................................................................ 15
3.2.1 Exergetic analysis ......................................................................................... 15
3.2.2 Economic analysis ........................................................................................ 16
3.2.3 Exergoeconomic analysis ............................................................................. 18
3.2.4 Environmental analysis ................................................................................ 20
3.2.5 Exergoenvironmental analysis ..................................................................... 21
3.3 Advanced exergy‐based analyses ....................................................................... 22
4. The algorithm and mathematical model ........................................................... 23
4.1 Description of algorithm model ......................................................................... 23
4.1.1 Program process flowchart ......................................................................... 26
4.1.2 Two significant data structures ................................................................... 27
4.1.2.1 Set of streams’ properties .................................................................... 28
4.1.2.2 Set of components ............................................................................... 31
4.1.2.3 General form of the component data structure .................................. 32
iv
4.2 Thermodynamic properties calculation ............................................................. 36
4.2.1 IAPWS‐IF97 for thermodynamic properties calculation of water and steam
.............................................................................................................................. 36
4.2.2 Thermodynamic properties calculation of some selected substances ....... 39
4.3 Exergetic analysis ............................................................................................... 41
4.3.1 Reference state ............................................................................................ 41
4.3.2 Physical and chemical exergy ...................................................................... 42
4.4 SPECO approach for exergoeconomic analysis .................................................. 47
4.4.1 Identification of exergy streams .................................................................. 48
4.4.2 Definition of fuel exergy and product exergy.............................................. 48
4.4.3 Cost balance ................................................................................................ 52
4.4.4 Auxiliary equations ...................................................................................... 54
4.4.5 Matrix formulation ...................................................................................... 61
5. Implementation of the energy and exergy based analyses program for the
energy conversion systems ................................................................................... 65
5.1 Combined cycle power plant .............................................................................. 65
5.1.1 Energetic analysis ........................................................................................ 66
5.1.2 Exergetic analysis ......................................................................................... 67
5.1.3 Exergoeconomic analysis ............................................................................. 70
5.1.4 Error analyses .............................................................................................. 72
5.1.4.1 Energetic analysis ................................................................................. 72
5.1.4.2 Exergetic analysis ................................................................................. 73
5.1.4.3 Exergoeconomic analysis ..................................................................... 74
5.2 IGCC Plant ........................................................................................................... 75
5.2.1 Energetic analysis ........................................................................................ 77
5.2.2 Exergetic analysis ......................................................................................... 79
5.2.3 Exergoeconomic analysis ............................................................................. 81
5.2.4 Error analyses .............................................................................................. 84
5.2.4.1 Energetic analysis ................................................................................. 84
v
5.2.4.2 Exergetic analysis ................................................................................. 84
5.2.4.3 Exergoeconomic analysis ..................................................................... 85
5.3 Simple refrigeration machine ............................................................................. 86
5.3.1 Energetic analysis ........................................................................................ 86
5.3.2 Exergetic analysis ......................................................................................... 86
5.3.3 Exergoeconomic analysis ............................................................................. 88
5.3.4 Error analyses .............................................................................................. 89
5.3.4.1 Energetic analysis ................................................................................. 89
5.3.4.2 Exergetic analysis ................................................................................. 90
5.3.4.3 Exergoeconomic analysis ..................................................................... 91
6. Conclusion ........................................................................................................ 92
6.1 Energetic Analysis ........................................................................................... 92
6.2 Exergetic analysis ............................................................................................ 93
6.3 Exergoeconomic analysis ................................................................................ 94
6.4 Summary and future work .............................................................................. 95
Appendix A ........................................................................................................... 97
Flow charts and simulation results of this program and the reference paper ........ 97
A.1 The combined cycle power plant ....................................................................... 98
A.2 The IGCC power plant with CO2 Capture ........................................................ 103
A.3 The compression refrigeration machine .......................................................... 111
Appendix B ..........................................................................................................113
Exergy rates and cost rates associated with fuel and product for defining
component models at steady state operation ....................................................... 113
Appendix C ..........................................................................................................121
Economic Analysis for the IGCC power plant with CO2 Capture ............................ 121
Appendix D ..........................................................................................................126
Thermal properties calculation of Ammonia ......................................................... 126
D.1 The vapor pressure equation for the Liquid‐Vapor coexisting phase ............. 126
D.2 The density for the Saturated Liquid and Vapor ............................................. 126
vi
D.3 The latent heat of vaporization and the enthalpy of the Saturated Liquid and
Vapor ...................................................................................................................... 127
D.4 The entropy of the Saturated Liquid and Vapor .............................................. 127
Reference ............................................................................................................128
vii
ListofTables
Table 2.1 Software for process simulation or thermophysical properties evaluation ... 5
Table 2.2 Several features of selected simulation software .......................................... 7
Table 4.1 Characteristics’ variables in a stream abstract data type ............................. 30
Table 4.2 Structure of components’ set ....................................................................... 31
Table 4.3 General form of component data structure ................................................. 35
Table 4.4 Basic equations and backward equations from IAPWS ................................ 37
Table 4.5 Comparisons between calculated results and international steam tables .. 38
Table 4.6 Properties of selected working fluids at Tref=298.15K and pref=1.0 bar ...... 40
Table 4.7 Constants for Eqs. (4.5) through (4.8) .......................................................... 40
Table 4.8 Standard molar chemical exergy for selected substances at
Tref=298.15 K(pref=1.019 atmfor ModelⅠ andpref=1.0 atmfor ModelⅡ) ..... 43
Table 5.1 Selected thermal results from the reference paper and the program ......... 66
Table 5.2 The selected results of the generated or supplied work .............................. 67
Table 5.3 The results of exergies for some selected streams ...................................... 68
Table 5.4 Selected exergetic results at the component level ...................................... 69
Table 5.5 The cost rates of selected streams ............................................................... 70
Table 5.6 Selected results of exergoeconomic analyses at component level .............. 71
Table 5.7 Selected thermal results from the reference paper and the program ......... 77
Table 5.8 The selected results of the generated or supplied work .............................. 78
Table 5.9 The results of exergies for some selected streams in IGCC plant ................. 79
Table 5.10 Selected exergetic results at the component level for IGCC ...................... 80
Table 5.11 The cost rates of some selected streams ................................................... 82
Table 5.12 Selected results of exergoeconomic analyses at component level ............ 83
Table 5.13 Selected thermal results of the refrigeration machine .............................. 86
Table 5.14 The results of exergies for the refrigeration machine ................................ 87
Table 5.15 Selected exergetic results at the component level .................................... 87
viii
Table 5.16 The cost rates of selected streams for the refrigeration machine ............. 88
Table 5.17 Selected results of exergoeconomic analyses at component level ............ 89
Table A.1.1 Results at component level for the combined cycle power plant from the
program ................................................................................................................ 99
Table A.1.2 Results at component level for the combined cycle power plant from the
reference paper .................................................................................................. 100
Table A.1.3 Results at stream level for the combined cycle power plant .................. 101
Table A.1.4 Results at stream level for the combined cycle power plant .................. 102
Table A.2.1 Results at stream level of the IGCC power plant with CO2 capture from
the program ....................................................................................................... 104
A.2.2 Results at stream level of the IGCC power plant with CO2 capture from the
reference ............................................................................................................ 107
Table A.2.3 Results at component level of the IGCC plant with CO2 capture from the
program .............................................................................................................. 109
Table A.3.1 Exergetic results of refrigeration machine from the program ................ 111
Table A.3.2 Exergoeconomic results of refrigeration machine from the program .... 111
Table A.3.3 Exergetic results of refrigeration machine from the reference............... 111
Table A.3.4 Exergoeconomic results of refrigeration machine from the reference ... 112
Table A.3.5 Thermodynamic data of streams from the program .............................. 112
Table A.3.6 Thermodynamic data of streams from the reference paper .................. 112
Table B.1 Exergoeconomic models of selected components used for programming 113
Table C.1 Parameters and assumptions used in the calculation of economic analysis
(all monetary values are expressed in mid‐2007 dollars) .................................. 121
Table C.2 Calculation of the allowance for funds used during construction (end‐2016
dollars) of IGCC power plant .............................................................................. 122
Table C.3 Annual tax depreciation amount for a life period of 20 years ................... 122
Table C.4 Year by year capital recovery schedule for the IGCC case .......................... 123
Table C.5 Year by year revenue requirement analysis for the IGCC case ................... 124
ix
Table C.6 Total investment cost rates of components for IGCC power plant ............ 125
x
ListofFigures
Figure 4.1 Algorithm flowchart .................................................................................... 26
Figure 4.2 Schematic of a component in a thermal system ......................................... 33
Figure 4.3 Component models in other process simulation software ........................ 34
Figure 4.4 Regions and equations of IAPWS‐IF97 ........................................................ 36
Figure 4.5 Schematic of a component to define fuel and product .............................. 49
Figure 4.6 The productive structure for the component shown in Fig. 4.5 ................. 50
Figure 4.7 Schematic of a heat exchanger ................................................................... 55
Figure 4.8 Schematic of a mixing device ...................................................................... 57
Figure 4.9 Schematic of a gasifier ................................................................................ 58
Figure 4.10 Schematic of a dissipative component ..................................................... 60
Figure 4.11 The cost equations in a matrix form ......................................................... 62
Figure 5.1 Relative errors of energetic results for the combined cycle power plant ... 72
Figure 5.2 Relative errors of exergetic results for the combined cycle power plant ... 73
Figure 5.3 Absolute values comparison of the specific costs of fuel and product for
the combined cycle power plant.......................................................................... 74
Figure 5.4 Absolute values comparison of the specific costs of streams .................... 75
Figure 5.5 Process flowchart of IGCC plant from the reference paper ........................ 76
Figure 5.6 Relative errors of energetic results of the IGCC case .................................. 84
Figure 5.7 Relative errors of exergies of the IGCC case ............................................... 85
Figure 5.8 Relative errors of energetic results for the compression refrigeration
machine ................................................................................................................ 90
Figure 5.9 Relative errors of exergetic results for the refrigeration machine .............. 90
Figure 5.10 Relative errors of the exergoeconomic results for the refrigeration
machine ................................................................................................................ 91
Figure 6.1 Exergy destructions of primary components of the combined cycle power
plant ..................................................................................................................... 94
xi
Nomenclature
Symbols
Ar argon B environmental impact rate [Pts/h]b specific environmental impact [Pts/GJ]
C cost rate [€/h] c specific cost [€/GJ] Cp constant‐pressure specific heat [J/K] Cv constant‐volume specific heat [J/K]
E exergy [J] e specific exergy [J/kg] E exergy rate [MW]
f exergoeconomic factor [%]
fb exergoenvironmental factor [%]
G Gibbs function [J] g specific Gibbs function [J/kg] H enthalpy [J] h specific enthalpy [J/kg] He Helium
HHV higher heating value [kJ/kg] LHV lower heating value [kJ/kg] m mass flow rate [kg/s]
NH3 ammonia
n polytropic exponent [‐] p pressure [bar] Q heat transfer [J] R gas constant [J/kg K] r relative cost difference [%] rb relative environmental impact difference [%]
S entropy [J/K] s specific entropy [J/kg K] T temperature [K]
TCO total concentration [kg/kg] U internal energy [J] u specific internal energy [J] V volume [m3]
v specific volume [m3/kg]
W work [J]
xii
W power [W]
X dryness [‐] x concentration [kmol/kmol, kg/kg]
Y component‐related environmental impact [Pts/h]
y exergy destruction ratio [%] Z investment cost rate [€/h]
coefficient of thermal expansion [‐]
exergetic efficiency [%] η efficiency [%] ρ density [kg/m3]
annual operating hours [h]
Indices
AV avoidable a,b,c separated exergy forms
c critical CH chemical exergy
CO construction environmental impact
D exergy destruction DI disposal environmental impact
dc dissipative component
DAF dry and ash free fuel EN energy stream
EN endogenous EX exogenous e exiting F exergy of fuel IC investment cost
in inlet i,j exergy flow indices k,Y,W component indices
L exergy losses l liquid M mechanical exergy
max maximal
OM,O&M operating and maintenance environmental impact
out outlet P exergy of product PH physical exergy q heat transfer ref reference
xiii
T thermal exergy
tot overall system
UN unavoidable w generating power 0 thermodynamic enviroment
Abbreviations
ASU air separation unit AGR acid gas removal
CC carrying charge CExC cumulative exergy consumption
ECT exergetic cost theory EEA exergy economics approach
EES engineering equation slover EFA engineering functional analysis FEA first exergoeconomic approach
HRSG heat recovery steam generator
IAPWS International Association for the Properties of Water and Steam
IF97 Industrial Formulation 1997
IGCC integrated gasification combined cycle
ISO International Organization for Standardization LIFOA Last‐In‐First‐Out approach PEC purchased equipment cost
SAA structural analysis approach SPECO specific exergy costing TFA thermoeconomic functional analysis
TRR total revenue requirement
WGS water gas shift
1
1.Introduction
The exergoeconomic analysis is a further evaluation method of the energy
conversion system principally focused on the cost rates of exergy streams and the
cost rates of exergy destructions. As an essential complement to the traditional
thermodynamic analysis (i.e. energy‐related analysis), a rapid growth of
exergoeconomic analysis occurred since 1980s. In the last decades, the
exergoeconomic analysis is more esteemed by the researchers; a lot of applications
using exergoeconomic analysis are presented. Simultaneously, various process
simulation software have been developed almost at the same period; one of the
most outstanding programs is Aspen Plus. In the past years, the emphases of the
improvements of the simulation programs are all laid on the First Law of
thermodynamics, the exergy‐based analyses are seldom covered and the
exergoeconomic analysis are not involved. Certainly, the energy‐based analyses are
the core and the foundation of all thermodynamic evaluation methods; the closer to
the reality is the simulation the better. However, for efforts of many years the degree
of accuracy of the energy‐based evaluation of simulation software is very high and
stable. Therefore, the further evaluation included exergetic analysis, exergoeconomic
analysis and exergoenviromental analysis should be considered in the simulation
program according to the researchers’ demand. For now, most researchers combined
Matlab, Excel or other computer‐assisted software with a process simulation
software to solve exergy‐based analyses problems that require exhaustively
understanding of the whole procedure of exergy‐based analyses and massive coding
works.
Hence, this thesis intends to develop a computer program for exergy‐based
analyses especially for the exergoeconomic analysis of the energy conversion systems.
To realize the foregoing purpose, the following works have been accomplished:
2
1. A database of parameters for the thermal properties calculation of usual
materials is built. The equations of the energetic analysis include ideal
gas model equations from Gatex, the basic equations and backward
equations of steam and water from IF97, etc.
2. A library of exergetic and exergoeconomic models of components is
found by the methodologies of thermal design and optimization (Bejan
A., Tsatsaronis G., Moran M. 1996) and the SPECO approach (Lazzaretto
A, Tsatsaronis G, 2006). The equations of the exergetic analysis and
exergoeconomic analysis are formulated with exergy balance, cost
balance and the fuel and product definitions.
3. The resulting matrix of the linear equations is solved by Gauss‐Jordan
elimination and the exergetic, and exergoeconomic variables are
calculated.
4. Three reference energy conversion systems are introduced to examine
the simulated calculations for each part of the program. The results of
the energetic, exergetic and exergoeconomic analyses are compared
with the corresponding data from the references. The relative errors of
the results and the causes of these differences are discussed.
All the coding work is completed in C++ programming language with the
Microsoft visual studio 2008. The organization of the dissertation is ordered
according to the exergoeconomic analysis procedure. Chapter 2 presents some
frequently used simulation and evaluation software for power plants and discusses
their advantages and disadvantages. Chapter 3 provides a comprehensive description
of conventional exergy‐based methods used in the exergoeconomic analysis program
and a short description of advanced exergy‐based methods not involved in the
software. Chapter 4 presents the structure of the program, all the algorithms and
mathematical models of components. All the equations and variables and the
original data resources are included. Chapter 5 presents some selected calculation
3
results of three referred energy systems contained a combined cycle power plant, an
IGCC power plant with CO2 capture and a compression refrigeration machine. The
comparison of the final results and the error analysis are considered at the same
time. Conclusions and further work are presented in Chapter 6. The process flow
charts of three cases, the unabridged results of each part of exergoeconomic analysis,
the economic analysis results for IGCC plant and all the exergoeconomic models of
components are listed in appendices.
4
2. Simulation and evaluation software for energy
conversionsystems
Nowadays, process simulation is used for the design, development, analysis,
optimization and failure diagnosis of technical processes such as: petroleum refining,
chemical plants, environmental systems, power plants, pharmacy, biological
processes, and similar technical functions. In the 1970s, related to the development
of the computer science and programming languages, process simulation made a
rapid progress simultaneously. However, the basis of process simulation which is the
modelling of chemical properties for working fluids began much earlier with the
development of thermodynamics (Rhodes C.L., 1996), notably the cubic equation of
states were precursory events of the 19th century. Various simulation and evaluation
software are published for distinct fields by different companies at present. Some of
them only can be applied to a very narrow area even a specific equipment (such as
piping system) or a particular reaction process, for example, BatchColumn from
ProSim; while some others have a broad range of applications for many industries
and can simulate very complex process like Aspen Plus from Aspen Technology. For
energy conversion systems, the modern simulation software is Aspen Plus,
Thermoflow, Gate‐cycle, ProSimPlus and Ebsilon Pro, etc.
2.1Processsimulationsoftware
Process simulation is a model‐based representation, which usually means a more
convenient, efficient and economical process for similar performance of an elaborate
process is built for prediction or guidance. Thus, the process simulation always uses
mathematical models of chemical, physical, biological, and other processes which
introduce approximations and assumptions or allow interpolation and extrapolation
within certain limits for facilitating the description of the process. There are two
types modeling method for existing process simulation software (Gani R.,
5
Pistikopoulos E.N., 2002); 80 percent of commercial simulation systems use the
sequential modular method which builds a mathematical model for each component
as a module, called unit operations, positioned and connected by product or streams
between modules; the others gain the required information by solving the
simultaneous equations; and the rest few combine the two methods together mostly
for the simulation of dynamic processes. In the program of this thesis all equations
are solved simultaneously, in which each component as a module has a set of
equations for the exergetic analysis, the definition of the P rule and F rule and the
formulation of auxiliary equations (elaborated below in Section 4.1.2.2‐4.1.2.3 and
4.4.2‐4.4.4) since these manipulations mainly based on the component level. Besides,
the calculation of the specific cost rates for the exergoeconomic analysis requires the
simultaneous equations (cost balance equations with auxiliary equations) which is
expressed as a matrix discussed in Section 4.4.5.
In general, the simulation software solves the mass and energy balance of the
process to find a stable operating point first, and then optimal conditions for a
considered process are determined which is essentially an optimization problem
ordinarily solved in an iterative process in computer. The following table lists some
common simulation software for process simulation or thermophysical properties
evaluation.
Table 2.1 Software for process simulation or thermophysical properties evaluation
Software Developer ApplicationsAriane ProSim Utilities management and power plant
optimization
ProSimPlus ProSim Process simulation and optimization
Aspen Plus Aspen Technology Process simulation and optimization
Aspen
HYSYS
Aspen Technology Process simulation and optimization
CADSIM
Plus
Aurel Systems Inc. Steady‐state and dynamic process simulation
ChemCAD Chemstations Software suite for process simulation
Ebsilon STEAG Process simulation and optimization
6
Professional
Cycle‐Tempo Asimptote Thermodynamic analysis and optimization of
energy conversion systems
Design II WinSim Inc. Process simulation
gPROMS PSE Ltd Advanced process simulation and modelling
PRO/ II SimSci Dynamic and steady‐state process simulation
system
VMGSim VMG General Purpose, Static, Sequential‐Modular
Process Simulator
Gate‐Cycle GE‐Energy Power plant performance prediction
Thermo‐Calc Thermo‐Calc
Software
Thermodynamic properties calculation
EES F‐Chart Engineering Equation Solver
REFPROP NIST Thermodynamic properties calculation
FactSage ThermFact Inc. &
GTT‐Technologies
Thermochemical Database System
HSC
Chemistry
Chemistry‐Software Thermodynamic calculation
2.2 Advantages and disadvantages of existing simulation
software
The functions of today’s simulation software become more powerful than before,
and lots of engineering problem can be managed by simulation software, such as:
1. New product and process development in which the amount of experimental
investigation can be reduced.
2. The project design included concept design, equipment design, and process
design. The simulation software can provide design parameters and compare
different design options so that saving time for engineers.
3. Optimization of the process operation conditions. The information can make full
use of existing equipment or locate the reasonable modification.
4. Fault diagnosis for the production process.
5. Economic evaluation of the simulation process.
7
6. Advanced process control, production management and operator training.
Existing process simulation software is normally with different focuses on
functions mentioned above. Some even only have one function, like Thermo‐Calc
that can calculate the thermodynamic properties. However, some simulation
software contains comprehensive functions, for example, ProSimPlus and Aspen Plus.
Several features of selected simulation software are compared in following Table 2.2.
Table 2.2 Several features of selected simulation software
Software Model
library
Application
field
Convergence
speed
Accuracy Model type Learning
cost
Aspen Plus Large Full range of
process
industries
Medium Very high Sequential
modular
High Very
complic‐at
ed
ChemCAD Small Mainly in
colleges and
universities
Very fast Low
Basically
needs
Sequential
modular
Low
Easy to
use
PRO/ II Large Oil refining
and
Chemical
Industry
Medium High Sequential
modular
High
HYSYS Large Oil refining
and
Chemical
Industry
Fast High Sequential
modular
High
Gatecycle Medium Power plant
design and
analysis
Fast High Sequential
modular
Medium
EES Small Chemical
equations
Very fast High Simultaneous
equations
Low
Ebsilon
Professional
Medium Power
system
Fast High Sequential
modular
Medium
Through the above table it can be seen, the process simulation software that
has a broad range of applications and powerful functions usually has relatively slow
convergence speed, and more complex operation, but more accurate results, more
closer to the actual industry. In addition, the software with narrow limits has rapid
8
convergence speed and is very easy to use but with low accuracy of results, more for
teaching and research. Moreover, most of the process simulation software is an open
system that can interact with the users by input and output files or user‐defined
components.
Generally, PRO/II is more accurate in the oil refining industry owing to the large
number of experiential data from factories in its model library. While Aspen Plus has
a better performance in the chemical industry for steady‐state process simulation
and HYSYS like PRO/II is often used for oil refining, but its advantage is in a dynamic
process simulation. The Design institutes and industries prefer to use these kinds of
simulation software. However, the database of ChemCAD is much smaller compared
to above‐mentioned software but the operation interface of ChemCAD is friendly so
that it usually adopted by colleges and universities. The Gatecycle and Ebsilon
Professional are specific simulation software aimed at power systems and suitable
for both industries and universities. Instead, EES is seen more like a engineering tool
for sovling the chemical equations.
2.2.1EbsilonProfessional
In this thesis, the first application in Section 5.1 that is the combined cycle power
plant was simulated by the simulation software Ebsilon Professional (Petrakopoulou
F, 2011). Ebsilon is the abbreviation for “energy balance and simulation of the load
response of power generating or process controlling network structures” (Ebsilon
Professional 2014). Ebsilon software is developed by STEAG Company that is “all in
one” solution for power plant projects. It can be used for engineering, acquisition
and planning for all kinds of power plants and other thermodynamic processes.
Ebsilon Professional comes with a powerful graphical editor and enables the
balancing of single components, groups of components, subsystems and complete
systems, regardless of the fact, whether these components or systems form an open
or a closed circuit. The graphical user interface is used to model cycles. The
9
calculation core of Ebsilon Professional creates and solves a set of equations for the
cycle.
The process simulation results can be imported in Ebsilon Professional or
exported from Ebsilon Professional. The data in the output file given by Ebsilon
Professional contains the full information of the combined cycle power plant, e.g.,
the flow sheet of the plant, the thermal properties of each material streams and
energy streams, the compositions of each working fluid. The exported file could be
Excel, DLL or Text files. Therefore, the program developed for exergoeconomic
analysis in this thesis will not simulate the combined cycle again but load the
exported text files from Ebsilon Professional. This can be achieved on a necessary
condition that the integration of the division of operation units is similar. In general,
the simulation software is the closer to the actual system the lower integration level.
While Ebsilon Professional just has an appropriate integration with the
exergoeconomic analysis program. How the program uses the input data to do the
exergoeconomic analysis discussed in Chapter 4.
2.2.2AspenPlus
Accordingly, the second application in Section 5.2 which is the IGCC (integration
gasification combined cycle) problem was simulated by Aspen Plus (Sorgenfrei M.
and Tsatsaronis G., 2013). With regard to the complicated energy conversion systems
like IGCC with CO2 capture, Aspen Plus has some advantages in dealing with these
kinds of power plants since it has a large amount of equipment models and abundant
thermophysical database.
Aspen Plus represented “Advanced System for Process Engineering” is the
market‐leading process optimization software that supports the full range of process
industries. Aspen Plus boasts the world’s most extensive property database and
handles solid, fluid and gas phase processes, making it the best choice for chemicals,
polymers, specialty chemicals, pharmaceuticals and biotech, biofuels, power, carbon
10
capture, minerals, metals and mining (Aspentech, 2014). Aspen Plus, as well as
Ebsilon Professional, can export the simulation results as a text file, but the
exergoeconomic analysis software cannot use the report file as input data directly.
There are two reasons that cause this situation. One is the information in the text file
has too many redundant data included all properties values within the whole
iterative procedure and the iterative time, etc. However, the exergoeconomic
analysis software only needs the flowsheet, the final thermophysical properties from
the iteration and the compositions of each material streams. The other is the
exergoeconomic analysis software doesn’t have parallel components model to Aspen
Plus for now. The convergence level of the exergoeconomic analysis software is much
higher than Aspen Plus. For example, the coal preparation unit of the second
application IGCC problem from Aspen Plus has dryer, mill and lock hopper units
respectively, but in the exergoeconomic analysis software there are no related
component and the coal preparation unit only can be treated as a whole unit. As a
result, the data from Aspen Plus should be preprocessed before going to an
exegoeconomic analysis. The primary work for pretreatment is to increase the
integrated level of the entire power plant and to redefine the operation units to
conform to the needs of the exergoecnomic analysis program. In the future work,
high integration is no longer required when more and more component models for
the exergoeconomic analysis are added into the model library of the program.
Economic evaluation of a process or capital cost assessment comparison of
different schemes is an important element of process engineering. The extended
functionalities of Aspen Plus contain Activated Economics, using the power of
Activated Economics, process engineers can execute relative cost analyses inside the
Aspen Plus user interfaces. Map and size equipment from unit operations and
consider preliminary capital and operating costs that is another advantage other
process simulation software do not have.
11
2.3The lackofexergoeconomicanalysis inprocess simulation
software
Exergoeconomic analysis as a relatively new methodology rapidly developed since
later 1980s that was during the same time as the development period of process
simulation software (e.g. Aspen Plus was designed by Massachusetts Institute of
Technology and other cooperators in 1976‐1981). Generally, the commercial
simulation software applies sophisticated mathematical model for process
simulation instead of the new method or incomplete theory. Most process
simulation software for now still only based on the energetic analyses, i.e., focused
on energy flows of a system. Through strict mass balances and energy balances of
the process, stream flow rates, compositions and properties can be predicted; in
addition chemical equilibriums are required when chemical reactions occur in the
facilities. The operating conditions of the equipment and the size of the components
can predicted as well. The properties determined by process simulation software
usually include temperature, pressure, mass flow rate and chemical compositions,
the enthalpy and entropy are also calculated automatically. For many years,
numerous efforts are made to find more precise and rapidly constringed models for
the calculation of properties. At this point, the engineers and researchers need to
combine two or more software together to solve the problems of exergy‐based
analyses, such as, EES or Matlab, but the procedure is both time‐consuming and
error‐prone. For many years of development, the conventional exergoeconomic
analysis methods have been mature and also have a lot of applications on complex
energy conversion systems (Petrakopoulou F, etc. 2011a, 2011b). Based on the
exergoeconomic analysis approach (Lazzaretto A, Tsatsaronis G, 2006), it is
appropriate to develop a process simulation program to treat the exergy‐based
problems, which can facilitate the assessment and improvement of the performance
of energy systems. This is also the original intention of this thesis.
12
3.Energyandexergybasedanalyses
3.1Stateoftheart
For many years thermodynamic analysis using the first law, i.e. energy‐based analysis,
has been used to determine which components and operational parameters affect
the total efficiency of an energy system. This method is simple and practicable, but
energy balances neither provide information regarding the degradation of energy
during a process nor quantify the usefulness or the quality of energy in the material
streams flowing through a system while the second law assesses the flow of work
known both as availability or exergy. The researchers in Europe usually trace back to
19th century when exergy as a concept was conceived first by Carnot, and then
developed by J. Willard Gibbs in 1873 and Stodola and Gouy (F.Bosnjakovic, 1938) in
1889. In America, Darsious proposed to use an independent parameter to evaluate
the efficiency in 1930. Moreover, then J. H. Keenan abstracted this kind of parameter
named “Availability” from point function in 1932, who also first introduced the idea
of combining exergy with costs. The term "exergy" was coined in 1956 by Zoran Rant
by using the Greek ex and ergon meaning "extraction of work". In the late 1950s, the
studies on the second law analysis methodologies and exergy costing were in an
embryonic stage and started in both Europe and America independently. Till the
1970s, a great deal of literatures and publications by many scientists established the
theoretical foundations of the exergy based methodology. These contributions
included that in the US, Obert and Gaggioli (1963) applied the exergy method to the
optimal selection of steam piping and then Gaggioli et al. presented several papers in
1977 and 1978 about available energy accounting method; Tribus and Evans (1962,
1965) studied desalination processes by exergy analysis, for which they coined the
word ‘‘thermoeconomics’’, and it is the beginning of a concrete formulation of
thermoeconomics; El‐Sayed and Evans (1970), El‐Sayed and Aplenc (1970) published
13
two important papers in which the mathematical foundation for thermal system
optimization was given; in Europe Bergmann and Schmidt (1965) assigned costs to
the exergy destruction in each component of a steam power plant and optimized
feed water heaters; Szargut (1967, 1971, 1974) analyzed of a simple cogeneration
plant using exergy costing procedure and introduced an ecological cost coefficient
into the literature; Beyer (1972, 1978, 1979) used structural analysis and
thermoeconomics to industrial production process.
