ZERO EMISSION COAL STUDY - Columbia...

ZERO EMISSION COAL STUDY

Final Report

Prepared for

THE NEW YORK STATE

ENERGY RESEARCH AND DEVELOPMENT AUTHORITY

Albany, NY

Barry N. Liebowitz

Project Manager

Prepared by

Columbia University

New York, NY

Klaus S. Lackner

Xinxin Li

Agreement No. 10087

NYSERDA December2010

Notice

This report was prepared by Klaus Lackner and Xinxin Li in the course of per-

forming work contracted for and sponsored by the New York State Energy Research

and Development Authority and the Columbia University. The opinions expressed

in this report do not necessarily re�ect those of the Sponsors or the State of New

York, and reference to any speci�c product, service, process, or method does not

constitute an implied or expressed recommendation or endorsement of it. Further,

the Sponsors and the State of New York make no warranties or representations, ex-

pressed or implied, as to the �tness for particular purpose or merchantability of any

product, apparatus, or service, or the usefulness, completeness, or accuracy of any

processes, methods, or other information contained, described, disclosed, or referred

to in this report. The Sponsors, the State of New York, and the contractor make

no representation that the use of any product, apparatus, process, method, or other

information will not infringe privately owned rights and will assume no liability for

any loss, injury, or damage resulting from, or occurring in connection with, the use

of information contained, described, disclosed, or referred to in this report.

ii

ZERO EMISSION COAL STUDY

Abstract

Choosing among di�erent technologies is di�cult and requires a means of mak-

ing comparisons across di�erent technologies. This paper proposes a computational

model, to evaluate di�erent technologies and to identify optimal technologies based

on a user supplied set of evaluation criteria to compare di�erent zero emission power

plant designs.

iii

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Summary 41.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Goal & Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 A numerical method for multiobjective optimization of zero emissionpower plants 112.1 A means required to compare di�erent technologies . . . . . . . . . . 122.2 Evaluation criteria based on a penalty model . . . . . . . . . . . . . . 16

3 A simple model for power plant pathway optimization 193.1 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Path-dependent shortest-path algorithms for optimizing a sequenceof power plant designs 404.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . 434.3 Literature review on shortest-path problem . . . . . . . . . . . . . . . 444.4 Path-dependent shortest-path algorithms . . . . . . . . . . . . . . . . 454.5 Branch and bound algorithm with bottom-up pruning . . . . . . . . . 474.6 Heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.7 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . 554.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5 Optimizing CO2 post-combustion capture technologies 635.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

iv

Table of Contents v

5.3 Modeling CO2 absorber physics . . . . . . . . . . . . . . . . . . . . . 685.4 Penalty model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.6 Discussion-Modeling Results . . . . . . . . . . . . . . . . . . . . . . . 85

6 Designing the software tool for advanced power plant modeling andoptimization 876.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896.3 A model of modules and pipes . . . . . . . . . . . . . . . . . . . . . . 916.4 Reconcile - An iterative procedure . . . . . . . . . . . . . . . . . . . . 936.5 Reconcile algorithm: numerical routine for solving a system of equations 976.6 Reconcile implementation . . . . . . . . . . . . . . . . . . . . . . . . 996.7 Discussion of Newton-Raphson method . . . . . . . . . . . . . . . . . 1006.8 Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026.9 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.10 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.11 Ongoing development . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

A Introduction to TEX 110A.1 What is TEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110A.2 The algorithm of breaking paragraphs into lines . . . . . . . . . . . . 111

Bibliography 112

List of Figures

3.1 Environmental Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 An example of pathways connecting y0 to various future technologies 343.3 Pathways end in an environment with CO2 regulations . . . . . . . . 373.4 Pathways end in an environment without CO2 regulations . . . . . . 373.5 Plant level penalties with CO2 regulations . . . . . . . . . . . . . . . 383.6 Plant level penalties without CO2 regulations . . . . . . . . . . . . . 383.7 Environmental penalties with CO2 regulations . . . . . . . . . . . . . 393.8 Environmental penalties without CO2 regulations . . . . . . . . . . . 39

4.1 An instance of a rooted tree . . . . . . . . . . . . . . . . . . . . . . . 424.2 An instance of depth �rst search strategy in branch and bound [?] . . 484.3 An instance of a graph for shortest-path problem . . . . . . . . . . . 524.4 An instance of a tree collapsed into a graph, path-dependent . . . . . 524.5 Visited nodes in branch-and-bound(BB) algorithm . . . . . . . . . . . 564.6 The optimal results given by BB and the brute-force approach . . . . 564.7 The visited nodes comparison between BB and the heuristic . . . . . 574.8 The optimal results given by the heuristic and the brute-force approach 574.9 The optimal path as a function of x in Heuristic . . . . . . . . . . . . 594.10 Visited nodes in the branch-and-bound and the hybrid algorithm . . . 61

5.1 An instance of the cross-section of a packing tower . . . . . . . . . . . 705.2 Single plant and pathway optimization, 6 design choices for 14 decision

points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.3 6 design results. Plant index comparison . . . . . . . . . . . . . . . . 805.4 Plant performance data of the 6 designs . . . . . . . . . . . . . . . . 815.5 21 design results. The optimal cost of a single plant and a sequence of

plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.6 21 design results. Plant index comparison . . . . . . . . . . . . . . . 825.7 Plant performance data of the 21 designs . . . . . . . . . . . . . . . . 835.8 87 design results. The optimal cost of a single plant and a sequence of

plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

vi

List of Figures vii

5.9 87 design results. Plant index comparison . . . . . . . . . . . . . . . 845.10 87 design results. 87 design results. 30 $/ton CO2 .The optimal cost

of a single plant and a sequence of plants . . . . . . . . . . . . . . . . 855.11 87 design results. 30 $/ton CO2 Plant index comparison . . . . . . . 86

A.1 Examples of breaking a pargraph into lines . . . . . . . . . . . . . . . 111

List of Tables

3.1 Regulatory factor for each item in the sequence . . . . . . . . . . . . 263.2 Summary of power plant designs and pathways designs . . . . . . . . 353.3 Module level, plant level and pathway level penalties . . . . . . . . . 36

6.1 Input File (Flowsheet) De�nition (Format) . . . . . . . . . . . . . . 109

viii

List of Tables 1

Abbreviations

z = a representation of a sequence of power plants �

y = a speci�c power plant con�guration

xi = a module, usually an operational unit, like a pump, a furnace, or an absorber

m = the number of modules in a power plant design

tj = the decision making time, j stands for its position in the sequence of decisions

Sxiis the size of a module xi

Sy(t) is the size of a power plant y(t)

PN = Penalty Number � unit

PNxi= Penalty number of a module � unit

PNy(t) = Penalty number of a power plant at time t� unit

PNz = Penalty number of a power plant pathway� unit

Di = di�usion coe�cient � m2 s−1

Dco2mea = di�usion coe�cient of co2 in mea� unit

Dmeamea = di�usion coe�cient of mea in mea� unit

cp = speci�c heat � J kg−1 K−1

List of Tables 2

Cp = molar heat capacity � J mol−1 K−1

dch = channel diameter � m

cpsi = cells per square inch - in−1

GHSV = gas hourly space velocity - h−1

k = reaction rate coe�cient

kc = mass transfer coe�cient � m s−1

kT = coe�cient of thermal conductivity � W m−1 K−1

Le = α/Di � Lewis number

mesh number = number of wires per linear inch � in−1

Nu = hL/kT � Nusselt number

Pr = cpν/kT � Prandtl number

R = reaction rate � (detailed below)

RTOF = turnover frequency � moli mol−1Pt s

−1

Rwc = reaction rate per unit washcoat volume � moli m−3 s−1

Rv = reaction rate per unit reactor volume � moli m−3 s−1

RW = reaction rate per unit catalyst weight � moli g−1 s−1

Sav = geometric surface area-to-volume ratio � m−1

SCO = 0.5 ·∆CO/∆O2 � Selectivity of CO

Sc = ν/Di � Schmidt number

Sh = kcL/Di � Sherwood number

T = temperature - Ctwc = washcoat thickness � m

v = super�cial gas velocity � m s−1

List of Tables 3

V̇ = volumetric �owrate � m3 s−1

WHSV = weight hourly space velocity - gCO gcat−1 h−1

xi = molar fraction of species i

z = axial coordinate � m

greek letters

α = kT/(ρcp)= thermal di�usivity � m2 s−1

χi = fractional conversion of species i

ε = void fraction

λ = 2 · CO2/CCO µ = dynamic viscosity � Pa s

ν = µ/ρ = kinematic viscosity � m2 s−1

ρcat - catalyst loading (grams of metal+support per reactor volume) � g m−3

ρwc - washcoat loading (grams of metal+support per washcoat volume) � g m−3

σv = volumetric site density � ρcatlPtDispMWPt

� molPt m−3

Chapter 11

Summary2

1.1 Background3

Traditional power plant modeling tools only measure the thermodynamic perfor-4

mance and economic cost of a power plant, optimization is often carried out to reach5

a compromise between plant e�ciency and generation costs of the individual plants.6

Today, increasingly stringent environmental constraints especially in response to cli-7

mate change, require a new modeling tool to evaluate di�erent power plant designs8

under various energetic, economical, environmental and infrastructural constraints.9

Choosing between di�erent low-emission power generation technologies has a pro-10

found impact not only on the cost-e�ciencies of individual power plants, but more11

importantly on the pathways connecting current power generation technologies to12

future technologies.13

The need to develop low-emission power generation technologies arose both from14

the rapid growing consensus that excess carbon dioxide will cause a signi�cant change15

4

Chapter 1: Summary 5

in climate that will have repercussions on a wide variety of human activities [Lackner 2001],16

and from the fact that power plants burning fossil fuel are a major source of carbon17

dioxide emissions, accounting for roughly one thirds of the global carbon emissions.18

In order to mitigate carbon dioxide from fossil fuel-�red power plants, a means is19

required to obtain a concentrated form of carbon dioxide with little incondensible im-20

purities, before it can be dispose of safely and permanently. The capture and storage21

of carbon dixoide (CCS) is one of the greatest challenge not only to power genera-22

tion infrastructure, but more importantly to the sustainable access to the cheap and23

abundant fossil fuel [Lackner 2001].24

A spectrum of low-emission power plants has been addressing environmental im-25

pact of impurities and undesirable combustion product from fossil fuel for some time.26

On one end of the spectrum include power plants with environmental control units27

for desulphurization, particulate removal and mercury emission control, etc. On the28

end of the spectrum is a special class of technologies zero emission power plants. Such29

plants produce power without emitting any atmospheric emissions, in some designs30

without a smoke stack. For example, a technology developed by the zero emission coal31

alliance (ZECA) generates electricity with hydrogen fuel cell producing only water,32

where clean hydrogen is derived from coal with a hydrogasi�er and a decarbonation33

reactor, followed by a calciner separating carbon dioxide together with impurities and34

underiable combustion by-product for sequestration [Lackner 2002].35

Zero emission power plants are yet to be built. Today, low-emission power plants36

minimized emissions of carbon dioxide to the atmosphere through separation and cap-37

ture of carbon dioxide by one of three general techniques: pre-combustion, oxy-fuel,38


and post-combustion de-carbonization [IPCC, 2005]. Governments and �rms eager to39

deploy low-emission thermal power plants must choose among three distinct types of40

power plant designs: the integrated gasi�cation combined cycle design (IGCC), which41

relies on pre-combustion separation of carbon dioxide in a gasi�er [IEA GHG, 2003],42

the oxy-fuel design which uses pure oxygen combustion to yield a nearly pure stream43

of carbon dioxide after combustion [Croiset and Thambimuthu, 2000], and the post-44

combustion de-carbonation design which relies on chemical absorption processes[Henderiks, 1994].45

Currently, there is no clear technological winner [MIT, 2007]. For both the IGCC and46

the oxy-fuel processes, the chief obstacle to broad deployment is the high capital and47

operational cost associated with each technique. Opportunities exist both for incre-48

mental modi�cations leading to near-term cost e�ciencies and for major redesigns49

leading to advanced next-generation power plant designs.50

The IGCC and oxy-fuel processes are not the only possible implementations of low-51

emission power plants. Instead, there is a broad range of potential designs which might52

incorporate a variety of components and approaches. For example, advanced zero53

emission power plant (AZEP) addresses the development of a speci�c, zero emissions;54

gas turbine-based, power generation process, which relies on a mixed-oxide membrane55

for oxygen production [Gri�n 2005]. Such a device is a critical component shared56

by a variety of oxygen-enhanced combustion and gasi�cation processes. This project57

examines a family of advanced thermal power plant designs, such as conventional oxy-58

fuel power plants with a separate cryogenic air separation unit and fuel cell designs59

which combine oxygen separation, carbon oxidation, and electricity generation in a60

single unit, as well as the many potential designs which lie in between these two61


extremes. For example, oxygen blown IGCC, oxy-fuel �uidized bed combustors and62

AZEP designs are each a variation along a continuum of plant designs.63

A wide range of choices for the next-stage designs away from the existing low64

e�ciency, and polluting fossil fuel power plants, will lead to di�erent technological65

pathways, which constitute a sequence of plant designs that builid on each other,66

connecting to the e�cient, economical and clean future technologies. The overall67

objectives of this project are to create conceptual plant designs and conduct engi-68

neering assessments of the component modules of a zero emission power plant; eval-69

uate di�erent power plant designs under various energetic, economic, environmental70

and infrastructural constraints; and perform optimization not just to the individual71

power plants alone, but pathways connecting current power generation technologies72

to future technologies.73

1.2 Goal & Objectives74

The goal of this project is to model the performance (energy and environmen-75

tal) of advanced concepts in power generation that produce zero CO2 emission from76

coal. Speci�cally, we model and evaluate di�erent power plant technologies and path-77

way options with a new metric, which will be critical in choosing between various78

low-emission power generation technologies with very di�erent design constraint and79

optimization criteria.80

The project is accomplished in phases. In Phase I, we de�ned the modules that81

can be used to build a zero-emission power plant and the range of operational criteria82

for their recombination to function in various modes by establishing the performance83


criteria, identifying key parameters, and creating computational models for each mod-84

ule. In Phase II, we focused on developing computational capability and databases85

to model various power plant designs based on these models. Di�erent plant process86

con�guarations are established, heat and mass balance for various plant designs are87

made, and di�erent power plant designs are assessed based on e�ciency, emissions88

and technical and economic feasibility.89

Speci�cally, this report is divded into following chapters. A novel numerical90

method is presented (Chapter 2) to evaluate di�erent technologies in order to iden-91

tify optimal technologies, based on a user supplied set of evaluation criteria. The92

ranking method used here for advanced power plant designs comparison has taken its93

inspiration from the typesetting system TEX, in which Donald Knuth demonstrated94

the power of these optimization algorithms for trading o� between text layouts with95

properties that are very di�erent and very di�cult to quantify.96

In Chapter 3, a very simple example is presented to show how the model can be97

used to select appropriate power plant modules and a wide range of technologies, to98

arrive at a sequence of plant designs that provides an advantageous technology path-99

way from today's power plant designs to a future design via a number of intermediate100

steps. Eight basic modules are chosen which forms 96 possible plant designs, of which101

17 are physically valid. The permutations of the 17 power plants in a pathway con-102

sisting of �ve di�erent power plants implemented in sequence, gives 106 variations.103

As a preliminary study, we didn't explore the entire space of all solutions. Instead,104

�ve unique pathways are chosen to show various aspect of penalties when forming a105

technology pathway. For example, a shorter path is favorable, but too many changes106


at the same time is undesirable. The modeling results are subjective because they107

depend highly on the user-supplied set of evaluation criteria. However, the bias input108

are exogenous to the model. This is because we want to give users the freedom to put109

their own preference to the model, such that they can get their customized solutions.110

This re�ects the �exibility of the model.111

To explore the entire space of solutions, we developed two combinatorial optimiza-112

tion algorithms (Chapter 4). The objective function is de�ned as the minimum of a113

nonlinear programming problem. The problem is solved by means of a branch-and-114

bound method, and a heuristic based on the label-correcting algorithm for solving115

shortest-path problem. The proposed algorithms are applied for practical problems116

on �nding the optimal sequence of various power plant designs.117

In Chapter 5, we study various post-combustion capture technologies using the118

ranking algorithms introduced in Chapter 4. In the �rst part of our work, we devel-119

oped a simple model for the absorber system. We �nd the optimum design given a120

speci�c sorbent strength by varying the packing tube radius and the absorber tower121

height. In the second part of our work, we studied various power plant designs with122

absorbers in a sequence and �nd the optimum sequence using the algorithm.123

As a part of the project, a computational software tool is developed to model124

the mass-energy balance of a module, and to implement the ranking method (Ap-125

pendix). This input-output model consists of modules and pipes, where each module126

respresent a fundamental operation unit (i.e a expander, an heat exchanger, a CO2127

absorber etc), and a pipe can be considered as a material or energy �ow. Each mod-128

ule is characterized by a set of parameters, which satisfy a system of equations. The129


program begins with a set of complete but inconsistent parameters, and �nd a con-130

sistent set of parameters through iteration. Upon �nding a reconciled system, The131

user may set one(or a few) parameter(s) free to a range, such that the software can132

�nd the optimum. The same method is used to �nd the optimum pathway. A library133

of �ve modules are built, and the manuals on coding a new module are included in134

the Appendix.135

The main contribution of this project is developing and implementing the opti-136

mization method to the problem of choosing optimum power plant designs that are137

path-dependent.138

Chapter 2139

A numerical method for140

multiobjective optimization of zero141

emission power plants142

In this chapter, a novel numerical method to optimize(rank) advanced power plant143

designs and technology pathways is introduced. The motivation is driven by the144

lack of appropriate methods to rank various technologies that are characterized by145

very di�erent properties, which are very di�cult to quantify. For example, power146

plant owners are faced with not only economic and energetic constraints, but also147

increasingly stringent environmental, infrastructural, and social constraints. The need148

to conceptually explore new power plant designs and compare di�erent technologies149

and technology pathways, calls for new methods which are e�cient, �exible and can150

deal with very complex systems.151

This novel modeling method borrows the concept from the typesetting algorithm152

11

Chapter 2: A numerical method for multiobjective optimization of zero emissionpower plants 12

TEX, which is very powerful in ranking di�erent typesetting layout as more or less153

optimum. When applied to power plant modeling, a perfect and unattainable power154

plant design is chosen as the anchor point. The actual power plant design compared155

to the anchor point design results in a penalty number, which captures the di�erence156

in various aspects between the actual plant design and the anchor point, where the157

anchor point is characterize with a zero penalty. Since penalty number is always158

positive and the anchor point is an absolute reference that holds constant under all159

circumstances, one can stop calculating the penalty as soon as the partial sum of the160

total penalty exceeds the current minimum. The algorithm is highly e�cient and161

