DEVELOPING A BASIS FOR PREDICTING AND ASSESSING

TRENDS IN CORE TRACKING IN THE BOILING WATER REACTOR COMMERCIAL POWER INDUSTRY

By

ANNA SMOLINSKA

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

2004

Copyright 2004

by

Anna Smolinska

To my family that has always been there for me. Thank you for your support and encouragement throughout my education.

iv

ACKNOWLEDGMENTS

I recognize Global Nuclear Fuel-Americas (GNF-A) for sponsoring this research

and providing all the necessary resources for the study. It was a great opportunity to do

research that focuses on an immediate challenge in the BWR industry today. I

specifically want to thank John Rea, an engineer at GNF-A, for realizing the need and

importance of this study, and mentoring me throughout the process. I learned a lot and

also had an opportunity to contribute useful knowledge to the BWR industry. Additional

GNF-A engineers that I want to recognize for giving advice and guidance throughout the

study are Ken Gardner and Atul Karve. It was very helpful to work with experienced

engineers in the nuclear field.

I acknowledge all the faculty of the University of Florida Nuclear and Radiological

Engineering Department for providing me with guidance and knowledge throughout my

education there. I particularly thank Professor James Tulenko for being my committee

chair and graduate advisor. I also want to thank Dr. Edward Dugan and Dr. Jacob Chung

for being on my advisory committee.

I acknowledge all of the organizations that provided me scholarships and

fellowships during my pursuit to acquire my nuclear engineering degrees. These

organizations include the University of Florida Nuclear and Radiological Engineering

Department, the National Academy for Nuclear Training (NANT), the American Nuclear

Society (ANS), and the Department of Energy (DOE).

v

Finally, I want to thank my family for their support and encouragement throughout

my education.

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv

LIST OF TABLES........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

ABSTRACT.......................................................................................................................xv

CHAPTER 1 BACKGROUND ..........................................................................................................1

Nuclear Basics ..............................................................................................................1 Characteristics of Nuclear Power .................................................................................4

Safety.....................................................................................................................4 Economics .............................................................................................................5 Environmental Benefits .........................................................................................6 Nuclear Waste .......................................................................................................7 Reprocessing and Recycling..................................................................................9

Introduction to US Commercial Nuclear Reactors.....................................................10 The PWR .............................................................................................................10 The BWR.............................................................................................................12

The BWR Reactor Assembly......................................................................................14 BWR Cycle Design.....................................................................................................21

2 INTRODUCTION ......................................................................................................25

3 METHODS.................................................................................................................29

4 REFERENCE MULTICYCLE...................................................................................32

Cycle Characteristics ..................................................................................................32 Reference Bundle........................................................................................................35 Cold Criticals ..............................................................................................................36

5 PLANT MEASUREMENT PERTURBATIONS ......................................................39

6 FUEL MANUFACTURING PERTURBATIONS.....................................................47

vii

7 CONCLUSION...........................................................................................................58

APPENDIX A REFERENCE CYCLE SPECIFICS...........................................................................60

Cycle N Characteristics ..............................................................................................60 Cycle N Rod Pattern Results ...............................................................................66 Cycle N Hot Excess and SDM ............................................................................76 Cycle N TIP Plots................................................................................................77

Cycle N+1 Characteristics ..........................................................................................80 Cycle N+1 Rod Pattern Results...........................................................................86 Cycle N+1 Hot Excess and SDM ........................................................................96 Cycle N+1 TIP Plots............................................................................................97

Cycle N+2 Characteristics ........................................................................................100 Cycle N+2 Rod Pattern Results.........................................................................106 Cycle N+2 Hot Excess and SDM ......................................................................117 Cycle N+2 TIP Plots..........................................................................................118

Cycle N+3 Characteristics ........................................................................................121 Cycle N+3 Rod Pattern Results.........................................................................127 Cycle N+3 Hot Excess and SDM ......................................................................137 Cycle N+3 TIP Plots..........................................................................................138

B FUEL BUNDLE FIGURES .....................................................................................141

LIST OF REFERENCES.................................................................................................153

BIOGRAPHICAL SKETCH ...........................................................................................155

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LIST OF TABLES

Table page 4-1 General Cycle Parameters ........................................................................................33

5-1 Description of Plant Measurement Perturbations.....................................................40

5-2 Summary of Results from Plant Measurement Perturbations ..................................40

6-1 Description of Fuel Manufacturing Perturbations....................................................48

6-2 Summary of Results from Fuel Manufacturing Perturbations .................................48

A-1 Bundle Information Cycle N ....................................................................................60