After that, in 1983, Tsatsaronis introduced some fundamental concepts of
thermoeconomics such as Fuel and Product and proposed the term
‘‘exergoeconomics’’ which was in a general sense expressing an accurate and
unambiguous characterization of a combination of economics and the exergy
concept. Since the 1980s, the exergoeconomic cost analysis rapidly expanded, and
the methodologies applied in design and optimization of thermal systems
comprehensively occurred. During this decade, there are two research trends in
exergoeconomic analysis. One is exergoeconomic accounting methods which is a
continuation of Obert and Gaggioli (1963), including Tsatsaronis and Winhold (1984,
1985, 1986), Valero and Lozano et al. (1986, 1989); and the other is Lagrangian‐based
approaches first introduced by Tribus and Evans (1965), including Tribus and EI‐Sayed
(1980, 1981), Evans et al. (1983) and Frangopoulos (1983, 1987). The important
contributions of conventional exergoeconomic analysis were done in the 1990s,
there were numerous publications and applications to power plants, combined heat
and power production or cogeneration facilities which included Von Spakovsky MR,
Curti V (1992), Tsatsaronis G, Pisa J (1994), Frangopoulos CA (1994), Von Spakovsky
MR (1994), Valero A, LozanoMA, Serra L, Torres C (1994), Hua B, Chen QL, Wang P
(1997), Kim SM, Oh SD, Kwon YH, Kwak HY (1998), Cerqueira SAAG, Nebra SA (1999), ,
Lazzaretto A, Tsatsaronis G (1999) etc. Since late 1990s, progressed innovative
methodologies of fuzzy logic and genetic algorithm methods have also been applied
to existing power plants and cogeneration facilities (Manolas DA, Frangopoulos CA,
14
Gialamas TP, Tsahalis DT, 1997; Cziesla F, Tsatsaronis G, 2002; Valdes M, Duran MD,
Rovira A, 2003; Mazur VA, 2005; Groniewsky A, 2013).
In the last ten years, the exergoeconomic analysis primarily applied to complex
systems, in which the Lagrangian‐based methods are limited because of the
weakness of the calculus method itself. If the component of the complex system fails
to achieve thermoeconomic isolation, the Lagrange multipliers vary from iteration to
iteration making the applicability of this method very difficult. Therefore, there have
been no new progresses or interesting applications of these methods. While, the
accounting methods do not have these limitations, and were rapidly developed in
recent years. The exergoenviromental analysis (Meyer et al., 2009; Tsatsaronis and
Morosuk, 2008a, 2008b) was developed to involve an ecological evaluation instead of
economic assessment into exergoecomonic analysis. Then advanced accounting
methods (Tsatsaronis, 2008) included advanced exergetic, advanced exergoeconomic
and advanced exergoenviromental analysis were proposed in order to describe the
interactions of the components and reveal the real potential of improvement. For
this objective, the thermodynamic efficiency, exergoeconomic costs and
environmental impacts are split into avoidable, unavoidable, endogenous and
exogenous parts, and also their combination, such as: avoidable endogenous,
avoidable exogenous parts or unavoidable endogenous, unavoidable exogenous
parts (Tsatsaronis, Kelly and Morosuk, 2006; Tsatsaronis and Morosuk, 2007, 2010;
Morosuk and Tsatsaronis, 2008a,2008b, 2009, 2010; Cziesla F et al, 2006; Kelly et al,
2009; Petrakopoulou F et al, 2012a, 2012b). Endogenous and exogenous parts can
provide detailed information about the mutual effects within plant components and
the whole plant, in addition, avoidable and unavoidable parts can reveal the
positions and the real potential of optimizations. These progresses effectively
prevent the optimization strategy to be misled as it may happen in the conventional
exergy‐based analyses.
15
3.2Exergy‐basedanalyses
In general, a rigorous evaluation of energy conversion systems consists of exergetic
analysis, exergoeconomic and exergoenvironmental analyses.
3.2.1Exergeticanalysis
The real thermodynamic inefficiencies in an energy conversion system are related to
exergy destruction and exergy loss. An exergetic analysis often aims to the calculation
of measures of performance which involves exergy destruction ratios, exergy loss
ratio and exergetic efficiencies. For a considered irreversible system, the exergy
destruction for the k‐th system component is kDE , . Thereafter the exergy loss ,
is only defined for the overall system. An exergy balance equation for the k‐th system
component can be written in a general form: kDkPkF EEE ,,, . The exergy of fuel
kFE , and the exergy of product kPE ,
have different definitions in different
approaches. In this thesis, the fuel and product definitions proposed by Lazzaretto
and Tsatsaronis (2006) are used. For the overall system, the exergy balance is:
, , , , 3.10
The exergetic efficiency is defined as the ratio between the exergy of product
and the exergy of fuel, for the component k:
kF
kD
kF
kPk E
E
E
E
,
,
,
, 1
(3.11)
For the overall system
totF
totLtotD
totF
totPtot E
EE
E
E
,
,,
,
, 1
(3.12)
The total exergy destruction totDE , is equal to the sum of exergy destructions within
the components, i.e. kDtotD EE ,, . In some applications, some components are
16
defined as dissipative component like condenser and throttling valve in which exergy
is destroyed without any useful product, thus, no exergetic efficiencies can be
defined.
Some exergetic variables associated with exergy destruction are defined for
characterizing the performance of a conversion system or the system component.
The exergy destruction ratio
totF
kDkD E
Ey
,
,,
(3.13)
can be used to compare dissimilar components to improve components with the
highest values of the exergy destruction kDE , . Alternatively, the component exergy
destruction rate can be compared to the total exergy destruction rate within the
system,
totD
kDkD
E
Ey
,
,,
*
(3.14)
In addition, the total exergy destruction ratio, i.e., Eq. (3.15) and the total exergy loss
ratio, i.e., Eq. (3.16) can be used to compare different energy conversion systems.
totF
totDtotD E
Ey
,
,,
(3.15)
totF
totLtotL E
Ey
,
,,
(3.16)
With a conventional exergetic analysis, the real thermodynamic inefficiencies within
the energy conversion system are identified.
3.2.2Economicanalysis
For the exergoeconomic analysis, we need the total capital investment cost, fuel
costs and operating, and maintenance (O&M) expenses that are determined by an
economic analysis. To estimate the major costs of a thermodynamic system, there
are many different approaches. In this thesis, the economic analysis is not part of the
17
considerations of the exergoeconomic analysis program. The values of the cost rate
kZ associated with capital investment cost and operating and maintenance
expenses for the k‐th component are all taken from other applications directly and
are not recalculated again. In these applications, the TRR (total revenue requirement)
method is used (Bejan et al., 1996). The procedure commonly involves four steps: 1.
Estimation of total capital investment; 2. Year by year analysis; 3. Calculation of
revenue requirements; 4. Levelized costs. For the first step, the most difficult part is
the estimation of the PEC (purchased equipment cost). The sources of the value of
PEC can be derived from vendors’ quotations, cost databases maintained by
engineering companies, commercial computer programs, literature or other
resources. However, most researchers cannot get exactly the same size equipment,
or the same year purchased equipment cost value from their sources. Thus, the
effect of size on equipment cost, i.e., Eq. (3.17) and the effect of the cost indices that
are basically inflation indicators on the time value of money, i.e., Eq. (3.18) should be
used in this case.
W
YwY X
XCC (3.17)
YX and WX are the sizes or capacities of the equipment and YC and WC are
the purchase costs of the same type of equipment in the same year but with
different sizes. The degression exponent α expresses that the increase in the
equipment cost is usually lower than the increase in the equipment size or capacity,
this value remains constant within a given size range and usually less than one.
ref
nowrefnow I
ICC (3.18)
The equipment cost for now nowC can be assembled from the known cost data refC
by using appropriate cost indices nowI and refI of now and the reference year.
Then using principles of economic evaluation, though the balance between the total
18
revenue requirements, annual CC (carrying charges), levelized fuel costs and levelized
operating and maintenance costs over the entire plant economic life, the cost rate
kZ for component k can be estimated by Eq. (3.19).
k k
kk PEC
PECMOCCZ
)&( (3.19)
is the annual operating hours, CC represents the annual carrying charges, O&M
indicates the levelized annual operating and maintenance costs and PEC expresses
the purchased equipment costs. The results of the cost rates kZ are important
input data introduced to the exergoeconomic analysis. More details about the
economic analysis can be found in Bejan et al. (1996) or other references.
3.2.3Exergoeconomicanalysis
Exergoeconomics combines exergy analysis with conventional cost analysis in order
to assess and improve the performance of energy systems (Tsatsaronis G, Lin L, Pisa J,
1993). The primary purpose of an exergoeconomic evaluation is to consider not only
the inefficiencies, but also the costs associated with these inefficiencies and the
investment expenditures required to reduce them. For this purpose, a specific cost
ic represented the cost of per unit exergy associated with the i‐th exergy stream (as
well as heat or work streams) is used. The cost rate iC of the exergy stream i can be
written as:
iii EcC (3.20)
To apply the exergoeconomic analysis to a system operating at steady state, cost
balances are formulated for each component separately shown as Eq. (3.21).
kwe
kekkqi
ki CCZCC ,,,, (3.21)
Here, the subscript i expresses the entering streams of component k, relatively,
subscript e is associated with the exiting streams of component k. q represents the
19
receiving heat transfer streams and w is the generating power streams. It should be
noticed that the terms kqC , and kwC ,
can be negative if there is a heat transfer
from the component or when a component receives power, and even non‐existent if
there is no heat transfer and power generation.
Generally, the cost balance equations are stated at the component level. Thus
for a system component, if the number of unknown cost of exiting exergy streams in
this component is higher than one, auxiliary equations are required. The auxiliary
costing equations are based on the F and P principles which are described below in
Section 4.4 or also see in Lazzaretto and Tsatsaronis (2006).
From the exergoeconomic evaluation, some effective variables are defined to
reveal the improvement of cost effectiveness for the considered system or find a
trade‐off between the investment cost and the component efficiency in an iterative
optimization. An important variable, which can be revealed only through a
exergoeconomic analysis, is the cost rate associated with exergy destruction for the
k‐th component. The appropriate expression is:
kDkFkD EcC ,,, (3.22)
where, kFc , is the specific cost of fuel.
Another variable is the relative cost difference in the k‐th component, shown as:
kF
k
k
k
kF
kFkP
c
Z
c
ccr
,,
,, 1
(3.23)
where, k is the exergetic efficiency of the component k, kFkpk EE ,, / .
In addition, the variable kf is the exergoeconomic factor defined for
component k by
kDk
kk CZ
Zf
,
(3.24)
From the definition of the exergoeconomic factor, conclusions can be made: a low
20
value of kf suggests improving the component efficiency and a high value of kf
suggests reducing the investment costs of this component.
3.2.4Environmentalanalysis
Analogous to the economic analysis, the environmental impact is calculated through
environmental analysis. Some of the approaches suggested combining an exergy
analysis with an environmental assessment with CExC (cumulative exergy
consumption) (Szargut J, 2002, 2004) and some suggested taking into account the life
cycle of components as the economic analysis (Meyer et al., 2009). The latter is much
prevalent in respect to the environmental analysis for recent years; moreover it
became part of the ISO (International Organization for Standardization) 14000
environmental management standards: in ISO 14040:2006 and 14044:2006. The
environmental impact of component k, kY , consists of construction (including
manufacturing, transport and installation), operating and maintenance(including
pollutant formation), and disposal:
dcdifDIk
OMk
COkk BYYYY ,
(3.25)
where, the terms COkY , OM
kY and DIkY correspond to construction, operating and
maintenance, and disposal environmental impact, however, the term dcdifB , is the
environmental impact rate associated with a dissipative component; this impact is
assigned to the productive component(s) served by the dissipative component.
The environmental impact rates related to dissipative components, dcdifB , , usually
are charged to the productive components in which chemical reaction occurs, and
should be zero for those which are not served by the dissipative components. In
some applications, the treatment of the cost rate of a dissipative component in
economic analysis, dcdifC , , is similar to the way in the environmental analysis.
21
3.2.5Exergoenvironmentalanalysis
The procedure for the exergoenvironmental analysis is highly consistent with the
corresponding exergoeconomic analysis. First, an exergy analysis of the energy
conversion system is carried out; then, an economic or an environmental analysis
follows; last, the cost rates or the environmental impacts are assigned to the exergy
streams in the system. Therefore, the environmental impact balance for component
k has a similar formulation with the cost balance, written as:
e
keki
ki BYB ,, (3.26)
with iii EbB . ib is the specific environmental impact (also called specific
environmental cost) which equals the average environmental impact per exergy unit
associated with the production of the i‐th exergy stream.
In an exergoeconomic analysis the cost rates kFC , and kPC ,
are calculated
from F and P rules, respectively. Similarly, in an exergoenvironmental analysis the
environmental impact rates kFB , and kPB ,
are calculated by the same F and P
rules, and the environmental impact of exergy destruction can be written as:
kDkFkD EbB ,,, (3.27)
Accordingly, the relative difference of specific environmental impacts kbr , is:
kF
kFkPkb b
bbr
,
,,,
(3.28)
In contrast to the exergoeconomic factor, the exergoenvironmental factor can be
written as:
kDk
kkb BY
Yf
,,
(3.29)
As a result of the high unification between exergoeconomic analysis and
exergoenvironmental analysis, the computer program developed here can calculate
22
the specific exergoenviromental impact of exergy streams only by replacing the input
value of kZ from the economic analysis to kY in the environmental analysis, but
without any other changes.
3.3Advancedexergy‐basedanalyses
As it was described in Section 3.1, the advanced exery‐based analyses appeared
only for few years, and the superiority of these approaches are that the interactions
of the components and the real potential of improvement can be quanfied;
simultaneously the optimization strategy, which may be misled by mutually affected
components, can be improved. The advanced exergy‐based analyses consist of
advanced exergetic analysis, advanced exergoeconomic analysis and advanced
exergoenvironmental analysis. These parts are not contained in this program for now;
they may be included in the future version of this program. Hence, only brief
overviews of the advanced exergy‐based analyses are discussed here, the
elaborations can be found in Morosuk and Tsatsaronis (2008b) and Kelly et al. (2009).
Generally, the basis of the advanced exergy‐based analyses is splitting the exergy
destruction into endogenous exergy destruction ENkDE ,
, exogenous exergy destruction
EXkDE ,
, avoidable exergy destruction AVkDE ,
, unavoidable exergy destruction UNkDE ,
and
their combination avoidable endogenous exergy destruction ENAVkDE
,,
, avoidable
exogenous exergy destruction EXAVkDE
,,
, unavoidable endogenous exergy destruction
ENUNkDE,
, , Unavoidable exogenous exergy destruction EXUN
kDE,
, . Then the cost rates of
exergy destruction for the exergoeconomic analysis (and the environmental impact
of exergy destruction for the exergoenvironmental analysis) are all split into
separated parts accordingly. While the investment costs and the component‐related
environmental impact can be split into avoidable and unavoidable part.
23
4.Thealgorithmandmathematicalmodel
4.1Descriptionofalgorithmmodel
With the development of science and technology, simulation technology has formed
a relatively complete theoretical system. Simulation and modeling are an inseparable
whole. The so‐called model can be a physical model, a mathematical model, or a
mathematical‐physical hybrid model. Physical models usually are scale models
simulated by the simulation object whose physical characteristics resemble the
physical characteristics of the system being modeled. Mathematical models,
especially the mathematical models of a continuous process, usually consist of a set
of nonlinear partial differential equations or algebraic expressions. Due to the rapid
development of computer technology, the use of mathematical models is more
general and flexible than using physical models. Simulation and modeling can be
applied to almost any situation, especially those which need onerous direct tests by
other methods; or those which practical tests are completely impossible. Therefore,
the simulation technology for chemical and energy systems has become an
indispensable and universal significance scientific instrument and engineering
practice method.
According to the different research purposes, mathematical models of
simulation systems are typically divided into steady‐state models and dynamic
models. The steady‐state model is a mathematical description of the relationships
between the input variables and output variables when a system or a process is at
steady state or equilibrium state; it reflects the static characteristics of the system or
the process. When the stable operating condition of the system changes, there are
always some kind of established mathematical relationships between the various
state parameters, these relationships can be expressed in formulas, curves, tables,
etc., so as to constitute steady‐state mathematical model. Dynamic mathematical
24
models are used to describe the mathematical relationships of parameters varying
with time when the system or process is in a non‐steady state. Theoretically, when
the time tends to infinity, all final steady state value of parameters decided by the
dynamic mathematical model should be exactly the same with those determined by
the steady state mathematical model.
Since the state parameters used in energetic analysis and exergetic analysis
which are considered below, are all in thermodynamic equilibrium state, the system
can be regarded in steady‐state. Exergoeconomic methods can be
divided into two main groups:
(1) Exergoeconomic accounting methods (e.g., Obert and Gaggioli, 1963;
Gaggioli, 1977; Tsatsaronis, 1984; Valero et al., 1986).
(2) Lagrangian‐based approaches (e.g., Evans and Tribus, 1965; Frangopoulos, 1
983; Tribus and El‐Sayed, 1980, 1981; Evans et al., 1983).
Exergoeconomic accounting methods calculate the average cost according to
the average number of external resources required for producing a unit of product.
This cost reflects the "static" performance of a system production. Lagrangian‐based
approaches aim to allow optimization of a system as a whole and the calculation
of marginal costs that reflect the “dynamic” performance of a system
production. Accounting and Lagrangian‐based methods are interrelated. When the
environment state and definitions of fuel and product are the same, the costs
calculated by both methods are the same. The cost balances and auxiliary equations
used in accounting methods can be obtained through derivatives in the
Lagrangian‐based approaches. However, Accounting methodologies have no
limitations with the complexity of the system being considered whereas
Lagrangian‐based methods are limited. In this thesis universality of the program is
more important, as a result, the SPECO approach that belongs to the accounting
methods is selected.
As it has been discussed in Chapter 3, the steps required to accomplish an
25
exergoeconomic analysis are:
(1) Energetic analysis
(2) Exergy analysis
(3) Economic analysis
(4) Exergoeconomic analysis
The economic feasibility of the construction and operation is not included in this
program. is associated both with the IC (investment cost) and O&M (operating
and maintenance cost) of component k ( & ), the calculated cost rates
are used as program users’ input for the exergoeconomic analysis.
To achieve the above‐described four steps in a computer program, an algorithm
was developed to realize this mathematic model. An algorithm always consists of two
elements: data and operations. And data is stored in the data structures (e.g., stream
data structure, component data structure); operations implement by functions. Data
structures and function established method will be elaborated below.
26
4.1.1Programprocessflowchart
Input data
Data input from
simulation software
Data input by manual operation
Input data analyze
Thermal properties calculate
Get incidence matrix
Initial data of material streams
Flow sheet
Flow sheet analyze
Components analyze by SPECO
approach
Streams data set
Components data set
Flow sheet sorted by streams
Flow sheet sorted by
components
Energetic and exergetic analyze
Specific cost of streams analyze
Costing equations associated with
streams entering the overall system
Auxiliary costing
equations
Cost balance
equations
Formulate coefficient matrix for specific cost
calculation
Check results
Right
Wrong
Check flow sheet
Wrong
Check the matrix is fulfilled or not
No
Solve equationsfailed
Specific cost
results
Exergoeconomic
analyze
Save results
End
Initial data
Enegetic and exergetic analysis
Exergoeconimic analysis
Figure 4.1 Algorithm flowchart
27
As the main process flows illustrated in Figure 4.1, the initial data for calculation
are taken from the process simulation software such as Ebsilon or Aspen plus when a
complex system is considered. Otherwise, if a simple case is considered, manual
work is also acceptable. The initial data consist of two main parts; one is thermal
properties of state parameters (i.e., independent variables associated with all
material and energy streams), the other is the flow sheet (i.e., a matrix indicated the
relations between streams and components) which is essential for process simulation.
Mass balance, energy balance, and exergy equations stated at the component level
can be formulated by combining thermal properties data and flow sheet. Solving
these equations, the results of exergetic analysis are obtained. These results not only
need to be outputted and shown in a list table but also should be stored for further
exergoeconomic analysis. Using the aforementioned methodology in section 3.2.3,
cost balance assigned to each component can be built. However, the number of
components is always less than the number of streams in and out the components.
Therefore, to solve this problem, in addition to the known values of cost rates
associated with the exergy streams supplied to the overall system from outside,
auxiliary equations which are formulated by the SPECO method in this thesis are
necessary. When the matrix for calculating costs is complete, the remaining question
is just how to solve the matrix. In this program, Gaussian elimination method and its
extensional method Gauss‐Jordan elimination (Golub, Gene H., and Van Loan,
Charles F., 1996; Lipschutz, Seymour, and Lipson, Mark, 2001.) are chosen to
implement this function. Then the calculated result of cost rate for each stream can
be used to further exergoeconomic analyses.
4.1.2Twosignificantdatastructures
In the early days of computer programming, the purpose of using computers was
mainly dealing with numerical problems. When using a computer to solve a specific
problem, it is usually necessary to go through the following steps: First, an
28
appropriate mathematical model should be found from the concrete issue, and then
an algorithm will be designed or selected for the mathematical model solution, and
finally the program compiling and debugging, testing, need to be repeated until a
final answer (Sartaj Sahni, 2005). The essence of seeking mathematical model is to
analyze the problem, extract operating objects and identify the relationships
between these operating objects, then these objects, relations, operations should be
described by mathematical form (Clifford A. Shaffer, 2011).
At that time, due to the operation objects are some simple integer, real or
Boolean data type, the programmer’s primary focus is on programming skills,
without attentions on data structures. In the wake of hardware and software
development and the expansion of computer application area, non‐numerical
problem is getting more and more important. According to statistics, today's
non‐numerical problems handling time occupy more than 85% of the machine time.
Such kind of issues related to more complex data structures, relationships between
data elements in general cannot be described by mathematical equations but with
logical operations. Consequently, the key in order to effectively solve these problems
is not only a mathematical analysis and calculation methods, but also a suitable data
structure.
In this exergoeconomic analysis program two data structures (i.e., set of streams,
set of components) are the most significant, which influence the entire calculation
through the data exchange between each other or the call and storage of data with
algorithms.
4.1.2.1Setofstreams’properties
The role of this data structure is used to record all relevant information with total
streams, simultaneously can be defined by a set of streams described in abstract data
type as well. Each stream contains lots of characteristics indicated by sub‐items of
the structure are shown in Table 4.1.
29
The sub‐item StreamNo can uniquely identify a data record of this stream, for
the reason that it can be treated as a key item or an index for data manipulation of
the set that refers to data classification, merging, sorting, access, retrieval, input,
output and other standard operations. Therefore if the initial input data is coming
from the export files of other simulation software, in order to facilitate the
calculation, the streams should be reordered by StreamNo, while StreamID is used to
record the original stream number. The usages of PhEStreamNo, ChEStreamNo and
EnStreamNo, are similar to the sub‐item StreamNo. The difference is these three sub
items are assigned only when the exergy streams for cost evaluation are separated to
physical and chemical. The most remaining items represent the thermal properties of
this stream. But the last nine entries attend to reveal the mesh relations or graph
structure of connections among streams and components, and that the values of
which will constitute a flow sheet matrix. The detailed explanation of the thermal
properties evaluation method will be expounded below.
30
Table 4.1 Characteristics’ variables in a stream abstract data type
Subitem Datatype Comments Subitem Datatype Comments
StreamNo int Stream’s serial number for both data input ways S double Specific entropy at working condition
StreamID int Stream ID only for recording original stream No. from other
process simulation software
Eph double Specific physical exergy at working condition
PhEStreamNo int Physical exergy stream No. only for cost analysis also
separated to physical and chemical
Ech double Specific chemical exergy at working condition
ChEStreamNo int Chemical exergy stream No. only for cost analysis also
separated to physical and chemical
Etot double Specific total exergy at working condition
EnStreamNo int Energy stream No. only for cost analysis also separated to
physical and chemical
Etot double Total exergy at working condition
Workingfluid char[] Material flow C double Specific cost rate
Composition vector Vector for storing composition of material flow Cph double Specific physical cost rate
X double Dryness of water steam Cch double Specific chemical cost rate
LHV double Low heating value Component1 char[] Component associated with this stream
HHV double High heating value Cp1No int Component No.
MassRate double Mass rate of material flow Direction1 int Stream direction entering or exiting component
T0
P0
h0
s0
T
P
h
double
double
double
double
double
double
double
Temperature at reference state
Pressure at reference state
Enthalpy at reference state
Entropy at reference state
Temperature at working condition
Pressure at working condition
Specific enthalpy at working condition
Component2
Cp2No
Direction2
Innerstream
Exergystream
Costcheck
char[]
int
int
Boolean
Boolean
Boolean
Another component associated with this stream
Component No.
Stream direction that entering or exiting component
The stream inside the system or from outside
The stream which is an exergy or energy stream
Cost rate of energy stream provided by system or at which
external resources are purchased from outside
31
4.1.2.2Setofcomponents
Another essential factor for this calculation is the data structure of components’ set.
Sub‐items in the structure are shown in Table 4.2.
Table 4.2 Structure of components’ set
Subitem Datatype Comments
ComponentNo int Component’s serial number
ComponentType char[] Component’s name
Compressor structure Data structure for defining compressors, fans, and
pumps
Turbine structure Data structure for defining turbines
Combustion_Chamber structure Data structure for defining a combustion chamber
Heater structure Data structure for defining heaters, reheaters,
economizers, condensers and preheaters
Steam_Generator structure Data structure for defining steam generator
Mixer structure Data structure for defining mixers and ejectors
Deaerator
Evaporator
Splitter
Gasifier
Throttling_valve
structure
structure
structure
structure
structure
Data structure for defining deaerators
Data structure for defining evaporators
Data structure for defining separators and splitters
Data structure for defining gasifier
Data structure for defining throttling valve
The intention of the sub‐item ComponentNo is similar as StreamNo in section
4.1.2.1; it can distinguish diverse components from each other. The following
sub‐item ComponentType declares what kind of component it is, and depending on
ComponentType properties associated with the component will be recorded in one
of the component structure from Table 4.2. Each component structure can be
considered as a mathematic model included data and operations reflected the
characteristics of a real facility or an abstract subsystem depending on different levels
of integration division. The division of integration is artificial according to the
purpose of research or probability for convenience. For now, this structure consists of
common plant components; more components’ model can be flexibly and lightly
32
appended in future work with a similar definition.
4.1.2.3Generalformofthecomponentdatastructure
A complex conversion power plant is composed of many various components, for
instance, compressors, gas turbine, steam turbines, etc. As that is presented in Table
4.2, each different component has always its specific definition within its data
structure. But meanwhile, the sub‐items of these components’ structure also have a
lot in common. As a result, a general form is extracted in Table 4.3. The comments of
sub‐items are shown in Table 4.3 as well. Some of the sub‐items represent the
thermal properties (i.e., T_inlet, P_inlet, h_outlet and s_outlet etc.) and
exegoeconomic parameters (i.e., c_inlet, c_outlet and cph_inlet etc.) associated with
incoming streams and outgoing streams of a component, and some are the
component characteristics (i.e., Ep, Ef, ε, cf and Cd etc.) evaluated by exergy‐based
method. Specific component structure differs in that evaluation method (i.e., SPECO
approach discussed in section 4.4) of exergy rates and cost rates associated with fuel
and product is particular.
The application of the first sixteen sub‐items in component structure is
demonstrated with the aid of Figure 4.2. It should be noticed that in real components
not all of the stream situations shown in Figure 4.2 exist simultaneously, and the
amount of streams with the same condition also can be more or less than the
general case. Generally, the component model construction for the process
simulation software is critical because the dependent variables of streams in a
process simulation are always under some constraint conditions (energy balance,
mass balance, cost balance etc.) which are stated at component level. Whereas there
are at least two streams corresponded with a component, which stream connected
with which component should be confirmed in a component model. And still when
the component contains lots of streams, as the schematic in Figure 4.2, different
streams should be marked in accord with the purpose of the component (e.g., fuel
33
stream, oxidizer stream, energy stream, hot stream or cold stream etc.).
Figure 4.2 Schematic of a component in a thermal system
To solve this problem, popular process simulation software all uses the graphical
representation for real component model, shown in Figure 4.3, in which the working
fluid of streams at component inlet and outlet are already defined and cannot be
changed by users. These definitions can be directly used in the component structures
which are built in this program when the input data are taken from Ebsilon. But when
the input data are by manual operation, the streams can be distinguished by the
sub‐item Workingfluid or an assemblage of sub‐items Workingfluid, T, P and
StreamMass in Table 4.3 expect for a special case seldom encountered in heat
exchanger in practical applications. The latter is illustrated by streams 11, 12, 25 and
26 in Figure 4.2. If the incoming streams are 11 for the hot stream and 25 for the cold
stream, when the outgoing streams 12 and 26 have identical material flows and mass
flow rates, these two streams cannot be differentiated automatically by the program
that which one belongs to the hot stream and which stream belongs to the cold
stream. Consequently, the streams’ serial number 12, 26 will be artificially used to
34
identify these two streams according to the rule which is the serial number of exiting
stream equals the serial number of entering stream plus one. This should be
observed carefully when the users start an analysis with this program and all initial
data for exergoeconomic analysis are inputted by themselves. Time permitting, a
graphical interface of the component model in this program also can be realized in
future work.