�exible, it can easily incorporate new constraints (which often results in additional162

penalties) into the existing structure, it also allows di�erent users assign customized163

preferences for di�erent penalties.164

In addition to rank various power plant designs, this method can also rank various165

sequences of power plants designs, in which a new design can either build upon the166

previous ones, or can be entirely new. In the next chapter, a simple model is developed167

to show the concept.168

2.1 A means required to compare di�erent technolo-169

gies170

Traditional power plant modeling tools only measure the thermodynamic per-171

formance and economic cost of a power plant, optimization is often carried out to172

reach a compromise between plant e�ciency and generation costs of the individual173


plants. Today, increasingly stringent environmental constraints especially in response174

to climate change, require a new modeling tool to evaluate di�erent power plant175

designs under various energetic, economical, environmental and infrastructural con-176

straints. Choosing between di�erent low-emission power generation technologies has177

a profound impact not only on the cost-e�ciencies of individual power plants, but178

more importantly on the pathways connecting current power generation technologies179

to future technologies. This project evaluate di�erent power plant technologies and180

pathway options with a new metric, which will be critical in choosing between various181

low-emission power generation technologies with very di�erent design constraint and182

optimization criteria.183

The need to develop low-emission power generation technologies arose both from184

the rapid growing consensus that excess carbon dioxide will cause a signi�cant change185

in climate that will have repercussions on a wide variety of human activities [Lackner 2001],186

and from the fact that power plants burning fossil fuel are a major source of carbon187

dioxide emissions, accounting for roughly one thirds of the global carbon emissions.188

In order to mitigate carbon dioxide from fossil fuel-�red power plants, a means is189

required to obtain a concentrated form of carbon dioxide with little incondensible im-190

purities, before it can be dispose of safely and permanently. The capture and storage191

of carbon dioxide (CCS) is one of the greatest challenge not only to power genera-192

tion infrastructure, but more importantly to the sustainable access to the cheap and193

abundant fossil fuel [Lackner 2001].194

A spectrum of low-emission power plants has been addressing environmental im-195

pact of impurities and undesirable combustion product from fossil fuel for some time.196


On one end of the spectrum include power plants with environmental control units197

for desulphurization, particulate removal and mercury emission control, etc. On the198

end of the spectrum is a special class of technologies zero emission power plants. Such199

plants produce power without emitting any atmospheric emissions, in some designs200

without a smoke stack. For example, a technology developed by the zero emission coal201

alliance (ZECA) generates electricity with hydrogen fuel cell producing only water,202

where clean hydrogen is derived from coal with a hydrogasi�er and a decarbonation203

reactor, followed by a calciner separating carbon dioxide together with impurities and204

underiable combustion by-product for sequestration [Lackner 2002].205

Zero emission power plants are yet to be built. Today, low-emission power plants206

minimized emissions of carbon dioxide to the atmosphere through separation and cap-207

ture of carbon dioxide by one of three general techniques: pre-combustion, oxy-fuel,208

and post-combustion de-carbonization [IPCC, 2005]. Governments and �rms eager to209

deploy low-emission thermal power plants must choose among three distinct types of210

power plant designs: the integrated gasi�cation combined cycle design (IGCC), which211

relies on pre-combustion separation of carbon dioxide in a gasi�er [IEA GHG, 2003],212

the oxy-fuel design which uses pure oxygen combustion to yield a nearly pure stream213

of carbon dioxide after combustion [Croiset and Thambimuthu, 2000], and the post-214

combustion de-carbonation design which relies on chemical absorption processes[Henderiks, 1994].215

Currently, there is no clear technological winner [MIT, 2007]. For both the IGCC and216

the oxy-fuel processes, the chief obstacle to broad deployment is the high capital and217

operational cost associated with each technique. Opportunities exist both for incre-218

mental modi�cations leading to near-term cost e�ciencies and for major redesigns219


leading to advanced next-generation power plant designs.220

The IGCC and oxy-fuel processes are not the only possible implementations of low-221

emission power plants. Instead, there is a broad range of potential designs which might222

incorporate a variety of components and approaches. For example, advanced zero223

emission power plant (AZEP) addresses the development of a speci�c, zero emissions;224

gas turbine-based, power generation process, which relies on a mixed-oxide membrane225

for oxygen production [Gri�n 2005]. Such a device is a critical component shared226

by a variety of oxygen-enhanced combustion and gasi�cation processes. This paper227

examines a family of advanced thermal power plant designs, such as conventional oxy-228

fuel power plants with a separate cryogenic air separation unit and fuel cell designs229

which combine oxygen separation, carbon oxidation, and electricity generation in a230

single unit, as well as the many potential designs which lie in between these two231

extremes. For example, oxygen blown IGCC, oxy-fuel �uidized bed combustors and232

AZEP designs are each a variation along a continuum of plant designs.233

A wide range of choices for the next-stage designs away from the existing low234

e�ciency, and polluting fossil fuel power plants, will lead to di�erent technological235

pathways, which constitute a sequence of plant designs that builid on each other,236

connecting to the e�cient, economical and clean future technologies. The overall237

objectives of this project are to create conceptual plant designs and conduct engi-238

neering assessments of the component modules of a zero emission power plant; eval-239

uate di�erent power plant designs under various energetic, economic, environmental240

and infrastructural constraints; and perform optimization not just to the individual241

power plants alone, but pathways connecting current power generation technologies242


to future technologies.243

2.2 Evaluation criteria based on a penalty model244

Power plant development leading to a zero emission plant design could move245

through a set of new plants, each designed to the best available knowledge at the246

time and with little regard to the long term goal, or to the basic knowledge that is247

embedded in previous designs. In such a strategy one may introduce technologies248

even though it is clear from the outset that they do not lend themselves to further249

advances, essentially locking-into a wrong path. For example, post combustion tech-250

nology, may well be in this category. Any R&D investment into �ue gas scrubbing251

is most likely made obsolete by the next generation of power plants. Alternatively,252

the goal could be achieved by a set of incremental improvements that are introduced253

in each new plant or in each upgraded plant, where changes are designed to build254

upon each other. In this example, by su�ering perhaps a little extra cost during each255

upgraded plant, the pathway may prevent itself from locking-into a wrong direction256

which will incur a much bigger cost to break away from. Oxyfuel combustion designs257

are likely to �t into this category.258

A consideration of the intermediate plant designs can reduce the long-term cost of259

power plant designs. However, a rational implementation of such an approach requires260

the means of making comparisons across di�erent technologies and across di�erent261

times. We propose a methodology by which we can make such an assessment. The262

method introduces a penalty function that can be applied to modules, plants, and263

sequences of plant designs. In optimizing the design, one varies design parameters so264


as to minimize the penalty function. The penalty function is zero for some perfect265

state of the system which is typically not attainable, and the penalty function is266

optimized by varying all the available design parameters. The penalty can be thought267

of as a sum of penalties for speci�c aspects of the plant, for example its e�ciency, its268

cost or its environmental impact. Individual modules may have component penalties.269

Some aspect of the penalty will depend on properties that can only be de�ned for the270

entire plant, or even for a sequence of plants.271

The relative weights of these penalties can be chosen appropriately by a user, who272

has speci�c goals. For example, penalties one may associate with having to build a273

new plant on a new site may vary for users in di�erent countries. Building new plants274

in China is likely to introduce a relatively small penalty for green�eld plants. The275

same decision in the West is likely to introduce a much bigger weight, because the276

political di�culties of opening up new sites are much larger. The di�erent weights277

may result in alternative development pathways.278

It is also recognized that the availability and maturity of novel technologies, as well279

as environmental thresholds for existing and potential criteria pollutants are likely280

to change over time, thus the weights for these penalties should not be considered281

as static. The dynamic nature of these penalty speci�cations, allow users to choose,282

instead of the best possible plant at a speci�c time ti, the best possible pathway283

connecting technologies from time t1 to time tn. Pursuing the optimal pathways284

on the basis of the minimum total pathway penalties helps users lower the cost of285

achieving the speci�c goals, even if it results in seemingly sub-optimal outcomes for286

individual plants.287


Much of the work we present is in de�ning an appropriate set of penalties on288

which the optimization rests. The underlying algorithms have been studied for other289

applications. The approach outlined here has taken its inspiration from the typeset-290

ting software TeX, in which Donald Knuth demonstrated the power of these penalty291

based optimization algorithms for trading o� between very di�erent and very di�-292

cult to quantify properties of text. We will show how very similar algorithms can be293

used to select appropriate modules, and power plants to arrive at a sequence of plant294

designs that provides an advantageous technology pathway from todays power plant295

designs to a future design that has far higher e�ciency, avoids all emissions to the296

air, and provides the CO2 produced in a concentrated stream ready for disposal.297

Chapter 3298

A simple model for power plant299

pathway optimization300

To demonstrate application of Knuth's ranking method on power plant modeling301

and optimization, a simple model is developed to show the concept. Before the con-302

struction of the simple model, let us consider a power plant explicitly in mathematical303

terms. For example, a hypothetical power plant design yj can be considered as a net-304

work of m modules (or components). yj = {x1, x2, ...xm}, where each module xi is305

an independent reactor speci�cation, iε[1,m]. Furthermore, a hypothetical pathway306

of power plant design evolvement zk can be considered as a sequence of power plant307

designs zk ={y0, y1, ...yn}, where yj is a hypothetical power plant �owsheet, jε[0, n].308

Note there are a number of possible pathways connecting initial technologies to future309

technologies, when comparing di�erent pathways, it is important to ensure the same310

initial design y0 for all possible pathways zk.311

This simple model considers eight basic modules, where three generation modules312

19

Chapter 3: A simple model for power plant pathway optimization 20

and �ve environmental modules can be combined to form three major plant designs313

in 32 di�erent ways, hence 96 di�erent power plant con�gurations. The generation314

modules include a subcritical boiler island, a supercritical boiler island, and an ul-315

trasupercritical boiler island. (The generation modules can again be divided into a316

network of water cycle modules and a sequence of fuel processing modules, which can317

again be combined di�erently, this project only considers the generation unit as a318

whole.) The environmental modules are �ue gas cleaning devices for SO2, NOx, �ne319

particulates, mercury, and CO2 emissions respectively. Each environmental module320

can be considered as an optional add-on to the main plant designs in a binary man-321

ner, hence the overall number of power plant con�gurations are 3x2x2x2x2x2 = 96.322

Besides the simplicity in notation, thinking plant con�gurations in such manner allow323

us to use the TEXalgorithm to our advantage. Since penalties are always positive, as324

soon as the penalty of one module (the partial sum of total penalties) exceeds the325

total penalty of current optimum, the class of plant con�gurations containing this326

module can be excluded from computation automatically (because the penalties are327

additive), hence considerably speeding up the algorithm. However, it's important to328

note that many of these con�gurations are not feasible in practice. For example, a329

selective catalytic reduction (SCR) can't be attached directly to a supercritical boiler330

island without adding a heat exchanger to lower the incoming �ue gas temperature.331

In another instance, the amine CO2 scrubber can't be directly added to the back332

of the boiler island, without pretreating the �ue gas with desulphurization unit to333

avoid sulfur poisoning. Infeasible con�gurations will be characterized with an in�nite334

penalty.335


The simple model considers a pathway with a �nite sequence of �ve items/ele-336

ments, where the state of each item/element is characterized with a set of di�erent337

environmental regulations. Therefore, a given plant con�guration will be charac-338

terized with a di�erent sets of regulatory states depending on its position in the339

sequence/pathway. In total, a given plant con�guration will have �ve di�erent sets of340

regulatory states for a sequence of �ve items. For the purpose of this simple model341

evaluation, the initial item of all possible pathways is a subcritical power plant con-342

�guration. Each item/element in the rest of the sequence can be chosen from the 96343

di�erent plant con�gurations. This simple model aims to rank these pathways and344

power plant designs, based on assigning penalty functions that scale with the devia-345

tion from a perfect state, which sets the anchor points against which various aspects346

in various levels of a pathway compare. The following section designs a hierarchy of347

di�erent levels of penalties incurred at the corresponding level of the model, namely:348

module level, plant level and pathway levels. Di�erent levels of penalties characterize349

performance speci�cally local to the corresponding level in the model. Together, they350

allow for rankings of di�erent power plant designs and pathways according to the ac-351

cumulated penalties respectively. In the following sections, we indenti�ed individual352

penalty variables (or aspects of penalties at di�erent penalty level), the anchor points353

for each penalty variable, and functions describing the behaviors of each penalty354

variable.355


3.1 Model Formulation356

3.1.1 Module level penalties357

Module level penalties characterize individual module performances independently358

from the rest of the plant. For example, cost and size of a module are strictly indepen-359

dent from the rest of the modules in a plant design, thus they belong to the module360

level in the penalty hierarchy. In comparison, cost per unit capacity ($/kW, M$/kW)361

or size per unit capacity (m2/kW, m3/kW) are not module level penalty variables,362

because the total power output of the whole plant (MW) measures the plant level363

performance, rather than module level performance.364

The module level penalties, their anchor points, and penalty functions for this365

simple model are summarized in Table 2. The sum of total module penalties for366

m modules in a speci�c plant design j equals a plant level penalty attribute to all367

modules in that plant, assuming there are m modules in a plant design (∑m

i=1Pjtot,i).368

One can also calculate this plant level penalty by adding the sum of each penalty369

speci�cations accounting for all modules in a plant design:370

∑m

i=1Pi =

∑m

i=1PTPI,i +

∑m

i=1POAM,i

where371

PTPI,i = α× TPI, i372

TPI,i is the Total Plant Investment for plant i;373

POAM,i = β ×OAM, i374

OAM,i is the annual Operational and Maintenance cost for plant i;375

α, β are constants;376


377

Due to the lack of data on physical size for modules examined in this example,378

the penalty calculation for size is not included in the simple model. Data on costs379

and emissions as a result of mass and energy balance calculations are produced using380

the integrated environmental control model (IECM), the plant performance data are381

attached in Appendix ??.382

3.1.2 Plant level penalty383

In addition to the sum of module level penalties as described above, plant level384

penalties also characterize energetic and environmental performance at plant level.385

3.1.3 Reconcile penalty386

This penalty Prec refers to plant con�gurations that don't reconcile. As stated387

earlier, many of the 96 con�gurations in the model are not feasible in practice. Infea-388

sible con�gurations will be characterized with an in�nite penalty. A fully reconciled389

plant con�guration has a zero penalty.390

Energy e�ciency penalty391

For energy e�ciencies, we penalize gross plant e�ciency and generation e�ciency392

separately. The former penalty measures gross power output as a fraction of total393

energy input (represented by the total potential energy embedded in the fuel); the394

latter penalty measures the net power output (which is gross output less internal395

power consumption) as a fraction of gross power output, indicating the amount of396


power consumed by the system itself. The need to separate the two speci�cation is to397

distinguish two kinds of plant designs with the same net plant e�ciency: one design398

with a high gross e�ciency but many energy-intensive additional units (i.e. auxiliary399

units and environmental control units), the other one with a low gross e�ciency to400

start with but few energy-intensive auxiliary units. It may come out to be the same,401

but the system's ine�ciency is captured separately, thus identifying the opportunities402

and incentives to reduce the ine�ciency respectively.403

Environmental penalty404

Environmental impact is penalized through a three-level environmental penalty405

hierarchy (Figure 3.1). The environmental penalty are evaluated as a product of reg-406

ulatory factor, compliance factor and quantitative factor. We consider environmental407

impacts at the plant level, because emissions are a measure of plant performance.408

For now, we assume all emissions are emitted at the smoke stack. One exception to409

this rule is when users are concerned with hazardous (poisonous) chemicals �owing410

around a plant, or with any chemical leakage from a single operation unit in a plant.411

In that case, an additional environmental penalty will be placed at the module level412

to punish poor seals, especially for modules that operate at positive pressures. This413

module level penalty is not considered in this simple model, but can be easily included414

for future optimization when required. Also, we penalize environmental impact only415

to the extent that it is due to atmospheric emissions for simplicity, of the model. At416

present, we do not penalize other environmental impacts such as solid waste discharge417

and water consumption, but they can be easily incorporated when needed.418


Figure 3.1: Environmental Penalty

Regulatory factor Regulatory factor accounts for various sets of regulatory states419

at each position, in this case time, along the pathway. If there is a regulation, the420

factor is one, if there is none, the factor is zero. It is also possible to assign a421

value that is between zero and one to capture a situation where the introduction of422

a regulation is either considered likely or desirable. The regulatory factor can be423

calculated according to the following equation.424

Freg

= 1 if there is a regulation on a speci�c kind of emissions at

a speci�c time

= 0 if there is no regulation on a speci�c kind of emissions at

a speci�c time

6= (0 ∧ 1) if there is no regulation on a speci�c kind of emissions,

but the regulation is expected to materialize at a future time

Table 3.1 describes the regulatory factors characterizing the regulatory states at425

each time along the pathway of the sequence of �ve power plant con�gurations. The426

�rst row are regulatory factors characterizing the initial plant con�guration of all427


Table 3.1: Regulatory factor for each item in the sequence

Time Freg,so2 Freg,pm Freg,nox Freg,Hg Freg,co2

t = 0 0 0 0 0 0t = 1 1 0 0 0 0t = 2 1 1 0 0 0t = 3 1 1 1 0 0t = 4 1 1 1 1 0t = 5 1 1 1 1 1

possible pathways.428

It is understandable that the regulatory states (quanti�ed as regulatory factors)429

change over time, since what's considered not harmful today might be considered430

as pollutants tomorrow, as a result of increasing scienti�c understanding on various431

emissions and their environmental impact over time. The necessity to have a top432

level regulatory factor is to capture di�erences in regulated emissions and unregulated433

discharge, and to ensure the corresponding technological and infrastructural change434

economically viable in a historical context. For example, the installation of �ue gas435

desulphurization unit (FGD) on the existing pulverize coal plants in US was driven by436

the regulation of sulfur emissions in 1990s as a result of amendments to clean air act.437

However the use of limestone to control SO2 emissions incurs unintended consequences438

of generating additional CO2 emissions 1 , which was considered not harmful at the439

time. In this situation, since no regulations on CO2 emissions were in place, the440

regulatory factor is zero. Since the environmental penalty is a product of regulatory441

1

SO2 + 12 O2 −−→ SO3 (3.1)

SO3 + CaCO3 −−→ CaSO4 + CO2 (3.2)


factor, compliance factor and quantitative factor, the overall environmental penalty442

of CO2 emissions is zero for all plant con�gurations at that time. From the algorithm443

point of view, once the regulatory factor is recognized as zero, the program does not444

have to proceed to calculate all other factors in the product function, hence speeding445

up the computational runtime by avoiding performing unnecessary calculations.446

As shown in table 3.1, this hypothetical exercise assumes environmental regula-447

tions for various emissions come in one at the time. This assumption have some448

degree of truth, because in reality, the process of introducing a new environmental449

regulation, or introducing a new criteria pollutant, is long and di�cult. It's rare that450

multiple regulations (or multiple criteria pollutants) are introduced at the same time.451