A-2 Cycle N Cold Critical Data ......................................................................................75

A-3 Cycle N Hot Excess and SDM Data.........................................................................76

A-4 Bundle Information Cycle N+1................................................................................80

A-5 Cycle N+1 Cold Critical Data ..................................................................................95

A-6 Cycle N+1 Hot Excess and SDM Data ....................................................................96

A-7 Bundle Information Cycle N+2..............................................................................100

A-8 Cycle N+2 Cold Critical Data ................................................................................116

A-9 Cycle N+2 Hot Excess and SDM Data ..................................................................117

A-10 Bundle Information Cycle N+3..............................................................................121

A-11 Cycle N+3 Cold Critical Data ................................................................................136

A-12 Cycle N+3 Hot Excess and SDM Data ..................................................................137

ix

LIST OF FIGURES

Figure page 1-1 PWR System ............................................................................................................12

1-2 The BWR System.....................................................................................................13

1-3 BWR Reactor Vessel Assembly...............................................................................14

1-4 A. Cross-Sectional View of BWR Core, B. Control Rod Banks .............................17

1-5 Cross-Sectional View of BWR Fuel Module ...........................................................18

1-6 BWR Fuel Assemblies and Control Rod Module ....................................................19

1-7 Cross-Sectional View of BWR Fuel Bundle............................................................20

1-8 Bias Eigenvalue Trend .............................................................................................22

2-1 Energy per Bundle as a Function of Number of Bundles in BWR Core .................27

2-2 Change in the Number of Bundles Needed for a 0.003 Error in Eigenvalue...........27

2-3 Change in the Total Fuel Cost for 0.003 Error in Eigenvalue (BWR).....................27

4-1 Thermal Margins for Cycles N to N+3 ....................................................................33

4-2 Reactor Power and Core Flow for Cycles N to N+3................................................34

4-3 Normalized Axial Core Parameters for Cycle N+3 .................................................34

4-5 Cold Critical Rod Patterns for MOC N+1................................................................37

5-1 Hot Delta Keff for Varied Flow by 5.0% Compared to Base Case..........................41

5-2 Hot Delta Keff for Varied Pressure by 2.0% Compared to Base Case ....................41

5-3 Hot Delta Keff for Varied Temperature by 0.4% Compared to Base Case .............42

5-4 Hot Delta Keff for Varied Power by 1.25% Compared to Base Case .....................42

5-5 Hot Delta Keff for Varied Power by 2.5% in Cycle N Compared to Base Case .....43

x

5-6 Hot Delta Keff for Varied Power by 2.50% Compared to Base Case .....................43

5-7 Delta Keff for Distributed Cold Critical Eigenvalues Compared to Base Case.......44

5-8 Delta Keff for Local Cold Critical Eigenvalues Compared to Base Case for the Power Increased 2.50% Case ....................................................................................44

5-9 Maximum Delta Keff Between Distributed and Any Local Cold Critical Eigenvalue Compared to Base Case..........................................................................45

5-10 Average Axial TIP Distributions for EOC N+3.......................................................46

6-1 Hot Delta Keff for Channel Geometry Variation Cases Compared to Base Case ...49

6-2 Hot Delta Keff for Clad Geometry Variation Cases Compared to Base .................49

6-3 Hot Delta Keff for Fuel Density Variation Cases Compared to Base Case.............50

6-4 Hot Delta Keff for Enrichment Variation Cases Compared to Base Case...............50

6-5 Delta Keff for Distributed Cold Critical Eigenvalues Compared to Base Case.......51

6-6 Delta Keff for Local Cold Critical Eigenvalues Compared to Base Case for Average Bundle Enrichment Increased 1.5% Case...................................................52

6-7 Maximum Delta Keff Between Distributed and Any Local Cold Critical Eigenvalue Compared to Base Case..........................................................................52

6-8 Average Axial TIP Distributions for BOC N+3.......................................................53

6-9 Average Axial TIP Distributions for BOC N+3.......................................................53

6-10 Hot Delta Keff for Gadolinium Concentration Variation Cases Compared to Base Case ................................................................................................................54

6-11 Delta Keff for Distributed Cold Critical Eigenvalues Compared to Base Case.......55

6-12 Delta Keff for Local Cold Critical Eigenvalues Compared to Base Case for Decreased Gadolinium Case ...................................................................................55

6-13 Maximum Delta Keff Between Distributed and Any Local Cold Critical Eigenvalue Compared to Base Case........................................................................56

6-14 Average Axial TIP Distributions for Cycle N+2 at 9811 MWd/MT .......................56

6-15 Average Axial TIP Distributions for EOC N ...........................................................57