Figure 4.3 Component models in other process simulation software
35
Table 4.3 General form of component data structure
Subitem Datatype Comments Subitem Datatype Comments
InletStreamNo int Incoming stream’s serial number OutletStreamPhEx double Physical exergy of outgoing stream
OutletStreamNo int Outgoing stream’s serial number InletStreamChEx double Chemical exergy of incoming stream
InletStreamMass double Mass rate of inlet stream OutletStreamChEx double Chemical exergy of outgoing stream
OutletStreamMass double Mass rate of outlet stream c_inlet double Specific cost of incoming stream
InletPhStreamNo int Incoming physical exergy stream’s serial number c_outlet double Specific cost of outgoing stream
InletChStreamNo int Incoming chemical exergy stream’s serial number cph_inlet double Specific physical cost of incoming stream
OutletPhStreamNo int Outgoing physical exergy stream’s serial number cch_inlet double Specific chemical cost of incoming stream
OutletChStreamNo int Outgoing chemical exergy stream’s serial number cph_outlet double Specific physical cost of outgoing stream
InletWorkingfluid char[] Incoming material flow cch_outlet double Specific chemical cost of outgoing stream
OutletWorkingfluid char[] Outgoing material flow Q double
The definitions of Q, W, Ep, Ef , ε, Sgen, Ed, y, y*, Cd,
cf, cp, r and f can be found in Chapter 3, Section 3.2
and Section 3.3
EnStreamNo int Energy stream’s serial number W double
EnStreamNewNo
T_inlet
T_outlet
P_inlet
P_outlet
h_inlet
h_outlet
int
double
double
double
double
double
double
Energy stream’s number for cost analysis separated
Temperature at inlet
Temperature at oulet
Pressure at inlet
Pressure at outlet
Specific enthalpy of incoming stream
Specific enthalpy of outgoing stream
Ep
Ef
ε
Sgen
Ed
y
y*
double
double
double
double
double
double
double
s_inlet double Specific entropy of incoming stream Cd double
s_outlet double Specific entropy of outgoing stream Cf double
InletStreamEx double Exergy of incoming stream Cp double
OutletStreamEx double Exergy of outgoing stream R double
InletStreamPhEx double Physical exergy of incoming stream F double
36
4.2Thermodynamicpropertiescalculation
In this thesis, the arguments of thermodynamic properties for a material stream
except water and steam are T (temperature) and p (pressure). For water and water
steam, p and T, T and x (dryness) or p and x are chosen for different regions, and the
functions of p, s; p, h; T, s; x, s can be chosen as well.
4.2.1 IAPWS‐IF97 for thermodynamic properties calculation of
waterandsteam
The working fluid water and water steam is widely used in energy conversion plants.
The thermodynamic properties calculation methods for water and steam are
maturely developed. The methodology that the IAPWS (The International Association
for the Properties of Water and Steam) release on IF97 (the IAPWS Industrial
Formulation 1997) is generally recognized in industrial and scientific fields.
The IAPWS‐IF97 consists of a set of equations for different regions that cover
the following range of validity:
273.15 K≤T≤1073.15K, p≤100 MPa
1073.15 K < T≤2273.15K, p≤10 MPa .
Figure 4.4 shows the five regions into which the entire range of validity of
IAPWS‐IF97 is divided.
Figure 4.4 Regions and equations of IAPWS‐IF97
37
The boundaries of the regions can be directly taken from Fig. 4.4 except for the
boundary between regions 2 and 3; this boundary is defined by the so‐called
B23‐equation. Both regions 1 and 2 are individually covered by a fundamental
equation for the specific Gibbs free energy g(p,T), region 3 by a fundamental
equation for the specific Helmholtz free energy f(ρ,T), where ρ is the density, and the
saturation curve by a saturation‐pressure equation ps(T). The high‐temperature
region 5 is also covered by a g(p,T) equation. These five equations, shown in
rectangular boxes in Fig. 4.4, form the so‐called basic equations (IAPWS, 1997). In
addition to the basic equations, for regions 1, 2, and 4 so‐called backward equations
are provided in form of T(p,h) and T(p,s) for regions 1 and 2, and Ts(p) for region 4.
These backward equations are numerically consistent with the corresponding basic
equations and make the calculation of properties as functions of p,h and of p,s for
regions 1 and 2, and of p for region 4 extremely fast. In this way, properties such as
T(p,h), h(p,s), and h’(p) can be calculated without any iteration from the backward
equation alone or by combination with the corresponding basic equation. But for
Region 3, the basic equation is f(ρ,T), while f(p,T) is more convenient for this program.
This function of p,T only can be established by iterations before supplementary
released on backward equations for a specific volume as a function of pressure and
temperature v(p,T) for Region 3 in 2005.
Table 4.4 Basic equations and backward equations from IAPWS
Document Region1 Region2 Region3 Boudary23 Region4 Region5
IF97 g(p,T) g(p,T) f(ρ,T) p(T) ps(T) g(p,T)
T(p,h) T(p,h) T(p) Ts(p)
T(p,s) T(p,s)
IF97‐S01 p(h,s) p(h,s)
IF97‐S03rev T(p,h)
v(p,h)
T(p,s)
v(p,s)
IF97‐S04 p(h,s) Ts(h,s)
IF97‐S05 v(p,T)
38
From 2001 to 2005, IAPWS released four supplementary for IAPWS‐IF97
included several backward equations for region 1, 2, 3 and 4, shown in Table 4.4. The
details and concrete expression of these equations will not be discussed here and
can be found in references (IAPWS, 2001, 2003, 2004, 2005). If the quality of wet
steam is known, thermodynamic properties of wet steam can be calculated based on
the equations from Region 4 as well. Region 5 of IAPWS‐IF97 is not the frequent area
for water and steam in energy conversion plants. But the calculation of region 5 is
still involved in this program with iteration.
The specific gas constant of ordinary water used for this formulation and the
values of the critical parameters are:
R =0.461526 kJ/kg ∙ K (4.1)
Tc= 647.096 K (4.2)
pc=22.064 MPa (4.3)
ρc=322 kg/m (4.4)
Table 4.5 Comparisons between calculated results and international steam tables
LocationP
[bar]
T
[℃]
Internationalsteamtables Resultsofthisprogram
h[kJ/kg] s[kJ/kg·K] h[kJ/kg] s[kJ/kg·K]
Region 1 10 25 105.761 0.36700 105.761282 0.366999
290 110 482.524 1.3953 482.523632 1.395257
800 260 1147.67 2.7368 1147.665905 2.736847
Region 2 0.01 10 2519.41 8.9953 2519.405022 8.995251
200 400 2816.84 5.5525 2816.836198 5.552468
900 750 3573.51 5.9470 3573.507647 5.947036
Region 3 240 370 1802.54 3.9649 1802.540109 3.964866
700 450 2123.43 4.3080 2123.425402 4.307995
1000 580 2759.87 5.0361 2759.866893 5.036122
Region 4 1 99.6059 2674.95
417.436
7.3588
1.3026
2674.949651
417.436506
7.358807
1.302560
80 295.009 2758.61
1317.08
5.7448
3.0277
2758.611082
1317.079790
5.744849
3.207651
210.43 370 2333.50
1892.64
4.7996
4.1142
2333.501248
1892.643277
4.799621
4.114155
Region 5 0.1 875 4338.32 10.791 4338.317352 10.791143
20 1425 5746.66 9.3440 5746.648534 9.343976
100 1850 6936.72 9.2246 6936.888538 9.224653
39
The calculation results of some randomly selected p,T compared with
international steam tables (Wagner W., Kretzschmar H.‐J., 2008) are shown in Table
4.5. The data in region 1, 2, 3 and 4 are exactly the same with international steam
table, while in region 5 there are minuscule errors but without impact to practical
application, thus it can be neglected.
4.2.2 Thermodynamic properties calculation of some selected
substances
To calculate the thermodynamic properties of selected substances as working fluids
for energy conversion plants, an ideal gas model for many real gases is used to create a
gas database in the program. The values given in Table 4.6 and 4.7 can be used
together with the equations (4.5) to (4.9) with y /1000 .
, 4.5
, 102 3
4.6
, ln2 2
4.7
, , , 4.8
, , 4.9
These four functions are valid for the temperature limit Tref<T<Tmax at pref= 1.0 bar.
The constants a,b,c and d are shown in Table 4.7 for various substances and =8.314
[kJ/kmol·K] is the universal gas constant (Bejan A., Tsatsaronis G., Moran M. 1996).
Then the thermodynamic properties of mixture real gases such as combustion gases,
flue gases can be calculated through function (4.10) and (4.11).
4.10
4.11
The terms and should be calculated using Eq. (4.6), (4.7) and (4.9), and
40
represents the mole fraction of the gas composition.
Table 4.6 Properties of selected working fluids at Tref=298.15K and pref=1.0 bar
Working
fluid* M
[kg/kmol] p,ref
[kJ/kmol] ref
[kJ/kmol] ref
[kJ/kmol·K]gref
[kJ/kmol]C(s) 12.01 8.53 0 5.740 ‐1711
S(s) 32.06 22.77 0 32.058 ‐9558
N2 28.01 29.49 0 191.610 ‐57128
O2 32.00 28.92 0 205.146 ‐61164
H2 2.02 29.13 0 130.679 ‐38961
CO 28.01 28.54 ‐110528 197.648 ‐169457
CO2 44.01 35.91 ‐393521 213.794 ‐457264
H2O 18.02 31.96 ‐241856 188.824 ‐298153
H2O(l) 18.02 75.79 ‐285829 69.948 ‐306685
CH4 16.04 35.05 ‐74872 186.251 ‐130403
SO2 64.06 39.59 ‐296833 248.094 ‐370803
H2S 34.08 33.06 ‐20501 205.757 ‐81847
NH3 17.03 35.59 ‐46111 192.451 ‐103491
*) Substance is in the gas phase unless denoted as liquid (l)
Table 4.7 Constants for Eqs. (4.5) through (4.8)
and T0<T≤Tmaxforselectedsubstance
Working
fluid* H+ + Tmax[K]
C(s) ‐2.101 ‐6.540 0.109 38.940 ‐0.146 ‐17.385 1100
S(s) ‐5.242 ‐59.014 14.795 24.075 0.071 0.000 368
N2 ‐7.069 51.539 24.229 10.521 0.180 ‐2.315 3000
O2 ‐9.589 36.116 29.154 6.477 ‐0.184 ‐1.017 3000
H2 ‐7.823 ‐22.966 26.882 3.586 0.105 0.000 3000
CO ‐120.809 18.937 30.962 2.439 ‐0.280 0.000 3000
CO2 ‐413.886 ‐87.078 51.128 4.368 ‐1.469 0.000 3000
H2O ‐253.871 ‐11.750 34.376 7.841 ‐0.423 0.000 3000
H2O(l) ‐289.932 ‐67.147 20.355 109.198 2.033 0.000 500
CH4 ‐81.242 96.731 11.933 77.647 0.142 ‐18.414 2000
SO2 ‐315.422 ‐43.725 49.936 4.766 ‐1.046 0.000 2000
H2S ‐32.887 1.142 34.911 10.686 ‐0.448 0.000 2000
NH3 ‐60.244 ‐29.402 37.321 18.661 ‐0.649 0.000 450
*) Substance is in the gas phase unless denoted as liquid (l)
In addition to the selected substances included in Table 4.7, there are some
41
other common working fluid for energy conversion systems such as He (Helium) and
Ar (Argon) which are the important compositions of air, or coal and coal ash. The
enthalpy and entropy of Helium and Argon at temperature T and pressure p can be
calculated with Eq. (4.12) and (4.13) when Helium and Argon are seen as ideal gases,
with constant heat capacities.
4.12
4.13
The term 5.19 kJ/kg ∙ K and 0.52 kJ/kg ∙ K can be found
in chemical handbook (David R. Lide, 2003). For coal and coal ash, the thermal
properties calculation will be discussed below simultaneously with the discussion of
the chemical exergy in Section 4.3.2.
4.3Exergeticanalysis
4.3.1Referencestate
Exergy is a measure of the deviation of the state of the system from the state of a
thermodynamic environment (Moran M.J.,Shapiro H.N.,1992; Bejan A., Tsatsaronis G.,
Moran M. 1996). The thermodynamic environment (reference state) in exergy‐based
analysis is a large thermodynamic system in equilibrium in which the state variables
(T0, p0) and the chemical potential of the chemical components contained in it
remain constant. Since our natural environment is not in equilibrium, there is a need
to model an exergy‐reference environment (e.g., Tsatsaronis G., Cziesla F, 2002, 2004;
Tsatsaronis G, 2007; Kotas T.J, 1995; Ahrends J, 1980; Szargut J. et al, 1988). Thus, the
thermodynamic environment model should be as close as possible to the physical
environment but is not identical with this. The temperature T0and pressure p0 of the
reference environment are often taken as standard state values, such as T0=298.15
K and p0 = 1.013 bar. However, these properties may be specified differently
depending on the application as the actual or average ambient temperature and
pressure, respectively, for the time and location at which the system under
42
consideration operates or is designed to operate. And although the intensive
properties of the environment are assumed to remain constant, the extensive
properties can change as a result of interactions with other systems. Therefore, in
this program, the values of the state variables (T0,p0) can be defined by users at the
beginning of the exergoeconomic analysis for the entire energy conversion system or
be changed for some material streams considered as from other systems among the
analysis as the occasion demands.
4.3.2Physicalandchemicalexergy
The total exergy of a system consists of nuclear, magnetic, electrical, surface tension
effects, physical, chemical, kinetic and potential exergy (Moran M.J.,Shapiro
H.N.,1992; Bejan A., Tsatsaronis G., Moran M. 1996). For many engineering
applications, only the changes in physical and chemical exergy are considered.
For a given mass flow rate, , the physical exergy associated with the i –th
material stream, , can be expressed as Eq. (4.14)
∙ 4.14
where the specific enthalpy , and specific entropy , at the reference
state (T0,p0) and the given temperature and pressure (T,p) can be calculated using
the equations in Section 4.2. The physical exergy of a working fluid can be further
split into its thermal exergy ( ) which is due to its temperature and mechanical
exergy ( ) which is due to its pressure. For any real fluids at any states, the physical
exergy of a point X defined at the given pressure p and the temperature T0 of the
environment is (Morosuk T., Tsatsaronis G, 2005):
4.15
, , 4.16
, , , , 4.17
43
This splitting may improve some results obtained from exergy‐based analysis (e.g.,
for the refrigeration system), but for now it is not included in this program and can be
involved in the future research.
Table 4.8 Standard molar chemical exergy for selected substances at
Tref=298.15 K(pref=1.019 atmfor ModelⅠandpref=1.0 atmfor ModelⅡ) (Bejan A.,
Tsatsaronis G., Moran M. 1996)
Substance Formula*) [kJ/kmol]ModelⅠ
ModelⅡ
Nitrogen N2(g) 639 720
3970
19870
9500
900
410260
236100
609600
275100
313400
88900
55600
‐
812000
337900
233700
331300
‐
831650
1 265800
1 361100
1 495840
2 003900
2 154000
2 805800
3 463300
3 303600
5 413100
722300
718000
1 363900
1 375700
Oxygen O2(g) 3951
Carbon dioxide CO2(g) 14176
Water H2O(g) 8636
Water H2O(l) 45
Carbon(graphite) C(s) 404589
Hydrogen H2(g) 235249
Sulfur S(g) 598158
Carbon monoxide CO2(g) 269412
Sulfur dioxide SO2(g) 301939
Nitrogen monoxide NO(g) 88851
Nitrogen dioxide NO2(g) 55585
Hydrogen peroxide H2O2(g) 133587
Hydrogen sulfide H2S(g) 799890
Ammonia NH3(g) 336684
Oxygen O(g) 231968
Hydrogen H(g) 320822
Nitrogen N(g) 453821
Methane CH4(g) 824348
Acetylene C2H2(g) ‐
Ethylene C2H4(g) ‐
Ethane C2H6(g) 1 482033
Propylene C3H6(g) ‐
Propane C3H8(g) ‐
n‐Butane C4H10(g) ‐
n‐Pentane C5H12(g) ‐
Benzene C6H6(g) ‐
Octane C8H18(g) ‐
Methanol CH3OH(g) 715069
Methanol CH3OH(l) 710747
Ethyl alcohol C2H5OH(g) 1 348328
Ethyl alcohol C2H5OH(l) 1 342086
The chemical exergy of an ideal gas l having the mole fraction in the
44
thermodynamic environmental gas phase is:
4.18
Then the chemical exergy of an ideal mixture of N ideal gases can be formulated as:
4.19
Here is the mole fraction of the substance l in the mixture gases working fluid at
temperature T0.
For calculating the chemical exergy the chemical composition of the
environment has to be specified. Two alternative standard exergy reference
environments have gained acceptance for engineering evaluations that are ModelⅠ
andModelⅡ inTable4.8(Bejan A., Tsatsaronis G., Moran M. 1996). The tabulated
standard chemical exergy values for substances contained in the environment model
at standard conditions (Tref,pref) facilitate the calculation of chemical exergy values
for a working fluid. The effect of small variations in the values of T0 and p0 (reference
environment by custom definition) on the chemical exergy of reference substances
might be neglected in practical applications. This program uses ModelⅠ as the
default value of standard chemical exergy, and ModelⅡ also can be called with a few
adjustments.
The standard chemical exergy of a substance not present in the environment
can be calculated by considering a reversible reaction of the substance with other
substances for which the values of standard chemical exergy are known(Bejan A.,
Tsatsaronis G., Moran M. 1996). The general form of this standard chemical exergy
can be formulated as:
∆ 4.20
The subscript denotes the products and denotes the reactants of the
reversible reaction, where the standard chemical exergies for the products and
reactants are assumed to be known. And ∆ is the change in Gibbs function of the
reaction, regarding each substance as separate at T0 and p0. This equation can be
45
written alternatively as:
4.21
In the above equations, the subscript represents the fuel. The terms and
are specific enthalpy and specific entropy that can be obtained by the functions in
Section 4.2.2. If the temperature and pressure respectively equal to T0 and p0, the
term in curly brackets on the right side of Eq. (4.21) corresponds to the standard
heating value: the higher heating value ( ) when water exits the system as a
liquid; and the lower heating value ( ) when water exits the system as vapor.
For energy conversion processes, calculation of the exergy of fossil fuels is
particularly important. ModelⅠ and ModelⅡ already contain some pure
hydrocarbon fuels which can be directly used for the exergy calculation. But for coal,
the model of the reversible reactor should be used. At assumption that 1 kg of DAF
(dry and ash free) coal entering the control volume, the chemical equation for the
reaction is described by:
⟶ 4.22
where c,h,o,n,s denote the number of atoms of carbon, oxygen, hydrogen, nitrogen
and sulfur in kmol/kg DAF, and [kmol/kgDAF]are the stoichiometric coefficients.
,2 , ,
2 ,
4 2
Thus the counterpart of Eq. (4.21) can be rewritten as:
,
,
4.23
Ignoring the slight difference between (T0,p0) and (Tref,pref), the standard specific
entropy can be found in Table 4.6 and the standard chemical exergy is given
in Table 4.8. To complete the calculation of Eq. (4.23), values of (the higher
46
heating value of the dry and ash free coal) and the absolute entropy are
required. In the absence of a measured value, [MJ/kg] can be estimated
by following equation (Eiserman W, Johnson P, Conger WI, 1980):
152.9 98.7673 8
4.24
And the estimating of absolute entropy [kJ/kg ∙ K] is:
37.1653 31.4767 exp 0.564682 20.1145
54.3111 44.6712 4.25
The terms c, h, o, n, s have identical meaning with that in the chemical equation
(4.22).
The specific chemical exergy of coal in [MJ/kg]can be estimated as:
% ∙%
∙ % ∙ 4.26
Through the estimated value of and the expression of the first curly
bracket in Eq. (4.21), the absolute enthalpy hDAF[kJ/kg]can be written as:
4.27
And then the enthalpy and entropy of coal at the state (T0,p0) has similar formation
with chemical exergy like the following equations:
% ∙%
∙ % ∙ 4.28
% ∙%
∙ % ∙ 4.29
The thermodynamic properties calculation of coal ash in solid form uses the Eq. (4.12)
and (4.13), but the specific heat will not remain constants instead it should be
calculated as (Eiserman W, Johnson P, Conger WI, 1980):
0.594 5.86 10 4.30
The term in Eq. (4.12) is equal to ‐940.9 MJ/kmol for coal ash and in
Eq.(4.13) is equal to 54.0kJ/kmol ∙ K. An average molecular weight of ash is 76.0
kg/kmol. Alien from enthalpy and entropy, the chemical exergy more correlate with
47
the ash composition. The standard chemical exergies of CaO, K2O, P2O5, MgO, SO3,
and Na2O are very large compared with that of SiO2, Al2O3, Fe2O3, and TiO2. It implies
that is sensitive to the total concentration of CaO, K2O, P2O5, MgO, SO3, and
Na2O in ash (TCO) (Song G, Shen L, Xiao J, et al, 2013). A correlation between
[kJ/kg] and TCO [wt%]is:
29.3761 30.67 4.31
When an average composition was concerned, the value of is 456.036kJ/kg.
4.4SPECOapproachforexergoeconomicanalysis
The SPECO (Specific Exergy Costing) method presents a general, systematic, simple
and unambiguous approach for developing the exergetic efficiencies of a thermal
system and its components (Lazzaretto A, Tsatsaronis G, 2006). Compared with
previous exergy‐based approaches included the EEA (Exergy Economics Approach)
(Gaggioli R A, 1980, 1983), FEA (First Exergoeconomic Approach) (Tsatsaronis G,
Winhold M, 1984, 1985, 1986), ECT (Exergetic Cost Theory) (Valero A, et al, 1986),
TFA (Thermoeconomic Functional Analysis) (Frangopoulos CA, 1987), EFA
(Engineering Functional Analysis) (Von Spakovsky MR, 1990), LIFOA (Last‐In‐First‐Out
Approach) (Tsatsaronis G, Lin L, 1993; Lazzaretto A, Andreatta R, 1995) and SAA
(Structural Analysis Approach) (Valero A, et al, 1992), it is chosen to realize an
exergoeconmic analysis using computer programming for three major reasons. First,
the productive structure derived from the application of TFA and EFA which is also
applied in SPECO can be helpful in understanding the fuel and product definitions of
components, facilitates modeling the real components and reflects the interactions
of exergy exchanges among components; Second, The SPECO method provides
general criteria for developing auxiliary costing equations associated with any system,
especially when the exergoeconomic analysis are considered with chemical, physical,
thermal and mechanical exergy separately; Third, a general matrix is formulated for
the SPECO approach that extends the application of the ECT matrix formulation to
calculation of average costs. The matrix formulation for the system of linear
48
equations was presented in conjunction with ECT, SAA and LIFOA, this type of
expressions are the most convenient formation for computer programming.
4.4.1Identificationofexergystreams
Using the SPECO method for exergoeconomic analysis, initially, a decision must be
made with respect to whether the analysis of the components should be conducted
using total exergy or separate forms of the total exergy of a material stream (e.g.,
thermal, mechanical and chemical exergies) (Lazzaretto A, Tsatsaronis G, 2006).
Consequently, all exergy streams associated with the incoming and outgoing material
and energy streams are identified after the decision is alternatively made by the
users of this program at the beginning of the analysis. In the first edition, the
separate form of total exergy involves physical and chemical exergies; thermal and
mechanical exergies are not included yet.
4.4.2Definitionoffuelexergyandproductexergy
After all streams in an energy conversion system are identified, a further
determination should be made which is the definition of fuel and product of
components. In general, different thermoeconomic analysis methods apply different
definitions; but for a given definition of fuel and product, diverse approaches
mentioned above lead to similar results. In SPECO method, the product is defined to
be the sum of all the exergy values to be considered at the outlet (including the
exergy of energy streams generated in the component) plus all the exergy increases
between inlet and outlet (i.e., the exergy additions to the respective material streams)
that are in accord with the purpose of the component. And the fuel is equal to all the
exergy values to be considered at the inlet (including the exergy of energy streams
supplied to the component) plus all the exergy decreases between inlet and outlet
(i.e., the exergy removals from the respective material streams) minus all the exergy
increases between inlet and outlet that are not in accord with the purpose of the
component. More detailed explanations refer to the literature (Lazzaretto A,
49
Tsatsaronis G, 2006). To make it clear, the definition of fuel and product in the SPECO
method applied to the component is illustrated here with Fig.4.5 and 4.6 which cover
all situations that might be encountered.
01112 EE
02526 EE
012 EE
Figure 4.5 Schematic of a component to define fuel and product (Lazzaretto A,
Tsatsaronis G, 2006)
According to the aforementioned definition of fuel, when the chemical composition
of a stream doesn’t change, the fuel should contain (the exergy of energy
streams supplied to the component), , (the exergy decreases
between inlet and outlet) and , due to the purpose of owning and operating
the component; the product involves (the exergy of energy streams generated in
the component), (the exergy increases between inlet and outlet
consistent with the purpose of the component) and at the outlet of the
component. Thus, the fuel ( ) and product ( ) for this component are:
4.32
4.33
Otherwise, if the composition of a stream changes because of mixing, separation or
chemical reaction and differences in the exergy streams need to be considered in
accord with the purpose of the component, the productive structure in Fig. 4.6 can
facilitate the understanding of fuel and product definitions better. In this case,
50
generally, when the analysis is conducted using only total exergies, a difference in
total exergy values between inlet and outlet of the considered material stream
should be used unless the chemical exergy represents the main exergy form of this
material stream and the purpose of the component dictates that the chemical
exergies at the inlet and outlet should be considered separately at the fuel and
product sides. As an example, if only total exergy are used, when is considered as
a fuel stream of an combustion chamber, is considered as an oxidizer stream and
is considered as an combustion gases at the outlet, the fuel can be expressed
using and the product is since the main exergy form in
stream 5 is the chemical exergy whereas in stream 9 and 8 is the physical exergy.
01112 EE
02526 EE
021 aa EE
0985 aaa EEE
0859 bbb EEE
)( 988cc eem
)( 595cc eem
021 bb EE
Figure 4.6 The productive structure for the component shown in Fig. 4.5 (Lazzaretto
A, Tsatsaronis G, 2006)
But if the exergy is divided into different forms when the researchers need more
accurate result particularly there is an exothermal chemical reaction occurs in a
energy conversion plant, as for streams 5a, 5b and 5c shown in Fig 4.6, the definition
of fuel and product becomes more complex. In Fig 4.6, two material streams 5 and 8
enter the component and exit as stream 9 ( ) after mixing with or
51
without chemical reaction. For form a in Fig. 4.6, and (the specific exergy of
stream 5 and stream 8 of the exergy form a) both decrease between inlet and outlet,
the exergy decrease can be written as and evidently be part of the
fuel. For the exergy form b, and both increase and the total increase is
which belongs to the product. However, for the exergy form c, the
specific exergy increases for stream 5 and decreases for stream 8. In this case,
according to the fuel definition, a specific exergy decrease is always interpreted as a
fuel, but a specific exergy increase should be distinguished by two subcases
depending on whether the increase is consistent with the purpose of the component
or not. In the first subcase, the specific exergy increase is incidental to the purpose of
the component (e.g., the increase in specific chemical exergy for the air mass flow
rate between inlet and outlet of a combustion chamber). The total difference
between inlet and outlet should be or ∆
. This difference ∆ obviously is part of the fuel of the component
whether the value is negative or positive. It should be noted that ∆ being positive
is a practically unknown but theoretically possible event (Lazzaretto A, Tsatsaronis G,
2006). In the second subcase, the specific exergy increase is desired for the
component, thus the fictitious auxiliary device in Fig. 4.6 is used to demonstrate the
separate exergy changes and seprate costs per exergy unit for separate streams at
the outlet. An imaginary state 9* is defined as the state in which the streams and
are not merged. Then the exergy difference belongs to fuel and
is part of the product. According to these two subcases, the equation
to define the fuel and product can be summarized respectively as follow:
Assuming subcase one applied to the exergy form c, the equations are
4.34
4.35
If subcase two applied to the exergy form c, the equations should be
4.36
4.37
52
It should be mentioned that in the paper (Lazzaretto A, Tsatsaronis G, 2006) it is
considered that making a distinction between physical and chemical exergy in
components in which the chemical exergy of each stream remains constant does not
in any way affect the results, while unnecessarily increases the required
computational efforts. These components include compressors, pumps, turbines and
heat exchangers, etc. As a result, only exergy differences between inlet and outlet for
every material streams are used in the definition of fuel and product, just like the
stream 1 and 2 in Fig. 4.5. But in this computer program, the efforts of computation
are no longer a problem that we are concerned with. And if the users make a
decision to use the separate form of exergy that discussed in section 4.4.1 when the
analysis begin, then the separate form of exergy will be used not only in the
components (e.g., combustion chamber, gasifier) where chemical composition of
material streams changes but also those (e.g., fan, condensor) where the chemical
reaction are not occur. As an example, (the difference of the separate
exergy form a between the stream 1 and 2 shown in Fig. 4.6) belongs to fuel, while
which equals zero and is not accord with the purpose of the component
(the difference of the separate exergy form b between the stream 1 and 2) is neither
part of fuel nor part of product. From the thermodynamic viewpoint maybe it’s not
meaningful at component level, but it’s necessary for using the program to analyze
the entire system. The reason will be discussed below in section 4.4.3.
4.4.3Costbalance
For the incoming and outgoing streams of the component, the general form of the
cost balance equations is represented as Eq. (3.21) in section 3.2.3. In order to do an
exergoeconomic analysis to a complex system, the cost balances should be
formulated for each system component separately. If there are k components in a
system, then there will be k cost balance equations. Moreover, for the kth
component, the equations can be written alternatively as:
, , 4.38
53
, , , , 4.39
These two equations in some particular situations cannot be used to calculate
the specific cost of the product of the kth component. For an instance, within a
mixing device as the second sub case for exergy form c in section 4.4.2, it is difficult
to calculate the specific cost of the product directly through the value of and .
Instead the separate costs per exergy unit , and , of the fictitious auxiliary
device at the imaginary state 9* are required (see section 3.3 in the paper presented
by Lazzaretto A, Tsatsaronis G, 2006). However, the separate costs , and ,
increase the number of unknowns for the cost balance equation and cannot be
described in a unified form with other components. It is adverse for the matrix
formulation and detrimental to computer programming. Thus in this thesis, the
separate costs are not needed and the value of is calculated from the cost
balance with the value of .
If the separate forms of exergy (e.g., physical and chemical for this program) are
used for exergoeconomic analysis, the cost balance equation can be written as:
, , , , , , , , 4.40
In previous discussion in section 3.2, for each component, the incoming streams from
upstream components are assumed to be known, so that the outgoing streams which
are unknown can be calculated through cost balance combined with auxiliary
equations. The specific cost rates with separate forms in the left part of the
equations are associated with the upstream components and can’t be calculated
from the total specific cost , directly. Therefore, regardless of which component
analyzed with separate forms of exergy streams, once the separate forms are used,
all streams of the whole system and each component whether there are chemical
reaction or not must use the separate form of exergy. And the specific cost of the
exergy streams supplied with a material stream to the overall system from outside as
known variables inputted into the program need to be separated as well.
54
4.4.4Auxiliaryequations
If the number of exiting exergy streams is n, when the unknown variables is larger
than one (n>1), only one equation, the cost balance is not enough to solve the
problem, then n‐1 auxiliary equations are needed. The auxiliary equations are
determined with the aid of the F and P principles in SPECO method (Lazzaretto A,
Tsatsaronis G, 2006). The F and P principles are derived from the fuel and product
definitions.