However, once the criteria pollutants are introduced (regulations are established), it452

is possible to raise the compliance standards (or lower the legal limits) for multiple453

emissions at the same time.454

Compliance factor Compliance factor evaluate whether a speci�c kind of emis-455

sions is compliant with the legal limit or not. Compliance factor hinge upon the fact456

that there is a regulatory factor for a speci�c kind of emissions. The legal limit against457

which compliance factor is measured, is normalized be an output-based emission rate458

in this study, expressed as lb/kWh, from the traditional input-based standard that459

re�ects an allowed amount of emissions per unit of fuel burned (lb/Btu). Output-460

based standards are preferable to traditional input-based standards, as they capture461

di�erences in e�ciency among sources in converting input energy (e.g., heat) to useful462

output (e.g., electricity) and therefore reward e�cient use of energy [E Roy, 1998]. In463

addition, the output-based standard capture emissions generated not only from the464


fuel source, but also from other sources that are converted to various emissions via465

both chemical process (i.e. reaction 3.2) and physical process (i.e. the injection of466

active carbon in order to control mercury emissions will introduce additional partic-467

ulates emissions), and therefore penalize the overall plant emissions, instead of only468

part of the emissions in a plant.469

If a speci�c kind of emissions is compliant with the regulation, then it receives a470

compliance factor of one, and the model proceeds to the quantitative factor calcula-471

tion. If it is not compliant with the regulation, it receives an in�nite overall environ-472

mental penalty. In this simple model, we penalized SO2, �ne particulates, NO, NO2,473

Hg, and CO2 emissions gradually for di�erent designs, assuming the corresponding474

regulations materialize over time. The legal limit for these emissions are assumed475

to be (lb/kWh)[?], (lb/kWh)[?], (lb/kWh)[?], (lb/kWh)[?], (lb/kWh)[?], (lb/kWh)[?]476

respectively, and they are assumed to be static for this exercise. Existing standards477

on the emissions are normalized to the output-based standards, the CO2 legal limit is478

chosen to be ???. The compliance factor can be calculated according to the following479

equation.480

Fcomp =

1 If a speci�c kind of emissions is compliant with the

regulation at a speci�c time

∞ If a speci�c kind of emissions is not compliant with the

regulation at a speci�c time

Quantitative factor Unlike the regulatory factor and compliance factor that ex-481

amine "qualitatively" the environmental impact of various emissions, this factor ex-482

amines the absolute emission quantitatively. Quantitative factors hinge upon the fact483


that a speci�c emission is regulated and is compliant with the regulation, the neces-484

sity to have a quantitative factor is to penalize the absolute emissions from a plant485

design, thus in essence rewarding plant designs with less emissions. For quantitative486

factors, we design di�erent functions to describe (penalize) the undesirability of a487

speci�c kind of emissions mathematically by scaling the emissions per unit output488

(lb/kWh) with a set of user-supplied scaling factor (penalty weight).489

The functions are carefully designed to characterize the environmental impact of490

various emissions. The function for CO2 is a linear function of the mass �ow rate CO2491

at the smoke stack of a power plant (equation 3.3), because its environmental impact492

is approximately linear to the amount of CO2 emitted. In comparison, the function for493

SO2 has several components as SO2 emissions have several aspects of environmental494

impact, both locally and regionally. At local level, aerosols of sulfuric acid and other495

sulfates contribute signi�cantly in the reduction of visibility and damage to material,496

it has also been recognized that there are some localized areas where asthmatics may497

be repeatedly exposed to short-term SO2 concentrations [Wark, K., 1997]. These local498

environmental impacts are not linear in the SO2 concentration, rather they show499

a much greater impact at higher concentrations []. Therefore, we design penalties500

attributed to the local impact as quadratic function to the concentration of SO2501

emissions at the smoke stack of a plant. At regional level, SO2 can be transported long502

distance by air masses and then be precipitated in the form of acid rain somewhere503

else. The function attributed to the regional impact of SO2 emissions is designed linear504

to its concentration at the smoke stack, because the amount of acid rain is linear to505

the amount of SO2 emissions. The overall quantitative factor for SO2 emissions can506


be calculated according to equation 3.4.507

Fquan,CO2 = k1 ∗ (mCO2) where mCO2 =lbCO2

kWh(3.3)

508

Fquan,SO2 = k2 ∗ (mSO2) + k3 ∗ (mSO2)2 where mSO2 =

lbSO2

kWh(3.4)

NOx like SO2 emissions, also contribute to acid rain formation, in addition to509

its local impact, thus it is penalized both locally and regionally. Regarding par-510

ticulate, we exclusively focused on their local impact. Mercury emissions has a511

more complex environmental impact, as elemental mercury emissions can be trans-512

ported and deposit in the watershed, and form methylmercury [?]. Harris and513

Rudd predicted that mercury emissions reductions will yield rapid (years) reductions514

in �sh methylmercury concentrations and will yield concomitant reductions in risk515

[Harris R. C., Rudd J.W.M. 2007]. Hence, we approximate the environment impact516

of mercury emissions linear to the mass �ow rate of the mercury emissions from the517

power plants. This function might change as we gain better scienti�c understand-518

ing of the environmental impact of mercury emissions in the future. Functions to519

calculate quantitative factors for all emissions are listed in Table 3.3520

Di�erent penalty functions for di�erent emissions show di�erent sensitivities to521

user-input weights. The relative weights depend on what users expect as conse-522

quences. For example, in the case of SO2 emissions, if users are mainly concern about523

local problems, then the penalty is dominated by the quadratic term, if the users524

are mainly concern about the long-distance problems, it's driven by the linear term.525

In essense these penalties are transferable, users that are less concerned about the526


long-distance problems may build extremely tall smokestacks hence transferring local527

sulfur pollution problems into regional sulfur problems.528

The sum of environmental penalty for a speci�c emission can be calculated by the529

following equation.530

PEM= FregM

× FcompM× FquanM

where531

M = SO2, particulates,NO,NO2,Hg,CO2.532

533

The sum of all plant level penalty speci�cations for a plant design adds up to the534

total penalty for that plant at time t, where t refers to the time in the sequence, t =535

0, 1, 2, 3, 4, 5.536

537

Ptot,t =∑m

i=1Pi,t

+Prec,t

+Pη(gross,t) + Pη(gen,t)

+PE(CO2,t)+ PE(SO2,t)

+ PE(NO,t)+ PE(NO2,t)

+ PE(Hg,t)+ PE(PM,t)

3.1.4 Pathway level penalty538

Mathematically, there are nm possible pathways, assuming there are m choic-539

es/items in the pathway, and each item can be chosen from n power plant con�g-540

urations. In the case of the simple model, the number of possible pathways are541

965 = 8.15E9. The ranking algorithm inspired by TEX can be implemented com-542


putationally such that the computer will examine all possible pathways and choose543

the optimal one. The implementation of the computational algorithm is beyond the544

scope of this project.545

Various pathways re�ect the evolution trajectory of power plant technologies. The546

simple model considers pathways with a �nite sequence of six items/elements, where547

the initial item of all possible pathways is a subcritical power plant con�guration.548

Each item/element in the rest of the sequence can be chosen from the 96 di�erent549

plant con�gurations.550

To compare and calculate penalties for di�erent pathways, we consider three as-551

pects of the penalty. The �rst penalty accounts for the sum of the plant level penalties552

for all the items in the path. The second penalty attempts to account for the ma-553

turity of a speci�c technology at the time of use, in the form of learning by doing,554

by counting the number of usage of this technology previously in the same pathway.555

This penalty is express as π2 ×Paverage ×K, where π2 is a constant, Paverage accounts556

for the average plant level penalty in a path, and K is the factor attempt to represent557

the learning gained throughout the entired pathway. The equation below explains K558

in greater details.559

K =∑5

t=1

{∑m

i=1

α

R(i) + ε

}2

Here R(i) is the number of usage of a speci�c technology i in a power plant, whose560

con�guration consists of a network of m modules. α and ε are both constant. Since561

R(i) is inversely related with K and the penalty, a larger R(i) entails smaller penalty.562

This is consistent with reality, the more we build, the more learning we have, hence563

less penalty we pay. On the other hand, if a technology has never been built before (if564


the technology is newly invented or newly introduced), R(i) is zero, hence the penalty565

function reaches its maximum. Note the summation starts with t=1, instead of t=0,566

hence all modules in the initial power plant, a subcritical power plant con�guration,567

by default is built once in any possible pathways.568

The last part of the pathway penalty accounts for the obsolete technologies through-569

out the pathway. It is expensive to introduce any new technologies, so once they are570

introduced, it is undesirable to remove them later. However, in reality, due to the571

lack of ability to "look ahead", technologies were found obsolete soon after being572

introduced at an expensive cost. For example, XXXX, TY. In author's opinion, the573

debate between post-combustion capture technology for CO2 capture versus boxful574

combustion technology �t right into this category. ANALYSIS The equation for this575

pathway level penalty is shown below:576

β ∗∑5

t=0Nobsolete

where Nobsolete is the number of technologies removed, and β is a constant.577

In summary, the total pathway penalty can be evaluated according to the following578

equation:579

Ptot = π1 ∗∑5

t=0Ptot,t

+π2 ∗ Paverage ∗∑5

t=0

{∑m

i=1

α

R(i) + ε

}2

+β ∗∑5

t=0Nobsolete

where580

Paverage =15*∑5

t=0Ptot,t581

582


Figure 3.2: An example of pathways connecting y0 to various future technologies

R(i) is the number of the times that i unit is being used before.583

π1= 0.01;584

π2= 0.000001;585

assume there are m new units, n plants. α, ε are both constants.586

587

Pursuing the optimal pathways on the basis of the minimum total pathway penal-588

ties helps users lower the cost of achieving the speci�c goals, even if it results in589

seemingly sub-optimal outcomes for individual plants.590

Table 3.3 summarize the categories of penalties at module level, plant level and591

pathway level, including the penalty variables for each category, anchor points against592

which penalty variables measure, and mathematical functions that describes the be-593

havior of each penalty variables. Figure 3.2 illustrate as an example on �ve di�erent594

pathways connecting y0 to various future technologies.595


Table3.2:

Summaryof

pow

erplantdesignsandpathwaysdesigns

y0{x

1,x

9}

subcritical

pulverized

coal

plant

y 1{x

2,x

9}

supercritical

pulverized

coal

plant

y 2{x

3,x

9}

ultra-supercritical

pulverized

coal

plant

y 3{x

1,x

4,x

5,x

9}

subcritical

plantwithSOxandparticulate

control

y 4{x

1,x

4,x

5,x

6,x

9}

subcritical

pow

erplantwithSOx,particulate

andNOxcontrol

y 5{x

1,x

4,x

5,x

6,x

7,x

9}

subcritical

pow

erplantwithSOx,particulate,NOxandmercury

control

y 6{x

1,x

4,x

5,x

6,x

7,x

8,x

9}

subcritical

pow

erplantwithSOx,particulate,NOx,mercury

and

CO

2control

y 7{x

2,x

4,x

9}

supercritical

pow

erplantwithSOxcontrol

y 8{x

2,x

4,x

5,x

9}

supercritical

plantwithSOxandparticulate

control

y 9{x

2,x

4,x

5,x

6,x

9}

supercritical

pow

erplantwithSOx,particulate

andNOxcontrol

y 10{x

2,x

4,x

5,x

6,x

7,x

9}

supercritical

pow


control

y 11{x

2,x

4,x

5,x

6,x

7,x

8,x

9}

supercritical

pow


and

CO

2control

y 12{x

3,x

4,x

5,x

6,x

7,x

9}

ultrasupercritical

pow


control

y 13{x

3,x

4,x

5,x

6,x

7,x

8,x

9}

ultrasupercritical

pow


and

CO

2control

z 1{y

0,y

2,y

4,y

5,y

6}

pathway

1z 2

{y0,y

1,y

7,y

8,y

9,y

10,y

11}

pathway

2z 3

{y0,y

1,y

7,y

8,y

9,y

10,y

12,y

13}

pathway

3z 4

{y0,y

13}

pathway

4z 5

{y0,y

1,y

7,y

8,y

9,y

10,y

12,y{1

2,tn}}

pathway

5x

1=

subcritical

boilerisland;x

2=

supercritical

boilerisland;x

3=

ultra-supercritical

boilerisland;

x4=wet

�uid

gasdesulphurization

unit(FGD);x

5=

electrostaticprecipitator

(ESP);x

6=

selectivecatalyticreductionunit(SCR);

x7=mercury

removal

unit(w

ithactive

carbon

injectionACI);x

8=

aminescrubber

(MEA);x

9=

smokestack;


Table3.3:

Modulelevel,plantlevelandpathway

levelpenalties

Penalties

Level

Penalty

Variable

Anchor

point

Behavioralfunctions

modulelevel

TPI(M$/yr)

TP

I 0=

0P

TP

I,i=α×

TP

I iOAM(M

$/yr)

OA

M0

=0

PO

AM,i

=β×

OA

Mi

plantlevel

η gro

ss,j

=M

Wgro

ss,j

HH

Vη g

ross,0

=1

Pηgro

ss,j

=γ×

(1−η g

ross,j)

η gro

ss,j

η gen,j

=M

Wn

et,j

MW

gro

ss,j

η gen

0=

1Pη

gen

,j=δ×

(1−η gen,j

)η gen,j

mC

O2,j

=C

O2em

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mC

O2,j

=0

Pqu

anC

O2

,j=

k1×

mC

O2,j

mS

O2,j

=SO

2em

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mS

O2,j

=0

Pqu

anSO

2,j

=k

2×

mS

O2,j+

k3×

mS

O2,j

2

mN

O,j

=N

Oem

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mN

O,j

=0

Pqu

anN

O,j

=k

4×

mN

O,j

+k

5×

m2 N

O,j

mN

O2,j

=N

O2em

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mN

O2,j

=0

Pqu

anN

O2

,j=

k6×

mN

O2,j+

k7×

m2 N

O2,j

mH

g,j

=H

gem

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mH

g,j

=0

Pqu

anH

g,j

=k

8×

mH

g,j

mP

M,j

=P

Mem

issionsfrom

smokestackj

Net

Pow

erOutputkW

hj

mP

M,j

=0

Pqu

anPM

,j=

k10×

mP

M,j

2

M=

SO

2,P

M,N

O,N

O2,H

g,C

O2

PE

M,j

=0

PE

M,j

=P

regM

,j×

Pco

mpM

,j×

Pqu

anM

,j

M=

SO

2,P

M,N

O,N

O2,H

g,C

O2

PE,j

=0

PE,j

=∑ P

EM

,j

pathway

level

Pk to

t,j

Pk to

t,j=

0P

k tot,

j=∑ m i=

1P

j tot,

i+

Pη(g

ross

,j)

+Pη(g

en

,j)

+P

E(M

,j)

Kk j

Kk j

=0

Pto

t,k=∑ n j=

1(ω×

Pk to

t,j×

Kk j)

Notes:

1.α,β,γ,δ,

k1,k

2,k

3,k

4,k

5,k

6,k

7,k

8,k

9,k

10,A,B,C,Dareallpenalty

weights

tobesupplied

byusers.

2.In

thismodel,theauthor

makeassumptionsof

theweights

asbelow

.α=

20,β=

20,γ=

5000,δ=

50000,k

1=

1E5,k

2=

1E3,k

3=

1E3

k4=

1E4,k

5=

1E4,k

6=

2E3,k

7=

2E3,k

8=

1E9,k

9=

1E5

3.Thecalculation

ofmaterialandenergy

balance

andcostsarecarriedoutusingtheIECM

model.

4.irepresentthenumber

ofmodules,jrepresentpow

erplants,krepresentpathways.


3.2 Results596

The two plots in Figure ?? show the total pathway penalties in an environment597

with and without CO2 regulations respectively. In the world without CO2 regulations,598

pathway z3 has more penalty than pathway z5, this is because the former pathway end599

with a plant design that introduces CO2 capture technologies, hence su�er the cost600

penalty, but due to the lack of regulations, this cost of introducing new technology601

didn't paid o�.602

Figure 3.3: Pathways end in an environ-ment with CO2 regulations

Figure 3.4: Pathways end in an environ-ment without CO2 regulations

Figure 3.5 and 3.6 show the breakdown of plant level penalty with and without603

CO2 regulations respectively, re�ecting author's concerns on environmental impact604

more than on the cost and e�ciency.605

Figure 3.7 and 3.8 show the breakdown of environmental penalties with and with-606

out CO2 regulations respectively. Note y12 and y12,tn are exactly the same designs607

built in di�erent time. When there's no CO2 regulation, they receive the same envi-608

ronmental penalty, but when at time tn, there is a CO2 regulations, y16,tn receives a609

much greater environmental penalty on CO2 emissions. Another interesting observa-610


Figure 3.5: Plant level penalties with CO2 regulations

Figure 3.6: Plant level penalties without CO2 regulations

tion from the results in environmental penalty plots is when power plants introduces611

CO2 scrubber, the overall environmental penalties are smaller than previous designs612

on the same pathways (i.e y6, y11, y13). This is because MEA sorbent are easily poi-613

son by impurities in the �ue gas, the inlet concentration of SO2 emissions is required614

to be controlled at a very low level when CO2 scrubber is install, hence the overall615

environmental penalty for plant designs with CO2 scrubber is much lower than other616


designs. However, this model doesn't take into account of the environmental impact617

of MEA leakage from the reboiler, should the users concern with the environmental618

impact of MEA leakage, the overall environmental penalties of plant designs with619

CO2 scrubber may not have a lower numeric value.620

Figure 3.7: Environmental penalties with CO2 regulations

Figure 3.8: Environmental penalties without CO2 regulations

Chapter 4621

Path-dependent shortest-path622

algorithms for optimizing a sequence623

of power plant designs624

Two combinatorial optimization algorithms for multi-variate technology designs625

that are path-dependent are proposed. The objective function is de�ned as the min-626

imum of a nonlinear programming problem. The problem is solved by means of a627

branch-and-bound method, and a heuristic based on the label-correcting algorithm628

for solving shortest-path problem. The proposed algorithms are applied for practical629

problems on �nding the optimal sequence of various power plant designs.630

40

Chapter 4: Path-dependent shortest-path algorithms for optimizing a sequence ofpower plant designs 41