A-1 Cycle N Assembly Locations by Bundle Type Number ..........................................60

xi

A-2 BOC Cycle N Exposure Distribution (GWD/T) ......................................................61

A-3 EOC Cycle N Exposure Distribution (GWD/T) ......................................................61

A-4 Cycle N Hot keff ......................................................................................................62

A-5 Cycle N Thermal Margins........................................................................................62

A-6 Cycle N Reactor Power and Core Flow ...................................................................63

A-7 Cycle N Core Pressure .............................................................................................63

A-8 Cycle N Core Inlet Temperature ..............................................................................64

A-9 Cycle N Core Bypass Flow ......................................................................................64

A-10 Cycle N BOC Axial Core Parameters ......................................................................65

A-11 Cycle N EOC Axial Core Parameters ......................................................................65

A-12 Cycle N BOC Cold Critical Rod Patterns ................................................................72

A-13 Cycle N MOC Cold Critical Rod Patterns ...............................................................73

A-14 Cycle N EOC Cold Critical Rod Patterns ................................................................74

A-15 Cycle N Predicted Hot Excess and SDM .................................................................76

A-16 Cycle N TIP results for 0 MWd/ST (BOC)..............................................................77

A-17 Cycle N TIP results for 4600 MWd/ST ...................................................................77

A-18 Cycle N TIP results for 8900 MWd/ST ...................................................................78

A-19 Cycle N TIP results for 15000 MWd/ST (EOR)......................................................78

A-20 Cycle N TIP results for 16450 MWd/ST (EOC)......................................................79

A-21 Cycle N+1 Assembly Locations by Bundle Type Number......................................80

A-22 BOC Cycle N+1 Exposure Distribution (GWD/T) ..................................................81

A-23 EOC Cycle N+1 Exposure Distribution (GWD/T) ..................................................81

A-24 Cycle N+1 Hot keff ..................................................................................................82

A-25 Cycle N+1 Thermal Margins....................................................................................82

A-26 Cycle N+1 Reactor Power and Core Flow...............................................................83

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A-27 Cycle N+1 Core Pressure .........................................................................................83

A-28 Cycle N+1 Core Inlet Temperature..........................................................................84

A-29 Cycle N+1 Core Bypass Flow..................................................................................84

A-30 Cycle N+1 BOC Axial Core Parameters..................................................................85

A-31 Cycle N+1 EOC Axial Core Parameters ..................................................................85

A-32 Cycle N+1 BOC Cold Critical Rod Patterns............................................................92

A-33 Cycle N+1 MOC Cold Critical Rod Patterns ...........................................................93

A-34 Cycle N+1 EOC Cold Critical Rod Patterns ............................................................94

A-35 Cycle N+1 Predicted Hot Excess and SDM.............................................................96

A-36 Cycle N+1 TIP results for 0 MWd/ST (BOC) .........................................................97

A-37 Cycle N+1 TIP results for 4600 MWd/ST ...............................................................97

A-38 Cycle N+1 TIP results for 8900 MWd/ST ...............................................................98

A-39 Cycle N+1 TIP results for 15000 MWd/ST (EOR)..................................................98

A-40 Cycle N+1 TIP results for 16250 MWd/ST (EOC)..................................................99

A-41 Cycle N+2 Assembly Locations by Bundle Type Number....................................100

A-42 BOC Cycle N+2 Exposure Distribution (GWD/T) ................................................101

A-43 EOC Cycle N+2 Exposure Distribution (GWD/T) ................................................101

A-44 Cycle N+2 Hot keff ................................................................................................102

A-45 Cycle N+2 Thermal Margins..................................................................................102

A-46 Cycle N+2 Reactor Power and Core Flow.............................................................103

A-47 Cycle N+2 Core Pressure .......................................................................................103

A-48 Cycle N+2 Core Inlet Temperature........................................................................104

A-49 Cycle N+2 Core Bypass Flow................................................................................104

A-50 Cycle N+2 BOC Axial Core Parameters................................................................105

A-51 Cycle N+2 EOC Axial Core Parameters ................................................................105

xiii

A-52 Cycle N+2 BOC Cold Critical Rod Patterns..........................................................113

A-53 Cycle N+2 MOC Cold Critical Rod Patterns .........................................................114

A-54 Cycle N+2 EOC Cold Critical Rod Patterns ..........................................................115

A-55 Cycle N+2 Predicted Hot Excess and SDM...........................................................117

A-56 Cycle N+2 TIP results for 0 MWd/ST (BOC) .......................................................118