In simple terms, the F principle means the cost per exergy unit associated with
the removed exergy of an exergy stream in a considered component must be equal
to the average specific cost associated with the removed exergy from upstream
component supplied to the same exergy stream, when the exergy difference of this
stream between inlet and outlet which is considered as a fuel.
The P principle refers to each exergy unit is supplied to all streams that belong
to the definition of product have the same average cost.
Applying the F and P principle, auxiliary equations can be obtained from Fig. 4.5.
From the F principle, the equations are:
4.41
4.42
The P principle leads to the equations as follows:
4.43
The number of equations gained from the F principle equals the sum of exiting
streams that were identified as a fuel. And the number of equations provided by the
P principle is always equal to the number of exiting exergy streams which were
identified as a product minus one. In the SPECO method, it is considered that each
exiting exergy stream is associated either with the fuel or with the product, so the
total number of exiting streams (i.e., number of unknowns) should be equal to the
number of equations (cost balance plus auxiliary equation provided by F and P
principle). Nevertheless it should be emphasized that there is a particular case which
55
is also discribed at the end of section 4.4.2. When the separate forms of exergy are
used for the component without chemical composition change, since the difference
of exergy between inlet and outlet is not included in fuel or product, one
additional auxiliary equation is needed. Here in this program, it is assumed that the
cost per exergy unit associated with this stream remains constant (i.e., ),
because no exergy transfer associated with the difference of this exergy between
inlet and outlet can be attributed to the purpose of the component.
Combining the fuel and product definition with the F and P principles applied to
components, the auxiliary equations of each specific component model are
determined and saved to the component data structure. In the following, the exergy
rates and the auxiliary costing equations associated with fuel and product for some
selected components at steady state operation are demonstrated. All the
components included in this program can be found in Appendix C.
1. Heat exchangers
Q
Figure 4.7 Schematic of a heat exchanger
The fuel and product of heat exchangers are varied because the purpose of heat
exchangers changes along with the temperature of the exergy streams at the inlet
and the outlet. For different definitions of fuel and product, different auxiliary
equations are formulated. The schematic of a heat exchanger in Fig. 4.7 can make the
demonstration easier. When the temperature ( ) of the hot stream at the inlet is
lower than the temperature ( ) of the reference state, in other words, the
temperatures of all the streams at the inlet and outlet are below the reference
temperature, the purpose of the heat exchanger is to increase the physical exergy of
the hot stream between inlet and outlet. Thus the exergetic efficiency of heat
exchanger and the auxiliary equation can be written as following, while :
56
4.44
4.45
When the temperature ( ) of the cold stream at the inlet is higher than the
temperature ( ) of the reference state, i.e. . This means the temperatures of
all the streams at the inlet and outlet are above the reference temperature. The
exergetic efficiency and the auxiliary equation should be:
4.46
4.47
If the temperature ( ) of the incoming cold stream is lower than the reference
temperature ( ), simultaneously, the temperature of the entering hot stream ( ) is
higher than , i.e. and , there are four subcase distinguished by
the temperature of the exiting hot stream ( ) and the temperature of the outgoing
cold stream ( ).
The first subcase is and , the purpose of the heat exchanger
dictates that is at the fuel side and belongs to product. As a result the
exergetic efficiency and the auxiliary equation from F principle are:
4.48
4.49
The second subcase is and , no exergy difference between
inlet and outlet are used, the purpose of the heat exchanger dictates that and
are associated with the fuel and and at the outlet are product. Then the
exergetic efficiency and the auxiliary equation from P principle are:
4.50
4.51
The third subcase is and , at this time the heat exchanger
should be treated as a dissipative component since there is no product here from
57
thermodynamic viewpoint, and no efficiency are used.
The fourth subcase is and , the purpose of the heat exchanger
dictates that belongs to product and is associated with fuel. The exergetic
efficiency and the auxiliary equation from F principle are:
4.52
4.53
Some of these cases may be practically unknown, but theoretically can be
encountered. So the software should cover all the possibilities in the heat exchanger.
2. Mixing devices
Figure 4.8 Schematic of a mixing device
As shown in Fig. 4.8, when total exergies are used, the exergetic efficiency of the
mixing device is:
,
, 4.54
For mixing devices, since there is only one exiting stream, the cost rate of the exiting
stream can be calculated directly through the cost balance. However, due to the
discussion in section 4.4.2 and the F and P principles, the specific cost of fuel and the
specific cost of the product are:
, 4.55
, 4.56
, 4.57
58
So the specific costs , and , of the imaginary state 3* do not necessarily
need to be considered explicitly in the analysis of a mixing device. When the total
exergy is split into physical and chemical exergies, the exiting streams become two,
separate exergy streams for each mass flow rate at the outlet need to be considered
only for the physical exergy. The fuel of the mixing device is:
,
4.58
The product of the mixing device is:
, 4.59
According to the fuel and product definition only one auxiliary costing equation is
required that is from F principle:
4.60
The specific cost of fuel and the specific cost of product are:
4.61
, 4.62
, 4.63
The specific costs , and , of the imaginary state 3* still do not need to be
calculated.
3. Gasification reactor
Figure 4.9 Schematic of a gasifier
59
It should be noted that in Fig. 4.9 when total exergies are considered, the
treatment of is determined by the physical exergy of stream 1, whereas the
treatment of , and depends on the chemical exergy of stream 2, 3 and 4.
In each stream, the dominating exergy form determines the treatment of total exergy.
Consequently, the exergetic efficiency of gasification reactor is:
4.64
And the auxiliary costing equation is derived from the F principle, which is:
4.65
If physical and chemical exergies are separately used, according to the
description in section 4.4.2, the fuel and the product of the gasification reactor are:
4.66
4.67
or
4.68
One auxiliary equation is determined by the F principle and two auxiliary
equations are derived from the P principle as follows:
4.69
4.70
4.71
The specific cost of fuel and the specific cost of the product are:
4.72
4.73
The unknowns , , and are calculated by combination of cost
balance and Eq. (4.69) to (4.71).
60
4. Dissipative components
auxC 0CdcZ
dcdifC ,
Figure 4.10 Schematic of a dissipative component
For the practical applications which contain dissipative components, all cost
associated with owning and operating a dissipative component must be charged
directly to the components served by it. As shown in Fig. 4.10, the exergy of the main
working fluid at the outlet is lower than at the inlet because of the exergy
destruction within the dissipative component, which is:
∆ 4.74
According to the F principle, the cost per unit of the main working fluid remains
constant between inlet and outlet, it can be written as:
4.75
If the rate of the total charges associated with the use of the auxiliary working
fluid is and the contribution of investment cost and operating and
maintenance expense is , the cost balance for the dissipative component
becomes (see Lazzaretto A, Tsatsaronis G, 2006):
, 4.76
The term , is a fictitious cost rate associated with the use of the
dissipative component being considered. When this cost rate , derived from a
dissipative component needs to be charged to another component, it can be added
61
to the cost rate of the latter component, the equation is:
, 4.77
In this program, all these dissipative components first are calculated as
productive components. In this case, if there is no auxiliary working fluid in the
dissipative component (e.g. throttling valve), the value of , can be calculated
through the following equation:
, ∆ 4.78
If auxiliary working fluid is used (e.g. condenser), compared Eq. (4.76) with Eq.
(4.79), it is obviously, the value of , is equal to the value of the cost rate
associated with the auxiliary working fluid at the outlet, i.e., , . The latter ,
can be obtained directly from the exergoeconomic analysis with the program
calculation.
, , 4.79
With the values of , for dissipative components, the users can recalculate
the term in Eq. (4.77) of the productive components served by these dissipative
components. For throttling valve used to control the mass flow rate in a pump should
be charged to the pump. And for the condenser, the fictitious cost rate could be
apportioned among all remaining plant components by using the entropy increase in
each component as a weighting factor. These decisions should be made by the users,
and it is not the consideration of this program. When the new are inputted to the
software, the cost rate per exergy unit for productive components update, and the
new efficiencies can be calculated correctly.
4.4.5Matrixformulation
An exergoeconomic analysis is an appropriate combination of an exergetic analysis
with economic principles. This is achieved through exergy costing, by which a specific
cost rate c is assigned to each exergy stream of the plant. Thus, if a general example
62
consisting of n components and l exergy streams (including j material streams and k
energy streams) is considered, for calculating the cost rates of each exergy stream a
system of linear equations is needed to be solved. It should be noted that l
equals j plus k ( ) when total exergies are used, alternatively, is equal to 2j
plus k ( 2 ) when chemical and physical exergies are considered separately.
Therefore, the number of components and the number of exergy streams are
inputted by the program users as an initial data for formulating the matrix form of
equations. As was first presented by Valero A, et al, in 1986 and also used in SPECO
method, these linear equations can be written in the form:
4.80
It is illustrated in Fig 4.11, and the separate forms of exergy are used.
PHE1
PHjE
CHE1
CHjE
ENE1
ENkE
APH
m,0
ACH
m,0
A en,0
PHc1
PHjc
CHc1
CHjc
ENc1
Z 1
Z n
PHb1
PHjb 0
CHb1
CHjb 0
ENb1
ENkb 0
ENkc
A ll
Figure 4.11 The cost equations in a matrix form (Lazzaretto A, Tsatsaronis G, 2006)
The vector of the unknown variables consists of the cost rates ( ,
63
and ) can be written alternatively as the product of two vectors ( ,
and ) and ( , and ). The vector refers to the exergy values of
all streams and can be calculated by the method discussed in section 4.2 and 4.3. The
matrix is composed of the sub‐matrices , , , , , , , , , .
The subscript m represents material stream, en represents energy stream, 0
represents the specific cost of this stream is known, Frefers to the fuel definition and
P refers to the product. and are the incidence matrices representing the
interconnections between all components and all exergy streams which can be
obtained from the flow sheet. The elements of these two matrices are ‐1 (for an
exergy stream entering a component), +1 (for a stream exiting a component), or 0
(when there is no interconnection between a stream and a component). As a result,
Eq. (4.81) represents the equations of cost balances for all the components of the
plant.
4.81
The matrices , and , are associated with the exergy streams supplied
with a material stream to the overall system from outside. Where, the matrix ,
refers to not only the energy streams supplied to the overall system from outside but
also the energy streams provided by the system itself. The elements of matrices , ,
, and , are similar to the matrices and , only consist of ‐1, +1 and
0. The equations associated with these matrices have the form:
4.82
The value of are the known variables from the specific cost at which all
external resources are purchased or the average costing of the electricity generated
by the system. The auxiliary equations of matrix forms and are placed
within the large matrix one below the other since each row of each matrix
supplies one auxiliary equation obtained from the F and P principles. The auxiliary
equations are either of the forms as Eq. (4.41) to (4.43). Thus the coefficients of
and are of one of the following forms:
1,
1 ,
1 ,
1 4.83
64
For this program, the F and P principles and the auxiliary equations of different
component are respectively recorded into the different component model of the set
of component data structure. Then the matrices and can be directly
obtained from the set of component data structure. When the large matrix is
loaded, the unknown variables of vector can be calculated. With the value of the
specific cost, it is the possible to perform the exergoeconomic analysis described in
Section 3.2.3.
65
5. Implementation of the energy and exergy based
analysesprogramfortheenergyconversionsystems
In this chapter, the exergoeconomic analysis program is applied to three different
types of thermal power plant cases. These cases are all from the published literature
of colleagues in the Institute for Energy Engineering in TU Berlin. And the
assumptions of these cases used in the simulation and the conventional
exergy‐based analyses are inherited by the exergoeconomic analysis program in this
dissertation. The selected results of each method (energetic, exergetic,
exergoeconomic) for the considered plants from the reference literature and the
program are presented in the respective sections and compared in Table 5.1‐5.17. In
addition, the unabridged results and the process flow chart diagrams are given in
Appendix A.
5.1Combinedcyclepowerplant
The combined cycle power plant is an important type of thermal power plants in use
on the power grid today, operating on carbon‐based fuels such as natural gas, and
petroleum products. The reference case of a combined cycle power plant from
Petrakopoulou F (2011) consists of conventional exergy‐based analyses and advanced
exergy‐based analyses; only the results of the conventional exergy‐based analyses
are necessary for the comparison here. It is appropriate to prove that the
exergoeconomic analysis program is working correctly, because the reference case
used the same approaches for exergoeconomic analyses. Petrakopoulou used Ebsilon
Professional to simulate the referred combined cycle power plant and Matlab to
perform the exergetic analysis and exergoeconomic analysis. In this dissertation, the
basic thermal data like temperature, pressure and compositions of working fluids are
exported from Ebsilon Professional as well, and packed as an output text file which
can be read in the exergoeconomic analysis program. The tiny deviations between
the values of these thermal properties with the reference case are negligible.
66
5.1.1Energeticanalysis
The process simulation software gives the enthalpy and entropy values of each
stream after an iterative simulation procedure. The program also has a database of
several substances listed in Table 4.7 for thermal properties calculation. The results
of some selected flows in combined cycle power plant are compared in Table 5.1.
Table 5.1 Selected thermal results from the reference paper and the program
Selectedenergeticanalysisresultsfromtheexergoeconomicanalysisprogram
Stream Mass[kg/s]
Workingfluid
T[K]
P[bar]
h[kJ/kg]
s[kJ/kgK]
1 614.5 Air 288.15 1.013 ‐69.3506 6.8391
2 614.5 Air 666.05 17 319.8104 6.8899
3 14 CH4 288.15 50 ‐4689.5029 9.510
53 14 CH4 288.15 17 ‐4689.5029 10.0693
4 628.5 Combustion
gases
1537.15 16.49 140.1646 7.9685
5 628.5 Combustion
gases
853.75 1.058 ‐693.0014 8.0388
19 94.6 Water 306.05 3.728 138.1683 0.4764
20 94.6 Water 408.75 3.616 570.4277 1.6936
Selectedenergeticanalysisresultsfromthereferencepaper1 614.5 Air 288.15 1.013 15.1555 6.8695
2 614.5 Air 666.05 17 406.3903 6.9207
3 14 CH4 288.15 50 32.6806 9.5187
53 14 CH4 288.15 17 32.6806 10.0778
4 628.5 Combustion
gases
1537.17 16.49 1497.7913 8.1490
5 628.5 Combustion
gases
853.78 1.058 642.4399 8.2220
19 94.6 Water 306.04 3.728 138.1683 0.4764
20 94.6 Water 408.77 3.616 570.4277 1.6936
As can be seen in Table 5.1, the values of enthalpy and entropy are not equal
except the water. Since the reference states of enthalpy and entropy calculation are
different between Ebsilon Professional and the program, the comparisons of the
absolute values of enthalpy and entropy are pointless, while the thermodynamic
67
properties calculation of water and steam are based on the same reference
(IAPWS‐IF97). However, the relative deviations of each substance from the exergetic
and exergoeconomic analysis program are accurate with small deflections compared
to the results from the reference paper. The results of the generated or supplied
power of some selected components are presented in Table 5.2.
Table 5.2 Selected results of the generated or supplied work
Components W[MW]From this thesis
W[MW]From reference
Compressor 239.14 242.68
SteamTurbine1 29.92 29.18
SteamTurbine2 36.11 35.21
SteamTurbine3 62.91 61.35
Condenser Pump 0.04 0.04
LowPressurePump 0.00 0.00
HighPressurePump 1.04 1.12
IntermediatePressurePump 0.03 0.03
GasTurbine 526.00 530.67
Net Power Output 284.00 288.00
Total energetic efficiency 0.589 0.583
5.1.2Exergeticanalysis
Most of the process simulation software does not provide the values of the physical
and chemical exergies for each material stream. The combined cycle power plant
from the reference paper uses another program named Gatex to calculate the
exergies, but the disadvantage is that researchers need to code the exergy balance
equations everytime for different applications, while the exergoeconomic analysis
program overcomes this problem. The results of exergies for some selected streams
from distinct sources are paralleled with each other in Table 5.3. However, the
derived rates of fuel exergies and product exergies at the component level are
contrasted in Table 5.4, accompanied by the exergy destructions and other exergetic
variables. The reference states of exergetic analysis are the same that the
temperature is 288.15 K and the pressure is 1.013 bar.
68
Table 5.3 The results of exergies for some selected streams
ResultsfromthereferenceStream Mass
[kg/s]Workingfluid
T[K]
P[bar]
EPH[MW]
ECH[MW]
Etot[MW]
1 614.5 Air 288.15 1.013 0.00 0.96 0.96
2 614.5 Air 666.05 17 231.30 0.96 232.25
3 14 CH4 288.15 50 8.15 721.47 729.62
53 14 CH4 288.15 17 5.9 721.47 727.37
4 628.5 Combustion
gases
1537.15 16.49 735.74 5.27 741.01
5 628.5 Combustion
gases
853.75 1.058 184.60 5.27 189.87
7 268.5 Combustion
gases
720.76 1.05 52.39 2.25 54.64
9 360 Combustion
gases
722.45 1.05 70.66 3.02 73.68
18 628.5 Combustion
gases
368.49 1.03 11.22 5.27 16.49
19 94.6 Water 306.05 3.728 0.24 0.24 0.47
20 94.6 Water 408.75 3.616 7.95 0.24 8.18
22 72.4 Water 413.25 3.616 6.49 0.18 6.67
31 22.1 Steam 487.23 4.1 17.95 0.06 18.01
41 65.2 Steam 833.79 124 103.35 0.16 103.51
Resultsfromtheexergoeconomicanalysisprogram1 614.5 Air 288.15 1.013 0.00 1.10 1.10
2 614.5 Air 666.05 17 230.13 1.10 231.24
3 14 CH4 288.15 50 8.15 719.51 727.66
53 14 CH4 288.15 17 5.9 719.51 725.41
4 628.5 Combustion
gases
1537.17 16.49 715.55 8.3 723.85
5 628.5 Combustion
gases
853.78 1.058 179.16 8.3 187.46
7 268.5 Combustion
gases
720.76 1.05 50.54 3.55 54.09
9 360 Combustion
gases
722.45 1.05 68.18 4.75 72.93
18 628.5 Combustion
gases
368.49 1.03 8.36 8.3 16.66
19 94.6 Water 306.04 3.728 0.24 0.24 0.47
20 94.6 Water 408.77 3.616 7.95 0.24 8.18
22 72.4 Water 413.25 3.616 6.49 0.18 6.67
31 22.1 Steam 487.23 4.1 17.95 0.06 18.01
41 65.2 Steam 833.79 124 103.35 0.16 103.51
69
The definitions of product exergy and fuel exergy of different components are
given in Chapter 4.4, and the detailed graphic demonstrations for each component
model are presented in Appendix B.
Table 5.4 Selected exergetic results at the component level
Resultsfromthereference
EF EP ED Eps yD*
Component [MW] [MW] [MW] [%] [%]
Compressor 242.68 231.30 11.38 95.3 1.56
CC 729.62 508.76 220.87 69.7 30.23
GT 551.15 530.67 20.47 96.3 2.8
Reheater 26.47 23.89 2.58 90.3 0.35
HPSH 35.07 31.72 3.35 90.5 0.46
HPEVAP 43.64 39.91 3.73 91.5 0.51
HPECON 28.92 24.91 4.00 86.2 0.55
IPSH 0.18 0.12 0.06 69.0 0.01
IPEVAP 6.10 5.67 0.38 92.9 0.06
IPECON 1.06 0.87 0.19 82.5 0.03
LPSH 1.43 1.04 0.38 73.3 0.05
LPEVAP 19.03 15.48 3.55 81.4 0.49
LPECON 11.49 7.71 3.78 67.1 0.52
HPST 31.29 29.18 2.11 93.2 0.29
IPST 37.39 35.21 2.18 94.2 0.3
LPST 70.99 61.35 9.64 86.4 1.32
ResultsfromtheexergoeconomicanalysisprogramCompressor 240.00 230.46 9.58 96.0 1.31
CC 725.43 505.78 219.65 69.7 30.14
GT 538.16 526.00 12.17 97.7 1.67
Reheater 26.10 23.89 2.21 91.5 0.30
HPSH 34.58 31.72 2.86 91.7 0.39
HPEVAP 43.21 39.91 3.30 92.3 0.45
HPECON 28.69 24.91 3.77 86.8 0.52
IPSH 0.18 0.12 0.05 69.6 0.01
IPEVAP 6.05 5.67 0.38 93.7 0.05
IPECON 1.05 0.87 0.18 83.2 0.02
LPSH 1.41 1.04 0.37 73.9 0.05
LPEVAP 18.84 15.48 3.36 82.2 0.46
LPECON 11.32 7.71 3.61 68.1 0.50
HPST 31.29 29.92 1.37 95.6 0.19
IPST 37.39 36.11 1.28 96.6 0.18
LPST 70.99 62.91 8.08 88.6 1.11
70
5.1.3Exergoeconomicanalysis
The economic analysis is not included in the exergoeconomic analysis program; the
investment costs of components are considered as input data for the
exergoeconomic calculation. And the detailed graphic demonstrations for the
auxiliary cost balance equations of each component model are presented in
Appendix B as well. The specific cost of selected streams and the cost rates of total
exergy are compared in Table 5.5 in which the thermal properties of each stream are
corresponding with the same stream in Table 5.3. The specific cost for fuel (in this
case is CH4) is 9.2 €/GJ, besides the specific cost of air and cooling water at the
reference state are assumed to be 0 €/GJ.
Table 5.5 Cost rates of selected streams
NO. Mass[kg/s]
Workingfluid
Etot[MW]
ci[€/GJ]
Ci[€/h]
Etot[MW]
ci[€/GJ]
Ci[€/h]
Fromthereference Fromtheprogram1 614.5 Air 0.96 0.00 0.00 1.10 0.00 0.00
2 614.5 Air 232.25 19.4 16198 231.24 19.10 15900
3 14 CH4 729.62 9.2 24037 727.66 9.2 24100
53 14 CH4 727.37 9.2 23962 725.41 9.2 24026
4 628.5 Combustion
gases
741.01 15.5 41252 723.85 15.62 40886
5 628.5 Combustion
gases
189.87 15.5 10570 187.46 15.62 10588
7 268.5 Combustion
gases
54.64 15.5 3042 54.09 15.62 3055
9 360 Combustion
gases
73.68 15.5 4102 72.93 15.62 4119
18 628.5 Combustion
gases
16.49 0.00 0.00 16.66 15.62 941
19 94.6 Water 0.47 26.1 44 0.47 20.45 34
20 94.6 Water 8.18 30.6 900 8.18 24.01 707
22 72.4 Water 6.67 31.1 748 6.67 24.68 593
31 22.1 Steam 18.01 25.3 1642 18.01 22.88 1484
41 65.2 Steam 103.51 20.3 7581 103.51 19.25 7173
The results of exergoeconomic variables from the reference and the program are
71
shown in Table 5.6, respectively.
Table 5.6 Selected results of exergoeconomic analyses at component level
Resultsfromthereference cF cP CD Z CD+Z f r
Component [€/GJ] [€/GJ] [€/h] [€/h] [€/h] [%] [%]Compressor 16.9 19.5 693 1423 2116 67.3 15.0
CC 9.2 13.7 7276 1017 8293 12.3 49.5
GT 15.5 16.9 1140 1627 2766 58.8 9.4
Reheater 15.5 19.4 143 111 255 43.7 25.4
HPSH 15.5 19.4 186 158 344 45.8 25.6
HPEVAP 15.5 19.0 207 185 392 47.1 23.1
HPECON 15.5 20.4 223 89 312 28.6 31.8
IPSH 15.5 35.4 3 4 7 56.3 128.8
IPEVAP 15.5 20.5 24 65 90 73.1 32.8
IPECON 15.5 22.3 10 5 16 33.4 44.2
LPSH 15.5 29.5 21.0 19 41 47.7 90.9
LPEVAP 15.5 24.2 197 174 372 46.9 56.4
LPECON 15.5 30.8 211 93 304 30.7 99.3
HPST 20.3 24.2 155 182 336 54.0 18.9
IPST 20.3 24.7 159 329 488 67.4 21.7
LPST 21.4 29.7 743 764 1508 50.7 38.5
Total 9.2 20.6 9897 6519 16416 39.7 124.8
Resultsfromtheexergoeconomicanalysisprogram
Compressor 16.97 19.39 585.2 1423 2008 70.9 14.3
CC 9.23 13.79 7297.5 1017 8314 12.2 49.5
GT 15.62 16.97 689.6 1627 2317 70.2 7.8
Reheater 15.62 18.49 125.2 111 236 47.0 17.4
HPSH 15.62 18.55 162.1 158 320 49.4 17.8
HPEVAP 15.62 18.33 187.1 185 372 49.7 16.4
HPECON 15.62 19.12 213.9 89 303 29.4 21.5
IPSH 15.62 31.63 3.1 4 7 55.2 126.1
IPEVAP 15.62 19.99 23.8 65 89 73.2 32.8
IPECON 15.62 20.52 10.2 5 15 33.5 44.2
LPSH 15.62 26.36 21.0 19 39 46.6 89.3
LPEVAP 15.62 22.28 195.4 174 368 46.9 56.4
LPECON 15.62 26.48 208.5 93 301 30.8 99.2
HPST 19.24 21.81 152.9 182 318 52.0 18.3
IPST 19.21 22.46 157.4 329 457 65.6 20.7
LPST 20.09 26.04 734.3 764 1431 48.7 37.2
Total 9.2 20.52 9720 6519 16513 39.4 124.4
72
5.1.4Erroranalyses
The relative errors can be defined by comparing the results from the exergoeconomic
analysis program and the reference paper. If A0 denotes the real value of Ai in a data
set A, then the relative error can be written as:
%100%1000
0
0
A
AA
A
A ii (5.1)
The reasons that lead to the systematic error are diverse and will be discussed
separately in the following sections.
5.1.4.1Energeticanalysis
Comparing the difference between enthalpy and entropy values for the same
working fluid respectively from the exergoeconomic analysis program and the
reference paper in Table 5.1, the relative deviations are shown in Figure 5.1.
Moreover, the work generated and supplied to the combined cycle power plant of
each component in Table 5.2 is contrasted in Figure 5.1 as well.
Figure 5.1 Relative errors of energetic results for the combined cycle power plant
Granted the exceptions or noises, such as point 7 in Figure 5.1, the relative deviations
‐0.08
‐0.06
‐0.04
‐0.02
0
0.02
0.04
1 2 3 4 5 6 7 8 9
Δhref
REΔh
Δsref
REΔs
Wref
REW
73
between two different sources are less than 3%, and the errors of enthalpy and
entropy are negative which means the absolute value of these energetic results is
lower than the reference value. In addition, the results of water and steam are totally
matched, the deviations all exist in the results of air and combustion product stream
indicate that the causes of these errors are most coming from the distinct
thermodynamic database of the working fluid and the state equations, and the
properties calculation for this program are described in Section 4.2 and 4.3.
5.1.4.2Exergeticanalysis
The relative errors of exergetic results of 16 principal components of the combined
cycle system from Table 5.4 are illustrated in Figure 5.2. The exergies of fuel and
product are lower than the reference values while the exergy efficiencies are higher
than the reference values. The interval of the results for 16 points in the rectangular
coordinate is among ‐2.5% to +2.5%. These deviations of exergetic results are caused
by the same reason with the energetic results.
Figure 5.2 Relative errors of exergetic results for the combined cycle power plant
But the relative errors of exergy destructions and the exergy destruction ratio
are bigger than other exergetic results. Since the exergy destruction is defined to be
‐0.03
‐0.02
‐0.01
0
0.01
0.02
0.03
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Ef‐REF [MW]
Ep‐REF [MW]
Ef [MW]
Ep [MW]
Eps‐REF [%]
Eps [%]
74
the difference between fuel exergy and product exergy, the errors from the fuel
exergy and product exergy will be accumulated only if the errors of the fuel are equal
to the errors of product.
5.1.4.3Exergoeconomicanalysis
The deflections of the cost rates of fuel and product of 16 components and the
overall system in Table 5.6 are illustrated in Figure 5.3. For fuel cost, the variations
are minimal. For the product cost, although the trend of these two polylines are the
same, but the average deviations are around 6% that cannot be accepted for a real
application. However, it should not happen if the value of fuel exergy, product exergy
and fuel cost has minuscule errors. According to the same cost balance equations,
the product cost rates can be calculated with these three variables, and the
deviations should be minimal as well.
Figure 5.3 Absolute values comparison of the specific costs of fuel and product for
the combined cycle power plant
The deviations of the fuel costs are derived from the same origin with the energetic
and exergetic analysis, i.e., the thermodynamic data libraries of the substances.
Otherwise, the reason results in the product cost deviations can be found in Figure
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
cf‐REF [€/GJ]
cf [€/GJ]
cp‐REF [€/GJ]
cp [€/GJ]
75
5.4. The significant point on the horizontal ordinate is point 9, which is the
combustion gases stream with stream No. 18 in Table 5.6 (also in Table A.1.3 and
Table A.1.4), the value of the specific cost is 0 €/GJ for the reference and 15.62 €/GJ
for the program. This stream is the exhaust gas at the outlet of the heat recovery
generator; the 0 value are personal setting by the reference paper that changes the
auxiliary equation and the cost balance equation of the low‐pressure economizer. As
opposed to the reference, the value of the specific cost is directly gained from the F
rule of the economizer in the program. As a result, the 0 value of the specific cost of
exhaust gas leads to much higher values of specific costs of the downstream flows,
which are the water and steam streams in this case, also can be seen in Table 5.6 and
Figure 5.4.