4.1 Problem statement631

Let us consider each power plant design in a sequence as a vertex in a path. A632

sequence of m power plant designs with a given initial design, can be represented by633

a path of m vertexes with a given source vertex S. Thus, the problem of �nding the634

optimal power plant pathway with the lowest penalty, can be considered the same as635

the problem of �nding the optimal path with the minimum path distance.636

Given a source vertex S and a sequence of m decision points, there is a pool of n637

available power plant designs from which only one design is chosen at each decision638

point. The same design can be chosen more than once in a path. All possible paths639

start with a shared source vertex S, and all paths have exactly m vertexes. The640

enumeration of all possible paths forms a rooted tree, in which any two vertexes are641

connected by exactly one arc. The �rst level for all paths is the root S. Except for the642

root, each vertex in the path has a parent, which is the vertex immediately before it643

on the same path. The vertexes on the last level of the tree are named leaves. The644

vertex that is not the root nor a leave, can be viewed as a subroot. A subtree is a645

smaller tree originated from a subroot, but with the same tree structure.646

Each path can be viewed as a branch of the tree, a path from the root to a subroot647

is named as a subbranch. Note in this discussion, subbranch always begins from the648

root. The whole tree has nm branches. On each level i (1<i<=m), there are n i649

vertexes. As an example, Fig 4.1 illustrates an instance of a rooted tree of four levels,650

the root is design S, three designs d1, d2, d3 are chosen repeatedly, forming a total of651

twenty-seven possible branches. To distinguish the same design choices on di�erent652

levels, each level of the tree is indexed with a time, i.e, t1, t2, t3, and t4.653


Figure 4.1: An instance of a rooted tree

The arc distance is characterized with a numerical value. Arc distance mea-654

sures the direct distance between the two ends. For example, the distance of arc655

S(t1)→d1(t2) is 20, the distance of arc d1(t2)→d1(t3) is 15. Each arc distance is656

non-negative, and more importantly, it is path-dependent. It depends not only on the657

pair of vertexes on both ends of the arc, but also on all previous vertexes on the same658

path. For example, consider path S(t1)→ d1(t2)→ d1(t3)→d1(t4) and path S(t1)→659

d2(t2)→ d1(t3)→d1(t4) in Figure 4.1. Both paths include arc d1(t3)→d1(t4) on the660

last level, however the arc distances are di�erent, one being 2, the other being 14.661

This is a result of di�erent path histories.662

In the case of power plant technology development, two di�erent technology path-663

ways may coincide in some choices, but the chosen technologies may cost di�erently664

in di�erent paths. On one hand, once a dominant technology is chosen, it is natural665

that one will choose new technologies compatible with the existing one. For exam-666

ple, one with an Apple computer is more likely to choose compatible Apple product667


when new electronic devices emerge (i.e. iphone). On the other hand, the cost of668

technology goes down as we gain experience in building it [?]. This has been seen669

most signi�cantly in the cost of personal computers in the last 30 years. As a result,670

technologies and components of technologies, that have been chosen in the path over671

and over again, are less costly than the same technologies in the path proceeded by672

various unrelated choices.673

The total path distance is the summation of all arc distance in a path. For674

example, the total distance of path S(t1)→ d1(t2)→ d1(t3)→d1(t4) is 20+15+2=37.675

The goal of this work is to �nd the path with the minimum distance number.676

4.2 Mathematical formulation677

min cost(Pst) (4.1)

cost(Pst) =∑

(i,j)∈Pst

c((i, j), Psi) (4.2)

where Pst is a full directed path in the tree, s is the root of the tree, t is a leaf678

on the tree. Psi is the preceding path of (i, j ) in Pst. For any arc (i, j ) where i<j,679

and any path P, let c be a function which assigns a value c((i, j), P ) to an (arc, path)680

pair. c((i, j), P ) is non-negative.681

The decision version of the problem is de�ne as PDSP = { <T, c, s, t, k>}: there682

exists a path Pst in T, s.t. cost(Pst) ≤ k. T= { s, T0, T1, T2, ...TN−1}. where PDSP683

is path-dependent shortest path, T is an N-ary rooted tree, T0, T1, T2, ...TN−1 are684


subtrees.685

The convention used here follows Bruno [?], the formulation follows Tan and Leong686

[?].687

4.3 Literature review on shortest-path problem688

Though the problem of �nding the shortest path has been studied extensively,689

the e�ort of most research has been focusing on non-path-dependent problems [?].690

Mathematical procedures to solve this set of problems often take advantage of the691

principle of dynamic programming, which states if a path is the shortest, then its692

subpath is also the shortest [?].693

There are two general procedures to solve the non-path-dependent shortest-path694

problems. Both algorithms maintain a distance label of a node, and iteratively up-695

date its distance label, until �nding the shortest path. One procedure is generic696

label-setting algorithm, which designates one label as permanent at each iteration697

(Dijkstra's algorithm [?]). The other is generic label-correcting algorithm, which698

considers all labels as temporary ones until the �nal step, when they all become per-699

manent [?]. Both algorithms require that the distance label of a current node depends700

only on the previous node, rather than the entire history.701

When taking into account of the path-dependency, the problem becomes much702

more complicated to solve. Tan and Long showed that the path-dependent shortest703

path, in general is NP-complete1 , whereas its special case can be solved by any704

1NP-complete represent the complexity of a problem in computer science. In computationalcomplexity theory, the complexity class NP-complete (abbreviated NP-C or NPC) is a class ofdecision problems. A problem L is NP-complete if it has two properties: 1)It is in the set of NP


shortest path procedure in polynomial time. The special case assumes that the cost705

doesn't depend on the entire path, but only the last su�x-k paths, therefore it can706

take advantage of the last k nodes [?].707

Unlike the partial path-dependent problem that Tan and Leong described, our708

problem is full path-dependent, which can not be transformed to a special case,709

therefore it can not be solved by shortest path procedure.710

4.4 Path-dependent shortest-path algorithms711

To �nd the true optimum, we can use brute-force search approach to examine712

every single path, and compare the distances of all possible paths. Since in total a713

tree has nm branches, the runtime2 of the brute-force search approach is O(nm). This714

is very computationally expensive, especially for a big tree.715

To improve that, we can design e�cient pruning procedures by removing the bad716

branches that are bigger than a bound, which is the current best path. Furthermore,717

we can tighten the bound by continuously updating the current best path to improve718

the e�ciency even more. When the current best is in�nity, we don't gain anything719

from pruning, as we need to explore essentially the entire space of solutions. When720

the current best is the true optimal, it prunes the tree most e�ciently. This method721

is called branch-and-bound method. It is a general algorithm for �nding optimal722

(nondeterministic polynomial time) problems: Any given solution to L can be veri�ed quickly (inpolynomial time)[?]. 2)It is also in the set of NP-hard problems: Any NP problem can be convertedinto L by a transformation of the inputs in polynomial time.

2runtime refers to the time during which a program is running (executing). The symbol O()means the complexity of the algorithm, which quanti�es the amount of resources needed to solve aproblem using an algorithm, such as time and storage.


solutions of various optimization problems, especially in discrete and combinatorial723

optimization [?]. The original branch and bound algorithm is proposed by A. H. Land724

and A. G. Doig in 1960 for linear programming [?]. The term "branch-and-bound"725

was �rst proposed by J.D.C Little in 1963 for traveling salesman problems [?]. It is726

the most widely used tool for solving large scale optimization problems that have a727

�nite but usually very large number of feasible solutions, for example vehicle routing,728

crew scheduling, and production planning[?].729

We develop a speci�c branch and bound algorithm, with a strategy that prunes730

the tree from bottom to top using best-�rst search strategy through an iterative731

procedure. The detail of the procedure is given in section4.5. This method is an732

exact approach for �nding the optimal solution, and it is very e�cient in detecting733

bad choices on the upper level of the tree. But if the bad choices are made on the lower734

level of the tree, or even on the leaves, the algorithm will not detect these bad choices735

in order to prune them o�, until the full tree is examined. In this extreme case, the736

branch and bound algorithm becomes essentially the brute-force search approach, and737

all branches are explored and compared. As mentioned before, this is computationally738

challenging.739

To gain a reasonable computational performance for solving the extreme case740

problems described above, we develop a second approach. This approach can solve741

the problem in polynomial time, rather than exponential time. However, it's not an742

exact approach that always gives the true optimum solution, rather it gives a good743

solution which is relatively close to the true optimal. To examine the accuracy of744

the second approach, we run the �rst approach (branch and bound algorithm) and745


compare the solutions of the two approaches. The detail of this approach is given in746

section 4.6.747

4.5 Branch and bound algorithm with bottom-up748

pruning749

Unlike the brute-force search approach which examines each branch independently750

and individually, this algorithm considers all possible branches forming a n-ary rooted751

tree as illustrated in Figure 4.1. For any subroot, there is a subbranch above it, and752

exactly n subtrees below it. n is the number of choices that a parent node can branch753

from at each level. For example, n is three in Figure 4.1. For subroot d1(t2), above it754

there is a subbranch S(t1)→ d1(t2), and below it there are exactly n subtrees rooted755

from d1(t3), d2(t3), and d3(t3) respectively.756

Assuming we are given a bound and a corresponding path. The distance of the757

bound is the distance of the full path. If a subbranch distance already exceeds the758

bound, one can immediately throw away the subbranch without having to look further759

into the n subtrees below it. This procedure is known as eager node evaluation [?].760

Taking advantage of the eager node evaluation approach, we �rst �nd a bound,761

and sort the tree such that we always keep the bound as the leftest branch. Then we762

re-examine the bound from its leave to its root. We can do so because the subbranch763

distance is not in�uenced by the choice behind it. In other words, future decisions do764

not change the cost of decisions in the past (i.e. past decisions are sunk cost).765

In terms of search strategy, we employ the depth �rst search(DFS) approach.766


Figure 4.2 shows a small search tree, the number in each node corresponds to the767

sequence, in which the nodes are processed when DFS is used [?]. The search strategy768

usually re�ects a trade o� between keeping the number of explored nodes in the search769

tree low, and staying within the memory capacity of the computer used [?].770

Figure 4.2: An instance of depth �rst search strategy in branch and bound [?]

Let's look at Figure 4.1 and walk over the steps in this algorithm. We assume771

the initial bound is in�nity, there is no corresponding path. First, we branch o� from772

the root to a full path by always choosing the local optimal at each step until we773

�nish. As illustrated, this path is S(t1)→d1(t2)→d1(t3)→ d1(t4) with a distance of774

37. Since 37 is less than in�nity, we update the bound as our current best and keep775

it on the leftest of all branches. Now that we have a bound and a corresponding776

path, we start pruning the tree from leaf of the current bound towards the root in777

an iterative manner. For example, in this case, we back o� from the leaf. First778

we back o� one step to d1(t3), since from d1(t3) to the last step, we only need779

to look at the local optimal, there is nothing to be changed. Therefore, we look780

at d2(t3), while maintaining the subbranch above as S(t1)→d1(t2). We notice the781

subbranch distance S(t1)→d1(t2)→d2(t3) is 20+30=50, and this is already greater782

than the 37. Immediately, we can throw away the whole subbranch, without having783


to look further. Next we look at d3(t3), while maintaining the subbranch above as784

S(t1)→d1(t2). The subbranch distance S(t1)→d1(t2)→d3(t3) is 20+20=40. It is785

greater than 37, therefore, we can throw away the whole subbranch. Now we are786

done on t3 level, we back o� two steps of the bound at d1(t2), and prune the tree in787

the same manner describe above. Whenever we �nd a full branch shorter than the788

current bound, we update the leftest branch to ensure it is always the shortest. This789

way, we have a tighter bound. We continuously tighten the bound as we prune the790

tree, it makes the algorithm even more e�cient. In this case, when we look at path791

S(t1)→d3(t2)→d1(t3)→d2(t4), we �nd the path distance to be 21+13+2=36. Since792

36 is smaller than 37, we update our bound as S(t1)→d3(t2)→d1(t3)→d2(t4). When793

we �nish pruning the tree, we �nd the current bound as the best path. In this case,794

the best path is S(t1)→d3(t2)→d1(t3)→d2(t4).795

This method is especially useful for problems in which very bad choices are made796

on the upper level of the tree. For problems in which very bad choices are made797

on the upper level of the tree, this method is very useful as one can prune the bad798

branches pretty quickly. But if the bad choices are on the lower level of the tree,799

or even on the leaves, the algorithm will not be able to detect them until the full800

tree is thoroughly examined. For example, if on each level except for the last level,801

the arc distance to each node are exactly the same, then one would not be able802

to throw away any subbranches, because all subbranches have the same length. If803

the di�erences only begin to appear on the last level, one would need to calculate804

and compare all branches. In this case, the branch and bound algorithm becomes805

essentially the brute-force search approach, and one ends up doing an exhaustive806


search of the full tree.807

In summary, this algorithm can �nd the optimum solution, which has the lowest808

distance number for a path-dependent problems. It is especially e�cient with prob-809

lems where bad choices are made on the upper level of the tree, and less e�cient when810

bad choices are made on the lower level of the tree. The worst case of this algorithm811

is a case of the brute-force search approach.812

The pseudocode of this algorithm is given below.813

• path is the path we are looking at (its lower level parts need to be de�ned the814

part from level on up, need not be de�ned815

• level is the current working level, all parts earlier in the path are de�ned816

• bound is the current best bound, it could be "in�nite"817

• bestpath is the current best path, it may be unde�ned at the outset, it may be818

de�ned819


Algorithm 4.5.1: FindBestPath(path, level, bound, bestPath)

Input:path, level, bound, bestpath

if (level ≡ nstep)

then

if (Penalty < bound)

then

bestPath← path;

bound← Penalty;

for i← 1 to nstep

Penalty(level, path, PowerP lant, allnodes);

for i← 1 to nstep

s[i]← i;

Bubblesort(Penalty[s[i]])

for i← 1 to nstep

do

if (P [s[i]] > bound)

then break;

FindBestPath(path, level + 1, bound, bestPath);

820

4.6 Heuristic821

To solve problems in which the distances of all branches are very similar to each822

other, it may be too expensive to use the branch and bound algorithm. In order to823

reach a reasonable computational cost , we seek alternative methods that would �nd824

a solution which is close to the best possible answer, i.e. a heuristic. The outcome of825

the heuristic may not be the optimum path, but it is a good path that is close to the826


optimum. The results can be compared with the results of the brute-force approach827

algorithm to verify the accuracy of the heuristic.828

This heuristic is based on the label-correcting algorithm, which is very e�cient in829

solving the shortest-path problem in polynomial time. In the shortest-path problem,830

a multi-ary or n-ary tree is collapsed into a graph. On each level of the graph, there831

are exactly n nodes, and each node represents a unique design choice. Di�erent paths832

are represented by connecting the nodes on each level with directed arc. An instance833

of the graph is shown in Figure 4.3.834

Figure 4.3: An instance of a graph forshortest-path problem

Figure 4.4: An instance of a tree collapsedinto a graph, path-dependent

The shortest-path problem is not path-dependent, each arc only has one value,835

regardless its past history. Therefore we can associate a numerical value or a distance836

label with each node, representing the subbranch distance from the root to that node.837

Di�erent paths give di�erent distance labels.838

Since it's not path-dependent, one can calculate the distance label of a node by839

considering only local information, namely the length of single arc. Therefore, instead840

of having to remember the full tree, one needs only remember the best path reaching841


each node on the that level. Since there are exactly n nodes on every level, one needs842

to keep the best n paths, each being the shortest for each node.843

One always works on two neighboring levels, each level has exactly n nodes, there-844

fore, the total number of enumeration for every pair of levels is n2 paths. On each845

level for each node, one iteratively reduces the distance label until the best path to846

reach that node is found.847

The procedure described above is essentially a label-correcting algorithm, which848

is a general procedure for successively updating the distance label until they satisfy849

the shortest path optimality condition. The total runtime of this algorithm is O(n2).850

The critical di�erence between our problem and the shortest-path problem lies851

in the di�erence in path-dependency. Figure 4.4 illustrates an instance of a tree852

that is path-dependent collapsed into a graph. As illustrated, the same arc may853

have multiple values, instead of just one value. For example, arc d1(t3)→d1(t4)854

has three values, and each one corresponds to a unique path histories. Speci�-855

cally, the distance of S(t1)→d1(t2) is 5 after subpath S(t1)→d1(t2)→d1(t3), 14856

after subpath S(t1)→d2(t2)→d1(t3), and 31 after subpath S(t1)→d3(t2)→d1(t3).857

What is more, the principal of dynamic programming no longer holds. For example,858

path S(t1)→d1(t2)→d1(t3)→d1(t4) is the shortest path in graph, however, subpath859

S(t1)→d1(t2)→d1(t3) is suboptimal compared to subpath S(t1)→d3(t2)→d1(t3).860

If we use the label-correcting algorithm to solve Figure 4.4, subpath S(t1)→ d1(t2)861

→ d1(t3) will be pruned out before reaching the last level. To avoid pruning out a862

good path early on, we modify the label-correcting algorithm, such that on every863

level, we keep more than n paths. In addition, we keep another x good paths, such864


that on every level we keep the total of x+n paths. The choice of x depends on865

ones preference of runtime versus accuracy (0 ≤ x ≤ (nm-n)). On one end of the866

spectrum, when x equals zero, in total we are keeping n paths on each level, this is867

essentially the non-path-dependent shortest-path algorithm. On the other end, when868

x equals nm-n, in total we are keeping nm paths, this is essentially the brute-force869

search approach. For simplicity, we assume x=2n in this work.870

We further improve the heuristic by introducing the concept of a bound. In this871

case, we �rst get a bound by running the shortest-path algorithm (x=0 ). Then we872

run the heuristic by assuming x=2n. We keep a maximum total of x+n subbranches873

on every level, such that all subbranch we keep are smaller than the bound. This874

way, we remember only the good path that are likely to be the best path. By using875

a bound, we prune out the bad subbranches early on, hence increasing the e�ciency876

and the accuracy of the algorithm.877

One can further improve the heuristic by gradually increase x. One can update878

the bound whenever a smaller optimal path is found for a given x. The price to pay879

in this scenario, is that one needs to prune the tree once for every value of x. Further,880

the optimal path does not change monotonically as x increases. In other words, by881

increasing the value x, one is not guaranteed to �nd a better path. A detail discussion882

is given in the following section.883

The limitation of this heuristic is that it may not be able to �nd the true optimum884

path. To examine the accuracy of the heuristic, we can compare results of the heuristic885

with the brute-force search approach. The detail of the comparison is given in the886

following section.887


4.7 Computational results888

We summarize the algorithms described in this chapter as following.889

• brute-force search or exhaustive search, explicitly enumerates the complete890

space of solutions, calculates and compares all possible solutions for optimality.891

• branch-and-bound algorithm By using a bound for the function to be opti-892

mized combined with the value of the current best solution enables the algorithm893

to search parts of the solution space only implicitly.894

• heuristic improves the label-correcting algorithm for the shortest path prob-895

lem, by remembering a few additional good subpaths (x subpaths) on each level,896

to avoid pruning out a good path early on. For simplicity, we assume x=2n.897

In this section, we present computational experiments conducted to evaluate the898

quality of the two approaches described above, namely the branch-and-bound algo-899

rithm and the heuristic. We tested the approaches on a sequence of examples with a900

feasible solution space ranging from thousands to trillions of paths. These particular901

example problems form 6-ary search trees of di�erent levels. On a small problem,902

a 5-level tree gives 1296 possible paths (64), on a big problem, a 15-level tree gives903