A-57 Cycle N+2 TIP results for 4600 MWd/ST .............................................................118

A-58 Cycle N+2 TIP results for 8900 MWd/ST .............................................................119

A-59 Cycle N+2 TIP results for 15000 MWd/ST (EOR)................................................119

A-60 Cycle N+2 TIP results for 16250 MWd/ST (EOC)................................................120

A-61 Cycle N+3 Assembly Locations by Bundle Type Number....................................121

A-62 BOC Cycle N+3 Exposure Distribution (GWD/T) ................................................122

A-63 EOC Cycle N+3 Exposure Distribution (GWD/T..................................................122

A-64 Cycle N+3 Hot keff ................................................................................................123

A-65 Cycle N+3 Thermal Margins..................................................................................123

A-66 Cycle N+3 Reactor Power and Core Flow.............................................................124

A-67 Cycle N+3 Core Pressure .......................................................................................124

A-68 Cycle N+3 Core Inlet Temperature........................................................................125

A-69 Cycle N+3 Core Bypass Flow................................................................................125

A-70 Cycle N+3 BOC Axial Core Parameters................................................................126

A-71 Cycle N+3 EOC Axial Core Parameters ................................................................126

A-72 Cycle N+3 BOC Cold Critical Rod Patterns..........................................................133

A-73 Cycle N+3 MOC Cold Critical Rod Patterns .........................................................134

A-74 Cycle N+3 EOC Cold Critical Rod Patterns ..........................................................135

A-75 Cycle N+3 Predicted Hot Excess and SDM...........................................................137

A-76 Cycle N+3 TIP results for 0 MWd/ST (BOC) .......................................................138

xiv

A-77 Cycle N+3 TIP results for 4600 MWd/ST .............................................................138

A-78 Cycle N+3 TIP results for 8900 MWd/ST .............................................................139

A-79 Cycle N+3 TIP results for 15000 MWd/ST (EOR)................................................139

A-80 Cycle N+3 TIP results for 16250 MWd/ST (EOC)................................................140

B-1 Fuel Bundle A ........................................................................................................142

B-2 Fuel Bundle B.........................................................................................................143

B-3 Fuel Bundle C.........................................................................................................144

B-4 Fuel Bundle D ........................................................................................................145

B-5 Fuel Bundle E.........................................................................................................146

B-6 Fuel Bundle F .........................................................................................................147

B-7 Fuel Bundle G ........................................................................................................148

B-8 Fuel Bundle H ........................................................................................................149

B-9 Fuel Bundle I ..........................................................................................................150

B-10 Fuel Bundle J..........................................................................................................151

B-11 Fuel Bundle K ........................................................................................................152

xv

Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering

DEVELOPING A BASIS FOR PREDICTING AND ASSESSING TRENDS IN CORE TRACKING IN THE BOILING WATER REACTOR

COMMERCIAL POWER INDUSTRY

By

Anna Smolinska

May 2004

Chair: James S. Tulenko Major Department: Nuclear and Radiological Engineering

The commercial nuclear industry produces about 20% of the electrical power in the

United States. Currently, there are104 nuclear power plants licensed to operate in the

United States. All of these reactors are referred to as light water reactors (LWRs). Of the

104 LWRs, 69 are pressurized water reactors (PWRs) and 35 are boiling water reactors

(BWRs). Since the coolant boils in the core, BWRs are more complicated than PWRs in

the aspect of designing a cycle. This study contributes knowledge and insight to the

cycle design process of a BWR.

When designing a BWR cycle, it is necessary to estimate the bias eigenvalue trend

or nuclear design basis (NDB). The NDB, which has a large effect on cycle parameters

and is plant and cycle specific, is used to compensate for any bias arising from the use of

the nuclear computer code package to perform core calculations combined with other

uncertainties that are discussed in this thesis. Currently, history of previous cycles of a

plant or similar plants is used as a basis for predicting the NDB. However, due to

xvi

constant demands of higher energy output per cycle, and unexpected events during a

cycle, predictions become challenging. In addition to known variations, there may also

be unrecognized events that may cause the eigenvalue and other plant parameters to vary.

Considering that safety and cost can be greatly affected by incorrect predictions, it is

important to understand the NDB trends when doing calculations for a future cycle, or

evaluating eigenvalue drift for a current cycle. To aid in developing a basis for making

predictions, various perturbations in the areas of fuel manufacturing and plant

measurement were studied in a multicycle analysis. These perturbations have a range of

effects on several different cycle parameters. The results of this study are intended to

assist in the prediction and assessment of trends in the BWR industry.