Figure 5.4 Absolute values comparison of the specific costs of streams
5.2IGCCPlant
An integrated gasification combined cycle (IGCC) is based on the coal gasification
technology that uses a gasifier to turn coal or other carbon‐based solid fuels into
syngas. The impurities in the syngas should be removed before it is combusted, and
the combustion process is similar to a combined cycle power plant. Then the excess
0
5
10
15
20
25
30
35
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ci‐REF [€/GJ]
ci [€/GJ]
76
heat is passed to a heat recovery steam generator. A lot of facilities that make the
IGCC much more complex are required for dealing with the pollutants, such as
hydrogen sulfide and carbon dioxide. In this thesis, the reference case uses the
conventional IGCC plant with CO2 capture from Sorgenfrei and Tsatsaronis (2014), in
which Aspen Plus 8.0 is used for process simulation and EES is used for the physical
and chemical exergy calculation. The process flow diagram can be seen in Figure 5.5
Figure 5.5 Process flowchart of IGCC plant from the reference paper (Sorgenfrei and
Tsatsaronis, 2014)
In the conventional IGCC plant with CO2 capture, pure oxygen is supplied to the
gasifier for inhibiting the nitric oxide generation and increasing the carbon capture
rate from the air separation unit. The carbon monoxide in the syngas is shifted to
hydrogen via the water‐gas shift reactor. The hydrogen sulfide and carbon dioxide
from the shift reactor can be captured in the acid gas removal unit. The hydrogen
sulfide is then turned into sulfur as a reusable byproduct in the Claus plant, and the
carbon dioxide is compressed and stored. These processes result in nearly
carbon‐free fuel into the combustion chamber. However, thermal properties of some
selected common substances in the existing database in this program are all in the
gas phase except water, but a more improved and comprehensive thermodynamic
properties database is necessary for the energetic and exergetic analysis of the air
77
separation unit and acid gas removal unit due to the liquid phase and liquid‐vapor
mixture working fluids. Simultaneously, there aren’t component models associated
with some equipment with chemical reactions like the absorber. Hence, a judicious
subsystem partition can result in a considerable simplification of the equipment,
which means the coal dryer, mill and lock hopper are seen as a unit named “Coal
preparation unit”. Likewise, the air separation equipment and the acid gas removal
equipment are also modeled as one single air separation unit and acid gas removal
unit in the exergoeconomic analysis program. The detailed schematic of the IGCC
case used for the program calculation is given in Figure A.2.
5.2.1Energeticanalysis
The enthalpy and entropy results from the reference are directly given by Aspen Plus
and the EES software. The numerical values are drawn a comparison with the
associated values from the program in Table 5.7. Contrasted with Table 5.1, the
enthalpy results from Aspen Plus (property method Redlich‐Kwong‐Soave with
Boston Matthias Alpha function, i.e., RKS‐BM is used) and the program should be
calculated using similar reference state or equation of state, while Ebsilon
Professional is distinct. Yet it is completely converse for the entropy results, which
are closer for Ebsilon and the program. Generally, the results from exergetic analysis
depend on the accuracy of the enthalpy and entropy value. If the exergy value from
different sources is consistent as well, the diverse ways to calculate the enthalpy and
entropy are all appropriate. The results of the generated or supplied work of the
pumps, compressors and turbines are presented in Table 5.8.
Table 5.7 Selected thermal results from the reference paper and the program
No. Mass
[kg/s]
Workin
gfluid
T
[K]
P
[bar]
h
[kJ/kg]
s
[kJ/kg]
h
[kJ/kg]
s
[kJ/kg]
Fromthereference Fromtheprogram
1 80.00 Coal 288.15 1.013 ‐1882.978 ‐ 27227.4 1.2731
2 178.81 N2 402.74 1.013 ‐175.642 0.3092 ‐175.894 7.2756
4 175.00 N2 523.15 1.100 235.538 0.5636 235.328 7.4001
78
6 257.80 Air 288.15 1.013 ‐10.359 0.1129 ‐10.148 6.8505
35 6.50 N2 428.02 56.0 133.932 ‐0.8262 135.102 6.0222
37 59.85 O2 393.70 45.0 83.406 ‐0.7202 88.864 5.7106
42 135.63 Raw gas 1823.13 40.0 ‐1267.601 4.4484 ‐1268.420 10.460
46 291.96 Raw gas 553.15 40.0 ‐3363.687 2.5117 ‐3359.916 8.5201
51 149.37 Raw gas 414.32 38.966 ‐4463.054 1.7002 ‐4456.662 8.3513
59 244.37 Shift gas 561.63 38.766 ‐8246.324 ‐3.6969 ‐8230.455 8.9239
62 206.52 Shift gas 302.51 34.896 ‐7855.132 ‐0.9846 ‐7843.075 7.4285
64 25.71 Clean gas 293.15 34.626 ‐911.598 ‐5.9782 ‐916.676 26.620
65 42.00 Syngas 418.28 34.126 ‐5137.749 ‐2.8971 ‐5131.770 22.084
72 1230.02 Air 288.15 1.013 ‐10.358 0.1129 ‐10.148 6.8505
73 1230.02 Air 705.99 19.45 425.582 0.1884 425.042 6.9270
74 1272.02
Exhaust
gas 1586.38 19.45 237.968 1.1130 257.757 8.4535
76 1272.02
Exhaust
gas 886.05 1.050 ‐660.883 1.2451 ‐657.391 8.5899
88 1272.02
Exhaust
gas 406.15 1.050 ‐1222 7.6790 ‐1222.063 7.6782
90 346.00 Water 295.15 2.041 92.47 0.3249 92.477 0.3249
133 199.11 Steam 863.15 164.0 3544 6.5970 3544.451 6.5970
135 214.01 Steam 830.85 35.0 3582 7.3230 3582.419 7.3224
140 244.20 Mixed 299.82 0.035 2257 7.5450 2255.094 7.5391
Table 5.8 The selected results of the generated or supplied work
Components W[KW]
From thesis
W[KW]
From reference
CM1 N2 1764 1783.54
CM1 O2 4801 4829
CM2 N2 753 767
CM2 O2 4758 4779
CM3 N2 811 836
CM3 O2 4776 4793
Compressor 2020 2141
Compressor 535293 524572
Gas Turbine 1164085 1147611
HP SteamTurbine 84770 84713
IP SteamTurbine 142651 142670
LP SteamTurbine 159167 158697
LPPump 6 6
HPPump 4803 4778
IPPump 564 572
Total energetic efficiency 0.343 0.332
79
5.2.2Exergeticanalysis
Applied the program to the IGCC power plant, the results of exergies at the streams
level are compared with the corresponding values from the reference paper in Table
5.9.
Table 5.9 The results of exergies for some selected streams in IGCC plant
No. Mass
[kg/s]
Workin
gfluid
EPH[MW]
ECH[MW]
Etot[MW]
EPH[MW]
ECH[MW]
Etot[MW]
Fromthereference Fromtheprogram1 80.00 Coal 0.000 2557.60 2557.60 0.000 2467.62 2467.62
2 178.81 N2 3.626 4.35 7.98 3.515 4.28 7.79
4 175.00 N2 12.833 4.49 17.33 12.824 4.49 17.32
6 257.80 Air 0.000 1.53 1.53 0.000 1.53 1.53
35 6.50 N2 2.419 0.17 2.59 2.406 0.17 2.57
37 59.85 O2 17.865 6.88 24.75 17.916 6.88 24.80
42 135.63 Raw gas 283.619 1649.36 1932.97 282.731 1648.68 1931.41
46 291.96 Raw gas 161.469 3550.40 3711.87 161.183 3548.96 3710.14
51 149.37 Raw gas 72.494 1649.66 1722.15 72.055 1649.89 1721.95
59 244.37 Shift gas 155.467 1567.13 1722.60 155.379 1570.93 1726.31
62 206.52 Shift gas 89.830 1565.62 1655.45 90.446 1564.42 1654.86
64 25.71 Clean gas 53.756 1426.82 1480.58 53.394 1423.47 1476.87
65 42.00 Syngas 69.058 1424.96 1494.01 68.184 1425.62 1493.81
72 1230.02 Air 0.000 7.30 7.30 0.000 7.30 7.30
73 1230.02 Air 509.418 7.30 516.72 508.177 7.30 515.47
74 1272.02
Exhaust
gas 1651.50 26.71 1678.21 1649.96 26.50 1676.46
76 1272.02
Exhaust
gas 436.593 26.71 463.30 435.852 26.50 462.35
88 1272.02
Exhaust
gas 52.000 26.71 78.71 51.746 26.50 78.24
90 346.00 Water 0.157 17.11 17.27 0.157 17.28 17.44
133 199.11 Steam 328.000 9.83 337.83 327.561 9.94 337.51
135 214.01 Steam 315.000 10.56 325.56 315.467 10.69 326.16
140 244.20 Mixed 21.000 12.02 33.02 20.587 12.20 32.78
The most representative streams are selected for the comparison, for example
the external raw materials into the IGCC system like the coal, the air and the water
streams; the inlet and outlet streams of the gasification process; the incoming raw
80
gas and the outgoing shift gas stream through the water gas shift reaction; the clean
gas stream out of the acid gas removal unit; all streams associated with gas turbine
system; the combustion gas stream before and after the heat recovery generator and
the water and steam streams in both upstream and downstream side of the steam
turbine. These significant flows can describe the performance of the IGCC power
plant in general.
The reference state of the exergetic analysis for IGCC power plant with CO2
capture is that the temperature is at 288.15 K, and the pressure is at 1.013 bar. The
selected exergetic results at the component level for the IGCC plant are presented in
Table 5.10.
Table 5.10 Selected exergetic results at the component level for IGCC
EF EP ED Eps yD yD*
Component [MW] [MW] [MW] [%] [%] [%]
CoalPrepareUnit 93.10 43.65 49.44 46.89 0.2 0.35
Gasifier 2353.49 1914.22 439.27 81.34 17.74 31.36
ASU 46.75 18.44 28.31 39.44 1.14 2.02
CM1 O2 4.8 4.28 0.52 89.15 0.021 0.037
CM1 N2 1.76 1.62 0.14 91.78 0.006 0.01
Syngas Cooler HP 180.27 129.75 50.52 72 2.04 3.607
Syngas Cooler IP 7.96 6.69 1.27 84.1 0.05 0.091
Scrubber Dissipative component 18.12 ‐ 0.732 1.294
WGS HT 750.667 701.287 49.375 93.42 1.994 3.533
Evaporator 69.18 61.05 8.13 88.25 0.33 0.58
WGS LT 230.757 220.196 10.56 95.42 0.426 0.754
Heater 34.33 19.96 14.37 58.14 0.58 1.026
AGR Dissipative component 180 ‐ 7.18 12.708
Saturator 18.08 14.79 3.29 81.79 0.133 0.235
Compressor 535.29 508.18 27.12 94.93 1.1 1.936
CC 1406.43 1073.6 332.83 76.34 13.44 23.762
GT 1214.11 1143.09 50.02 94.15 2.02 3.571
HPSH1 36.86 34.95 1.90 94.84 0.077 0.136
HPSH2 64.07 58.02 6.06 90.55 0.245 0.432
IPSH1 91.16 84.53 6.63 92.73 0.268 0.473
IPSH2 0.186 0.18 0.006 96.98 0.0002 0.0004
IPSH3 25.02 21.29 3.72 85.12 0.15 0.266
IPEVAP 96.54 82.87 13.67 85.84 0.552 0.976
Preheater IP 32.31 27.42 4.89 84.87 0.197 0.349
81
LPSH 1.45 1.16 0.29 80 0.012 0.021
LPEVAP 31.14 25.26 5.88 81.12 0.237 0.42
Preheater LP 0.62 0.556 0.062 89.9 0.0025 0.004
Economizer 4.77 2.51 2.27 52.5 0.09 0.162
Turbine LP 169.1 159.17 9.93 94.13 0.401 0.709
Turbine IP 148.43 142.65 5.78 96.11 0.233 0.412
Turbine HP 88.44 84.77 3.67 95.85 0.148 0.262
Total 2476.44 824.74 1400.68 33.30 49.35 100
Since there are no identical detailed exergetic analysis results at the component
level from the reference case, in addition, the fuel and product exergy are redefined
in separated exergy forms for the exergetic and exergoeconomic analysis in the
program as above‐mentioned, the exergetic results for IGCC case will not be
compared in this thesis. But it doesn’t affect the validity and accuracy of the
calculation of the program, because the fuel and product exergy and other exergetic
parameters are derived from the fuel and product definition of component model
and the exergies of streams. The fuel and product definition of the component for
the IGCC case are the same as the combined cycle case (SPECO approach), and the
exergies of all streams are highly accurate in Table A.2.1. Therefore, the same
consideration are applied to the exergoeconomic analysis, and the results of the
exergoeconomic variables at the component level are not compared too. The
detailed graphic demonstrations for specific facilities of IGCC case such as gasifier,
WGS, saturator, coal preparation unit and ASU are presented in Appendix B.
5.2.3Exergoeconomicanalysis
In IGCC plant, the chemical and physical of streams are supplied or generated at
different unit costs, therefore, the specific cost of the chemical and physical exergy
are separated for the exergoeconomic analysis of the IGCC case in the program,
which is trying to improve the accuracy of the thermoeconomic analysis. Commonly,
taking these differing unit costs into consideration will at least double the amount of
computation, the definition of the fuel and product should be modified as well. As a
result, for the complex power system like IGCC with CO2 capture, the researchers
82
didn’t implement the separated cost before. However, this program will provide an
option to apply this separation by the predefined component model library.
The selected results of exergoeconomic analysis arranged by the sequence of
streams are shown in Table 5.11, and that at the component level are listed in Table
5.12.
Table 5.11 The cost rates of some selected streams
No. Mass
[kg/s]
EPH[MW]
ECH[MW]
Etot[MW]
cPH
[$/GJ]
cCH
[$/h]
ci [$/GJ]
Ci [$/h]
1 80.00 0.00 2467.62 2467.62 0.00 1.30 1.30 11548.44
2 178.81 3.51 4.28 7.79 56.49 124.88 94.03 2637.23
4 175.00 12.82 4.49 17.32 56.49 124.88 74.23 4627.95
6 257.80 0.00 1.53 1.53 0.00 0.00 0.00 0.00
35 6.50 2.41 0.17 2.57 55.986 124.88 60.46 559.92
37 59.85 17.92 6.88 24.80 127.01 124.88 126.42 11285.45
42 135.63 282.73 1648.68 1931.41 17.25 4.59 6.44 44777.74
46 291.96 161.18 3548.96 3710.14 18.88 4.59 5.21 69547.74
51 149.37 72.06 1649.89 1721.95 18.94 4.59 5.19 32154.69
59 244.37 155.38 1570.93 1726.31 37.71 1.92 5.14 31962.28
62 206.52 90.45 1564.42 1654.86 27.52 1.92 3.32 19782.50
64 25.71 53.39 1423.47 1476.87 27.52 5.91 6.69 35556.49
65 42.00 68.18 1425.62 1493.81 89.87 3.62 7.55 40617.32
72 1230.02 0.00 7.30 7.30 0.00 0.00 0.00 0.00
73 1230.02 508.18 7.30 515.47 16.92 0.00 16.68 30947.92
74 1272.02 1650 26.50 1676.46 12.49 0.12 12.29 74174.07
76 1272.02 435.85 26.50 462.35 12.49 0.12 11.78 19602.17
88 1272.02 51.75 26.50 78.24 12.49 0.12 8.30 2337.28
90 346.00 0.16 17.28 17.44 51.25 0.00 0.46 28.92
133 199.11 327.56 9.94 337.51 28.34 0.00 27.51 33421.52
135 214.01 315.47 10.69 326.16 25.43 0.00 24.59 28877.64
140 244.20 20.59 12.20 32.78 26.00 0.00 16.33 1927.17
The exergoeconomic analysis is not included in the reference IGCC case; the
investment costs kZ of the components are calculated by economic analysis. The
fuel cost (here is coal at 1.3 $/GJ) and the purchased equipment cost of different
equipments is quoted from the case 6‐Shell IGCC power plant with CO2 capture of
the final report of cost and performance baseline for fossil energy plants volume 1
83
(2013, Revision 2a). The total revenue requirement method introduced in section
3.2.2 is applied for economic analysis of the IGCC power plant, and the results are
presented in Appendix C.
Table 5.12 Selected results of exergoeconomic analyses at component level
cF cP CD Z CD+Z f rComponent [$/GJ] [$/GJ] [$/h] [$/h] [$/h] [%] [%]
CoalPrepareUnit 56.49 965.32 1005.4 12632.582 13637.982 92.63 1608.83
Gasifier 965.32 1950.6 6108.5 7.591 6116.091 0.12 102.07
ASU 24.4 295.016 2486.7 9794.174 12280.874 79.75 1109.08
CM1 O2 24.4 43.65 42.9 253.718 296.618 85.54 78.89
CM1 N2 24.4 48.49 12.7 127.695 140.395 90.95 98.75
Syngas Cooler HP 18.876 28.14 3433.21 893.562 4326.772 20.65 49.08
Syngas Cooler IP 18.876 24.91 86.16 59.236 145.396 40.74 31.97
Scrubber ‐ ‐ 586.6 586.6 100.0 ‐
WGS HT 0.8136 1.169 144.62 752.553 897.173 83.88 43.68
Evaporator 37.7 44.7 1103.85 430.071 1533.921 28.04 18.57
WGS LT 0.4316 0.927 16.41 376.276 392.686 95.82 114.78
Heater 37.7 77.1 1951.04 752.479 2703.519 27.83 104.51
AGR ‐ ‐ 15773.96 15773.956 100.0
Saturator 239.57 314.95 2840.3 1173.2 4013.5 29.23 31.46
Compressor 13.9 16.92 1356.3 4174.088 5530.388 75.48 21.73
CC 3.66 5.47 4388.85 2608.805 6997.655 37.28 49.45
GT 12.486 13.9 2248.4 3652.327 5900.727 61.90 11.32
HPSH1 12.486 15 85.48 230.553 316.033 72.95 20.13
HPSH2 12.486 15.44 272.2 344.42 616.62 55.86 23.66
IPSH1 12.486 15.3 298.1 547.728 845.828 64.76 22.54
IPSH2 12.486 18.9 0.25 3.917 4.167 94.00 51.37
IPSH3 12.486 19.2 167.3 349.259 516.559 67.61 53.77
IPEVAP 12.486 17.68 614.4 934.781 1549.181 60.34 41.60
Preheater IP 12.486 16.2 219.73 148.285 368.015 40.29 29.75
LPSH 12.486 23.33 12.96 32.192 45.152 71.30 86.85
LPEVAP 12.486 19.95 264.24 414.274 678.514 61.06 59.78
Preheater LP 12.486 19.98 2.81 12.196 15.006 81.27 60.02
Economizer 12.486 30.22 101.94 57.973 159.913 36.25 142.03
Turbine HP 28.34 30.125 374.77 169.253 544.023 31.11 6.30
Turbine IP 25.43 27.3 528.75 428.691 957.441 44.77 7.35
Turbine LP 26 28.74 929.82 636.242 1566.062 40.63 10.54
Total 1.3 24.4 40806.6 77767.9 118574.6 65.59 1776.92
84
5.2.4Erroranalyses
5.2.4.1Energeticanalysis
The relative errors of the enthalpy results of 21 points in the rectangular coordinate
which represent 21 streams in Table 5.7 expect coal are slight. The overall accuracy is
higher than Figure 5.1, which means the enthalpy results of the working fluids from
the program are more closed to the values from Aspen Plus than that from Ebsilon
Professional. For the entropy results, only point 17 to point 21 that represent the
water and steam streams in Table 5.7 are compared. The entropy results of water
from the reference paper is obtained by EES, which are also calculated based on the
steam table IAPWS‐97, resulting in the same outcome with the program. The relative
errors of most supplied and generated work from Table 5.8 are among ‐2% to +2%.
Figure 5.6 Relative errors of energetic results of the IGCC case
5.2.4.2Exergeticanalysis
22 streams in Table 5.9 are taken into consideration; the relative errors of the
chemical, physical and total exergies are shown in Figure 5.7. The deviations of most
‐0.08
‐0.06
‐0.04
‐0.02
0
0.02
0.04
0.06
0.08
0.1
1 2 3 4 5 6 7 8 9 101112131415161718192021
href [kJ/kg]
sref [kJ/kg]
h [kJ/kg]
s [kJ/kg]
Wref [MW]
W [MW]
85
points are within the range of ±1% so that the exergy estimate of the program is
satisfactory. Point 1 has the biggest deviation since the coal properties calculation
method discussed in Section 4.3.2 is an approximate approach.
Figure 5.7 Relative errors of exergies of the IGCC case
5.2.4.3Exergoeconomicanalysis
Without the information of exergoeconomic analysis from reference paper, no error
analysis is performed to the IGCC case. But through Table 5.10 and 5.13, it can be
seen that the total exergy efficiency of the IGCC power plant is 0.333, the net power
output is 824.74MW and the specific cost of the output electricity is 24.4 $/GJ,
implying the general performance obtained from the exergetic, and exergoeconomic
analysis is appropriate.
‐0.04
‐0.03
‐0.02
‐0.01
0
0.01
0.02
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
EPH‐Ref [MW] ECH‐Ref [MW] Etot‐Ref [MW]
EPH [MW] ECH [MW] Etot [MW]
86
5.3Simplerefrigerationmachine
A simple compression refrigeration machine system from the reference paper
(Morosuk T, Tsatsaronis G, 2007) is implemented here without the advanced
exergoeconomic analysis. The process flow diagram is shown in Appendix A.3, and
the results of the numerical analysis are presented in Table 5.13‐5.17.
5.3.1Energeticanalysis
R717 (Ammonia or NH3) is used as the refrigerant in the refrigeration machine of the
reference, only the thermal properties of gas phase of R717 can be calculated with
Table 4.7, the liquid phase, and saturated line are calculated in this program based on
the thermal properties of critical state and the method from the literature (Chen Z S,
Cheng W L, Hu P, 2001, 2003).
Table 5.13 Selected thermal results of the refrigeration machine
No. Mass
[kg/s]
Working
fluid
T
[K]
P
[bar]
h
[kJ/kg]
s
[kJ/kg]
h
[kJ/kg]
s
[kJ/kg]
Fromthereference Fromtheprogram
1 0.09186 R717 248.15 1.51 1430 5.981 1430 5.979
2 0.09186 R717 426.15 11.67 1810 6.166 1829 6.194
3 0.09186 R717 303.15 11.67 341.6 1.488 343.7 1.499
4 0.09186 R717 248.15 1.51 341.6 1.594 343.7 1.601
6 6.45 Water 293.15 1 83.93 0.296 84.01 0.296
7 6.45 Water 298.15 1 104.8 0.367 104.9 0.367
8 9.942 Air 268.15 1 268.3 6.757 ‐30.35 6.782
9 9.942 Air 258.15 1 258.2 6.719 ‐40.46 6.743
As the comparison in Table 5.13, the thermal results of the program are
acceptable for energetic analysis.
5.3.2Exergeticanalysis
In the reference paper, in order to define appropriate exergetic efficiencies for the
87
components, the physical exergy associated with each material stream are split into
its thermal and mechanical parts. But in this program, this split is not applied and can
be realized in the future work. The reference state of exergy‐based analysis for this
case is 293.15 K and 1 bar.
Table 5.14 The results of exergies for the refrigeration machine
No Mass[kg/s]
Workin
gfluid
ePH
[kJ/kg]eCH
[kJ/kg]Etot[KW]
ePH
[kJ/kg]eCH
[kJ/kg]Etot[KW]
Fromthereference Fromtheprogram1 0.09186 R717 67.5 19841 1828.8 67.7 19841 1828.8
2 0.09186 R717 393.2 19841 1858.7 403.8 19841 1859.7
3 0.09186 R717 296.1 19841 1849.8 294.5 19841 1849.6
4 0.09186 R717 264.9 19841 1846.9 264.7 19841 1846.9
6 6.45 Water 0 49.9 321.9 0 49.9 321.9
7 6.45 Water 0.176 49.9 323 0.176 49.9 323
8 9.942 Air 1.138 5.2 63 1.142 5.2 63.1
9 9.942 Air 2.285 5.2 74.4 2.296 5.2 74.5
5 work 34.9 36.65
The chemical exergy of the flowing stream has no contribution in this energy
system, the exergy fuel and the product exergy in Table 5.15 only associated with the
physical exergy in Table 5.14.
Table 5.15 Selected exergetic results at the component level
Exergeticresultsfromtheprogram
EF EP ED Eps yD*
Component [MW] [MW] [MW] [%] [%]
CM 36.65 30.87 5.778 84.24 24.03
CD 10.04 1.137 8.903 11.33 37.03
TV 21.57 18.82 2.737 86.85 11.38
EV 18.10 11.47 6.625 63.39 27.55
ResultsfromthereferencepaperCM 34.9 29.92 4.981 85.7 22.28
CD 8.919 1.138 7.781 12.76 34.41
TV 21.82 18.95 2.868 86.85 12.83
EV 18.14 11.41 6.721 62.9 30.07
88
5.3.3Exergoeconomicanalysis
The cost rates associated with thermal and mechanical exergy are not considered
here too. Instead, the cost rates of physical exergy are calculated in the program, and
the fuel of the compression refrigeration machine is the power supplied to the
compressor, which is known through the market price of electricity. Here, the price is
assumed to be 0.1 €/KWh, equal to 27.78 €/GJ.
Table 5.16 The cost rates of selected streams for the refrigeration machine
Resultsfromtheexergoeconomicanalysisprogram Mass EPH ECH Etot cPH cCH ci Ci
stream [kg/s] [KW] [KW] [KW] [€/GJ] [€/GJ] [€/GJ] [€/GJ]
1 0.09186 67.7 19841 1828.8 59.4 0 0.20 1.33
2 0.09186 403.8 19841 1859.7 53.32 0 1.06 7.12
3 0.09186 294.5 19841 1849.6 53.32 0 0.78 5.19
4 0.09186 264.7 19841 1846.9 59.4 0 0.78 5.20
6 6.45 0 49.9 321.9 0 0 0.00 0.00
7 6.45 0.176 49.9 323 643.31 0 2.26 2.63
8 9.942 1.142 5.2 63.1 61.617 0 11.09 2.52
9 9.942 2.296 5.2 74.5 111.28 0 34.08 9.14
5 34.9 27.78 3.67
Resultsfromthereferencepaper1 0.09186 67.5 19841 1828.8 60.12 0 0.20 1.34
2 0.09186 393.2 19841 1858.7 53.51 0 1.04 6.96
3 0.09186 296.1 19841 1849.8 53.51 0 0.79 5.24
4 0.09186 264.9 19841 1846.9 60.12 0 0.79 5.27
6 6.45 0 49.9 321.9 0 0 0.00 0.00
7 6.45 0.176 49.9 323 588.34 0 2.07 2.40
8 9.942 1.138 5.2 63 61.617 0 11.06 2.51
9 9.942 2.285 5.2 74.4 112.37 0 34.31 9.19
5 34.9 27.78 3.49
The cost rates of the chemical exergy in Table 5.16 are all 0 because no increase
or decrease occurs in chemical exergy form within any of the components. The cost
rates of the fuel and the product of each component are obtained from the cost rates
of physical exergy. Different from the other two power plants discussed above, the
condenser and the throttling valve in this case are considered to be productive
89
components, and the exergoeconomic variables of them are compared in Table 5.17.
Table 5.17 Selected results of exergoeconomic analyses at component level
Resultsfromtheexergoeconomicanalysisprogram
cF cP CD Z CD+Z f rComponent [€/GJ] [€/GJ] [€/h] [€/h] [€/h] [%] [%]
CM 27.78 52.098 0.558 2.125 2.703 78.6 87.5
CD 53.32 643.31 1.709 0.707 2.416 29.3 1106
TV 52.13 59.838 0.514 0.0068 0.5204 1.31 14.8
EV 59.40 160.44 1.417 2.756 4.173 66.0 170
Resultsfromthereferencepaper
CM 27.78 51.581 0.489 2.125 2.623 81.0 90
CD 52.86 588.34 1.481 0.707 2.188 32.3 1013
TV 52.13 59.356 0.538 0.0068 0.5448 1.25 13.86
EV 60.12 76.864 1.456 2.756 4.212 65.4 170
5.3.4Erroranalyses
5.3.4.1Energeticanalysis
Figure 5.8 shows that the biggest relative error of enthalpy and entropy for 8 streams
in Table 5.13 is only 1%. It demonstrates that the program is also adaptable to the
cooling system, and the accuracy is much higher than the combined cycle system and
the IGCC power plant. Of course, the primary reason for the improvement of the
precision is probably because the complexity of the system. The point 2 on the
horizontal ordinate of the biggest relative error is the R717 in the supercooled area
suggests that the thermal properties evaluation of ammonia in supercooled area in
the program has some distinction with the reference paper.
90
Figure 5.8 Relative errors of energetic results for the compression refrigeration
machine
5.3.4.2Exergeticanalysis
The relative deviations of the physical exergy are similar to errors of the enthalpy in
Figure 5.8. Moreover, the errors of the exergetic parameters at the component level
from Table 5.15 are illustrated in Figure 5.9. Since the simple refrigeration system
only has four components, the relative error of the point 2, i.e., the condenser, is
significantly affected by the incoming stream that is the stream 2 in Table 5.16 and
also is the point 2 with the biggest relative errors in Figure 5.8.
Figure 5.9 Relative errors of exergetic results for the refrigeration machine
‐0.002
0
0.002
0.004
0.006
0.008
0.01
0.012
1 2 3 4 5 6 7 8
href [kJ/kg]
sref [kJ/kg]
h [kJ/kg]
s [kJ/kg]
‐0.15
‐0.1
‐0.05
0
0.05
0.1
0.15
1 2 3 4
Ef‐REF [KW]
Ep‐REF [KW]
Eps‐REF %
Ef [KW]
Ep [KW]
Eps %
91
5.3.4.3Exergoeconomicanalysis
In Figure 5.10, the fuel and the product cost rates of four components are
approximate except the product cost rates of the condenser. For the condenser, the
large amount of deviation of the fuel exergy and minuscule difference of the product
exergy in Figure 5.9 results in the significant increase in the product cost rates. The
origin of this variation can be traced back to the thermodynamic data of the R717
stream at the inlet of the condenser (the point 2 in Figure 5.8). It reveals that the
deviations are exaggerated during the entire exergy‐based analysis.
Figure 5.10 Relative errors of the exergoeconomic results for the refrigeration
machine
‐0.02
0
0.02
0.04
0.06
0.08
0.1
1 2 3 4
cf‐ref (€/GJ)
cp‐ref (€/GJ)
cf (€/GJ)
cp (€/GJ)
92
6.Conclusion
In this dissertation, a computer program for the exergoeconomic analysis of energy
conversion systems has been developed based on the SPECO method. The input data
pretreatment functions of the thermal properties calculation part and the exergetic
analysis of considered energy systems have been realized too. Three typical energy
systems have been introduced to examine whether the program is running
appropriately or not. And the results of the calculation from the program are
inspected and compared with the values from the reference papers in Chapter 5. A
combined cycle power plant with the most comprehensive results of each step of the
whole exergoeconomic analysis is primarily used to find out the accuracy of the
program output data step by step. The IGCC power plant with CO2 capture case is
focused on the capability of handling complicated systems and the exergoeconomic
analysis with separated exergy forms. The last simple compression refrigeration
machine is aimed at the exergy‐based calculation when the operating temperature is
lower than the environment temperature. A short summary of the results of the
energetic analysis, the exergetic analysis and the exergoeconomic analysis for three
different cases are presented below, respectively.