7.84E10 possible paths (614). Problems forming search trees with all levels between 5904

to 15 are also explored. We pruned the trees with the branch-and-bound algorithm905

and the heuristic respectively. We also provided the brute-force search approach to906

calibrate ourselves.907

The algorithms are coded in C++ and tests are carried out on a PC with AMD64908

architecture under Linux system Ubuntu. Without going into the details of the science909


and engineering aspect of the examples right now (the details are given in the later910

chapter), here is the summary of the results with a numerical method focus.911

4.7.1 Verifying branch-and-bound algorithm912

First, we compare the the branch-and-bound algorithm with the brute-force search913

approach over a set of 6-ary search trees with a height from 5 levels to 15 levels. When914

working with an extreme problem, the branch-and-bound algorithm degenerates into915

the brute-force search approach. In that case, every node on the tree has to be visited916

exactly once. Further, whenever a node is visited, the program triggers a function917

call which calculates the distant number. From a computational point of view, this918

calculation is the most expensive task for each iteration. Therefore, comparing the919

actual nodes visited using the branch-and-bound algorithm against all nodes in the920

tree, is a good measurement of the algorithm e�ciency.921

Figure 4.5: Visited nodes in branch-and-bound(BB) algorithm

Figure 4.6: The optimal results given byBB and the brute-force approach

Figure 4.5 illustrates the number of visited nodes against all nodes for all levels922

considered. First of all, we were successful in discarding bad branches and nodes using923


the algorithm over all level of problems considered. Secondly, none of the problems924

degenerate into the brute-force search approach. Lastly, as the tree level increases, the925

fraction total of the nodes visited decreases considerably. Therefore, for large trees,926

the branch-and-bound algorithm is especially e�cient compared to using brute-force927

search approach.928

We calibrated ourselves by comparing the results given by the branch-and-bound929

algorithm and the brute-force search approach. Figure 4.6 illustrates that the results930

of the branch-and-bound algorithm agrees with the brute-force search approach over931

all levels considered.932

4.7.2 Verifying Heuristic933

Secondly, we compare the visited nodes of the heuristic with the branch-and-bound934

algorithm to show that heuristic is actually more e�cient. The heuristic assumes935

x=2n, therefore it remembers a maximum total of 3n paths on each level of the tree.936

Figure 4.7 illustrates the visited nodes of both the branch-and-bound algorithm and

Figure 4.7: The visited nodes comparisonbetween BB and the heuristic

Figure 4.8: The optimal results given bythe heuristic and the brute-force approach

937

the heuristic, over a set of 6-ary search trees from 5 levels to 15 levels. As illustrated,938


the visited nodes for both branch-and-bound algorithm and the heuristic increases as939

the tree levels increases. Further, The heuristic is more e�cient compared with the940

branch-and-bound algorithm over all levels considered. Lastly, as the number of tree941

level increases, the fraction of visited nodes decreases considerably. The fraction total942

of visited nodes of the heuristic compared to the branch is bound is 47 percentage at943

5 levels, and only 2 percentage at 15 levels.944

We compare the optimal results give by the heuristic and the brute-force approach945

to calibrate ourselves. Note in this comparison, we ran the heuristic assuming x=2n.946

Figure 4.8 illustrates that for these speci�c sets of problems, the optimal results found947

using the heuristic agrees with brute-force approach at lower levels, speci�cally from948

5 levels to 11 levels. At higher levels, namely from 12 level to 15 levels, the heuristic949

gives suboptimal solutions compared to the results given by the brute force search950

approach.951

As mentioned earlier, heuristic is not an exact method, therefore it does not952

guarantee to always give the optimal results. Figure 4.9 illustrates the optimal results953

given by heuristic as the number of additional subpath x increases for a 6-ary trees of954

15 levels. Firstly, when x=0, this heuristic is essentially the shortest path algorithm.955

Since it ignores the path-dependency nature in the problem, the results given is956

suboptimal. Secondly, the optimal result changes as x changes. Lastly, the change of957

the optimal result is not monotonic as x increases. The details interpretation of the958

results are given in the discussion section.959


Figure 4.9: The optimal path as a function of x in Heuristic

4.8 Discussion960

We have shown that the branch-and-bound algorithm is indeed more e�cient than961

the brute-force search approach, as illustrated in Figure 4.5. In these speci�c sets of962

problems, the branch-and-bound algorithm becomes more e�cient as the tree level963

increases. Further, Figure 4.6 illustrates that the results given by the branch-and-964

bound algorithm agrees with the brute-force search approach over all levels considered.965

Despite the improved e�ciency, the branch-and-bound algorithm can still take966

up to nine minutes in solving a 6-ary tree of 15 levels. For a large tree with a large967

number of steps and a great number of choices for each step, the runtime can increase968

considerably. To improve the algorithm even more, we proposed a heuristic to obtain969

a good solution in a reasonable time. We have shown in Figure 4.7 that the heuristic970

is indeed more e�cient than the branch-and-bound algorithm. The fraction total of971

visited nodes compared with the branch-and-bound algorithm decreases as the tree972

level increases, indicating an increased e�ciency gain with larger trees. We compare973


the results given by the brute-force approach and the heuristic assuming x=2n. We974

have shown in Figure 4.8 that the heuristic coincides with the brute-force approach975

over lower levels of the tree, but disagree at higher levels.976

The heuristic does not guarantee to �nd the optimal solution, it is not an exact977

method. To calibrate ourselves, we ran the heuristic for a 6-ary tree of 15 levels, by978

slowly increase x from zero to nine times the design options. Figure 4.9 illustrated979

that, given di�erent x, the results may not coincide with the optimal results given980

by the exact method. Further, the di�erences between the optimal and suboptimal981

results are very small, this is problem-speci�c. Given a di�erent tree, the di�erence982

may be more dramatic. Lastly, the change in the optimal results is not monotonic983

with the increase of x. This is because though some of the x partial paths look984

promising on the upper level, they can later become terrible choices. An extreme985

case is when the partial path is locked-in to a wrong path, which later becomes too986

expensive to escape from. Additionally, keeping x additional subpaths on early levels,987

can crowd out the true optimal subpath, resulting in suboptimal results. In fact, this988

is the case when x is between 2n and 8n, as illustrated in Figure 4.9. When x=n, the989

results given by the heuristic agree with the exact method. This is because keeping990

only n additional subpaths did not crowd out the true optimal. It is worth to note991

that, these results are problem-speci�c. Given a di�erent tree, the range of x value,992

in which optimal solution is crowded out may be di�erent.993

In addition to the two approaches discussed above, we can combine the two ap-994

proaches for a hybrid algorithm. Speci�cally, we can �rst run the heuristic to get995

a good bound, then we can run the branch-and-bound algorithm with the bound996


obtained from the heuristic. Theoretically, the hybrid algorithm should be more ef-997

�cient than the branch-and-bound because it starts with a tighter bound, therefore998

making the pruning more e�cient. We implemented the hybrid algorithm. Figure999

4.10 illustrates the number of discarded nodes using the branch-and-bound and the1000

hybrid algorithm over a set of 6-ary trees of 5 levels to 15 levels, the di�erences are1001

illustrated as dots. The results showed that, �rst there are di�erence in the number1002

of discarded nodes over all levels considered. Secondly, the di�erences are very small.1003

We believe this is a re�ection of the nature of this speci�c set of problems, rather1004

than generic to the algorithm.

Figure 4.10: Visited nodes in the branch-and-bound and the hybrid algorithm

1005

So far we have presented the results of deterministic discrete optimization. Firstly,1006

we have assume that the decision maker is a rational economic person, and is willing1007

invest the cost upfront, and receive the bene�t much later. However, if the decision1008

maker wants immediate grati�cation, rather than the true global optimal, he may1009

prefer a suboptimal solution, which gives the optimal bene�t in the short run. Sec-1010

ondly, although the cost of technology and the environmental penalty are expected to1011

change over time, we do not intend to forecast the technology development. Rather,1012


we treat these changes as exogenous to the model, and are given by the user as1013

input to the model. Finally, the uncertainties in the technology development, and1014

potentially emerging new technology choices over time are beyond the scope of this1015

research.1016

Chapter 51017

Optimizing CO2 post-combustion1018

capture technologies1019

In this chapter, we study various post-combustion capture technologies using the1020

ranking algorithms described in Chapter 4. In the �rst part of our work, we developed1021

a simple model for the absorber system. We are given a CO2 mitigation target,1022

by varying parameters like the sorbent strengh, the packing tube radius and the1023

absorber tower height, we can �nd the optimum design. In the second part of our1024

work, we studied various power plant designs with absorbers in a sequence and �nd1025

the optimum sequence using the algorithms described in the previous chapter. By1026

comparing the results from the �rst part and the second part, we can that one can1027

get di�erent answers when looking at the same problem di�erently.1028

63

Chapter 5: Optimizing CO2 post-combustion capture technologies 64

5.1 Motivation1029

Post-combustion capture technology captures carbon dioxide in a large point1030

source (i.e coal-�red power plant or cement plant), by separating carbon dioxide1031

from the �ue gas via chemical or physical absorption. This procedure can be used for1032

capturing carbon dioxide from power plants as an �end-of-the-pipe" approach, leaving1033

the existing technology designs relatively unchanged. Therefore, it is especially at-1034

tractive for governments and companies who are eager to deploy low-emission power1035

plants.1036

The technology of absorbing carbon dioxide from a mixed gas stream is well stud-1037

ied and widely used in chemical industry for gas treatment. However, it has not1038

been used in coal-�red power plant for CO2 separation. Traditionally, gas treatment1039

systems are designed to absorb as much CO2 as possible while meeting the economic1040

constraints. Drawing from the experience in chemical industry, power plant designs1041

with CO2 capture using post-combustion capture technology, often target for 90 per-1042

cent capture percentage or even higher are assumed (i.e. DOE, ieaghgt). Further,1043

technoeconomic studies of the power plant system with CO2 absorber, often takes1044

the CO2 absorber as a preoptimized module. While the absorber itself is optimized1045

locally, it may not be the optimal design when evaluating the entire power plant.1046

It is our view that, low capture percentage range may o�er economic opportunities1047

for reoptimizing the absorber system integrated with the power plant, by taking1048

advantage of weaker and cheaper sorbent.1049

On one end of the spectrum, as one attempt to capture the last percentage of CO21050

from the �ue stack, it is conceivable that the capture cost rises signi�cantly. This1051


is because as the partial pressure of CO2 approaches equilibrium, the driving force1052

for absorption decreases signi�cantly, making it very di�cult to collect the last bit.1053

Theoretically, to capture one hundred percent of CO2, one needs to build an in�nitely1054

tall absorber tower. Though one can capture as much as CO2 possible, the cost per1055

ton of CO2 captured is very expensive in this case.1056

On the opposite extreme, if one were to capture only very little CO2, the cost1057

is very little. For example, by licking one's �nger tip and simply put it in the air,1058

one can capture in�nitely small percentage CO2 from the air on the wetted �nger tip1059

surface. The cost of doing so is nill.1060

Between the two ends of the spectrum, there is an optimum capture cost ($/ton1061

CO2), which is associated with an optimum absorber design using an optimum sor-1062

bent. In such a design, design parameters like the sorbent strength, packing geometry,1063

and �ow pattern and �ow rates, are reoptimized at each targeted capture percentage1064

for the lowest cost per ton of CO2 captured, (rather than the lowest cost per ton of1065

gas treated.)1066

By connecting optimality at each capture percentage, one can generate a cost1067

curve of optimum capture costs in a power plant, at di�erent capture percentage.1068

Such curve is useful to decision-makers not only in building one plant at a time, but1069

more importantly, building a smoother pathway in the large scale carbon sequestration1070

project deployment and technology commercialization.1071

This chapter studies the subject of optimizing post-combustion capture power1072

plants via redesigning absorber-desorber system for various capture percentage using1073

various sorbent. In the �rst part of this chapter, we optimize a single plant design.1074


In the second part of this chapter, we optimize a sequence of plant designs using the1075

algorithms introduced in Chapter 4.1076

A post-combustion capture power plant using monoethanolamine is modeled with1077

the program introduced in the Chapter X. The modeling procedure strictly followes1078

Perrys' chemical engineering handbook and take (Oexemanne,2008) as reference (sec-1079

tion 5.3). The cost model is described in section 5.4. Optimization parameters include1080

packing tube radius, column height, capture percentage, choice of sorbent, etc. Re-1081

sults are presented in section 5.5. The optimization results show that for the perfectly1082

strong sorbent, CO2 capture percentage is insensitive to the design of the column as1083

long as the pressure drop remains the same. For imperfect sorbent, the optimized1084

packing is XXX for YYY capture percentage, and XX2 FOR YYY2 captuer per-1085

centage. This result is compared to the DOE study and the Oxemanne 2008 study,1086

the implications and limitation of the result are discussed, and further research is1087

proposed.1088

5.2 Literature Review1089

Many research workers have studied optimizing post-combustion capture tech-1090

nologies (DOE, IEAGHGT, etc). In the DOE study, a 300 MW subcritical power1091

plant with 90 percent CO2 captured using MEA sorbent is considered as the refer-1092

ence case. To simulate lower capture percentage in the full-size plant, the method1093

bypasses �uegas such that lower capture percentage in the full-size plant can be con-1094

sidered equivalent (in term of CO2 captured per hour), to 90 percent capture rate in1095

a much smaller plant. The optimization result is a capture system with the largest1096


column, due to the economies of scale. This study however, failed to account for1097

various capture system designs. For example, for various CO2 capture percentage in1098

power plants, one can choose to pack the absorption tower loosely or densely, one1099

can also choose to use weaker or stronger sorbent. For a perfectly strong sorbent1100

in the laminar �ow, when the schmit number is close to 1, the CO2 absorption rate1101

as a fraction of total is approximately the same as the pressure drop as the fraction1102

of total. If loose packing in a taller absorber give you the same pressure drop as1103

dense packing in a shorter absorber, a perfectly strong sorbent in the laminar �ow is1104

insensitive to the size and packing of the column as long as the pressure drop is the1105

same. However for imperfect sorbents, the design of column matters.1106

The DOE study also failed to take advantage of various sorbent with various1107

binding energies. For example, when the weaker sorbent is used (i.e. slightly alkaline1108

sorbent, seawater, etc), less energy per ton of carbon dioxide is needed for CO21109

regeneration.1110

In addition, when studying optimization with various sorbent, it is important1111

to fully integrate the capture system into the power plant. In the post-combustion1112

capture system, substantial amount of steam is extracted from the steam turbine1113

for CO2 regeneration in the stripper. Therefore, globally optimized power plant can1114

operate with the lowest cost and the lowest energy penalty of the entire system.1115

However, due to the lack of software tools suited for this purpose, many studies have1116

used separate softwares for power plant modeling, and for capture system modeling.1117

Since it is usually di�cult to fully integrate the two softwares, optimization is often1118

carried out locally in the capture system based on the pre-determined power plant1119


operating condition (i.e Oexmann, 2008). With the help of the newly developed1120

software tool (described in the previous chapter), it is possible to fully integrate the1121

capture system into the power plant designs, and carry out global optimization.1122

The literature review on a DOE study (2007) on carbon capture from existing coal-1123

�red power plants, found a deceasing CO2 avoidance cost ($/ton CO2 capture) with1124

increase in CO2 capture percentage, implying the more you scrub the cheaper/easier1125

it becomes. This result is counter-intuitive, but a closer examination on this report1126

found the assumption of bypassing a portion of �ue gas, essentially equivalent to1127

scrubbing a smaller power plant. The cost reduction is caused by the economics of1128

scale with larger absorption columns at higher capture percentage. Applying absorber1129

designs for high capture percentage range (90 percent or above) to all capture ranges,1130

will likely to result in sub-optimality.1131

Unlike the DOE approach, we aim to study the CO2 avoidance cost ($/ton CO21132

capture) as a function of capture percentage without bypassing any �ue gas for a hy-1133

pothetical sorbent in a hypothetical column design. Five capture technology options1134

are identi�ed among a wide range of technological options. A cost curve (that may or1135

may not continuous) combining these candidate technologies across di�erent capture1136

ranges will be constructed.1137

5.3 Modeling CO2 absorber physics1138

A post-combustion capture power plant using monoethanolamine is modeled with1139

the program introduced in the Chapter X. For the purpose of this discussion, the1140

modeling details of the power plant island is included in the appendix, while this1141


chapter focuses on the modeling detail of CO2 absorber.1142

Let us consider a hypothetical packed bed absorber tower for CO2 absorption us-1143

ing a hypothetical sorbent. The uptake rate of the absorption tower is characterized1144

by a surface area and a mass transfer coe�cient. Speci�cally, the surface area is de-1145

termined by the packing geometry, whereas the mass transfer coe�cient is determined1146

by the packing geometry, the sorbent strength, and the hydrodynamic condition of1147

the absorber.1148

For the simplicity of the discussion, the packing structure inside the absorber1149

can be considered as bundles of evenly divided tubes, the length of the which equals1150

the absorber height. This type of structured packing is rare in reality, however this1151

treatment greatly simpli�es the packing geometry, hence allowing us to understand1152

the physics of packed bed column with a rather simple model.1153

Consider the packing arrangement such that all tubes are identical, and are set1154

up in parallel to each other. An example of the cross sectional view of the absorber1155

column is shown in Figure 5.1, where 33 small tubes packed in a big column [?].1156

The tube wall is fully coated with sorbent which is continuously refreshed. The1157

overall tower diameter and volumetric �ue gas �ow rate are known, hence we can1158

determine the average gas velocity. For practical purposes, we don't know if the1159

sorbent combines with CO2 chemically or physically.1160

5.3.1 Di�usion process1161

In the laminar or somewhat turbulent �ow, we can make the following argument1162

about the absorption process. During CO2 absorption, momentum transfer to the1163


Figure 5.1: An instance of the cross-section of a packing tower

wall, follows the similar di�usion equation (equation 5.2), as that of the CO2 transfer1164

to the wall (equation 5.1). Momentum transfer coe�cient and mass transfer coe�cient1165

are on the same order of magnitude, their ratio is measured with Schmidt number,1166

as given in equation 5.3. When the Schmidt number approaches unity, the value of1167

momentum transfer coe�cient equals the value of mass transfer coe�cient.1168

τ = −µ× ∂vz∂r

(5.1)

JCO2,g = −ρD∇CO2 = −ρD∂yCO2

∂r(5.2)

Sc =ν

D=

µ

ρD(5.3)

In the center of the tube, both momentum and CO2 are at their maximum. On1169

the wall, momentum always go to zero. CO2 will also go to zero if a perfect sorbent is1170


coated on the wall, and is continuously refreshed (i.e. no CO2 loading in the sorbent).1171

