A computer program for the exergoeconomic analysis of ...

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



5.1.4 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




5.2.4 Error analyses .............................................................................................. 84


v



5.3 Simple refrigeration machine ............................................................................. 86




5.3.4 Error analyses .............................................................................................. 89




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


modular

Medium

EES Small Chemical

equations

Very fast High Simultaneous

equations

Low

Ebsilon

Professional

Medium Power

system


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



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


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


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.


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


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.


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.


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


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


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


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.


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.


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


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.


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


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


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


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


PHE3 ‐ PHE4

PHE2 ‐ PHE1

PHC3 ‐ PHC4

PHC2 ‐ PHC1


1T > 0T , 3T < 0T 1E ‐ 2E + 3E 4E

& 2T > 0T , 4T > 0T 1C ‐ 2C + 3C 4C


PHE1 ‐ PHE2

+ PHE3 PHE4

PHC1 ‐ PHC2

+ PHC3 PHC4


& 2T < 0T , 4T > 0T 1E + 3E 2E + 4E

1C + 3C 2C + 4C


PHE1 + PHE3

PHE2 + PHE4

PHC1 + PHC3

PHC2 + PHC4


& 2T > 0T , 4T < 0T Dissipative

component

& 2T < 0T , 4T < 0T 1E + 3E ‐ 4E 2E

1C + 3C ‐ 4C 2C

115


PHE1 + PHE3

‐ PHE4 PHE2

PHC1 + PHC3

‐ PHC4 PHC2

PHc3 = PHc4

Evaporator

3E ‐ 4E 2E + 5E ‐ 1E

with steam drum 3C ‐ 4C 2C + 5C ‐ 1C


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


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


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


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


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


120

PHE3 ‐ PHE4

PHE2 ‐ PHE1

PHC3 ‐ PHC4

PHC2 ‐ PHC1


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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