1

CHAPTER 1 BACKGROUND

Electricity is an essential part of everyday life. People depend on electricity

constantly, and expect it to be readily available. There are many different energy

sources, which all have individual advantages and disadvantages. These energy sources

include coal, natural gas, nuclear, hydropower, geothermal, solar, wind, and biomass.

Out of all commercial energy sources, the second largest contributor of electricity in the

United States is nuclear power. The commercial nuclear industry produced about 20% of

the electricity generated in the United States in 2002, only behind the coal contribution of

50% [1]. Nuclear reactors also supplied about 16% of the world’s power in 2002,

making them the third largest contributor after coal and hydropower [2]. In the United

States, the first generation of commercial nuclear reactors began operation in the late

1950s, early 1960s. Currently, there are104 nuclear power plants licensed to operate in

the United States. All of these reactors are referred to as light water reactors (LWRs)

because of their use of regular water as opposed to heavy water. Of the 104 LWRs, 69

are pressurized water reactors (PWRs) and 35 are boiling water reactors (BWRs) [1]. As

a result of the significant contribution from nuclear reactors to both the United States and

the world’s electricity market, nuclear power is extremely valuable and has potential for

significant technological advances.

Nuclear Basics

Nuclear energy comes from a process called nuclear fission. Fission is the energy

releasing process, where a heavy nucleus splits into nuclei with smaller mass numbers.

2

The fission process occurs when a heavy fissionable nucleus captures a neutron. The

captured neutron puts the nucleus in an excited state, which causes it to split. When the

nucleus splits, it produces smaller nuclei that are called fission products. In addition to

these fission products, there is also a release of additional neutrons and energy during the

event. The additional neutrons may then go on and cause more fissions to result in a self

sustaining fission chain reaction. This process occurs when neutrons that are released

from one fission event proceed to cause another fission event and so on.

The only naturally occurring isotope that undergoes fission is uranium-235. Since

uranium-235 can fission following the absorption of a zero energy neutron, it is said to be

fissile. Other fissile isotopes are uranium-233, plutonium-239, and plutonium-241.

Nuclei like uranium-238 that can only fission when struck by energetic neutrons are

called fissionable but not fissile. There are also isotopes that are referred to as fertile.

Fertile isotopes are not fissile themselves, but can become fissile after neutron absorption.

Uranium-238 and thorium-232 are fertile isotopes [3]. These different isotopes have

certain probabilities or cross sections that are associated with the fission process,

depending on the energy of the incoming neutron. When neutrons are released from a

fission reaction they are high energy or fast neutrons, however, low energy or thermal

neutrons are the ones that have very high probability of causing fission in uranium-235.

As a result of the necessary characteristics to sustain the fission process, there are two

main ingredients to a light water thermal reactor. The ingredients include having enough

uranium-235 and sustaining a sufficient population of thermal neutrons. Since the natural

element of uranium contains 0.72 atom percent of uranium-235, with the remaining part

made up of uranium-238 and a trace of uranium-234, the process of enrichment is used to

increase the amount of uranium-235 for LWR nuclear fuel. To maintain a sufficient

3

population of thermal neutrons, nuclear power plants use a moderator to slow down the

fast neutrons produced by fission. In LWRs, water is used as both the moderator and the

coolant. Due to the high population of thermal neutrons in the reactor, which cause an

elevated occurrence of fission in the fuel, the fuel becomes used up or depleted. As the

fuel depletes, the number of uranium-235 atoms is decreased and the amount of fission

products is increased. Also, other isotopes are created by neutron absorption like

plutonium-239 and uranium-236. Fission products end up acting like a poison in the fuel

because they absorb neutrons without resulting in a fission and releasing energy.

The parameter that describes the intensity of the fission process is called the

multiplication factor or eigenvalue, designated by k. This factor is defined as the number

of fissions or fission neutrons in one generation divided by the number of fissions or

fission neutrons in the preceding generation. The eigenvalue can be used to describe

three different cases. One case is when k is less than 1, and the process is said to be

subcritical because the number of fissions decreases with time. The second case is when

k is greater than 1; the process is then described as supercritical because the number of

fissions increases with time. The final case is when k is equal to 1; this last condition is

described as critical and occurs when the chain reaction continues at a constant rate. The

nuclear industry utilizes this final condition to produce electricity from the energy that is

released from the controlled fission process. This energy is released within fuel pellets,

which are located in fuel rods, which are part of the fuel bundles in the core of a nuclear

plant. The released energy is converted to heat, which is transferred from the fuel rods to

water, which is then used to make steam, and finally goes through a turbine that creates

electricity.