Therefore, given the shared boundary conditions on the wall and at the tube center,1172

we argue that the fractional total of CO2 and the fractional total of momentum1173

across the tube radius are approximately the same. In other words, if one percent of1174

momentum is lost, then one percent of CO2 lost too.1175

Nevertheless, momentum doesn't go away as CO2 does, because the momentum1176

lost is continuously replenished by pressure drop. If one percent of momentum is1177

replenished, then one percent of pressure is lost. Therefore, if one wants to take out1178

a certain fraction of the CO2, one needs to take out the same fraction of the �ue gas1179

pressure.1180

For a sorbent which meets the boundary condition of zero CO2 concentration on1181

the wall, as long as the pressure drop is kept constant, the CO2 capture percentage1182

is also kept constant. Therefore, the packing structure inside the bed can be either1183

long tubes with big openings, or short tubes with narrow openings. Since the latter1184

is more favorable for economic reasons, one can reduce the tube opening, to the point1185

where the boundary condition doesn't hold. The tube radius at this point is de�ned as1186

critical radius rc. Each sorbent with a unique binding strength, has a unique critical1187

radius. The value of rc is relatively small for strong sorbent, and big for weak sorbent.1188

When the tube radius is smaller than rc, it is undesirable to continue reducing the1189

tube radius for higher mass transfer coe�cient. This is because with a small opening,1190

the CO2 uptake rate is small due the limitation on the wall, but one still need to pay1191

for the big pressure drop. Therefore, the proportion of the momentum taken out to1192

the CO2 taken out is suddenly unfavorable.1193


Since the uptake rate, speci�cally the mass transfer, is greatly in�uenced by the1194

packing geometry, huge opportunities exist to redesign the packing structure for var-1195

ious sorbents. It is our view that one can redesign the packing structure for each1196

sorbent with a unique binding strength and a unique critical radius, for the lowest1197

cost per ton of CO2 capture. This optimum design correspond to a capture percent-1198

age for the chosen sorbent. Therefore, for a given capture percentage target, one can1199

select the optimum sorbent with the optimum design for the lowest cost of per ton of1200

CO2 capture.1201

5.3.2 Interfactial partial pressure and concentration1202

CO2 transfer on the wall side is given by the following equation1203

JCO2,w = kl × (PCO2,w − P ∗CO2) (5.4)

For the simplicity of the problem, we assume that the mass transfer pro�le across the1204

tube is linear, and the boundary layer in the gas side is the tube radius.1205

JCO2,g = −ρDPCO2,in − PCO2,w

rt(5.5)

Consider steady state, the CO2 �ux on the wall is always in equilibrium1206

JCO2,g = JCO2,w (5.6)

One can solve for the boundary condition as1207

PCO2,w =kl × P ∗CO2 + ρD

rt× PCO2,in

kl + ρDrt

(5.7)

PCO2,in > PCO2,w > P ∗CO2 is the condition for absorption, PCO2,in < PCO2,w < P ∗CO21208

is the condition for desorption.1209


The CO2 �ux on the wall can be expressed as1210

JCO2 =ρDkl(PCO2,in − P ∗CO2)

ρD + klrt(5.8)

The interfatial liquid side CO2 concentration can be found with Henry's law.1211

Cco2,w = HkPco2,w (5.9)

5.3.3 Vapor Liquid Equilibrium1212

This correlation is taken from [Gabrielsen, 2005]1213

P ∗CO2 = KCO2103XCO2Xamine,0θavg

(Xamine,0 ∗ (1− 2 ∗ θavg))2(5.10)

lnKCO2 = A+B

T+ CXamine,0θavg +D

√Xamine,0θavg (5.11)

A = 30.96 ± 1.861214

B = -10584 ± 6701215

C = -7.187 ± 4.271216

D = 01217

1218

5.3.4 liquid side mass transfer coe�cient1219

Liquid size mass transfer coe�cient is determined by the packing geometry, the1220

hydrodynamic conditions, and the sorbent strength.1221


physical mass transfer coe�cient1222

Penetration theory1223

k0l = (5.12)

Enhancement factor1224

5.3.5 CO2 absorption1225

Enhancement factor for the sorbents are:1226

E =Ha×

√(E∞−E)E∞−1

tanh×[Ha×√

(E∞−E)E∞−1

](5.13)

where1227

Ha =

√DCO2,AM × k2 × CMEA

KL

(5.14)

1228

E∞ = [1 +DMEA,amCMEA

γDCO2,am × CCO2,i

] (5.15)

k2 = 4.4× 108exp[−5400

T] (5.16)

For desorption1229

K−1 = 3.95× 1010exp[−6863.8

T] (5.17)

Sources are1230

5.3.6 Pressure Drop1231

Pressure drop is given by Hagan-Poiseuille equation.1232

Q =4Pπrt4

8µh(5.18)


By rearranging the equation, we give the pressure drop as a function of height and1233

radius.1234

4P =8µhQ

πrt4(5.19)

To maintain the same pressure drop, one needs to maintain a constant hrt4. Hence,1235

the tube height (also the absorber height) can be expressed as a following equation1236

h =4Pπ8µQ

rt4 (5.20)

5.3.7 Uptake rate1237

rCO2 = ApJCO2 (5.21)1238

Ap = 2πhR2

rt(5.22)

5.4 Penalty model1239

5.4.1 Plant penalty model1240

The overall plant penalty model follows the same method described in Chapter1241

X. The details of other modules are listed in the appendix, since this chapter focuses1242

on the absorber.1243

5.4.2 CO2 absorber capital cost1244

For the absorber, there are two parts of the cost in capital cost, �rst it's the1245

total tower cost, secondly it's the packing cost. These calculation follows the man-1246


ual[INCLUDE CITATION!]1247

The capital cost can be calculated based on the scaling law1248

Capex = C0× V α

V0α (5.23)

Assume the absorber height is 25 percent taller than the tube height, to account for1249

the sorbent distributor, the volume of the absorber column is given as below.1250

V = πR21.25h (5.24)

If we replace h with equation ??, we give the volume as below1251

V = 1.25πR24Pπ8µQ

rt4 (5.25)

5.4.3 CO2 absorber operation and Maintenance(OAM) cost1252

For the absorber, operation and maintenance cost here includes variable oam cost1253

and �xed oam cost. Variable oam costs include sorbent makeup cost, and the pump1254

cost. Fixed oam costs is estimated to be 2 percent of the absorber capital cost.1255

5.4.4 Unit cost of CO2 captured1256

Since we keep the pressure drop constant, if we only account for capital cost in1257

the total capture cost, the unit cost of CO2 captured is given as1258

$

tonCO2

=Capex

rCO2

(5.26)

This equation can be simpli�ed to1259

$

tonCO2

= kart(4α−3) + kbrt

(4α−2) (5.27)


where1260

ka = ktotD

Pin− P ∗CO2

(5.28)

kb = ktotktotkl

Pin− P ∗CO2

(5.29)

ktot =C0παR2αCα

C1DklV0α (5.30)

Equation 5.27 gives the unit cost of CO2 captured as a function of tube radius1261

and α. Since α is usually 0.6 for chemical reactor [?, ?, ] the minimum unit cost of1262

CO2 captured correspond to a tube radius between zero and in�nity.1263

5.4.5 Parameters1264

We would like to �nd the optimum absorber by changing the radius and the height1265

of the packing tube. So the two parameters we have are tube radius rt, and height h.1266

State the source of constant Equilibrium1267

5.4.6 Mass conservation1268

Two mass conservation equations are postulated in this model. Firstly, the di�er-1269

ence between mathrmCO2 �ow rate (kg/s) on both sides of the absorber equals the1270

total mathrmCO2 absorption.1271

φCO2 = CO2, in− CO2, out (5.31)

Secondly, the di�erence between �ue gas �ow rate (kg/s) on both sides of the absorber1272

are only caused by mathrmCO2 absorption. This is a gross assumption, assuming1273


zero mathrmSOx or mathrmH2O reacts with the sorbent. In reality, this equation1274

needs to take into account the e�ect of mathrmSOx and mathrmH2O. For the1275

simplicity of the model, we use the following equation.1276

FlueGas, in− FlueGas, out = CO2, in− CO2, out (5.32)

5.5 Results1277

• Single plant optimizaiton gives the optimal single plant at time t (t =t1,1278

t2, ... tn). It is a discrete optimization, in which the penalty of all designs1279

at the corresponding decision time are calculated. The one with the lowest1280

penalty is the optimum design. At each decision time t, one can �nd an optimal1281

design. Since each decision is viewed as independent, the factor of learning and1282

transitional costs are ignored. Therefore, the cost of the same design does not1283

change when it is chosen repeatedly.1284

• Local plant optimization simply puts the optimized single plant designs in1285

a sequence, giving a sequence of n designs for n decision points. In this case,1286

the decisions are viewed as a sequence of interdependent choices. Therefore,1287

learning and transitional costs between immediate decisions play a role in the1288

penalty of each choice in the sequence.1289

• Global optimization �nds the optimal sequence of designs, by comparing1290

all possible sequences of designs. In this case, an earlier cost may prevent the1291

sequence from locking in to the wrong path, incurring a much bigger costs later.1292


5.5.1 Global optimum favors earlier costs for future bene�t1293

In this section, we �rst ran the model with 6 design choices for a 14 plant sequence.1294

Then we ran it with 21 designs for a 15 plant sequence. Finally, we increases the1295

number of designs to 87 designs, and optimize for a 15 plant sequence. In1296

Result1. 6 design choices with 14 decision times1297

Figure 5.2 illustrates the single plant optimum at 14 decision points, both in-1298

dependently and sequentially. It also illustrates the global optimum of a 14-plant1299

sequence in comparison. In both optimizations, we are given 6 design choices at each1300

time. The 6 choices are: NoScrubber, WeakAbsorber, StrongAbsorber, Absorber.

Figure 5.2: Single plant and pathway optimization, 6 design choices for 14 decisionpoints

1301

As illustrated in Figure 5.2, Firstly, when viewed as independent decisions, the1302

same designs chosen repeatedly have the same cost. In comparison, when they are1303

viewed as a sequence of decisions, the cost decreases as more units are built. Secondly,1304

we can see that single plant optimum favors immediate bene�t at the cost of lock-in1305


at time t11. Sequence optimum favors early costs for future bene�t. Thus by paying1306

a little extra at time t2 and t6, it gains the bene�t of learning for the rest of the1307

sequence.1308

Figure 5.6 compares the series of chosen plant index for both single plant opti-1309

mization and sequence optimization. As seen, they are di�erent

Figure 5.3: 6 design results. Plant index comparison

1310


Figure 5.4: Plant performance data of the 6 designs

Figure 5.5: 21 design results. The optimal cost of a single plant and a sequence ofplants

Result2. 21 design choices with 15 decision times1311

Result 3. 87 design choices with 15 decision times. Only CO2 cap1312

Result 3. 87 design choices with 15 decision times. CO2 cap and trade,1313

assume 30 $/ton CO21314

5.5.2 Parametric study of technical performance based on mo-1315

noethanolamine1316

This should be part of the sorbent chapter1317



Impact of MEA%, loading1318

The �rst part of the results look at choosing the optimized packing structure for1319

sorbents with di�erent concentration. Three cases are chosen for comparison, in case1320

1, MEA concentration is chosen to be 45% by weight, in case 2, MEA concentration1321

is chosen to be 35% by weight, in case 3, MEA concentration is chosen to be 25% by1322

weight.1323

The preliminary results show that to choose the optimum tube radius, di�erent1324

MEA concentration does not have a signi�cant impact. Di�erent loading also does1325

not have a signi�cant impact. This is because, given the choice of tube radius, MEA1326

concentration can have a impact on the equilibrium partial pressure of the CO2 with1327

regard to the sobent, and hence change the the CO2 �ux. But this impact is in-1328

signi�cant, compared with the impact of the di�erent packing area as a result of the1329


Figure 5.7: Plant performance data of the 21 designs

decreasing tube radius. The same case is true with di�erent loading.1330

This result compared with literature XXX, BBB, CCC1331


Figure 5.8: 87 design results. The optimal cost of a single plant and a sequence ofplants



Figure 5.10: 87 design results. 87 design results. 30 $/ton CO2 .The optimal cost ofa single plant and a sequence of plants

5.6 Discussion-Modeling Results1332

5.6.1 Limitation1333

: The advantage of optimizing over the entire integrated system is mostly obvious1334

in green�eld plants. When it comes to retro�t, it may or may not be more advanta-1335

geous than using two separate softwares, due to the limitation in how much you can1336

improved on the existing power plant, and the room for improvement/remodi�cation1337

due to the age of that power plant. If the existing power plant is relatively new,1338


Figure 5.11: 87 design results. 30 $/ton CO2 Plant index comparison

changed operating conditions from the design operation conditions may be allowed,1339

for older generation power plants, this may be too di�cult hence one can get the same1340

result using two separate softwares. In addition, retro�t is highly site-speci�c. It is1341

yet another question (and still an open question) whether it's better o� to retro�t the1342

existing �eet or build new ones. From purly engineering point of view, it is likely to1343

retire the existing �eet and build new ones, however, this will be subject to a range1344

of factors like policies, public opinion, and the economy.1345

Chapter 61346

Designing the software tool for1347

advanced power plant modeling and1348

optimization1349

6.1 Summary1350

In this chapter, a software tool for advance power plant modeling and optimiza-1351

tion is designed and developed. The motivation for this work is driven by the lack of1352

process modeling and optimization tool for advanced power plant optimization exer-1353

cise. This is con�rmed by the observation in the limitation of chapter 3, where the1354

existing software can not meet the requirement of the optimization exercise. This1355

chapter will explain in detail the design and the development of the software tool.1356

The software is designed as a model of modules and pipes, in which a module is1357

a basic operation unit (i.e. pressure pump, absorber, boiler, etc), and a pipe is the1358

87

Chapter 6: Designing the software tool for advanced power plant modeling andoptimization 88

material and energy �ow that connects the modules, each pipe is connected on both1359

ends. A module is characterized by a set of parameters, some of the parameters are1360

properties and �ow rate carried in the pipes, others are known only the module itself.1361

The program starts with a user-provided input �le which describes a power plant of1362

modules and pipes characterized by a complete but inconsistent set of parameters.1363

The program then reconciles the inconsistencies in the over-determined parameters1364

through an iterative process, until it �nds the solution. The penalty of the reconciled1365

power plant is then calculated. Up to this point, the program has calculated the1366

penalty number for a physically consistent(coherent) power plant which operates in1367

one speci�c conditions and of one speci�c size. To study the impact of parameters1368

of interest on the power plant penalty, instead of specifying a �xed value for the1369

parameter, one needs to specify a range and a current value of the parameter if1370

it is continuous, otherwise one need to specify a set of discrete values for discrete1371

parameters. The program calls the reconcile routine to �nd each possible physically1372

consistent system provided the parameters fall into the range speci�ed above. Each1373

reconciled system has one unique penalty number. The optimization routine compares1374

the penalty numbers of all reconciled systems and �nd the optimized system with the1375

lowest penalty number. In this way, one can �nd the optimized plant design and the1376

optimized operating condition for systems of interest.1377

Similarly, one can use this method to �nd the optimum pathway for a sequence of1378

power plant designs. First reconcile will �nd the physically consistent set of parame-1379

ters for each plant design. Then the penalty of the sequence will be calculated, where1380

the pathway penalty is the sum of all plant level penalty in addition to pathway level1381


penalties (see Chapter X). A sequence of power plant designs is a discrete parameter,1382

where each plant design is an element in the set. Optimization will run through each1383

possible combination of elements in the set, calculate the pathway penalty for each1384

combination, and �nd the optimized pathway with the lowest penalty.1385

This chapter will describe in detail the program design, and introduce its main1386

functionality. Currently seven modules and six pipes are developed. The module li-1387

brary includes boiler, steam turbine, condenser, pressure pump, CO2 absorber, split-1388

ter, generic source and sink. The pipe library includes heat �ow, work �ow, �ue gas1389

�ue, water �ow, coal �ow, and sorbent �ow.1390

6.2 Motivation1391

There is a lack of process modelling and simulation, in particular to evaluate1392

the potential of CO2 capture by various sorbent for various capture percentage, in1393

comparison to solvents such as MEA, which is often aiming for 90-95 % capture1394

percentage only.1395

When considering the integration of the capture and compression sub-processes1396

into the overall process of a coal-�red power plant, the simulation of the CO2 capture1397

process and the power plant modeling are often carried out in two independent soft-1398

ware respectively (i.e Oexmann, 2008). Therefore, it becomes very di�cult (unstable)1399

and in�exible to conduct optimization, which will �nd optimum process parameters1400

for the overall system (instead of only part of the system, i.e. the power plant, or the1401

CO2 capture process) that shows the lowest penalty.1402

Furthermore, the objective function of the optimization is often minimizing energy1403


loss in CO2 post-combustion capture process (due to the nature of such modeling1404

tools), capital cost of the overall integrated system are subsequently calculated based1405

on the result of the optimization. In reality, business decisions are made often with1406

the goal of minimizing cost, where the capital cost of the entire plant is not only a1407

function of power loss, but also a number of other factors, for example the operating1408

temperature of the furnace, the number of stages in steam turbine, etc.1409

Nonetheless, power plants today are faced with multiple competing objectives, in1410

addition to the objective of minimize the cost. The objectives to meet environmen-1411

tal constraints, infrastructural constraints, and energetic constraints, in addition to1412

economic constraints, demand a tool that will allow users (�rms and policy maker)1413

make informed decisions to choose the optimum power plant design, and the optimum1414

pathways for building a sequence of power plants.1415

To satisfy the need and requirement stated above, a software tool which allows1416

users to conduct multi-objective optimization on very complex systems, and highly1417

�exible is developed.1418

The author uses this software to �nd the optimum sorbent in post-combustion pro-1419

cess for various capture percentage which would give the lowest penalty.(environmental1420

impact, infrastructural impact, energetic impact, and economic impact).1421

6.2.1 Limitation1422

The advantage of optimizing over the entire integrated system is mostly obvious1423

in green�eld plants. When it comes to retro�t, it may or may not be more advanta-1424

geous than using two separate softwares, due to the limitation in how much you can1425


improved on the existing power plant, and the room for improvement/remodi�cation1426

due to the age of that power plant. If the existing power plant is relatively new,1427

changed operating conditions from the design operation conditions may be allowed,1428

for older generation power plants, this may be too di�cult hence one can get the same1429

result using two separate softwares. In addition, retro�t is highly site-speci�c. It is1430

yet another question (and still an open question) whether it's better o� to retro�t the1431

existing �eet or build new ones. From purly engineering point of view, it is likely to1432

retire the existing �eet and build new ones, however, this will be subject to a range1433

of factors like policies, public opinion, and the economy.1434

6.3 A model of modules and pipes1435

The purpose of "design" is to create a clean and relatively simple internal struc-1436

ture, sometimes also called architecture, for a program [B Stroustrup, 2000]. This1437

program is designed with a modules-and-pipes structure which I will explain in greater1438

details below.1439

A module is a generic concept as illustrated in (Figure ??), the module can be at1440

some level any thing you like it to be (for example it could be an operation unit, it1441

can also be a power plant). A module has a number of inputs and it has a number of1442

outputs . A model (�owchart) of a power plant has only two fundamental components:1443

they are modules and pipes, a fully developed plant can be think of as combination1444