6.1EnergeticAnalysis
The energetic analysis is always the first procedure of an exergoeconomic analysis for
energy conversion systems. The results of this part from the reference paper are all
coming from the commercial popular simulation software with very high precision.
As already discussed in Chapter 5, the results of the exergetic analysis and the
exergoeconomic analysis are significantly influenced by the outcomes of the
energetic analysis. Seen the relative error analysis for the three considered systems,
the average relative deviation of the common gases is 1.05% for the enthalpy and
0.92% for the entropy, and completely no difference occurs for the water and steam
flows. But the comparison of the energetic results sometimes is inconvenient due to
93
the distinct reference state of different simulation software. Hence, the contrast of
exergy values of each material stream is more intuitively clear.
6.2Exergeticanalysis
The physical exergies of the working fluids are directly related to the enthalpy and
entropy, and the average relative deviation of the total exergy of 67 streams in Table
A.1.3 that belong to the combined cycle power plant is 0.56%. Similarly, the average
relative deviation of the total exergy of 151 streams in Table A.2.1 from the IGCC case
is 0.86%. The sample of the compression refrigeration machine is too small; the
average deviation is pointless, and the relative errors of each stream have been
presented in Section 5.3.4.2. All the exergetic variables at the component level are
derived from the exergy of streams and the component models; the errors are
enlarged among the numerical calculation. Take the combined cycle power plant for
example; the average relative deviations of the fuel and product exergies of these
flows basically remain steady, which are 0.89% and 0.59% separately. As a result, the
average relative deviation of the exergetic efficiency is 1.25%; however, for the
exergy destructions this value is greatly increased to 14.2%. But for a general
estimate of energy conversion systems by the exergy‐based analysis, what the
researcher concerned is that which components are the most inefficient facilities and
with the highest exergy destructions rather than the true value of the exergy
destruction. Figure 6.1 shows that the point 1, 2, 3 and 16 represented air
compressor, combustion chamber, gas turbine and low‐pressure steam turbine are
the most influential equipment in the combined cycle power plant. This conclusion
can be acquired from both exergy destruction results in Figure 6.1 even a big
variation exists. Consequently, the errors of exergy destructions do not affect the
implementation of the program, and it can be significantly improved by modifying
the calculation method of thermal properties of substances in the future.
94
Figure 6.1 Exergy destructions of primary components of the combined cycle power
plant
Although the definition of the exergetic efficiency of the IGCC power plant is
adjusted and formulated by physical and chemical exergy instead of total exergy, the
degree of accuracy remains unchanged no matter which kind of exergy form is used.
The exergy calculation of the refrigerant R717 and the exergetic analysis of the third
refrigeration machine case are appropriate only the precision of super cooling area of
the refrigerant should be improved.
6.3Exergoeconomicanalysis
The average relative error for the fuel cost rates of the combined cycle is 1.23% that
is a little bit expanded than the fuel exergy but acceptable. For the product cost rates,
the mean value is about 0.54% for the compressor, combustion chamber and gas
turbine but grows to 6.75% for other components as a result of the different
definitions of the product for the low pressure economizer. A detailed explanation is
in Section 5.1.4.3. The exergoeconomic analysis for the IGCC case can’t compare to
any reference data, but the correctness of the calculation still can be roughly
confirmed because the cost balance for the overall system is fulfilled, the total
exergetic efficiency and the cost rate of electricity are in the reasonable range. It also
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Ed‐REF [MW] Ed [MW]
95
can be proved by the refrigeration machine case since the cost rate of physical exergy,
and chemical exergy are split too. The average relative deviation of the physical
exergy cost of 9 streams is 1.5%. For the fuel and the product cost rates at the
component level, the difference is less than 1%. The cost rates associated with the
exergy destruction is similar to the exergy destruction; big errors exist, but the
components that have ultimate cost associated with the inefficient is the same.
6.4Summaryandfuturework
In general, the program provides a fast way to apply the exergoeconomic analysis to
common energy conversion systems. It can read text files or Excel files as the initial
data input of exergoeconomic analysis that makes the connection to other simulation
software easier and more flexible. It also reveals that the exergoeconomic accounting
method, especially the SPECO approach, is suitable and convenient to be realized by
a computer program. When complex systems are considered and the separated
exergy forms are used, the exergoeconomic analysis with the program will save more
times for the researchers.
The precision of the parameters that are directly obtained from the thermal
properties database is highest while the degree of the accuracy drops quickly for the
exergetic and exergoeconomic variables that are indirectly gained through other
calculated results. Therefore, the average relative errors of the enthalpy, entropy,
exergy and specific cost for each material flow similar to the average relative errors
of the fuel exergy, the product exergy and the cost rates associated with these
exergies for the component are all below 1.5%. However, the exergy destruction and
other variables bound up with the exergy destruction are not very precise. But as has
been discussed above, this inaccuracy does not prevent the researchers from
acquiring correct conclusions of the exergy‐based analyses. Consequently, the
program is suitable for a probable evaluation to an energy conversion system.
Nonetheless, for numerical analysis and process simulation, the precision is the
higher, the better. The accuracy of the program can be significantly improved by
96
using a more accurate equation of state, more comprehensive substances databases
or better approach for liquid and solid phase.
Simultaneously, the library of the components exergoeconomic models need to
be extended by more specialized equipment and components with chemical
reactions so that the program can be applied to the much larger scope. Perhaps, the
user‐defined component function is another possibility.
In addition, splitting the physical exergy into the thermal exergy and mechanical
exergy also can be achieved by some modification works in the future. The
exergoenvironmental analysis has identical procedure with the exergoeconomic
analysis, the only distinguish is that the input data of investment cost kZ should be
instead by the environmental impact kY and the cost rate iC will be changed to
the impact rate iB .
Finally, the program for now is still a fundamental trial edition; there are a lot of
works to accomplish it.
97
AppendixA
Flowchartsandsimulationresultsofthisprogramandthe
referencepaper
98
A.1Thecombinedcyclepowerplant
99
Table A.1.1 Results at component level for the combined cycle power plant from the program
EF EP ED Eps yD* cF cP CD Z CD+Z f rComponent (MW) (MW) (MW) (%) (%) (€/GJ) (€/GJ) (€/h) (€/h) (€/h) (%) (%)Compressor 240.00 230.46 9.58 96.0 1.31 16.97 19.39 585.2 1423 2008 70.9 14.3
CC 725.43 505.78 219.65 69.7 30.14 9.23 13.79 7297.5 1017 8314 12.2 49.5 GT 538.16 526.00 12.17 97.7 1.67 15.69 16.97 689.6 1627 2317 70.2 7.8
Reheater 26.10 23.89 2.21 91.5 0.30 15.69 18.49 125.2 111 236 47.0 17.4 HPSH 34.58 31.72 2.86 91.7 0.39 15.69 18.55 162.1 158 320 49.4 17.8
HPEVAP 43.21 39.91 3.30 92.3 0.45 15.69 18.33 187.1 185 372 49.7 16.4 HPECON 28.69 24.91 3.77 86.8 0.52 15.69 19.12 213.9 89 303 29.4 21.5
IPSH 0.18 0.12 0.05 69.6 0.01 15.69 31.63 3.1 4 7 55.2 126.1 IPEVAP 6.05 5.67 0.38 93.7 0.05 15.69 19.99 23.8 65 89 73.2 32.8 IPECON 1.05 0.87 0.18 83.2 0.02 15.69 20.52 10.2 5 15 33.5 44.2
LPSH 1.41 1.04 0.37 73.9 0.05 15.69 26.36 21.0 19 39 46.6 89.3 LPEVAP 18.84 15.48 3.36 82.2 0.46 15.69 22.28 195.4 174 368 46.9 56.4 LPECON 11.32 7.71 3.61 68.1 0.50 15.69 26.48 208.5 93 301 30.8 99.2
HPST 31.29 29.92 1.37 95.6 0.19 19.24 21.81 152.9 182 318 52.0 18.3 IPST 37.39 36.11 1.28 96.6 0.18 19.21 22.46 157.4 329 457 65.6 20.7 LPST 70.99 62.91 8.08 88.6 1.11 20.09 26.04 734.3 764 1431 48.7 37.2
Cond. Pump 0.04 0.04 0.00 92.2 0.00 20.00 77.01 0.7 7 8 91.0 310.0 HP Pump 1.04 0.96 0.09 91.8 0.01 20.00 33.40 11.7 40 50 76.6 81.4 IP Pump 0.02 0.02 0.01 77.4 0.00 20.00 141.45 0.7 8 8 91.0 614.6 LP Pump 0.00 0.00 0.00 84.9 0.00 20.00 466.60 0.1 3 2 97.3 1858.4 Deaerator 0.56 0.53 0.03 95.4 0.00 22.90 38.04 2.3 28 28 92.0 61.6
Mixer 1 1.81 1.63 0.18 90.1 0.02 19.21 21.33 12.9 0 13 0.0 12.2 Mixer 2 0.63 0.58 0.04 92.9 0.01 19.24 20.70 3.2 0 3 0.0 21.2 Mixer 3 0.18 0.18 0.00 99.9 0.00 15.74 15.76 0.0 0 0 0.0 0.1
Condenser 12.43 - 7.53 - 1.03 20.69 - 946.4 91 1032 8.3 - Total 728.77 414.90 293.47 56.93 40.27 9.2 20.52 9720 6519 16513 39.4 124.4
100
Table A.1.2 Results at component level for the combined cycle power plant from the reference paper
EF EP ED Eps yD* cF cP CD Z CD+Z f rComponent (MW) (MW) (MW) (%) (%) (€/GJ) (€/GJ) (€/h) (€/h) (€/h) (%) (%)Compressor 242.68 231.30 11.38 95.3 1.56 16.9 19.5 693 1423 2116 67.3 15.0
CC 729.62 508.76 220.87 69.7 30.23 9.2 13.7 7276 1017 8293 12.3 49.5 GT 551.15 530.67 20.47 96.3 2.8 15.5 16.9 1140 1627 2766 58.8 9.4
Reheater 26.47 23.89 2.58 90.3 0.35 15.5 19.4 143 111 255 43.7 25.4 HPSH 35.07 31.72 3.35 90.5 0.46 15.5 19.4 186 158 344 45.8 25.6
HPEVAP 43.64 39.91 3.73 91.5 0.51 15.5 19.0 207 185 392 47.1 23.1 HPECON 28.92 24.91 4.00 86.2 0.55 15.5 20.4 223 89 312 28.6 31.8
IPSH 0.18 0.12 0.06 69.0 0.01 15.5 35.4 3 4 7 56.3 128.8 IPEVAP 6.10 5.67 0.38 92.9 0.06 15.5 20.5 24 65 90 73.1 32.8 IPECON 1.06 0.87 0.19 82.5 0.03 15.5 22.3 10 5 16 33.4 44.2
LPSH 1.43 1.04 0.38 73.3 0.05 15.5 29.5 21.0 19 41 47.7 90.9 LPEVAP 19.03 15.48 3.55 81.4 0.49 15.5 24.2 197 174 372 46.9 56.4 LPECON 11.49 7.71 3.78 67.1 0.52 15.5 30.8 211 93 304 30.7 99.3
HPST 31.29 29.18 2.11 93.2 0.29 20.3 24.2 155 182 336 54.0 18.9 IPST 37.39 35.21 2.18 94.2 0.3 20.3 24.7 159 329 488 67.4 21.7 LPST 70.99 61.35 9.64 86.4 1.32 21.4 29.7 743 764 1508 50.7 38.5
Cond. Pump 0.04 0.04 0.01 78.8 0.00 20.00 84.2 1 7 8 91.3 321.6 HP Pump 1.12 0.96 0.17 85.3 0.02 20.00 36.7 12 40 52 77.3 83.8 IP Pump 0.03 0.02 0.01 65.3 0.00 20.00 147.4 1 8 8 91.4 637.6 LP Pump 0.00 0.00 0.00 67.2 0.00 20.00 406.5 0 3 3 97.4 1934.4 Deaerator 0.56 0.53 0.03 95.4 0.00 25.1 41.2 2 28 30 92.4 64.3
Mixer 1 1.81 1.63 0.18 90.1 0.02 20.3 22.8 13 0 13 0.0 12.2 Mixer 2 0.63 0.58 0.04 92.9 0.01 20.3 24.7 3 0 3 0.0 21.3 Mixer 3 0.18 0.18 0.00 99.9 0.00 15.5 15.5 0.0 0 0 0.0 0.1
Condenser 12.43 - 9.24 - 1.26 21.4 - 712 91 803 11.3 - Total 730.58 412.54 300.41 56.5 41.12 9.2 20.6 9897 6519 16416 39.7 124.8
101
Table A.1.3 Results at stream level for the combined cycle power plant
from the program
Stream jm jT jP jPHE , jCHE ,
jtotE , jc jC
j (kg/s) (°C) (bar) (MW) (MW) (MW) (€/GJ) (€/h)1 614.50 15.00 1.01 0.00 1.10 1.10 0.00 0.00 2 614.50 392.90 17.00 230.13 1.10 231.24 19.10 15900.00 3 14.00 15.00 50.00 8.15 719.51 727.66 9.20 24100.00 4 628.50 1264.03 16.49 715.55 8.3 723.85 15.69 40886.00 5 628.50 580.64 1.06 179.16 8.3 187.46 15.69 10589.00 6 268.50 580.64 1.06 76.54 3.55 80.09 15.69 4524.00 7 268.50 447.61 1.05 50.54 3.55 54.09 15.69 3055.00 8 360.00 580.64 1.06 102.62 4.75 107.37 15.69 6065.00 9 360.00 449.30 1.05 68.18 4.75 72.93 15.69 4119.00
10 628.50 448.58 1.05 118.72 8.3 127.02 15.69 7175.00 11 628.50 341.18 1.04 75.67 8.3 83.97 15.69 4743.00 12 628.50 257.92 1.04 47.08 8.3 55.38 15.69 3128.00 13 628.50 257.35 1.04 46.91 8.3 55.21 15.69 3118.00 14 628.50 237.62 1.04 40.88 8.3 49.18 15.69 2778.00 15 628.50 234.08 1.04 39.83 8.3 48.13 15.69 2719.00 16 628.50 229.27 1.04 38.42 8.3 46.72 15.69 2639.00 17 628.50 156.37 1.03 19.65 8.3 27.94 15.69 1578.00 18 628.50 95.34 1.03 8.36 8.3 16.66 15.69 941.00 19 94.60 32.89 3.73 0.24 0.24 0.47 20.45 34.00 20 94.60 135.62 3.62 7.95 0.24 8.18 24.01 707.00 21 95.40 140.01 3.62 8.55 0.24 8.79 24.68 781.00 22 72.40 140.01 3.62 6.49 0.18 6.67 24.68 593.00 23 7.20 140.01 3.62 0.65 0.02 0.67 24.68 60.00 24 7.20 140.49 25.13 0.67 0.02 0.69 26.84 67.00 25 7.20 216.62 24.38 1.54 0.02 1.56 24.01 135.00 26 7.20 222.62 24.38 7.21 0.02 7.23 20.97 546.00 27 7.20 237.92 23.16 7.33 0.02 7.35 21.21 561.00 28 72.40 305.14 23.16 79.35 0.18 79.53 19.45 5568.00 29 72.40 560.64 22.00 103.24 0.18 103.42 19.23 7160.00 30 72.40 317.23 4.10 65.85 0.18 66.03 19.23 4571.00 31 22.10 214.08 4.10 17.95 0.06 18.01 22.88 1484.00 32 22.10 146.37 4.32 16.91 0.06 16.96 22.69 1386.00 33 0.80 146.37 4.32 0.63 0.00 0.63 22.69 52.00 34 23.00 140.01 3.62 2.06 0.06 2.12 26.81 205.00 35 23.00 140.02 4.32 2.06 0.06 2.12 27.06 207.00 36 23.00 146.37 4.32 17.54 0.06 17.60 22.70 1438.00 37 65.20 140.01 3.62 5.84 0.16 6.01 26.81 580.00 38 65.20 141.75 134.56 6.80 0.16 6.96 27.63 693.00 39 65.20 325.17 130.53 31.72 0.16 31.88 21.01 2411.00 40 65.20 331.17 130.53 71.63 0.16 71.79 19.58 5060.00 41 65.20 560.64 124.00 103.35 0.16 103.51 19.25 7173.00 42 65.20 313.21 23.16 72.06 0.16 72.22 19.25 5005.00 43 94.60 293.03 4.10 83.62 0.24 83.86 20.03 6047.00 44 94.60 32.88 0.05 12.63 0.24 12.87 20.03 928.00 45 94.60 32.88 0.05 0.20 0.24 0.44 20.03 32.00 46 5177.40 15.00 1.01 0.00 8.06 8.06 0.00 0.00 47 135.60 15.00 1.01 0.00 0.34 0.34 0.00 0.00 48 74.00 16.00 1.01 0.00 0.18 0.19 0.00 0.00 49 5239.00 22.88 1.01 1.84 7.52 9.36 0.00 0.00 50 7396.20 22.88 1.33 3.51 18.47 21.98 ‐ ‐ 51 7396.20 16.00 1.01 0.05 18.47 18.53 ‐ ‐ 52 7396.20 16.00 1.37 0.32 18.47 18.80 ‐ ‐ 53 14.00 15.00 17.00 5.90 719.51 725.41 ‐ ‐ 54 498.50 392.90 17.00 186.69 0.89 187.59 ‐ ‐ 55 512.50 1435.04 16.49 681.78 9.43 691.21 ‐ ‐ 56 116.00 392.90 17.00 43.44 0.21 43.65 ‐ ‐ 57 116.00 392.90 16.49 43.15 0.21 43.36 ‐ ‐ 58 ‐ ‐ ‐ ‐ C1 239.14 16.97 14610.00 59 ‐ ‐ ‐ ‐ ST1 29.92 21.81 2349.00 60 ‐ ‐ ‐ ‐ ST2 36.11 22.46 2920.00 61 ‐ ‐ ‐ ‐ ST3 62.91 26.04 5897.00 62 ‐ ‐ ‐ ‐ COND P 0.04 20.00 3.00 63 ‐ ‐ ‐ ‐ LPP 0.00 20.00 0.00 64 ‐ ‐ ‐ ‐ HPP 1.04 20.00 75.00 65 ‐ ‐ ‐ ‐ IPP 0.03 20.00 2.00 66 ‐ ‐ ‐ ‐ GT1 284.00 16.97 17350.00 67 ‐ ‐ ‐ ‐ tot 413.45 20.00 29768.00
102
Table A.1.4 Results at stream level for the combined cycle power plant
from the reference paper
Stream jm jT jP jPHE , jCHE ,
jtotE , jc jC
j (kg/s) (°C) (bar) (MW) (MW) (MW) (€/GJ) (€/h)1 614.50 15.00 1.01 0.00 0.96 0.96 0.00 0.00 2 614.50 392.90 17.00 231.30 0.96 232.25 19.40 16198.00 3 14.00 15.00 50.00 8.15 721.47 729.62 9.20 24037.00 4 628.50 1264.03 16.49 735.74 5.27 741.01 15.50 41252.00 5 628.50 580.64 1.06 184.60 5.27 189.87 15.50 10570.00 6 268.50 580.64 1.06 78.86 2.25 81.11 15.50 4515.00 7 268.50 447.61 1.05 52.39 2.25 54.64 15.50 3042.00 8 360.00 580.64 1.06 105.73 3.02 108.75 15.50 6054.00 9 360.00 449.30 1.05 70.66 3.02 73.68 15.50 4102.00
10 628.50 448.58 1.05 123.05 5.27 128.33 15.50 7144.00 11 628.50 341.18 1.04 79.42 5.27 84.69 15.50 4715.00 12 628.50 257.92 1.04 50.50 5.27 55.77 15.50 3105.00 13 628.50 257.35 1.04 50.32 5.27 55.59 15.50 3095.00 14 628.50 237.62 1.04 44.22 5.27 49.49 15.50 2755.00 15 628.50 234.08 1.04 43.16 5.27 48.43 15.50 2696.00 16 628.50 229.27 1.04 41.74 5.27 47.01 15.50 2617.00 17 628.50 156.37 1.03 22.71 5.27 27.98 15.50 1558.00 18 628.50 95.34 1.03 11.22 5.27 16.49 0.00 0.00 19 94.60 32.89 3.73 0.24 0.24 0.47 26.10 44.00 20 94.60 135.62 3.62 7.95 0.24 8.18 30.60 900.00 21 95.40 140.01 3.62 8.55 0.24 8.79 31.10 986.00 22 72.40 140.01 3.62 6.49 0.18 6.67 31.10 748.00 23 7.20 140.01 3.62 0.65 0.02 0.67 31.10 75.00 24 7.20 140.49 25.13 0.67 0.02 0.69 34.40 85.00 25 7.20 216.62 24.38 1.54 0.02 1.56 27.60 155.00 26 7.20 222.62 24.38 7.21 0.02 7.23 22.10 574.00 27 7.20 237.92 23.16 7.33 0.02 7.35 22.30 590.00 28 72.40 305.14 23.16 79.35 0.18 79.53 20.60 5885.00 29 72.40 560.64 22.00 103.24 0.18 103.42 20.30 7553.00 30 72.40 317.23 4.10 65.85 0.18 66.03 20.30 4822.00 31 22.10 214.08 4.10 17.95 0.06 18.01 25.30 1642.00 32 22.10 146.37 4.32 16.91 0.06 16.96 25.10 1531.00 33 0.80 146.37 4.32 0.63 0.00 0.63 25.10 57.00 34 23.00 140.01 3.62 2.06 0.06 2.12 31.10 237.00 35 23.00 140.02 4.32 2.06 0.06 2.12 31.50 240.00 36 23.00 146.37 4.32 17.54 0.06 17.60 25.10 1588.00 37 65.20 140.01 3.62 5.84 0.16 6.01 31.10 674.00 38 65.20 141.75 134.56 6.80 0.16 6.96 31.90 800.00 39 65.20 325.17 130.53 31.72 0.16 31.88 22.90 2628.00 40 65.20 331.17 130.53 71.63 0.16 71.79 20.80 5363.00 41 65.20 560.64 124.00 103.35 0.16 103.51 20.30 7581.00 42 65.20 313.21 23.16 72.06 0.16 72.22 20.30 5290.00 43 94.60 293.03 4.10 83.62 0.24 83.86 21.40 6465.00 44 94.60 32.88 0.05 12.63 0.24 12.87 21.40 992.00 45 94.60 32.88 0.05 0.20 0.24 0.44 21.40 34.00 46 5177.40 15.00 1.01 0.00 8.06 8.06 0.00 0.00 47 135.60 15.00 1.01 0.00 0.34 0.34 0.00 0.00 48 74.00 16.00 1.01 0.00 0.18 0.19 0.00 0.00 49 5239.00 22.88 1.01 1.84 7.52 9.36 0.00 0.00 50 7396.20 22.88 1.33 3.51 18.47 21.98 ‐ ‐ 51 7396.20 16.00 1.01 0.05 18.47 18.53 ‐ ‐ 52 7396.20 16.00 1.37 0.32 18.47 18.80 ‐ ‐ 53 14.00 15.00 17.00 5.90 721.47 727.37 ‐ ‐ 54 498.50 392.90 17.00 187.64 0.78 188.41 ‐ ‐ 55 512.50 1435.04 16.49 704.31 5.80 710.10 ‐ ‐ 56 116.00 392.90 17.00 43.66 0.18 43.84 ‐ ‐ 57 116.00 392.90 16.49 43.37 0.18 43.55 ‐ ‐ 58 ‐ ‐ ‐ ‐ C1 242.68 16.90 14775.00 59 ‐ ‐ ‐ ‐ ST1 29.18 24.20 2542.00 60 ‐ ‐ ‐ ‐ ST2 35.21 24.70 3130.00 61 ‐ ‐ ‐ ‐ ST3 61.35 29.70 6549.00 62 ‐ ‐ ‐ ‐ COND P 0.04 20.00 3.00 63 ‐ ‐ ‐ ‐ LPP 0.00 20.00 0.00 64 ‐ ‐ ‐ ‐ HPP 1.12 20.00 81.00 65 ‐ ‐ ‐ ‐ IPP 0.03 20.00 2.00 66 ‐ ‐ ‐ ‐ GT1 288.00 16.90 17534.00 67 ‐ ‐ ‐ ‐ tot 412.54 20.00 29669.00
103
A.2TheIG
CCpow
erplan
twithCO
2Cap
ture
M
5
6
104
Table A.2.1 Results at stream level of the IGCC power plant with CO2 capture from the program
Stream Mass(kg/s)
T(C)
P(bar)
h(kJ/kg)
s(kJ/kgK)
EPH
(MW)
ECH
(MW)
Etot(MW)
c($/GJ)
cPH
($/GJ)
cCH($/GJ)
C($/h)
1 80.0000 15.000 1.013 27227.40 1.273 0.00 2467.62 2467.62 1.30 0.00 1.30 11548.44 2 178.8148 129.592 1.013 ‐175.89 7.276 3.51 4.28 7.79 94.03 56.49 124.88 2637.23 3 76.2105 129.592 1.013 27299.37 1.309 4.37 2350.73 2355.09 3.09 965.32 1.30 26171.75 4 175.0000 250.000 1.100 235.33 7.400 12.82 4.49 17.32 74.23 56.49 124.88 4627.95 5 76.2105 50.000 1.013 27246.79 1.285 0.88 2350.73 2351.61 1.66 965.32 1.30 14071.98 6 257.8000 15.000 1.013 ‐10.15 6.850 0.00 1.53 1.53 0.00 0.00 0.00 0.00 8 196.6900 17.719 1.100 ‐7.65 6.787 1.39 5.05 6.44 161.57 295.02 124.88 3745.53 9 59.8498 17.719 4.450 ‐6.61 6.033 6.65 6.88 13.53 208.48 295.02 124.88 10155.16 10 15.1900 17.719 1.100 ‐7.65 6.787 0.11 0.39 0.50 161.57 295.02 124.88 289.26 11 181.5000 17.719 1.100 ‐7.65 6.787 1.28 4.66 5.94 161.57 295.02 124.88 3456.27 12 175.0000 17.719 1.100 ‐7.65 6.787 1.24 4.49 5.73 161.57 295.02 124.88 3332.49 13 6.5000 17.719 1.100 ‐7.65 6.787 0.05 0.17 0.21 161.57 295.02 124.88 123.78 14 6.5000 276.644 8.000 263.71 6.864 1.66 0.17 1.83 62.39 56.127 124.88 411.42 17 59.8498 104.451 10.000 73.61 6.063 10.93 6.88 17.81 168.88 196.58 124.88 10827.72 18 6.5000 35.000 8.000 10.35 6.258 1.15 0.17 1.32 64.82 56.127 124.88 308.09 19 75.0000 25.000 9.200 105.69 0.367 0.11 3.75 3.86 0.00 0.00 0.00 0.00 20 75.0000 29.594 9.200 124.88 0.431 0.17 3.75 3.92 7.71 174.04 0.00 108.73 21 75.0000 25.000 9.200 105.69 0.367 0.11 3.75 3.86 0.00 0.00 0.00 0.00 22 75.0000 37.106 9.200 156.26 0.533 0.31 3.75 4.06 30.27 391.04 0.00 442.49 23 59.8498 35.000 10.000 9.07 5.874 10.32 6.88 17.20 167.90 196.58 124.88 10397.99 25 6.5000 146.384 20.500 126.23 6.300 1.83 0.17 2.00 61.88 56.126 124.88 444.51 27 59.8498 120.242 21.200 88.57 5.906 14.53 6.88 21.41 143.61 152.48 124.88 11069.63 28 75.0000 25.000 9.200 105.69 0.367 0.11 3.75 3.86 0.00 0.00 0.00 0.00 29 75.0000 27.144 9.200 114.65 0.397 0.14 3.75 3.89 2.39 66.57 0.00 33.43 30 6.5000 35.000 20.500 10.35 5.979 1.68 0.17 1.84 62.35 56.126 124.88 413.80 31 67.2000 25.000 9.200 105.69 0.367 0.10 3.36 3.46 0.00 0.00 0.00 0.00 32 67.2000 40.122 9.200 168.86 0.574 0.35 3.36 3.70 35.36 378.63 0.00 471.28 33 59.8498 35.000 21.200 9.07 5.678 13.70 6.88 20.58 143.25 152.48 124.88 10612.24 35 6.5000 154.872 56.000 135.10 6.022 2.41 0.17 2.57 60.46 55.986 124.88 559.92 37 59.8498 120.554 45.000 88.86 5.711 17.92 6.88 24.80 126.42 127.01 124.88 11285.45 38 9.7626 1549.978 40.000 ‐10526.60 2.680 12.56 4.63 17.19 10.03 13.25 1.30 620.49 39 9.7626 349.000 40.000 ‐12100.44 1.337 0.97 4.63 5.60 3.37 13.25 1.30 67.91 40 250.0000 15.000 1.013 63.08 0.224 0.00 12.49 12.49 0.00 0.00 0.00 0.00 41 250.0000 70.000 1.013 293.08 0.955 4.88 12.49 17.36 9.50 33.83 0.00 593.77 42 135.6322 1549.978 40.000 ‐1268.42 10.460 282.73 1648.68 1931.41 6.44 17.25 4.59 44777.74 43 156.3294 288.307 41.000 ‐3347.17 8.533 87.72 1900.27 1987.99 5.25 19.59 4.59 37560.89 44 291.9618 900.000 40.000 ‐2371.27 9.714 349.41 3548.96 3898.37 5.87 18.88 4.59 82338.67 45 291.9618 315.800 40.000 ‐3304.85 8.617 169.14 3548.96 3718.10 5.24 18.88 4.59 70088.78 46 291.9618 280.000 40.000 ‐3359.92 8.520 161.18 3548.96 3710.14 5.21 18.88 4.59 69547.74 47 291.9618 280.030 39.310 ‐3359.86 8.527 160.59 3548.96 3709.54 5.21 18.95 4.59 69547.74 48 156.3294 280.030 39.310 ‐3360.08 8.528 86.00 1900.27 1986.27 5.21 18.94 4.59 37239.38 50 135.6324 280.030 39.310 ‐3359.87 8.527 74.60 1648.69 1723.29 5.21 18.94 4.59 32308.36