4

Nuclear reactors enhance and control the fission chain reaction to maintain a

critical system, which is a complicated process that requires very detailed calculations.

The calculations take into account every process in the system and its physical

environment. In nuclear reactors the eigenvalue is referred to as keff (k effective), since

the power reactor is a finite system, which allows for the leakage of neutrons. Another

parameter that is used in the industry is reactivity, designated by ρ. Reactivity is a

measure of the change in the eigenvalue and is defined as the ratio of the eigenvalue

minus one, the quantity divided by the eigenvalue. Also, the neutron flux is a parameter

used to describe the distribution of neutrons in the core and approximates the number of

neutrons per cm^3/sec. (It is advantageous to maintain a flat or constant flux in the

reactor core to burn the fuel evenly.) These parameters are among the many that are

calculated when assessing a nuclear system. Besides reactivity based calculations, many

thermal hydraulic parameters are also calculated. There is a necessary coupling that has

to exist between the reactivity and thermal hydraulic calculations. To accomplish this

task, extensive computer codes have been developed throughout the history of the nuclear

industry.

Characteristics of Nuclear Power

Nuclear power seems to be controversial among the general public. This view is

largely due to the public’s lack of knowledge about the facts of the technology. In effect,

nuclear power is a reliable and beneficial source of electricity that is safe, economical,

and environmentally friendly.

Safety

There are many factors that contribute to the safety of nuclear power plants. These

factors include: having a security program and an operational review process regulated

5

by the federal government, continual plant modernization or upgrading, and advanced

containment structures, which act as a final shield to prevent the release of radiation.

Resulting from the efficient design and operation of U.S. nuclear plants, a negligible

amount of radiation is emitted. You receive more radiation flying roundtrip from New

York to Los Angeles, than you would receive living next door to a nuclear power plant

for a year [4]. The statistical field of risk assessment was used in the development of the

safety standards used in nuclear power plants. As a result, nuclear power plants have

extremely extensive safety features that were developed to satisfy very strict safety

standards. Safety systems proved to be effective during the one major nuclear power

plant accident in the United States, which occurred at the Three Mile Island Unit in 1979.

After scientific studies, the results showed that there was no serious reactivity release,

even though one third of the fuel in the reactor core melted. Although the accident did

not have any serious effect on the environment and did not endanger the public, the

industry took steps to further improve the already stringent safety systems and procedures

in nuclear power plants to ensure that a similar accident would not occur again [4].

Economics

Nuclear energy has apparent economic advantages. These advantages include:

abundant fuel with low cost and stable price, improving plant performance, and plant

longevity through license renewal. Currently, nuclear power is competitive with coal and

natural gas in price, while having higher price stability. When comparing the average

nuclear reactor and fossil steam (includes coal and fossil fuel) plant production expenses

(in dollars per megawatt-hour) in 2001, the expenses for nuclear power were 17.98 (13.31

for operation and maintenance and 4.67 for fuel) and 23.14 (5.01 for operation and

maintenance and 18.13 for fuel) for fossil steam.[1] Even though operation and

6

maintenance is expensive for nuclear reactors, which is an area that could always be

improved with new procedures and equipment, the price of the fuel is very competitive.

The fuel used in nuclear power plants is enriched uranium, which is produced from the

common and abundant natural element of uranium. One uranium fuel pellet, the size of

the tip of your little finger, is comparable to 17,000 cubic feet of natural gas, 1,780

pounds of coal, or 140 gallons of oil [4]. The improving performance and continual

modernization of nuclear power plants results in more electricity for a lower price.

Another important factor in the economic future of nuclear power is the opportunity to

receive license renewal. The initial operating license that was given to the nuclear plants

at their start of operation was for a time period of 40 years. Since the first commercial

nuclear plants started to operate in the late 1950s, the license for many plants is about to

or has already expired. There is an opportunity for a renewal of that license, which many

plants have already received or are in the process of applying for. If approved, this

renewal can extend plant operation for another 20 years, creating significant savings in

the nuclear industry by avoiding the immediate expense of building new power plants.

Finally, given that nuclear power plants have no green house gas emissions, they do not

have compliance costs like the fossil fuel industry [4].

Environmental Benefits

Out of all energy sources, nuclear energy has one of the lowest impacts on the

environment. Nuclear plants do not emit harmful gasses; they occupy a small amount of

land; and the water they release contains no harmful pollutants. Since no harmful gasses

are emitted, nuclear power plants do not contribute to problems like global warming,

ground-level ozone formation, smog, and acid rain. The only product given off by a

nuclear plant, besides electricity, is heat. Additionally, natural external water sources are

7

used in some nuclear power plants for cooling, and because this water is kept so clean, it

is not unusual to have nature parks on plant sites. Also, the small area required by

nuclear power plants leaves the environment in the surrounding area practically

undisturbed, while producing a large amount of electricity. This is a beneficial aspect to

the undisturbed plant life and wildlife in the area.