(a network) of modules and pipes. For a �owchart of a power plant design, the blocks1445

of the �owcharts are the modules, the streams and pipes are the lines (or streams)1446

connecting them.1447


A module has to have the feature that it is connected with a number of pipes. For1448

example, a furnace is a module that takes coal and air, and puts out heat and �ue1449

gas. The �ue gas is the combustion product of coal and air, air is air, and coal we1450

can specify some ten parameters that is speci�c to coal, thus we de�ne the furnace.1451

The pipes connect the furnace are the coal coming in, the air coming in, the �ue gas1452

going to the stack, and the heat going out the other end. We decided as a structural1453

decision, that we have a handful of modules which only has pipes that going out1454

or pipes coming in, as sources and sinks. For example, the atmosphere is a source1455

module that would give you as much as you like.1456

A pipe can be think of as a stream carrying material and/or energy, every pipe1457

has to have the feature that both ends of a pipe is connected to a module . A pipe1458

stores three copies of datasets, a copy of a dataset at the inlet of the pipe, a copy1459

of a dataset at the outlet of the pipe, and a iterative copy of a dataset, with which1460

the pipe reinitialize (writes to) both the inlet copy and the outlet copy after each1461

iteration (Figure ??). Note the inlet of the pipe is the outlet of the block that pipe1462

connects to at the front end, the outlet of the pipe is the inlet of the block that the1463

pipe connects to at the back end.1464

We can describe any network (or �owcharts) as a set of pipes and modules, so1465

every module has a name, every pipe has a name, and both ends of every pipe is1466

connected to a module. We describe any power plant as a network with the format1467

in the input �le(Table 6.1). Once all modules and pipes are connected, we make sure1468

that it is connected properly, by iteratively optimize the inputs and outputs until1469

every connection is converged (internally consistent). The pipe can also count and1470


store the number iterations before they are internally consistent.1471

The system is hierarchical, a module can be a network of modules and pipes itself.1472

The structure of the program allow us to build very complicated things out of very1473

simple things, hence making it easy to extend the complexity a power plant design1474

relatively easily.1475

6.4 Reconcile - An iterative procedure1476

Think of the stream as being de�ned by a number of parameters p1, p2, ?, pn. On1477

the base class level this all you really know. A stream has a direction, it is supposed1478

to go from left to right (although there is nothing wrong with a physical �ow that1479

points in the opposite direction; some �ows may change directions). As a result we1480

have three �avors of the parameters: those on the input side of the pipe (which is1481

the output of the module), those on the output side, and a reconciled version. The1482

pipe has functions, to take the reconciled version and write it into the input and the1483

output. The pipe has a function that creates the reconciled version from the input1484

and output version. The pipe will need to know the number of parameters is has.1485

During construction of the �ow chart, the user can (must?) set all the values in the1486

reconciled version. These amount to the �rst guesses and they are then automatically1487

propagated to the input and output versions. In additions there have to be functions1488

for the modules to read, and to write the end of the pipe they are connected to. This1489

pretty much de�nes the base class of the pipe. One more important feature is that each1490

pipe has a �ag of how it reconciles. There are in e�ect three options for the reconcile.1491

One is the input will overwrite the output, and thus de�ne the reconciled value. The1492


second is that the output overwrites the input and thus de�nes the reconciled value.1493

The third is that the reconciled value is constructed as an average of the input and1494

the output, and both input and output are overwritten. The �rst option is used if1495

the input is �xed from the outside. (For example the amount of coal coming in is1496

speci�ed.) Because the input is �xed the iteration cannot change it. You could get1497

around this by de�ning a module which only has an output, which is held constant1498

in every iteration. (This may be a simpler implementation). The other case handled1499

by the �rst option is that the pipe is an output pipe that drains to the outside and1500

that is not speci�ed in its output, it takes whatever it can get. This, too could be1501

handled by a trivial module that can absorb anything coming in. An example is that1502

the electric output of the power plant is speci�ed. The second option has two cases1503

analogous to those handled in option one. Now the input is unspeci�ed, whatever1504

the downstream module "sucks in" is OK. For example, the amount of coal shoveled1505

in, will ultimately be determined by the amount of electricity generated. The other1506

situation is on the downstream end, if the output of the pipe overrules the input, then1507

the output is predetermined. E..g, the electricity is �xed. Finally, the third option is1508

sort of typical, the two sides of the pipe must agree and they have equal voting rights,1509

because both of them are attached to a module. In the future it is also possible, to1510

have an algorithm, which takes the entire �ow chart and tries to reconcile all the �ows1511

everywhere. E.g. think of all the mismatches adding up in squares, and then �nding1512

a solution directly.1513

On the module side one can load in all the input and output pipe parameters. It1514

probably would be useful to allocate space for a single array, x1, ?, xm, which contains1515


all those parameters. Then there is again an option to reconcile these numbers, by1516

using a set of equations Fkx1,?xm=0 There is a special subset of these functions,1517

Gkx1,?xm;x01,?,x0m=0 Here, the parameters with the subindex 0, refer to a �xed1518

set of parameters, which for example give the starting value of the parameters at the1519

beginning of an iteration. For example, the constraining equations may relate in�ows1520

and out�ows in a way that mass and energy is conserved, but they can be scaled by1521

an arbitrary factor. The "0-parameter" could introduce the average size of the plant1522

measured by all the in�ows and out�ows and it will hold this parameter constant1523

during the optimization. In other words, the "0-parameters" would be �xed during1524

one cycle of reconciliation of parameters, but they would be reset every time the1525

module is connected to new �ux values. The idea is that between the F constraints,1526

and G constraints, there are just enough equations to exactly �nd one solution to the1527

problem. (In some future implementations, we will �ag out, if we do not have enough1528

equations, or if we have too many, or if it is just impossible to solve the equations.)1529

The module now needs a set of methods which call in the stu� from the pipelines,1530

�ll all the parameters, and then call the reconciliation routine. By default this may1531

be a steepest descend iteration scheme, that starts with the initial guesses, and then1532

moves forward until the proper solution has been found. You may want to de�ne an1533

error bar you would accept. In e�ect, you will work out the solutions for each module1534

separately. Then you have all modules internally consistent, but the pipelines are1535

now inconsistent. Then you make the pipelines internally consistent, but this will1536

ruin the modules again. Hopefully, the iterations converge toward a global solution.1537

Then we can create an iterative scheme. We begin with a user guess which is fed into1538


all the streams. These by de�nition are consistent. Each module will internally re-1539

adjust all the inputs and outputs until we have a consistent solution for the module.1540

This, however, will create a discrepancy across the length of the pipe, which is �xed1541

in the next iteration step, but this will destroy the balance in the module again.1542

We do this until things have converged. Better convergence may be achieved, if we1543

create intermediate modules. I.e, at some point we can create a hierarchy of modules,1544

which will make it easier to do all the plumbing. Immediate actions: Create the full1545

structure in the pipes and in the base module. Decide whether the pipes come in three1546

�avors, or whether you want to add an out-side world module. E.g. a coal supply1547

unit, which only has an output, and it can either deliver as much coal as you like, e.g.1548

its reconciliation step is to accept the out�ow it has, or it could be a predetermined1549

�ow, in which case its reconciliation will bring it back to the design in�ow. The same1550

of course works for the out�ow side.1551

The advantage of the latter method is that it removes an additional layer of1552

complexity from the pipes. It may become even more interesting if the boundary1553

conditions become more complex. For example, you may decide that air �ow has to1554

be adjusted so that the air coming through has 1So my suggestion for the decision is1555

to handle the outside world on the module level. Try out a simple steepest descend.1556

My suggestion is to create a trial unit with the furnace. You have air, coal as input1557

streams, heat, �ue gas as output streams. Temperature is for now a �xed parameter.1558

Excess oxygen (could be zero) is a �xed parameter, heat �ow follows from the heat of1559

combustion. Air �ow, coal �ow, and heat �ux and �ue gas stream are tied together1560

with equations. You could �x the heat �ux with one more equation (e.g. x3 - x03 =1561


0), or you could impute three heat �uxes from coal input, heat output, and air input.1562

The goal is to hold this average constant. This last equation will �x the size of the1563

unit, and it depends on the initial guess, so it will change from guess to guess, as it1564

must in order to provide just the right amount of electricity.1565

6.5 Reconcile algorithm: numerical routine for solv-1566

ing a system of equations1567

A set of m parameters x1, x2...xm satisfy a set of equations as below.1568

Fi(x1, x2, ...xm) = 0

where i is the equation number, i∈ [1, k] , k ≥ m.1569

This can be simpli�ed to1570

Fi(xj) = 0

where j∈ [1,m] .1571

For a complete system, with the initial guess of all the parameters, you'll get1572

Fi(x(0)j ) = A

(0)i

After n'th iteration, you'll get1573

Fi(x(n)j ) = A

(n)i (6.1)

Take Fi(x(n)j + ∆x

(n)j ) for Taylor series expansion including the �rst derivatives,1574

you'll get.1575

Fi(x(n)j + ∆x

(n)j ) = Fi(x

(n)j ) +

m∑j=1

(δFi(x

(n)j )

δxj×∆x

(n)j ) (6.2)


Assume at n'th iteration the system converges. You'll have1576

Fi(x(n)j + ∆x

(n)j ) = 0 (6.3)

Given Equation(1) (2) and (3), you can have1577

m∑i=1

(δFi(x

(n)j )

δx(n)j

×∆x(n)j ) = −A(n)

i (6.4)

Equation(4) can be simpli�ed to a linear system of equations of ∆x(n)j :1578

Gi(∆x(n)j ) = 0 (6.5)

For each iteration of n, you can use a linear solver (i.e matrix solve) to �nd ∆x(n)j .1579

Subsequently, you can solve for x(n+1)j based on the following equation1580

x(n+1)j = x

(n)j + ∆x

(n)j (6.6)

The iteration continues, until∑m

j=1 |∆x

(n)j

x(n)j

| < ε, where ε = 0.1%. 0.1 is generically1581

conservative assumption, it's somewhat arbitrary [?].1582

Finding the optimized step for the true optimum But you may say, I don't1583

dare to go this far because the steps are too large. But the direction is correct1584

because it follows the gradient. So if this is not stable, you can go in smaller steps1585

by introducing λi, and modify Equation (4) to1586

m∑i=1

(δFi(x

(n)j )

δx(n)j

×∆x(n)j ) = −λi × A(n)

i (6.7)

If assume λi = 1, you are actually directly solving Equation (4), but the system1587

may be unstable (or fail to converge). λi = 13is a generically conservative assumption,1588

it is more stable, but it needs more iterations.1589


The next thing you can do is to vary λi such that1590

min ‖A(n+1)i (λi)‖

or1591

min∑k

{A(n+1)i (λi) · A(n+1)

i (λi)}

where λi ∈ [0, 1]. When λi = 0, A(n+1)i (λi) = A

(0)i .1592

Equation (6) is modi�ed to1593

x(n+1)j (λi) = x

(n)j + λi ×∆x

(n)j (6.8)

If you plot ‖A(n+1)i (λi)‖ against λi, the slope of the plot is negative because if it's1594

all di�erentiable, it starts with a negative slope.1595

Typically the lowest point is neither 13or 1. The more nonlinear it is, the further it1596

is away from 1. If the problem is strictly linear, then the optimum is λi = 1.1597

6.6 Reconcile implementation1598

Let M(n)ij be a k-by-k Jacobian matrix, where1599

M(n)ij =

δFi(x(n)j )

δx(n)j

You need a linear solver to solve equation1600

Ci ×M (n)ij = Bj (6.9)

where1601

Ci = ∆x(n)j


1602

Bj = −λi × A(n)i

Ci = Bj × (M(n)ij )−1

Once this is solved, you can solve for xj iteratively.1603

1604

Once xj is solved, you can calculate Ani by plug in the xj into equation (1).1605

Then you can say, let me calculate various value of ‖A(n+1)i (λi)‖ for various choice of1606

λi.1607

1608

λi =λi2

else1609

you found the optimum.1610

6.7 Discussion of Newton-Raphson method1611

The method described above is essentially Newton-Raphson method. It is a highly1612

e�cient and powerful method for �nding successively better approximations to zeroes1613

(or roots) of a real-value function[?]. In general its convergence rate is quadratic (the1614

error is essentially squared at each step), which means that the number of accurate1615

digits roughly doubles in each step.1616

Though it's a powerful technique, there are some limitation with the method. For1617


example, the method may fail to converge if the derivative of the function is not1618

continuous, or if the derivative is zero (where the tangent line overshoots the desired1619

root), or if the initial guess is too far from true zero.1620

To increase the convergence stability, a number of studies (Press et al.(1992))1621

presented various improvement of Newton-Raphson method. However, the imple-1622

mentation of the improved method is beyond the scale of this work.1623

Another limitation on Newton's method, comes from the requirement that the1624

derivative be calculated directly. This is di�cult in most practical problems, where1625

functions may be given by a long and complicated formula, and hence an analytical1626

expression for the derivative may be di�cult to obtainable. In these situations, it may1627

be appropriate to approximate the derivative by using the slope of a line through two1628

points on the function, or the Secan method. This has slightly slower convergence1629

than Newton's method but does not require the existence of derivatives. The Secan1630

method is a popular choice by developers of large scale computer systems, because the1631

use of a di�erent quotient in place of the derivative in Newton's method implies that1632

the addition code to compute the derivative need not be maintained. In practice,1633

the advantages of maintaining a smaller code base usually outweigh the superior1634

convergence characteristics of Newton's method.[?] Having said that, this work chose1635

Newton-Raphson method because of the current development is still relatively small1636

scale, Secant method may be a consideration for future development.1637


6.8 Penalty1638

As described in the previous chapter, there are three levels of penalties in the1639

program: module level penalty, plant level penalty, and pathway level penalty.1640

Module level Penalty1641

Module level penalty characterize various module properties attribute to the mod-1642

ule alone, compared to a perfect anchor point. For example, module capital cost,1643

module operating and maintenance cost, etc.1644

Module capital cost is calculated by scaling the capital cost of the individual1645

operating units in a reference plant (equation 6.8). Inline with EPRITAG[], the1646

reference plant is chosen to be a 500 MW plant, the capital cost of pulverize PC,1647

subcrital PC, and supercritical PC is taken from the DOE Parson 2000 study. The1648

breakdown of module size and cost of the reference plant are listed in table ??. Scaling1649

factor is chosen to be 0.28 based on EPRI TAG [?]. Unit size are measure by di�erent1650

parameters in di�erent modules (Table ??).1651

CapCost = CapCostref ∗ ScalingFactor

1652

ScalingFactor = { size

sizeref}α

1653

Pm,capcost = Constant1× CapCost

Module operating and maintenance costs consists of �xed cost, and variable cost.1654

The breakdown of the operating and maintenance costs can be found in table ??.1655


Labor cost is included in plant operating and maintenance costs, rather the module1656

operating and maintenance costs, to account for researcher and other workers in1657

addition to the operating labor at the at the power plant.1658

Pm,oamcost = Constant2×OAMCost

Implementation of the module level penalty is relatively easy. A penalty function1659

is created as virtual function in each module, to account for the calculation of module1660

level penalty. A size function is created also as virtual function in each module, to1661

account for di�erent measurement of unit sizes.1662

Plant level penalty1663

On plant level, penalties includes thermal e�ciency penalty, plant capital cost,1664

plant operating and maintenance (OAM) cost, plant infrastructural penalty, and emis-1665

sion penalty, in which capital cost and emission penalty are functions of time. There1666

are a number of assumptions: �rst, we assume that the same technology becomes1667

cheaper as time passes by. In other words, the same power plant design has unique1668

a capital cost number at each time, but multiple cost numbers for a period of time.1669

Since we calculate the plant cost by adding up the module capital cost and module1670

OAM cost, a correction factor at plant level is added to account for the time.1671

Plant footprint and e�ciencies are physical measures and the preference of the1672

footprint and e�ciencies are considered to be constant. However, one can argue that1673

as time goes by, less land is available hence the penalty of plant footprint should be1674

a function of time as well.1675


In terms of emissions, we assume each time is characterized by a set of emissions1676

regulatory state. In this work, we designed regulatory states as shown in table X.1677

Instead of trying to predit when CO2 regulation comes into force, we use ti to represent1678

the time that CO2 regulation comes into force, whenever that is.1679

Pplant = Pη +∑

Pmodule + Pinfrtr + Pemissions

where1680

Pη = checkproposal1681 ∑

Pmodule = TF ×∑

Pm,capcost +∑

Pm,oamcost1682

TF = tbeta1683

Pinfrtr = 1.25 ∗∑

Pm,footprint1684

Pm,footprint = Constant× footprint

where the fudge factor 1.25 accounts for additional room in the power plant that's1685

not occupied by any modules. The cross section area of each module can be found in1686

table ??.1687

Pemissions =∑

Pemissions,M

where M include SO2, PM, NOX, Hg and CO2 emissions.1688

Pemissions,SO2 = KSO2 × SO2Emissions1689

Pemissions,PM = KPM × PMEmissions


1690

Pemissions,NOx = KNOx ×NOxEmissions1691

Pemissions,Hg = KHg ×HgEmissions1692

Pemissions,CO2 = KCO2 × CO2Emissions

Implementation of plant level penalty is straight forward. A penalty function at1693

�owsheet (plant) level is created, to account for various aspect of plant level penalty,1694

i.e. e�ciency, emissions, and module level penalty summation.1695

Pathway level penalty1696

Pathway level penalties characterize penalties due to three aspects. Firstly, the1697

introduction of a new technology, which was not used in the immediately previous1698

design; Secondly, the removal of an existing technology which was used in the imme-1699

diately previous design; Lastly, the introduction of a brand new technology, which1700

was not used in any of the previous designs.1701

Additionally, each choice in the sequence is characterized by a regulatory state,1702

describing the stringency and the threshold of the emission level one has to obey,1703

otherwise, an in�nite penalty will be applied. For example, in the �rst choice, no1704

emission regulation is applied. Gradually, SOx,NOx,PM,Hg and CO2 regulations1705

and emission standards will be added to characterize the regulatory states for each1706

additional choice.1707

Ppathway = checkproposal

CONSTANTS ARE CHOSEN TO BE BECAUSE...1708


Implementation of pathway level penalties applies exhaustive search in this work.1709