105
51 149.3656 141.170 38.966 ‐4456.66 8.351 72.06 1649.89 1721.95 5.19 18.94 4.59 32154.69 52 21.0000 160.000 75.000 679.62 1.935 2.60 1.05 3.65 0.00 0.00 0.00 0.00 53 7.2668 141.170 38.966 596.50 1.748 0.69 0.36 1.05 195.91 299.46 0.00 740.27 54 244.3657 241.354 38.766 ‐7685.65 9.353 173.90 1684.34 1858.24 6.00 37.00 2.80 40161.02 55 244.3657 275.000 38.766 ‐7626.33 9.465 180.53 1684.34 1864.87 6.18 37.71 2.80 41509.76 56 244.3657 519.681 38.766 ‐7632.21 9.813 223.31 1592.18 1815.50 6.47 37.71 2.08 42262.31 57 244.3657 488.619 38.766 ‐7693.69 9.734 213.86 1592.18 1806.04 6.30 37.71 2.08 40978.82 58 244.3657 210.000 38.766 ‐8227.55 8.863 144.68 1592.18 1736.86 5.05 37.71 2.08 31586.01 59 244.3657 288.482 38.766 ‐8230.45 8.924 155.38 1570.93 1726.31 5.14 37.71 1.92 31962.28 60 244.3657 154.783 38.766 ‐8482.41 8.412 129.85 1570.93 1700.78 4.65 37.71 1.92 28495.75 61 244.3657 30.000 38.766 ‐9067.24 7.054 95.52 1552.70 1648.22 4.00 37.71 1.92 23708.43 62 206.5197 29.361 34.896 ‐7843.07 7.429 90.45 1564.42 1654.86 3.32 27.52 1.92 19782.50 63 37.8460 29.361 34.896 ‐13410.09 8.864 0.183 1.89 2.073 18.73 27.52 1.92 3925.92 64 25.7109 20.000 34.626 ‐916.68 26.620 53.39 1423.47 1476.87 6.69 27.52 5.91 35556.49 65 41.9965 145.129 34.126 ‐5131.77 22.083 68.18 1425.62 1493.81 7.55 89.87 3.62 40617.32 66 193.7144 145.129 34.126 613.15 1.789 19.23 9.67 28.90 36.99 55.60 0.00 3848.66 67 193.7144 145.146 35.000 613.28 1.789 19.25 9.67 28.92 37.05 55.67 0.00 3857.42 68 16.2892 15.342 35.000 67.76 0.229 0.06 0.81 0.87 4.23 66.37 0.00 13.23 69 16.2892 15.000 1.000 63.08 0.224 0.00 0.81 0.81 0.00 0.00 0.00 0.00 70 210.0037 135.331 35.000 571.29 1.687 18.20 10.49 28.68 37.48 59.09 0.00 3870.65 71 210.0000 200.000 35.000 853.18 2.328 38.65 10.49 49.14 43.73 55.60 0.00 7736.34 72 1230.0210 15.000 1.013 ‐10.15 6.850 0.00 7.30 7.30 0.00 0.00 0.00 0.00 73 1230.0210 432.843 19.450 425.04 6.927 508.18 7.30 515.47 16.68 16.92 0.00 30947.92 74 1272.0180 1313.228 19.450 257.76 8.453 1649.96 26.50 1676.46 12.29 12.49 0.12 74174.07 76 1272.0180 612.900 1.050 ‐657.39 8.590 435.85 26.50 462.35 11.78 12.49 0.12 19602.17 78 1272.0180 577.700 1.050 ‐700.76 8.540 399.00 26.50 425.49 11.72 12.49 0.12 17945.57 79 1272.0180 514.000 1.050 ‐778.48 8.445 334.93 26.50 361.42 11.58 12.49 0.12 15065.67 80 1272.0180 416.000 1.050 ‐896.14 8.285 243.76 26.50 270.26 11.27 12.49 0.12 10968.09 81 1272.0180 415.788 1.050 ‐896.39 8.285 243.58 26.50 270.07 11.27 12.49 0.12 10959.71 82 1272.0180 386.800 1.050 ‐930.73 8.234 218.56 26.50 245.06 11.15 12.49 0.12 9835.32 83 1272.0180 260.400 1.050 ‐1077.93 7.987 122.03 26.50 148.52 10.28 12.49 0.12 5496.26 84 1272.0180 208.900 1.050 ‐1136.71 7.871 89.72 26.50 116.22 9.67 12.49 0.12 4044.10 85 1272.0180 206.400 1.050 ‐1139.54 7.865 88.27 26.50 114.77 9.63 12.49 0.12 3979.14 86 1272.0180 145.600 1.050 ‐1208.00 7.712 57.14 26.50 83.63 8.57 12.49 0.12 2579.62 87 1272.0180 144.200 1.050 ‐1209.56 7.709 56.52 26.50 83.02 8.54 12.49 0.12 2551.82 88 1272.0180 133.000 1.050 ‐1222.06 7.678 51.75 26.50 78.24 8.30 12.49 0.12 2337.28 89 101.8000 10.800 2.100 45.58 0.163 0.02 5.08 5.11 0.00 0.00 0.00 0.00 90 346.0000 22.000 2.041 92.48 0.325 0.16 17.28 17.44 0.46 51.25 0.00 28.92 91 38.58 22.000 2.041 92.48 0.325 0.02 1.93 1.94 0.46 51.25 0.00 3.22 92 38.58 120.200 2.000 504.68 1.530 2.52 1.93 4.45 17.21 30.36 0.00 275.73 93 307.4200 22.000 2.041 92.48 0.325 0.14 15.35 15.49 0.46 51.25 0.00 25.69 94 307.4200 120.200 2.000 504.68 1.530 20.10 15.35 35.45 43.60 76.91 0.00 5565.50 95 346.0000 120.200 2.000 504.68 1.530 22.62 17.28 39.90 40.66 71.72 0.00 5841.23 96 315.8100 120.200 2.000 504.68 1.530 20.65 15.77 36.42 40.66 71.72 0.00 5331.56 97 30.19 120.200 2.000 504.68 1.530 1.97 1.51 3.48 40.66 71.72 0.00 509.67 98 116.7000 120.200 2.000 504.68 1.530 7.63 5.83 13.46 40.66 71.72 0.00 1970.15 99 199.1100 120.200 2.000 504.68 1.530 13.02 9.94 22.96 40.66 71.72 0.00 3361.41 100 30.19 120.240 3.212 504.89 1.530 1.98 1.51 3.49 41.02 72.29 0.00 514.86
106
101 116.7000 120.700 41.260 509.51 1.532 8.14 5.83 13.97 40.68 69.82 0.00 2045.18 102 199.1100 122.700 195.100 528.81 1.540 17.28 9.94 27.22 40.02 63.06 0.00 3922.72 103 30.1900 135.600 3.187 570.33 1.693 2.53 1.51 4.04 38.13 60.81 0.00 554.86 104 135.2600 120.700 41.260 509.51 1.532 9.43 6.76 16.19 36.62 62.84 0.00 2133.62 105 63.71 122.700 195.100 528.81 1.540 5.53 3.18 8.71 40.02 63.06 0.00 1255.17 106 40.142 135.600 3.187 570.33 1.693 3.37 2.00 5.37 69.03 110.10 0.00 1335.68 107 128.42 120.700 41.260 509.51 1.532 8.95 6.41 15.37 36.62 62.84 0.00 2025.72 108 135.4 122.700 195.100 528.81 1.540 11.75 6.76 18.51 40.02 63.06 0.00 2667.55 109 63.71 355.700 177.200 2520.67 5.127 66.58 3.18 69.76 44.11 46.22 0.00 11078.06 110 6.8400 120.700 41.260 509.51 1.532 0.48 0.34 0.82 36.62 62.84 0.00 107.90 111 40.142 133.850 3.027 2725.35 6.989 28.63 2.00 30.63 28.56 30.56 0.00 3149.47 112 30.19 133.850 3.027 2725.35 6.989 21.53 1.51 23.04 28.56 30.56 0.00 2368.66 113 6.8400 247.400 38.020 2801.91 6.091 7.17 0.34 7.51 26.18 27.43 0.00 708.17 114 135.4 355.700 177.200 2520.67 5.127 141.50 6.76 148.26 29.62 31.04 0.00 15811.01 115 30.19 188.900 3.000 2843.08 7.264 22.69 1.51 24.19 28.31 30.19 0.00 2465.81 116 128.42 250.400 40.020 1087.57 2.797 36.37 6.41 42.79 23.54 27.69 0.00 3626.18 117 20.1200 250.400 40.020 1087.57 2.797 5.70 1.00 6.70 23.54 27.69 0.00 568.13 118 20.1200 247.400 38.020 2801.91 6.091 21.09 1.00 22.10 8.19 8.58 0.00 651.30 119 108.3 250.400 40.020 1087.57 2.797 30.67 5.41 36.08 23.54 27.69 0.00 3058.05 120 108.3 247.400 38.020 2801.91 6.091 113.54 5.41 118.95 19.46 20.38 0.00 8331.88 121 26.9600 247.400 38.020 2801.91 6.091 28.26 1.35 29.61 12.75 13.36 0.00 1359.48 122 135.26 247.400 38.020 2801.91 6.091 141.80 6.76 148.56 18.12 18.98 0.00 9691.36 123 116.7 247.400 38.020 2801.91 6.091 122.35 5.83 128.17 18.12 18.98 0.00 8361.54 124 116.7 380.000 36.760 3172.98 6.746 143.64 5.83 149.47 18.28 19.02 0.00 9835.20 125 95.0000 380.000 36.760 3172.98 6.746 116.93 4.74 121.67 18.28 19.02 0.00 8006.37 126 21.7000 380.000 36.760 3172.98 6.746 26.71 1.08 27.79 18.28 19.02 0.00 1828.82 127 6.8000 380.000 36.760 3172.98 6.746 8.37 0.34 8.71 18.28 19.02 0.00 573.09 128 6.8000 400.000 36.760 3220.01 6.817 8.55 0.34 8.89 18.29 19.02 0.00 585.38 129 14.9 380.000 36.760 3172.98 6.746 18.34 0.74 19.08 18.28 19.02 0.00 1255.74 130 199.11 355.700 177.200 2520.67 5.127 208.08 9.94 218.02 34.26 35.90 0.00 26889.06 131 199.11 494.000 167.900 3268.23 6.248 292.61 9.94 302.55 28.95 29.94 0.00 31534.36 132 214.01 358.900 36.760 3122.48 6.667 257.45 10.69 268.14 26.58 27.68 0.00 25653.32 133 199.11 590.000 164.000 3544.45 6.597 327.56 9.94 337.51 27.51 28.34 0.00 33421.52 134 199.11 357.342 36.760 3118.71 6.661 239.12 9.94 249.06 27.21 28.34 0.00 24397.59 135 214.01 557.700 35.000 3582.42 7.322 315.47 10.69 326.16 24.59 25.43 0.00 28877.64 137 214.01 224.400 3.000 2915.86 7.416 167.04 10.69 177.73 23.90 25.43 0.00 15290.74 139 244.2000 220.000 3.000 2906.89 7.398 189.69 12.20 201.88 24.43 26.00 0.00 17756.55 140 244.2000 26.670 0.035 2255.09 7.539 20.59 12.20 32.78 16.33 26.00 0.00 1927.17 142 244.2000 26.670 0.035 111.84 0.391 0.21 12.20 12.41 0.44 26.00 0.00 19.78 143 244.2000 26.680 2.000 112.05 0.391 0.26 12.20 12.46 0.64 30.95 0.00 28.92 144 18.5600 247.400 38.020 2801.91 6.091 19.46 0.93 20.38 18.12 18.98 0.00 1329.82 145 18.5600 120.700 41.260 509.51 1.532 1.29 0.93 2.22 11.06 18.98 0.00 88.44 146 75.0000 15.000 1.013 63.08 0.224 0.00 3.75 3.75 0.00 0.00 0.00 0.00 147 75.0000 75.000 1.013 314.02 1.016 1.72 3.75 5.47 614.84 1950.61 0.00 12107.36 148 13851.0000 15.000 1.013 63.08 0.224 0.00 691.78 691.78 0.00 0.00 0.00 0.00 149 13851.0000 24.030 1.013 100.87 0.354 8.03 691.78 699.81 0.87 76.03 0.00 2198.55 150 9.952 133.850 3.027 2725.35 6.989 7.10 0.50 7.59 28.56 30.56 0.00 780.82 151 9.952 135.600 3.187 570.33 1.693 0.84 0.50 1.33 162.77 259.60 0.00 780.82
107
A.2.2 Results at stream level of the IGCC power plant with CO2 capture from the
reference
Stream Mass(kg/s)
T(C)
P(bar)
h(kJ/kg)
s(kJ/kgK)
EPH
(MW)ECH
(MW)Etot(MW)
1 80.0000 15.000 1.013 ‐1882.98 ‐ 0.00 2557.60 2557.60 2 178.8148 129.592 1.013 ‐175.64 0.309 3.63 4.35 7.98 3 76.2105 129.592 1.013 ‐1023.78 ‐ ‐ ‐ 2557.50 4 175.0000 250.000 1.100 235.54 0.564 12.83 4.49 17.33 5 76.2105 50.000 1.013 ‐1139.57 ‐ ‐ ‐ 2557.50 6 257.8000 15.000 1.013 ‐10.36 0.113 0.00 1.53 1.53 8 196.6900 17.719 1.100 ‐7.53 ‐0.050 1.39 5.05 6.44 9 59.8498 17.719 4.450 ‐7.67 ‐0.388 6.69 6.88 13.57 10 15.1900 17.719 1.100 ‐7.53 ‐0.050 0.11 0.39 0.50 11 181.5000 17.719 1.100 ‐7.53 ‐0.050 1.28 4.66 5.94 12 175.0000 17.719 1.100 ‐7.53 ‐0.050 1.23 4.49 5.73 13 6.5000 17.719 1.100 ‐7.53 ‐0.050 0.05 0.17 0.21 14 6.5000 276.644 8.000 264.12 0.027 1.67 0.17 1.83 17 59.8498 104.451 10.000 72.21 ‐0.356 10.91 6.88 17.80 18 6.5000 35.000 8.000 8.87 ‐0.584 1.15 0.17 1.32 19 75.0000 25.000 9.200 ‐16033.36 ‐9.484 0.14 3.75 3.89 20 75.0000 29.594 9.200 ‐16011.24 ‐9.411 0.21 3.75 3.96 21 75.0000 25.000 9.200 ‐16033.36 ‐9.484 0.13 3.75 3.87 22 75.0000 37.106 9.200 ‐15975.09 ‐9.293 0.33 3.75 4.08 23 59.8498 35.000 10.000 6.79 ‐0.547 10.30 6.88 17.18 25 6.5000 146.384 20.500 125.71 ‐0.542 1.83 0.17 2.00 27 59.8498 120.242 21.200 85.84 ‐0.517 14.50 6.88 21.38 28 75.0000 25.000 9.200 ‐16033.36 ‐9.484 0.14 3.75 3.89 29 75.0000 27.144 9.200 ‐16023.03 ‐9.450 0.17 3.75 3.92 30 6.5000 35.000 20.500 6.58 ‐0.872 1.68 0.17 1.84 31 67.2000 25.000 9.200 ‐16033.36 ‐9.484 0.13 3.36 3.48 32 67.2000 40.122 9.200 ‐15960.58 ‐9.246 0.41 3.36 3.76 33 59.8498 35.000 21.200 4.13 ‐0.751 13.65 6.88 20.53 35 6.5000 154.872 56.000 133.93 ‐0.826 2.42 0.17 2.59 37 59.8498 120.554 45.000 83.41 ‐0.720 17.87 6.88 24.75 38 9.7626 1549.978 40.000 ‐ ‐ ‐ ‐ 39 9.7626 349.000 40.000 ‐ ‐ ‐ ‐ 40 250.0000 15.000 1.013 ‐ ‐ ‐ ‐ 41 250.0000 70.000 1.013 ‐ ‐ ‐ ‐ 42 135.6322 1549.978 40.000 ‐1267.60 4.448 283.62 1649.36 1932.97 43 156.3294 288.307 41.000 ‐3351.09 2.524 87.88 1901.04 1988.92 44 291.9618 900.000 40.000 ‐2383.19 3.693 348.32 3550.40 3898.73 45 291.9618 315.800 40.000 ‐3291.78 2.636 171.97 3550.40 3722.37 46 291.9618 280.000 40.000 ‐3363.69 2.512 161.47 3550.40 3711.87 47 291.9618 280.030 39.310 ‐3363.69 2.519 160.85 3550.40 3711.26 48 156.3294 280.030 39.310 ‐3363.69 2.519 86.13 1901.04 1987.17 50 135.6324 280.030 39.310 ‐3363.69 2.519 74.73 1649.36 1724.08 51 149.3656 141.170 38.966 ‐4463.05 1.700 72.49 1649.66 1722.15 52 21.0000 160.000 75.000 ‐15369.94 ‐7.677 3.03 1.05 4.08 53 7.2668 141.170 38.966 ‐15463.04 ‐7.889 0.80 0.39 1.19 54 244.3657 241.354 38.766 ‐7715.05 0.221 175.15 1654.40 1829.55 55 244.3657 275.000 38.766 ‐7654.20 0.336 181.95 1654.40 1836.35 56 244.3657 519.681 38.766 ‐7654.25 0.688 223.26 1583.48 1806.74 57 244.3657 488.619 38.766 ‐7715.10 0.610 213.90 1583.48 1797.38 58 244.3657 210.000 38.766 ‐8246.43 ‐0.257 145.11 1583.48 1728.58 59 244.3657 288.482 38.766 ‐8246.32 ‐0.193 155.47 1567.13 1722.60 60 244.3657 154.783 38.766 ‐8531.04 ‐0.781 127.29 1567.13 1694.42 61 244.3657 30.000 38.766 ‐9117.21 ‐2.327 92.93 1567.13 1660.06 62 206.5197 29.361 34.896 ‐7855.13 ‐0.985 89.83 1565.62 1655.45 63 37.8460 29.361 34.896 ‐16004.14 ‐9.410 0.23 1.96 2.19 64 25.7109 20.000 34.626 ‐911.60 ‐5.978 53.76 1426.82 1480.58 65 41.9965 145.129 34.126 ‐5137.75 ‐2.897 69.06 1424.96 1494.01 66 193.7144 145.129 34.126 ‐15446.93 ‐7.844 22.35 9.94 32.28 67 193.7144 145.146 35.000 ‐15446.78 ‐7.844 22.37 9.94 32.31 68 16.2892 15.342 35.000 ‐16077.18 ‐9.645 0.07 0.81 0.89 69 16.2892 15.000 1.000 ‐16082.44 ‐9.648 0.00 0.81 0.81 70 210.0037 135.331 35.000 ‐15495.68 ‐7.962 21.14 10.75 31.90 71 210.0000 200.000 35.000 ‐15164.87 ‐7.210 45.18 10.49 55.67 72 1230.021 15.000 1.013 ‐10.36 0.113 0.00 7.30 7.30 73 1230.021 432.843 19.450 425.58 0.188 515.37 7.30 522.67 74 1272.018 1313.228 19.450 237.97 1.113 1651.50 26.71 1678.21 76 1272.018 612.900 1.050 ‐660.88 1.245 436.59 26.71 463.30 78 1272.018 577.700 1.050 ‐704.30 8.535 397.09 26.71 423.80
108
79 1272.018 514.000 1.050 ‐781.70 8.440 337.68 26.71 364.39 80 1272.018 416.000 1.050 ‐898.60 8.282 243.01 26.71 269.72 81 1272.018 415.788 1.050 ‐898.80 8.281 243.12 26.71 269.83 82 1272.018 386.800 1.050 ‐932.90 8.231 218.07 26.71 244.78 83 1272.018 260.400 1.050 ‐1079.00 7.985 122.40 26.71 149.11 84 1272.018 208.900 1.050 ‐1137.00 7.870 90.77 26.71 117.48 85 1272.018 206.400 1.050 ‐1140.00 7.864 89.16 26.71 115.87 86 1272.018 145.600 1.050 ‐1208.00 7.713 58.00 26.71 84.71 87 1272.018 144.200 1.050 ‐1210.00 7.709 56.93 26.71 83.64 88 1272.018 133.000 1.050 ‐1222.00 7.679 52.66 26.71 79.37 89 101.8000 10.800 2.100 45.58 0.163 0.02 5.08 5.11 90 346.0000 22.000 2.041 92.48 0.325 0.16 17.28 17.44 91 38.58 22.000 2.041 92.48 0.325 0.02 1.93 1.94 92 38.58 120.200 2.000 504.68 1.530 2.52 1.93 4.45 93 307.4200 22.000 2.041 92.48 0.325 0.14 15.35 15.49 94 307.4200 120.200 2.000 504.68 1.530 20.10 15.35 35.45 95 346.0000 120.200 2.000 504.68 1.530 22.62 17.28 39.90 96 315.8100 120.200 2.000 504.68 1.530 20.65 15.77 36.42 97 30.19 120.200 2.000 504.68 1.530 1.97 1.51 3.48 98 116.7000 120.200 2.000 504.68 1.530 7.63 5.83 13.46 99 199.1100 120.200 2.000 504.68 1.530 13.02 9.94 22.96 100 30.19 120.240 3.212 504.89 1.530 1.98 1.51 3.49 101 116.7000 120.700 41.260 509.51 1.532 8.14 5.83 13.97 102 199.1100 122.700 195.100 528.81 1.540 17.28 9.94 27.22 103 30.1900 135.600 3.187 570.33 1.693 2.53 1.51 4.04 104 135.2600 120.700 41.260 509.51 1.532 9.43 6.76 16.19 105 63.71 122.700 195.100 528.81 1.540 5.53 3.18 8.71 106 40.142 135.600 3.187 570.33 1.693 3.37 2.00 5.37 107 128.42 120.700 41.260 509.51 1.532 8.95 6.41 15.37 108 135.4 122.700 195.100 528.81 1.540 11.75 6.76 18.51 109 63.71 355.700 177.200 2520.67 5.127 66.58 3.18 69.76 110 6.8400 120.700 41.260 509.51 1.532 0.48 0.34 0.82 111 40.142 133.850 3.027 2725.35 6.989 28.63 2.00 30.63 112 30.19 133.850 3.027 2725.35 6.989 21.53 1.51 23.04 113 6.8400 247.400 38.020 2801.91 6.091 7.17 0.34 7.51 114 135.4 355.700 177.200 2520.67 5.127 141.50 6.76 148.26 115 30.19 188.900 3.000 2843.08 7.264 22.69 1.51 24.19 116 128.42 250.400 40.020 1087.57 2.797 36.37 6.41 42.79 117 20.1200 250.400 40.020 1087.57 2.797 5.70 1.00 6.70 118 20.1200 247.400 38.020 2801.91 6.091 21.09 1.00 22.10 119 108.3 250.400 40.020 1087.57 2.797 30.67 5.41 36.08 120 108.3 247.400 38.020 2801.91 6.091 113.54 5.41 118.95 121 26.9600 247.400 38.020 2801.91 6.091 28.26 1.35 29.61 122 135.26 247.400 38.020 2801.91 6.091 141.80 6.76 148.56 123 116.7 247.400 38.020 2801.91 6.091 122.35 5.83 128.17 124 116.7 380.000 36.760 3172.98 6.746 143.64 5.83 149.47 125 95.0000 380.000 36.760 3172.98 6.746 116.93 4.74 121.67 126 21.7000 380.000 36.760 3172.98 6.746 26.71 1.08 27.79 127 6.8000 380.000 36.760 3172.98 6.746 8.37 0.34 8.71 128 6.8000 400.000 36.760 3220.01 6.817 8.55 0.34 8.89 129 14.9 380.000 36.760 3172.98 6.746 18.34 0.74 19.08 130 199.11 355.700 177.200 2520.67 5.127 208.08 9.94 218.02 131 199.11 494.000 167.900 3268.23 6.248 292.61 9.94 302.55 132 214.01 358.900 36.760 3122.48 6.667 257.45 10.69 268.14 133 199.11 590.000 164.000 3544.45 6.597 327.56 9.94 337.51 134 199.11 357.342 36.760 3118.71 6.661 239.12 9.94 249.06 135 214.01 557.700 35.000 3582.42 7.322 315.47 10.69 326.16 137 214.01 224.400 3.000 2915.86 7.416 167.04 10.69 177.73 139 244.2000 220.000 3.000 2906.89 7.398 189.69 12.20 201.88 140 244.2000 26.670 0.035 2255.09 7.539 20.59 12.20 32.78 142 244.2000 26.670 0.035 111.84 0.391 0.21 12.20 12.41 143 244.2000 26.680 2.000 112.05 0.391 0.26 12.20 12.46 144 18.5600 247.400 38.020 2801.91 6.091 19.46 0.93 20.38 145 18.5600 120.700 41.260 509.51 1.532 1.29 0.93 2.22 146 75.0000 15.000 1.013 63.08 0.224 0.00 3.75 3.75 147 75.0000 75.000 1.013 314.02 1.016 1.72 3.75 5.47 148 13851.0 15.000 1.013 63.08 0.224 0.00 691.78 691.78 149 13851.0 24.030 1.013 100.87 0.354 8.03 691.78 699.81 150 9.952 133.850 3.027 2725.35 6.989 7.10 0.50 7.59 151 9.952 135.600 3.187 570.33 1.693 0.84 0.50 1.33
109
Table A.2.3 Results at component level of the IGCC plant with CO2 capture from the program
EF EP ED Eps y yD* cF cP CD Z CD+Z f rComponent (KW) (KW) (KW) (%) (%) (%) ($/GJ) ($/GJ) ($/h) ($/h) ($/h) (%) (%)
CoalPrepareUnit 9310 4365 4944 46.89 0.2 0.353 56.49 965.32 1005.4 12632.582 13637.982 92.63 1608.83 Gasifier 2353486 1914217 439269 81.34 17.74 31.361 1.67 4.586 2640.7 17456.379 20097.079 86.86 174.61 ASU 46750 18440 28309.6 39.44 1.14 2.021 24.4 295.016 2486.7 9794.174 12280.874 79.75 1109.08 Heater 18164 11588 6575 63.8 0.27 0.469 19 31.05 449.4 54.074 503.474 10.74 63.42 CM1 N2 1764 1619 145 91.78 0.006 0.010 24.4 48.49 12.7 127.695 140.395 90.95 98.75 CM1 O2 4801 4280 521 89.15 0.021 0.037 24.4 43.65 42.9 253.718 296.618 85.54 78.89 Heater 511 59 452 11.52 0.0183 0.032 56.127 513.055 712.6 5.464 718.064 0.76 774.12 Heater 607 200 408 32.89 0.016 0.029 196.58 615.5 288.4 12.758 301.158 4.24 213.10 CM2 N2 753 675 78 89.64 0.0032 0.006 24.4 56.12 6.85 70.257 77.107 91.12 130.00 CM2 O2 4758 4209 549 88.46 0.0222 0.039 24.4 44.33 48.24 253.703 301.943 84.02 81.68 Heater 152 25 127 16.35 0.005 0.009 56.126 373.793 134.85 2.737 137.587 1.99 521.91 Heater 833 243 590 29.17 0.024 0.042 152.48 538.65 323.98 13.893 337.873 4.11 253.26 CM3 N2 811 729 82 89.93 0.0033 0.006 24.4 55.66 7.17 74.899 82.069 91.26 128.11 CM3 O2 4776 4219 557 88.35 0.0225 0.040 24.4 44.32 48.89 253.718 302.608 83.84 81.64 Mixer 120409 99367 21042 82.5 0.85 1.502 17.25 20.9 1306.67 0 1306.67 0.00 21.16 Compressor 2020 1727 292 85.5 0.012 0.021 24.4 51.72 25.68 144.136 169.816 84.88 111.97 Syngas Cooler HP 180270 129746 50523 72 2.04 3.607 18.876 28.14 3433.21 893.562 4326.772 20.65 49.08 Syngas Cooler IP 7962 6694 1268 84.1 0.05 0.091 18.876 24.91 86.16 59.236 145.396 40.74 31.97 ThrottlingValve Dissipative component 596 0.024 0.043 0 0 Scrubber Dissipative component 18119 0.732 1.294 586.6 586.6 100.00 Mixer 49323 34240 15083 69.42 0.609 1.077 19.02 110.49 1032.77 0 1032.77 0.00 480.91 Heater 9453 6633 2820 70.17 0.114 0.201 37.7 56.5 383.04 65.249 448.289 14.56 49.87 WGS HT 750667 701287 49375 93.42 1.994 3.525 0.8136 1.169 144.62 752.553 897.173 83.88 43.68 Evaporator 69180 61050 8130 88.25 0.328 0.580 37.7 44.7 1103.85 430.071 1533.921 28.04 18.57 WGS LT 230757 220196 10561 95.42 0.426 0.754 0.4316 0.927 16.41 376.276 392.686 95.82 114.78 Heater 25595 20454 5141 79.9 0.2076 0.367 37.7 52.5 689.35 399.163 1088.513 36.67 39.26 Heater 34331 19961 14370 58.14 0.58 1.026 37.7 77.1 1951.04 752.479 2703.519 27.83 104.51 AGR Dissipative component 177999 7.18 12.708 15773.956 15773.956 100.00 Saturator 18083 14790 3293 81.79 0.133 0.235 239.57 314.95 2840.3 1173.2 4013.5 29.23 31.46
110
Pump 25 21 5 81.04 0.0002 0.000 24.4 118.67 0.42 6.538 6.958 93.96 386.35 Mixer 2464 1356 1108 55.04 0.045 0.079 55.67 101.15 222 0 222 0.00 81.70 Pump 76 55 21 72.67 0.0008 0.001 24.4 66.37 1.83 6.538 8.368 78.13 172.01 CombustionChamber 1406425 1073599 332826 76.34 13.44 23.762 3.66 5.47 4388.85 2608.805 6997.655 37.28 49.45 Compressor 535293 508177 27116 94.93 1.1 1.936 13.9 16.92 1356.3 4174.088 5530.388 75.48 21.73 Gas Turbine 1214107 1143085 71022 95.88 2.02 5.071 12.486 13.9 2248.4 3652.327 5900.727 61.90 11.32 HPSH1 36856 34954 1902 94.84 0.077 0.136 12.486 15 85.48 230.553 316.033 72.95 20.13 HPSH2 64072 58016 6056 90.55 0.245 0.432 12.486 15.44 272.2 344.42 616.62 55.86 23.66 Turbine HP 88443 84770 3673 95.85 0.148 0.262 28.34 30.125 374.77 169.253 544.023 31.11 6.30 Mixer 415 408 6 98.44 0.0003 0.000 19.02 19.32 0.44 0 0.44 0.00 1.58 Turbine IP 148427 142651 5776 96.11 0.233 0.412 25.43 27.3 528.75 428.691 957.441 44.77 7.35 IPSH1 91162 84531 6632 92.73 0.268 0.473 12.486 15.3 298.1 547.728 845.828 64.76 22.54 Mixer 803 764 39 95.08 0.0016 0.003 25.43 26.74 3.6 0 3.6 0.00 5.15 Turbine LP 169100 159167 9933 94.13 0.401 0.709 26 28.74 929.82 636.242 1566.062 40.63 10.54 IPSH2 186 181 6 96.98 0.0002 0.000 12.486 18.9 0.25 3.917 4.167 94.00 51.37 IPSH3 25015 21293 3722 85.12 0.15 0.266 12.486 19.2 167.3 349.259 516.559 67.61 53.77 IPEVAP 96535 82865 13670 85.84 0.552 0.976 12.486 17.68 614.4 934.781 1549.181 60.34 41.60 Preheater IP 32308 27419 4889 84.87 0.197 0.349 12.486 16.2 219.73 148.285 368.015 40.29 29.75 LPSH 1445 1157 288 80 0.012 0.021 12.486 23.33 12.96 32.192 45.152 71.30 86.85 LPEVAP 31136 25258 5879 81.12 0.237 0.420 12.486 19.95 264.24 414.274 678.514 61.06 59.78 Preheater LP 619 556 62 89.9 0.0025 0.004 12.486 19.98 2.81 12.196 15.006 81.27 60.02 LP Pump 6.2 4.5 1.7 72.5 0.00007 0.000 24.4 320 0.15 4.644 4.794 96.87 1211.48 Economizer 4773 2505 2268 52.5 0.09 0.162 12.486 30.22 101.94 57.973 159.913 36.25 142.03 HP Pump 4803 4261 542 88.72 0.022 0.039 24.4 36.6 47.6 139.4 187 74.55 50.00 IP Pump 564 506 57 89.83 0.0023 0.004 24.4 41.15 5.03 25.506 30.536 83.53 68.65 Condenser 20376 8033 12343 39.42 0.498 0.881 26 76.03 1155.44 291.169 1446.609 20.13 192.42 COND Pump 51 48 3 94.34 0.00011 0.000 24.4 52.59 0.254 4.644 4.898 94.81 115.53 Mixer 149 22 127 14.67 0.005 0.009 30.95 210.93 14.16 0 14.16 0.00 581.52 Total 2476443 824738 1400677 33.3 49.35 100.000 1.3 24.4 40806.654 77767.9 118574.554 65.59 1776.92
A.3
C
T
Co
C
3Thecom
Table A.