Nuclear Waste

Although there are many benefits to nuclear power, an existing challenge is the

disposal of the nuclear waste. On the positive side, the risks that nuclear wastes pose to

man decrease with time, and the volume of nuclear waste produced is much smaller than

the volume of waste produced by other industries, per amount of product (electricity).

There are several classes of radioactive waste and there are several possible methods of

disposal. In decreasing severity, the different classes of nuclear waste are: high-level

wastes, transuranic wastes, low-level wastes, and uranium mill tailings. The most

problematic classes are the high-level and transuranic (elements with Z > 92) wastes.

High-level nuclear wastes were also generated from the country’s nuclear weapons

program. The disposal methods that have been considered include: deep geologic

disposal, transmutation (the use of nuclear reactions to alter the waste into isotopes that

are either stable or very reactive to cause them to decay to stable isotopes), ice sheet

disposal, outer space, and sub-seabed disposal [5]. Though a few of these concepts may

be farfetched, geologic disposal is very realistic and is in the process of being completed.

The Nuclear Waste Policy Act was passed by Congress in December 1982 and

signed into law by the president in January 1983. This act included detailed procedures

and corresponding dates for the completion of all tasks leading to the disposal of high-

level nuclear waste. The contents of the act included: establishing a repository site

8

screening process, establishing the Nuclear Waste Fund, requiring that licensed

repositories will use environmental protection standards set by the Environmental

Protection Agency, and establishing a schedule that leads to federal waste acceptance for

disposal starting in 1998 [6]. The Nuclear Waste Fund required the utilities to pay 1 mill

($0.001) per kilowatt-hour of nuclear electricity generated after April 7, 1983, as well as

paying a one time fee per kilogram of heavy metal in spent fuel (an amount equivalent to

1 mill/kWh(e) generated by that spent fuel) discharged before April 7, 1983. The

government guaranteed the utilities that if they paid the fee they would have no other

responsibility for the waste disposal, besides storing it prior to disposal. Through this

fund the government collected about $2.3 billion for the waste discharged before April 7,

1983 and collects about $300 to $400 million per year. As estimated in 1984, the total

cost for high-level waste disposal would cost between $25 and $35 billion dollars [5].

After some arising problems, the Congress drafted and adopted the Nuclear Waste

Policy Amendments Act in late 1987, which was supposed to put the repository program

“back on track”. The amendments act mainly named Yucca Mountain in Nevada as the

only site to be considered for the development of a repository, linked the development of

monitored retrievable storage with the repository licensing, established the Nuclear

Waste Technical Review Board to review the work done by the Department of Energy

(DOE) relating to the repository and transportation of the waste, and offered Nevada

financial benefits if the state agrees to permit the development of the repository at Yucca

Mountain. The prediction of the opening of the Yucca Mountain repository is currently

2010 [6]. If the repository actually does open by 2010 it will be 12 years delayed at that

time, which is a significant inconvenience to the nuclear industry.

9

Reprocessing and Recycling

The reprocessing and recycling of nuclear materials has many benefits. Some of

these benefits are that less uranium would have to be mined, and that there would be less

high-level waste being produced. The nuclear materials that could be used for

reprocessing and recycling include the spent fuel discharged from nuclear reactors and

the highly enriched material from nuclear weapons that are being disassembled. Fresh

fuel that goes into nuclear reactors consists of UO2 enriched in uranium-235. After this

fuel is used, it exits the nuclear reactor with almost all of its original uranium-238, one-

third of the uranium-235 originally in the fuel, plutonium, fission products, and

transuranics. Reprocessing allows for the recovery of the uranium and plutonium from

the spent fuel. The left over spent fuel is then considered high-level waste, and the

recovered uranium and plutonium is recycled back into the reactor. This fuel that

contains a mixture of UO2 and PuO2 is called mixed-oxide fuel or MOX fuel [5].

In the mid 1970s, the nuclear power industry was ready to add reprocessing and

recycling to the nuclear fuel cycle. Unfortunately, at the same time, the issue of weapons

proliferation was a big debate during the presidential campaign. Gerald Ford, the

president at the time, announced that reprocessing and recycling of civilian spent fuel

should not proceed unless the risks of proliferation are reduced to an acceptable level.