In order to �nd the best sequence of �owsheets from a list of all possible �owsheets,1710

one needs to build the sequence as you go. This is similar to Knuth's line breaking1711

algorithm, in which a paragraph layout is being built as one optimize for the best1712

layout. Potential breakpoints are identi�ed and grouped into a list (named "active1713

list"), the penalties of breaking at each individual breakpoints are calculated and1714

compared for the best layout. Similarly, in the �owsheetlist (or pathway construction),1715

the penalties of connecting the existing but incomplete pathway, with all possible1716

plant designs, towards a complete pathway, are calculated and compared. Such that1717

the choice with the lowest pathway penalty is chosen.1718

First-�t, best-�t and optimum-�t. In order to look ahead, demerits are calculated1719

such that the square of pathway level penalties are summed up, rather than simple1720

addition. Understand and explain why doing so will help you look ahead, redesign1721

and implement the pathway penalty functions.1722

Discuss whether one needs to stop as soon as the partial sum exceed the local1723

optimum??1724

Discuss weather one needs to compare every two �owsheets thoroughly, concep-1725

tually.1726

Optional: Implementation procedure First, one need to extract the block1727

names of the two �owsheets under comparison.1728

During the implementation, when a module is created, the count will increase by1729

one, if the count is zero, then the module is a new technology that has been used1730

before.1731


A list of existing modules, routine that compares the existing module with the1732

module being created, if used before, counts adds one, otherwise, additional penalty1733

for new technology.1734

6.9 Parameter1735

Continuous Parameter1736

The parameters at �owsheet level are continuous. It has a range and a current1737

value. The value within the range is continuous.1738

Discrete Optimization1739

The parameters at �owsheetlist level are discrete. For example, the choice of the1740

plant designs at a speci�c time.1741

6.10 Optimization1742

The optimization at both �owsheet level and �owsheetlist level are discrete. The1743

method is an exhaustive search. The basic assumption is that between any steps, we1744

assume it's monotonic. The limitation is that the choice of steps is very important.1745

If the step is too big, then it may or may not be monotonic between any steps. If the1746

steps are too small, then it's expensive computationally.1747


6.11 Ongoing development1748

6.11.1 FlowsheetBlock: Creating types on the �y1749

By connecting basic modules from the software library, one can create new modules1750

with new con�gurations that do not exist before. One can further use the new modules1751

repeatedly as new "basic modules" in future designs. Therefore, one is no longer1752

limited to using only the library that came with the software, instead, one can create1753

his/her own library serving for a speci�c purpose. This is especially attractive to1754

engineers with speci�c focus of research. The ability to allow researchers build their1755

own libraries on the �y, and the ability to use the new libraries repeatedly in future1756

work, is revolutionary compared to existing modeling tools (for example Aspen Plus).1757

The implementation of such feature is hierarchical, where a graph consists of1758

subgraphs. For example, given a graph consists of many basic modules, one can1759

replace a basic module(s) with a subgraph(s), which consists of a number of basic1760

modules or subgraphs, creating di�erent levels of details based on one's preference.1761

This allows researchers describe the module physics/chemistry at the level of details1762

in a customized manner.1763


Table 6.1: Input File (Flowsheet) De�nition (Format)

%Flowsheet: 〈name〉: size : e�ciency : fuel type%Blocks: Block NumberType1: Name1, Name2, ..., NamekType2: Name1, Name2,......, Namej...Type i: Name1, Name2,......, Namej%Streams: Stream NumberType1: Name1, Name2, ....., NamekType2: Name1, Name2,......, Namej...Type i: Name1, Name2,......, Namej%ConnectName1: (inputS1,....,inputSi) B1 (outputS1,....,outputSi)Name2: (inputS1,....,inputSi) B2 (outputS1,....,outputSi)...Namei: (inputS1,....,inputSi) Bi (outputS1,....,outputSi)%End Flowsheet :〈name〉

Appendix A1764

Introduction to TEX1765

This report is written in LATEX a typesetting program using TEX language.1766

A.1 What is TEX1767

TEX is a typesetting language invented by Donald Knuth. It is famous for a well1768

designed and extremely e�cient strategy and computational algorithm for ranking1769

di�erent typesetting layouts as more or less optimal [Knuth 1981]. In this approach,1770

an ideal typesetting layout is considered as the anchor point, the di�erences between1771

the actual typesetting layout and the anchor point is penalized with a numeric penalty.1772

Di�erent aspects of the layout incur di�erent penalties. The relative weights of these1773

penalties can be chosen appropriately by a user, who has speci�c goals, as in the1774

typesetting example, a speci�c aesthetic approach. The algorithm calculates the1775

penalties and determines an optimal layout with the least penalty.1776

TEX penalize an actual layout compare to an ideal layout, in several aspects. For1777

110

Appendix A: Introduction to TEX 111

example, if a paragraph is too dense, there is a penalty, if it's too sparse, there's1778

another penalty. If there is hyphenation, there's additional penalty. Users can choose1779

their own weights on these penalties. For example, a user with weak vision may1780

choose to put a relatively big weight on dense penalty, while preferring sparse layout1781

with large font. On the other hand, a user who's motivated to save space, might put a1782

relatively big weight on sparse penalty, while concerns little with a dense layout. An1783

optimal layout for a user with weak vision might be a disaster for a user motivated to1784

save space. TEX provides a method to allow users choose optimal layout with their1785

own taste in a �exible and e�cient manner.1786

A.2 The algorithm of breaking paragraphs into lines1787

r

Figure A.1: Examples of breaking a pargraph into lines

Bibliography1788

[Lackner 2001] T.M. Yegulalp, K. Lackner H.J.Ziock A Review of Emerging Tech-1789

nologies for Sustainable use of Coal Power Generation. International Journal1790

of Surface Mining Reclamation and Environment, 2001 (15), pp 52-681791

[Lackner 2002] K. Lackner Can Fossil Carbon Fuel the 21st Century. International1792

Geology Review, 2002 (44), pp 1122-11331793

[Gri�n 2005] T. Gri�n, S.G.Sundkvist, K Asen, T Bruun Advanced Zero Emission1794

Gas Turbine Power Plant Journal of Engineering for Gas Turbines and Power,1795

2005 (127), pp 81-851796

[Knuth 1981] D. E. Knuth, M.F. Plass Breaking Paragraphs into Lines Software-1797

Practice and Experience, 1981 (11), pp 1119-11841798

[MIT, 2007] Ansolabehere, S et al. The Future of Coal: An interdisciplinary MIT1799

study Massachusetts Institute of Technology, Cambridge MA, 20071800

[IPCC, 2005] IPCC IPCC special report on carbon dioxide capture and storage Cam-1801

bridge University Press, 2005, 442 p.1802

112

Bibliography 113

[Henderiks, 1994] Hendriks, C. Carbon dioxide removal from coal-�red power plants,1803

Dissertation Utrecht University, Netherlands, 259 pp.1804

[Croiset and Thambimuthu, 2000] Croiset, E. and K.V. Thambimuthu Coal combus-1805

tion in O2/ CO2 Mixtures Compared to Air Canadian Journal of Chemical1806

Engineering, 78, 402-407.1807

[IEA GHG, 2003] IEA GHG Potential for improvements in gasi�cation combined1808

cycle power generation with CO2 Capture IEA Greenhouse Gas R& D Pro-1809

gramme, UK, 2003.1810

[Unruh, 2000] Unruh, G. C. Understanding carbon lock-in Energy Policy 2000,28,1811

817-830.1812

[Unruh, 2002] Unruh, G. C. Escaping carbon lock-in Energy Policy 2002, 317-325.1813

[Unruh, 2006] Unruh, G. C. Globalizing carbon lock-in Energy Policy 2006,34, 1185-1814

1197.1815

[B Stroustrup, 2000] B Stroustrup The C++ Programming Language Addison-1816

Wesley, ISBN 0-201-88954-4 and 0-201-70073-5.1817

[U Siegenthaler, 1987] Siegenthaler, U. and Oeschger, H Biospheric CO2 Emissions1818

During the Past 200 years reconstructed by Deconvolution of Ice Core Data1819

Tellus 1987, 398, 140-1541820

[Keeling, C.D. et al, 1995] Keeling, C.D., Whorf, T.P. Wahlem, M. and van der1821

Plicht, J. Interannual Extremes in the Rate of Rise of Atmospheric Carbon1822

Dioxide since 1980 Nature 1995, 375, 666-6701823

Bibliography 114

[B. Federico, 2009] Barrai Federico Thesis Proposal: The interaction between trans-1824

port processs and chemical kinetics in selective catalytic reactors1825

[M Hillier, 2002] Mark S. Hillier and Frederick S. Hillier Conventonal optimization1826

techniques International Series in Operations Research & Management Science1827

, 48, 3-201828

[C. A. Coello, 2002] Carlos A. Coello Evolutionary Multi-objective Optimization: A1829

critical review International Series in Operations Research & Management Sci-1830

ence , 48, 1171831

[Sarker, R et al, 2002] Sarker, R; Mohammadian, M; Yao, X Evolutionary Optimiza-1832

tion Secaucus, NJ, USA: Kluwer Academic Publishers, 2002.1833

[Miettinen, 1998] Miettinen, K. M. Nonlinear Multiobjective Optimization Kluwer1834

Academic Publishers, Boston, Massachusetts.1835

[K. Jordal, O. Bolland, 2005] K. Jordal, O. Bolland Optimization with generic algo-1836

rithms of a gas turbine cycle with H2-separation membrane reactor for CO21837

capture International Journal of Green Energy, 2, 167-1801838

[Goldberg, D. E. 1989] Goldberg, D. E. Genetic Algorithms in Search, Optimization1839

& Machine Learning. USA: Addison-Wesley Publ. Co.1840

[B. Möller et al, 2006] B. Möller, M. Assadi, I. Potts CO2-free power generation in1841

combineed cycles - Integration of post-combustion separation of carbon dioxide1842

in the steam cycle Energy, 31, 1520-15321843

Bibliography 115

[B. Möller et al, 2003] B. Möller, et al, Optimization of an SOFC/GT system with1844

CO2-capture Energy, 31, 1520-15321845

[M. Valdes et al, 2003] M. Valde s, M. D. Dura n, A Rovira Thermoeconomic opti-1846

mization of combined cycel gas turbine power plants using genetic algorithms1847

Applied Thermal Engineering, 23, 2169-21821848

[F. Cotana, 2003] F. Cotana, M. Goretti Environmental impact of power plants:1849

Comparative criteria of evaluation ??,??, ??1850

[A. Chatzimouratidis, 2007] A. Chatzimouratidis, P.A.Pilavachi Multicritria evalua-1851

tion of power plants impact on the living standard using the analytic hierarchy1852

process Energy Policy, 36, 20081853

[W. Hensen, 2006] W. Hensen, et al Custom process unit models in a �owsheet1854

simulator-user experiences Co-LaF meeting, Cannes (F), 20061855

[E Roy, 1998] Ellen Roy The Uniform Generation Performance Standard: Connect-1856

ing Electricity Industry Restructuring and Air Quality Improvement The Elec-1857

tricity Journal, Volume 11, Issue 1, January-February 1998, Pages 56-631858

[EPA, 2009] Michigan Air Permits system- Acid Rain Program The science of Acid1859

Rain Source: U.S. EPA Airmarkets and Acid Rain Project websites1860

[Wark, K., 1997] Wark, K., Warner, C.F., Air Pollution, Its Origin and Control1861

(Third ed.) Prentice Hall, 31-371862

[D. W. Keith et al, 2004] D. W. Keith, J. F. DeCarolis, et al The in�uence of large-1863

Bibliography 116

scale wind-power on global climate. Proceedings of the National Academy of1864

Sciences, 101: 16115-16120.1865

[K. S. Lackner, et al, 2001] Lackner, K. S., Grimes, P., and Ziock, H. J. Capturing1866

carbon dioxide from air. In Proceedings of the First National Conference on1867

Carbon Sequestration,Washington, DC.1868

[Howes R, Fainberg A. 1991] Howes R, Fainberg A. The Energy Sourcebook: A Guide1869

to Technology, Resources and Policy, Ruth Howes, Anthony Fainberg (eds).1870

American Institute of Physics: New York.1871

[Harris R. C., Rudd J.W.M. 2007] Harris R. C., Rudd J.W.M. Whole-ecosystem1872

study shows rapid �sh-mercury response to changes in mercury deposition1873

PNAS, 104, 20071874

[Lackner 2001] T.M. Yegulalp, K. Lackner H.J.Ziock A Review of Emerging Tech-1875

nologies for Sustainable use of Coal Power Generation. International Journal1876

of Surface Mining Reclamation and Environment, 2001 (15), pp 52-681877

[Lackner 2002] K. Lackner Can Fossil Carbon Fuel the 21st Century. International1878

Geology Review, 2002 (44), pp 1122-11331879

[Gri�n 2005] T. Gri�n, S.G.Sundkvist, K Asen, T Bruun Advanced Zero Emission1880

Gas Turbine Power Plant Journal of Engineering for Gas Turbines and Power,1881

2005 (127), pp 81-851882

[Knuth 1981] D. E. Knuth, M.F. Plass Breaking Paragraphs into Lines Software-1883

Practice and Experience, 1981 (11), pp 1119-11841884

Bibliography 117

[MIT, 2007] Ansolabehere, S et al. The Future of Coal: An interdisciplinary MIT1885

study Massachusetts Institute of Technology, Cambridge MA, 20071886

[IPCC, 2005] IPCC IPCC special report on carbon dioxide capture and storage Cam-1887

bridge University Press, 2005, 442 p.1888

[Henderiks, 1994] Hendriks, C. Carbon dioxide removal from coal-�red power plants,1889

Dissertation Utrecht University, Netherlands, 259 pp.1890

[Croiset and Thambimuthu, 2000] Croiset, E. and K.V. Thambimuthu Coal combus-1891

tion in O2/ CO2 Mixtures Compared to Air Canadian Journal of Chemical1892

Engineering, 78, 402-407.1893

[IEA GHG, 2003] IEA GHG Potential for improvements in gasi�cation combined1894

cycle power generation with CO2 Capture IEA Greenhouse Gas R& D Pro-1895

gramme, UK, 2003.1896

[Unruh, 2000] Unruh, G. C. Understanding carbon lock-in Energy Policy 2000,28,1897

817-830.1898

[Unruh, 2002] Unruh, G. C. Escaping carbon lock-in Energy Policy 2002, 317-325.1899

[Unruh, 2006] Unruh, G. C. Globalizing carbon lock-in Energy Policy 2006,34, 1185-1900

1197.1901

[B Stroustrup, 2000] B Stroustrup The C++ Programming Language Addison-1902

Wesley, ISBN 0-201-88954-4 and 0-201-70073-5.1903

Bibliography 118

[U Siegenthaler, 1987] Siegenthaler, U. and Oeschger, H Biospheric CO2 Emissions1904

During the Past 200 years reconstructed by Deconvolution of Ice Core Data1905

Tellus 1987, 398, 140-1541906

[Keeling, C.D. et al, 1995] Keeling, C.D., Whorf, T.P. Wahlem, M. and van der1907

Plicht, J. Interannual Extremes in the Rate of Rise of Atmospheric Carbon1908

Dioxide since 1980 Nature 1995, 375, 666-6701909

[B. Federico, 2009] Barrai Federico Thesis Proposal: The interaction between trans-1910

port processs and chemical kinetics in selective catalytic reactors1911

[M Hillier, 2002] Mark S. Hillier and Frederick S. Hillier Conventonal optimization1912

techniques International Series in Operations Research & Management Science1913

, 48, 3-201914

[C. A. Coello, 2002] Carlos A. Coello Evolutionary Multi-objective Optimization: A1915

critical review International Series in Operations Research & Management Sci-1916

ence , 48, 1171917

[Sarker, R et al, 2002] Sarker, R; Mohammadian, M; Yao, X Evolutionary Optimiza-1918

tion Secaucus, NJ, USA: Kluwer Academic Publishers, 2002.1919

[Miettinen, 1998] Miettinen, K. M. Nonlinear Multiobjective Optimization Kluwer1920

Academic Publishers, Boston, Massachusetts.1921

[K. Jordal, O. Bolland, 2005] K. Jordal, O. Bolland Optimization with generic algo-1922

rithms of a gas turbine cycle with H2-separation membrane reactor for CO21923

capture International Journal of Green Energy, 2, 167-1801924

Bibliography 119

[Goldberg, D. E. 1989] Goldberg, D. E. Genetic Algorithms in Search, Optimization1925

& Machine Learning. USA: Addison-Wesley Publ. Co.1926

[B. Möller et al, 2006] B. Möller, M. Assadi, I. Potts CO2-free power generation in1927

combineed cycles - Integration of post-combustion separation of carbon dioxide1928

in the steam cycle Energy, 31, 1520-15321929

[B. Möller et al, 2003] B. Möller, et al, Optimization of an SOFC/GT system with1930

CO2-capture Energy, 31, 1520-15321931

[M. Valdes et al, 2003] M. Valde s, M. D. Dura n, A Rovira Thermoeconomic opti-1932

mization of combined cycel gas turbine power plants using genetic algorithms1933

Applied Thermal Engineering, 23, 2169-21821934

[F. Cotana, 2003] F. Cotana, M. Goretti Environmental impact of power plants:1935

Comparative criteria of evaluation ??,??, ??1936

[A. Chatzimouratidis, 2007] A. Chatzimouratidis, P.A.Pilavachi Multicritria evalua-1937

tion of power plants impact on the living standard using the analytic hierarchy1938

process Energy Policy, 36, 20081939

[W. Hensen, 2006] W. Hensen, et al Custom process unit models in a �owsheet1940

simulator-user experiences Co-LaF meeting, Cannes (F), 20061941

[E Roy, 1998] Ellen Roy The Uniform Generation Performance Standard: Connect-1942

ing Electricity Industry Restructuring and Air Quality Improvement The Elec-1943

tricity Journal, Volume 11, Issue 1, January-February 1998, Pages 56-631944

Bibliography 120

[EPA, 2009] Michigan Air Permits system- Acid Rain Program The science of Acid1945

Rain Source: U.S. EPA Airmarkets and Acid Rain Project websites1946

[Wark, K., 1997] Wark, K., Warner, C.F., Air Pollution, Its Origin and Control1947

(Third ed.) Prentice Hall, 31-371948

[D. W. Keith et al, 2004] D. W. Keith, J. F. DeCarolis, et al The in�uence of large-1949

scale wind-power on global climate. Proceedings of the National Academy of1950

Sciences, 101: 16115-16120.1951

[K. S. Lackner, et al, 2001] Lackner, K. S., Grimes, P., and Ziock, H. J. Capturing1952

carbon dioxide from air. In Proceedings of the First National Conference on1953

Carbon Sequestration,Washington, DC.1954

[Howes R, Fainberg A. 1991] Howes R, Fainberg A. The Energy Sourcebook: A Guide1955

to Technology, Resources and Policy, Ruth Howes, Anthony Fainberg (eds).1956

American Institute of Physics: New York.1957

[Harris R. C., Rudd J.W.M. 2007] Harris R. C., Rudd J.W.M. Whole-ecosystem1958

study shows rapid �sh-mercury response to changes in mercury deposition1959

PNAS, 104, 20071960

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