ComponenCM
CD
TV
EV
Table A.3.2
mponentCM
CD
TV
EV
Table A.3
ComponenCM
CD
TV
EV
mpressi
.3.1 Exerget
Ent (KW
36
10
21
18
Exergoecon
cF (€/GJ)
27.78
53.32
52.13
59.40
3.3 Exerget
Ent (KW
34
8.9
21
18
ionrefrig
tic results o
EFW) (K.65 30
.04 1.
.57 18
.10 1
nomic resul
cP(€/GJ)52.098
643.31
59.838
160.44
ic results of
EFW) (K4.9 29
919 1.
.82 18
.14 1
111
geration
f refrigerati
EPKW) (0.87 5
.137 8
8.82 2
1.47 6
ts of refrige
CD(€/h)0.558
1.709
0.514 0
1.417
f refrigeratio
EPKW) (9.92 4
.138 7
8.95 2
1.41 6
nmachin
ion machine
ED E(KW) (5.778 8
8.903 1
2.737 8
6.625 6
eration mac
Z (€/h)2.125
0.707
0.0068
2.756
on machine
ED E(KW) (4.981 8
7.781 1
2.868 8
6.721 6
ne
e from the p
Eps(%) (%84.24 1
11.33 2
86.85
63.39 1
chine from t
CD+Z(€/h)2.703
2.416
0.5204
4.173
e from the r
Eps(%) (%85.7 1
12.76
86.85
62.9 1
program
y y%) (%15.77 24
24.29 37
7.47 11
18.08 27
the program
f (%) (78.6
29.3 1
1.31
66.0
reference
y y%) (%14.27 22
22.3 34
8.2 12
19.26 30
D*
%).03
.03
.38
.55
m
r%)87.5
1106
14.8
170
D*
%).28
.41
.83
.07
112
Table A.3.4 Exergoeconomic results of refrigeration machine from the reference
cF cP CD Z CD+Z f rComponent (€/GJ) (€/GJ) (€/h) (€/h) (€/h) (%) (%)
CM 27.78 51.581 0.489 2.125 2.623 81.0 90
CD 52.86 588.34 1.481 0.707 2.188 32.3 1013
TV 52.13 59.356 0.538 0.0068 0.5448 1.25 13.86
EV 60.12 162.73 1.456 2.756 4.212 65.4 170
Table A.3.5 Thermodynamic data of streams from the program
Stream T(C)
P(bar)
h(kJ/kg)
s(kJ/kgK)
EPH
(kJ/kg)
ECH
(kJ/kg)
Etot(KW)
cPH
(€/GJ)
c(€/GJ)
C(€/h)
R717 (m = 0,09186 kg/s)
1 ‐25 1.51 1430 5.979 67.7 19841 1828.8 59.4 0.20 1.33
2 153 11.67 1829 6.194 403.8 19841 1859.7 53.32 1.06 7.12
3 30 11.67 343.7 1.499 294.5 19841 1849.6 53.32 0.78 5.19
4 ‐25 1.51 343.7 1.601 264.7 19841 1846.9 59.4 0.78 5.20
Water ( 76m = 6,45 kg/s)
6 20 1 84.01 0.296 0 49.9 321.9 0 0.00 0.00
7 25 1 104.9 0.367 0.176 49.9 323 643.31 2.26 2.63
Air ( 98m = 9,942 kg/s)
8 ‐5 1 ‐30.35 6.782 1.142 5.2 63.1 61.617 11.09 2.52
9 ‐15 1 ‐40.46 6.743 2.296 5.2 74.5 111.28 34.08 9.14
5 Compressor 36.65 27.78 3.67
Table A.3.6 Thermodynamic data of streams from the reference paper
Stream T(C)
P(bar)
h(kJ/kg)
s(kJ/kgK)
EPH
(kJ/kg)
ECH
(kJ/kg)
Etot(KW)
cPH
(€/GJ)
c(€/GJ)
C(€/h)
R717 (m = 0,09186 kg/s)
1 ‐25 1.51 1430 5.981 67.5 19841 1828.8 60.12 0.20 1.34
2 153 11.67 1810 6.166 393.2 19841 1858.7 52.86 1.04 6.96
3 30 11.67 341.6 1.488 296.1 19841 1849.8 52.86 0.79 5.24
4 ‐25 1.51 341.6 1.594 264.9 19841 1846.9 60.12 0.79 5.27
Water ( 76m = 6,45 kg/s)
6 20 1 83.93 0.296 0 49.9 321.9 0 0.00 0.00
7 25 1 104.8 0.367 0.176 49.9 323 588.34 2.07 2.40
Air ( 98m = 9,942 kg/s)
8 ‐5 1 268.3 6.757 1.138 5.2 63 61.617 11.06 2.51
9 ‐15 1 258.2 6.719 2.285 5.2 74.4 112.37 34.31 9.19
5 Compressor 34.9 27.78 3.49
113
AppendixB
Exergyratesandcostratesassociatedwithfuelandproduct
fordefiningcomponentmodelsatsteadystateoperation
Table B.1 Exergoeconomic models of selected components used for programming
Component Assum‐
putions
Schematic Exergyandcost
rateoffuel
Exergyandcost
rateofproduct
Compressor
Pump or
Fan
W
3E = CMW
3C
3E = CMW
3C
2E ‐ 1E
2C ‐ 1C
PHE2 ‐ PHE1
PHC2 ‐ PHC1
Turbine
Auxiliary equation W
1E ‐ 2E 3E = TW
1C ‐ 2C 3C
1c = 2c
PHE1 ‐ PHE2
3E = TW
PHC1 ‐ PHC2
Auxiliary equation PHc1 = PHc2 3C
Heat
exchanger
3T ≥ 0T
Q
1E ‐ 2E 4E ‐ 3E
1C ‐ 2C 4C ‐ 3C
Auxiliary equation 1c = 2c
PHE1 ‐ PHE2
PHE4 ‐ PHE3
PHC1 ‐ PHC2
PHC4 ‐ PHC3
114
Auxiliary equation PHc1 = PHc2
1T ≤ 0T
3E ‐ 4E 2E ‐ 1E
3C ‐ 4C 2C ‐ 1C
Auxiliary equation 3c = 4c
PHE3 ‐ PHE4
PHE2 ‐ PHE1
PHC3 ‐ PHC4
PHC2 ‐ PHC1
Auxiliary equation PHc3 = PHc4
1T > 0T , 3T < 0T 1E ‐ 2E + 3E 4E
& 2T > 0T , 4T > 0T 1C ‐ 2C + 3C 4C
Auxiliary equation 1c = 2c
PHE1 ‐ PHE2
+ PHE3 PHE4
PHC1 ‐ PHC2
+ PHC3 PHC4
Auxiliary equation PHc1 = PHc2
& 2T < 0T , 4T > 0T 1E + 3E 2E + 4E
1C + 3C 2C + 4C
Auxiliary equation 2c = 4c
PHE1 + PHE3
PHE2 + PHE4
PHC1 + PHC3
PHC2 + PHC4
Auxiliary equation PHc2 = PHc4
& 2T > 0T , 4T < 0T Dissipative
component
& 2T < 0T , 4T < 0T 1E + 3E ‐ 4E 2E
1C + 3C ‐ 4C 2C
115
Auxiliary equation 3c = 4c
PHE1 + PHE3
‐ PHE4 PHE2
PHC1 + PHC3
‐ PHC4 PHC2
PHc3 = PHc4
Evaporator
3E ‐ 4E 2E + 5E ‐ 1E
with steam drum 3C ‐ 4C 2C + 5C ‐ 1C
Auxiliary equation 3c = 4c
12
1122
ee
ecec
=
15
1155
ee
ecec
PHE3 ‐ PHE4
PHE2 + PHE5
‐ PHE1
PHC3 ‐ PHC4
PHC2 + PHC5
‐ PHC1
Auxiliary equations PHc3 = PHc4 PHPH
PHPHPHPH
ee
ecec
12
1122
=
PHPH
PHPHPHPH
ee
ecec
51
5511
Mixing
)( 322 eem )( 131 eem
unit )( 32,3222 ececm )( 1131,31 ececm
Auxiliary equation 2c = 2,3c
)( 322PHPH eem +
CHE1 + CHE2
‐ CHE3
)( 131PHPH eem
)( 32,3222PHPHPHPH ececm
+ CHC1 + CHC2
‐ CHC3
)( 1131,31PHPHPHPH ececm
Auxiliary equation PHc2 = PHc 2,3 CHCHCH cmcmcm 221133
116
Combustion 1E ‐ 4E 3E ‐ 2E
chamber
1C ‐ 4C 3C ‐ 2C
Auxiliary equation 1c = 4c
CHE1 + CHE2
‐ CHE3 ‐
CHE4
PHE3 + PHE4
‐ PHE1 ‐
PHE2
CHC1 + CHC2
‐ CHC3 ‐
CHC4
PHC1 + PHC2
‐ PHC3 ‐
PHC4
Auxiliary equation CHc1 = CHc4
CHCH
CHCH
EE
CC
21
21
=
CHCH
CHCH
EE
CC
43
43
PHPH
PHPHPH
emE
ecmC
244
2244
=
PHPHPH
PHPHPHPH
emmEE
ecmmCC
24213
224213
)(
)(
Deaerator
1E ‐ 341 )( emm ‐
4E
)( 232 eem
1C ‐ 3341 )( ecmm ‐
4C
332 ecm ‐ 2C
Auxiliary equations 1c = 4c
PHE1 ‐ PHemm 341 )( ‐
PHE4
)( 232PHPH eem
PHC1 ‐ PHecmm 3341 )( ‐
PHC4
332 ecm PH ‐ PHC2
Auxiliary equation PHc1 = PHc4
117
Steam
1E + 2E ‐( 3E + 4E ) 6E ‐ 5E + 8E ‐ 7E
generator 1C + 2C ‐( 3C + 4C ) 6C ‐ 5C + 8C ‐ 7C
Auxiliary equations 3c = 4c =
21
21
EE
CC
56
56
EE
CC
=78
78
EE
CC
CHE1 + CHE2
‐ CHE3 ‐
CHE4 ‐( PHE3
+ PHE4 ‐
PHE1 ‐ PHE2
)
PHE6 ‐ PHE5
+ PHE8 ‐
PHE7
CHC1 + CHC2
‐ CHC3 ‐
CHC4 ‐( PHC3
+ PHC4 ‐
PHC1 ‐ PHC2
)
PHC6 ‐ PHC5
+ PHC8 ‐
PHC7
Auxiliary equations PHc3 = PHc4 =
PHPH
PHPH
EE
CC
21
21
CHc1 = CHc3
CHCH
CHCH
EE
CC
21
21
=
CHCH
CHCH
EE
CC
43
43
PHPH
PHPH
EE
CC
56
56
=
PHPH
PHPH
EE
CC
78
78
Throttling 2p < 1p ,
Dissipative
component TVDE , = 1E ‐ 2E
valve 2T ≥ 0T
2p < 1p ,
1T < 0T ME1
‐ ME2
Mc1 = Mc2
TE2 ‐ TE1
Auxiliary equation
118
Gasifier
1E ‐ 4E 3E ‐ 2E
1C ‐ 4C 3C ‐ 2C
Auxiliary equation 1c = 4c
CHE1 + CHE2
‐ CHE4 CHE3
+ PHE3 + PHE4
‐
PHE1 ‐ PHE2
CHC1 + CHC2
‐ CHC4 CHC3
+ PHC3 + PHC4
‐
PHC1 ‐ PHC2
Auxiliary equation CHc2 = CHc4 CHc3 = PHPH
PHPHPH
emE
ecmC
244
2244
=PHPHPH
PHPHPHPH
emmEE
ecmmCC
24213
224213
)(
)(
Coal preparation
4
2
3
1
N2, moisture Prepared
coalcoal
N2
3E ‐ 4E 2E ‐ 1E
unit 3C ‐ 4C 2C ‐ 1C
Auxiliary equation 3c = 4c
PHE3 ‐ PHE4
+
PHemm 121 )( +
CHE3 ‐ CHE4
+
CHemm 121 )(
PHE2 ‐ PHem 12 + CHE2
‐
CHem 12
PHC3 ‐ PHC4
+
PHPHecmm 1121 )(
+ CHC3 ‐ CHC4
+
CHCHecmm 1121 )(
PHC2 ‐ PHPHecm 112 +
CHC2 ‐ CHCHecm 112
Auxiliary equation PHPHPH cmcmcm 441133 PHPH
PHPHPHPH
ee
ecec
12
1122
=
119
CHCH
CHCHCH
emmE
ecmmC
1213
11213
)(
)(
= CHc4
CHCH
CHCHCHCH
ee
ecec
12
1122
Air separation
4E = ASUW 3E + 2E ‐ 1E
Unit 4C 3C + 2C ‐ 1C
Auxiliary equation
12
1122
ee
ecec
=
13
1133
ee
ecec
4E = ASUW PHE3
+ PHE2 ‐ PHE1
+
CHE3 + CHE2
‐ CHE1
4C PHC3
+ PHC2 ‐ PHC1
+
CHC3 + CHC2
‐ CHC1
Auxiliary equation
PHPH
PHPHPHPH
ee
ecec
12
1122
=
PHPH
PHPHPHPH
ee
ecec
13
1133
PHPHPH
PHPHPH
EEE
CCC
123
123
=
CHCHCH
CHCHCH
EEE
CCC
123
123
CHc3 = CHc2
Saturator 3E ‐ 4E 2E ‐ 1E
3C ‐ 4C 2C ‐ 1C
Auxiliary equation 3c = 4c
120
PHE3 ‐ PHE4
PHE2 ‐ PHE1
PHC3 ‐ PHC4
PHC2 ‐ PHC1
Auxiliary equation PHc3 = PHc4
Water Gas
Shift
reactor
PHE1 ‐ PHE2
+ CHE1 ‐
CHelseH emm 2,2 )(
2
CHHHH emm
222)( 1,2,
= CHHH em
22
PHPHEc 11 ‐ PHPHEc 22
+ CHCH Ec 11 ‐
CHelse
CHelseH ecmm 2,2,2 )(
2
CHHH
CHH emc
222 2,
Auxiliary equation PHPH cc 21
CHc1 = CHelsec 2,
CHelse
CHelseH ecmm 2,2,2 )(
2
+ CHHH em
22 =
CHCHecm 222
Scrubber
Dissipative
component
Acid gas removal
Dissipative
component
121
AppendixC
Economic Analysis for the IGCC power plant with CO2
Capture
Table C.1 Parameters and assumptions used in the calculation of economic analysis
(all monetary values are expressed in mid‐2007 dollars)
Parameter(units) ValueAverage general inflation rate (%)
Average nominal escalation rate of all costs except fuel (%)
Average nominal escalation rate of coal (%)
Beginning of design and construction period
Date of commercial operation
Plant economic life (years)
Plant life for tax purpose (years)
Plant financing fractions and required returns on capital
5.0
5.0
3.0
Jan. 1, 2014
Jan. 1, 2017
25
20
Type of financing Common Equity
50
15
Debt
Financing fraction (%) 50
Required annual return (%) 9
Resulting average cost of money (%) 12
Average combined income tax rate (%) 30
Average property tax rate (% of PFI)
Average insurance rate (% of PFI)
Average capacity factor (%) 80
Labor position for operating and maintenance 30
Average labor rate ($/h) 34.65
Annual fixed operating and maintenance costs (106$) 58.21
Annual variable operating and maintenance costs at full capacity
(106$) 34.63
Unit cost of coal ($/GJ) 1.3
Allocation of plant‐facilities investment to the individual years of
design and construction (%)
Jan.1‐Dec.31, 2014 40
Jan.1‐Dec.31, 2015 30
Jan.1‐Dec.31, 2016 30
The case 6‐Shell IGCC power plant with CO2 capture from the final report of cost
and performance baseline for fossil energy plants volume 1 (2013, Revision 2a) is the
reference case for economic analysis. The Eq. 3.17 is used to adjust the fixed capital
122
costs of similar‐sized components. The capacities of the equipment are
recommended as YX and WX . To simplify the calculation, the amount of work of
turbines, compressors and pumps, the heat capacity of heat exchangers and the
mass flow rates for some other facilities are used. The exponent α is referred from
Chapter 7 of Bejan, Tsatsaronis and Moran (1996), if no corresponding value exists,
0.6 is taken. In addition, through the Eq. 3.18, the equipment cost of the calculation
year (2014) can be estimated by the known cost of the reference year (2007) with
CEPCI (the chemical engineering plant cost index), which is 579.7 for end‐2014 and
525.4 for end‐2007 (Chemical Engineering Journal).
Table C.2 Calculation of the allowance for funds used during construction (end‐2016
dollars) of IGCC power plant
year Commonequity debt
Escalated
investment
AFUDC Escalated
investment
AFUDC
2014 659911414 329955707 137995148 329955707 79325580
2015 519680238 259840119 60604488 259840119 35856223
2016 545664250 272832125 19747733 272834125 12013064
Table C.3 Annual tax depreciation amount for a life period of 20 years
Yearofcommercial
year MACRS depreciationfactor(%)
AnnualTaxdepreciation($)
1 2017 3.75 71388950
2 2018 7.219 137428488
3 2019 6.677 127110405
4 2020 6.177 117591878
5 2021 5.713 108758685
6 2022 5.285 100610827
7 2023 4.888 93053116
8 2024 4.522 86085555
9 2025 4.462 84944670
10 2026 4.461 84925633
11 2027 4.462 84944670
12 2028 4.461 84925633
13 2029 4.462 84944670
14 2030 4.461 84925633
123
15 2031 4.462 84944670
16 2032 4.461 84925633
17 2033 4.462 84944670
18 2034 4.461 84925633
19 2035 4.462 84944670
20 2036 4.461 84925633
21 2037 2.231 42472335
100 1903705333
Table C.4 Year by year capital recovery schedule for the IGCC case
Yearofcommercialoperation
year AnnualTaxdepreciation($)
DeferredIncomeTaxes
RecoveryofComnonEquityAFUDC
TotalCapitalRecovery
1 2017 76148213 ‐1427779 8800814 83521248
2 2018 76148213 18384082 8800814 103333109
3 2019 76148213 15288658 8800814 100237685
4 2020 76148213 12433099 8800814 97382126
5 2021 76148213 9783142 8800814 94732169
6 2022 76148213 7338784 8800814 92287811
7 2023 76148213 5071471 8800814 90020498
8 2024 76148213 2981203 8800814 87930230
9 2025 76148213 2638937 8800814 87587964
10 2026 76148213 2633226 8800814 87582253
11 2027 76148213 2638937 8800814 87587964
12 2028 76148213 2633226 8800814 87582253
13 2029 76148213 2638937 8800814 87587964
14 2030 76148213 2633226 8800814 87582253
15 2031 76148213 2638937 8800814 87587964
16 2032 76148213 2633226 8800814 87582253
17 2033 76148213 2638937 8800814 87587964
18 2034 76148213 2633226 8800814 87582253
19 2035 76148213 2638937 8800814 87587964
20 2036 76148213 2633226 8800814 87582253
21 2037 76148213 ‐10102763 8800814 74846264
22 2038 76148213 ‐22844464 8800814 62104563
23 2039 76148213 ‐22844464 8800814 62104563
24 2040 76148213 ‐22844464 8800814 62104563
25 2041 76148213 ‐22844464 8800814 62104563
1903705333 220020366 2123730694
124
Table C.5 Year by year revenue requirement analysis for the IGCC case
Year Capitalrecovery
Returnoncommonequity
Interestondebt
Incometaxes
Fuelcost O&Mcosts Totalrevenuerequirement
2017 83521248 161392244 96835346 74367661 83660000 151226600 651003099
2018 103333109 155043637 93026182 51834968 86169800 158787930 648195626
2019 100237685 147209141 88325485 51572752 88754894 166727327 642827284
2020 97382126 139606802 83764081 51170164 91417541 175063693 638404407
2021 94732169 132218630 79331178 50653763 94160067 183816877 634912684
2022 92287811 125029205 75017523 50016938 96984869 193007721 632344067
2023 90020498 118023106 70813864 49281638 99894415 202658107 630691628
2024 87930230 111187056 66712234 48442170 102891248 212791013 629953951
2025 87587964 104507776 62704666 45921887 105977985 223430563 630130841
2026 87582253 97854166 58712499 43076051 109157325 234602092 630984386
2027 87587964 91200984 54720590 40218976 112432044 246332196 632492754
2028 87582253 84547374 50728424 37373140 115805006 258648806 634685003
2029 87587964 77894192 46736515 34516065 119279156 271581246 637595138
2030 87582253 71240582 42744349 31670229 122857530 285160309 641255252
2031 87587964 64587400 38752440 28813155 126543256 299418324 645702539
2032 87582253 57933790 34760274 25967319 130339554 314389240 650972430
2033 87587964 51280609 30768365 23110244 134249741 330108702 657105625
2034 87582253 44626999 26776199 20264408 138277233 346614137 664141229
2035 87587964 37973817 22784290 17407333 142425550 363944844 672123798
2036 87582253 31320207 18792124 14561497 146698316 382142086 681096483
2037 74846264 24667025 14800215 24446123 151099266 401249191 691108084
2038 62104563 18969042 11381425 34745831 155632244 421311650 704144755
2039 62104563 14226687 8536012 32713393 160301211 442377233 720259099
2040 62104563 9484332 5690599 30680955 165110248 464496094 737566791
2041 62104563 4741977 2845186 28648517 170063555 487720899 756124697
125
Table C.6 Total investment cost rates of components for IGCC power plant
No ComponentType PEC ZCI ZOM Zk($/h)1 CoalPrepareUnit 270026000 7480.8651 5151.7167 12632.582 2 Eco 162264 4.4954 3.0958 7.591 3 Gasifier 373136400 10337.4604 7118.9183 17456.379 4 ASU 209354000 5799.9935 3994.1802 9794.174 7 Eco 1155841 32.0217 22.0518 54.074 8 Compressor1 N2 2729527 75.6195 52.0755 127.695 9 Compressor1 O2 5423323 150.2490 103.4694 253.718
10 HE 116788 3.2355 2.2282 5.464 11 HE 272715 7.5554 5.2030 12.758 12 CM2 N2 1501771 41.6054 28.6517 70.257 13 CM2 O2 5423000 150.2401 103.4632 253.703 14 HE 58507 1.6209 1.1162 2.737 15 HE 296962 8.2271 5.6656 13.893 16 CM3 N2 1601003 44.3546 30.5449 74.899 17 CM3 O2 5423321 150.2490 103.4693 253.718 18 Condenser 880497 24.3935 16.7986 41.192 19 Membrane Wall 1777961 49.2571 33.9210 83.178 21 CM 3080962 85.3557 58.7804 144.136 22 Syngas Cooler HP 19100200 529.1565 364.4050 893.562 23 Syngas Cooler IP 1266194 35.0789 24.1572 59.236 24 Throttlingvalve 0 0.0000 0.0000 0.000 26 Scrubber 12538786 347.3775 239.2224 586.600 28 HE 1394721 38.6397 26.6093 65.249 29 HT‐WGS 16086084 445.6527 306.8999 752.553 30 Evaporator 9192924 254.6830 175.3881 430.071 31 LT‐WGS 8043042 222.8264 153.4499 376.276 32 HE 8532259 236.3798 162.7835 399.163 33 HE 16084504 445.6090 306.8697 752.479 35 AGR 337174000 9341.1494 6432.8062 15773.956 36 Saturator 25077573 694.7551 478.4449 1173.200 37 Saturator Pump 139745 3.8715 2.6661 6.538 39 Pump 139745 3.8715 2.6661 6.538 40 CombustionChamber 55764150 1544.9034 1063.9016 2608.805 41 Compressor 89222640 2471.8454 1702.2426 4174.088 42 Gas Turbine 78069810 2162.8648 1489.4623 3652.327 43 HPSH1 4928148 136.5306 94.0221 230.553 44 HPSH2 7362108 203.9616 140.4587 344.420 45 Steam Turbine HP 3617837 100.2294 69.0232 169.253 47 Steam Turbine IP 9163428 253.8658 174.8253 428.691 48 IPSH1 11707892 324.3582 223.3701 547.728 50 Steam Turbine LP 13599901 376.7749 259.4670 636.242 52 IPSH2 83732 2.3197 1.5975 3.917 54 IPSH3 7465538 206.8271 142.4320 349.259 56 IPEV 19981287 553.5664 381.2149 934.781 57 IP Preheater 3169656 87.8129 60.4726 148.285 59 LPSH 688114 19.0637 13.1282 32.192 62 LPEV 8855257 245.3282 168.9459 414.274 64 LP Preheater 260704 7.2226 4.9739 12.196 65 Throttlingvalve 0 0.0000 0.0000 0.000 66 LPPump 99264 2.7500 1.8938 4.644 67 Economizer 1239196 34.3310 23.6421 57.973 72 HPPump 2979728 82.5511 56.8490 139.400 73 IPPump 545210 15.1046 10.4018 25.506 79 Condenser 6223838 172.4267 118.7421 291.169 80 CondenserPump 99264 2.7500 1.8938 4.644
126
AppendixD
ThermalpropertiescalculationofAmmonia
D.1 The vapor pressure equation for the Liquid‐Vapor
coexistingphase
The vapor pressure equation is (Lester Hour and John S. Gallagher, 1978):
1 1 1 1 ] (D.1)
The coefficients of the vapor pressure equation are =‐7.296510; =1.618053;
=‐1.956546; =‐2.114118; =405.4 K; =111.85 atm, and the subscript c
indicates the critical point.
D.2ThedensityfortheSaturatedLiquidandVapor
The generalized corresponding‐states equation of the density for the Saturated Vapor
is (Chen Z S, Cheng W L, Hu P. 2003):
0.0198 0.11| 0.82| 0.07 1 (D.2)
in which, / ; 0.256 1.85 0.066 1 ; ⁄ ;
⁄ ; ⁄ . In this equation, the item will significantly affect the
results only when the item is large than 0.98.
The generalized corresponding‐states equations of the density for the Saturated
Liquid are (Chen Z S, Cheng W L, Hu P. 2003):
∙ ∆ (D.3)
∆ ∆ . . ∆ (D.4)
∆ (D.5)
where the subscript b represent the boiling point.
127
D.3The latentheatofvaporizationand theenthalpyofthe
SaturatedLiquidandVapor
The generalized corresponding‐states equation of the latent heat of vaporization for
ammonia is (Chen Z S, Cheng W L, Hu P. 2003):
∆ , ∆. . | ∆ |
(D.4)
The generalized corresponding‐states equation of the enthalpy of the Saturated
Liquid is (Chen Z S, Cheng W L, Hu P. 2003):
∆ ∆ . . ∆ (D.5)
∆ (D.6)
The enthalpy of the Saturated Vapor is formulated as the following equation:
∆ (D.7)
where represent the enthalpy of the Saturated Vapor and ∆ ∆ , ∙ ∆ ,
in which the item ∆ , is the latent heat of vaporization on boiling point.
D.4TheentropyoftheSaturatedLiquidandVapor
For the calculation of the entropy of the Saturated Liquid, the reference state should
be chosen, according to the current common practice, the reference temperature T0=
273.15 K, the pressure p0=1 bar, the entropy of the Saturated Liquid at the reference
state is s0 = 1. 0 kJ / (kgK). Then the equation of the entropy of the Saturated Liquid
can be written as:
(D.8)
The entropy of the Saturated Vapor is formulated as the following equation:
∆ (D.9)
128
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