Later, President Jimmy Carter deferred reprocessing and recycling indefinitely. In 1981,

President Regan lifted the ban; however, since there were no reprocessing facilities in the

U.S., the technology was never fully developed, and since the materials to make nuclear

fuel were abundant, there was not incentive to pursue reprocessing. Despite its lack of

success in the United States, reprocessing and recycling is a part of the nuclear cycle in

countries such as France, Japan, England, the Soviet Union, and China [5].

10

Introduction to US Commercial Nuclear Reactors

Made to withstand a very harsh environment, nuclear power plants are very

complicated structures that have an extensive amount of safety features. Both the PWR

and BWR operate continuously for a period of 18 to 24 months, after which, a portion of

the fuel in the core has to be replaced. The period of time from when new fuel is added

to the core until the next refueling is called a cycle. There are extensive calculations that

go into the design of a cycle. The cycle has to meet the customer/utility needs, as well as

maintain all safety requirements. Cycle calculations are done to determine the type of

fresh fuel that will be used, the amount of fresh fuel necessary for the cycle, the

arrangement of the fuel within the core, whether the core meets reactivity and thermal

hydraulic limits, and the operation characteristics for the cycle. Extensive calculations

are also done to perform a full safety analysis. Although the primary objectives of PWRs

and BWRs are they same, they are very different systems, each having their own

advantages and disadvantages. The basic method of operation for each system is

described in the following paragraphs.

The PWR

The physical structure of the PWR is more complicated than that of a BWR. This

is primarily due to the fact that the PWR operates with one primary loop that is connected

by heat exchangers to a secondary loop. Connected by large pipes, the components of the

primary loop include: the reactor vessel, the coolant pumps, the pressurizer and the

steam generators. The primary loop is maintained at about 15 MPa (~2175 psi) to

prevent boiling. In the primary loop, water is heated up in the pressure vessel, where the

core containing the nuclear fuel is located. The water is pumped into the pressure vessel

at about 290°C (~550°F) and exits at about 325°C (~615°F). The water in a PWR

11

contains boron, which acts as a primary control of the power in the reactor. After the

water exits the pressure vessel, it travels through large pipes to the steam generators. The

steam generators are very large heat exchangers, which serve the purpose of transferring

the heat from the water of the primary loop to the water of the secondary loop. There are

several thousand tubes within the steam generator that carry the water of the primary

loop. The tubes in a U-tube steam generator enter at the bottom of the steam generator

and exit at the bottom of the steam generator (having a U shape). These tubes are

externally cooled by water from the secondary loop that enters near the bottom of the

steam generator and is heated up to the state of boiling to produce steam. At the top of

the steam generator there are various steam separators that separate the water from the

steam, and as a result, improve the quality of the steam. The steam has to be of high

quality in order to minimize damage to the blades of the turbine generator. After leaving

the steam generator, the steam passes through the turbine. When the steam exits the

turbine, it passes through condensers, and then is pumped back to the steam generator. In

this system the steam is not radioactive since the secondary loop contains coolant that is

not radioactive. Even though the structure of a PWR is more complicated than that of a

BWR, the plant calculations and cycle design are much simpler because of the fact that

the fuel within the core is much less complex. The PWR produces steam that is at about

293°C (~560°F) and at 6 MPa (~870 psi), which results in an overall efficiency in the

range of 32-33 percent [3]. Below, in Figure 1-1, is a simplified illustration of the PWR

system.

12

Figure 1-1. PWR System

The BWR

The BWR is a structurally simplified system with only one major loop, as opposed

to a primary and secondary loop. Because boiling of the coolant/moderator is permitted

in the BWR core, pressure is maintained at approximately 7 MPa (~1015 psi), about half

of the pressure that is maintained in the primary loop of the PWR. In a BWR, the water

enters the core at about 280°C (~536°F) and the portion that exits is at about 290°C

(~554°F).[3] Since steam is produced in the pressure vessel of the BWR, no steam

generators are necessary. To improve the steam quality, the steam passes through the

steam separators at the top of the vessel, and then it goes straight to the turbine. In this

case, the steam that reaches the turbine is radioactive because it comes straight from the

13

core. After passing through the turbine, the steam goes through condensers and then it is

pumped back into the reactor vessel through large pipes. The BWR produces steam that

is at about 290°C (~554°F) and 7MPa (~1015 psi), which results in an overall efficiency

of 33-34 percent [3]. Since there is boiling in the core, the fuel design and the plant

calculations of a BWR become more complicated than that of a PWR. Below is a

simplified illustration of the BWR system. This study contributes knowledge and insight

to the cycle design process of a BWR system, which will be further discussed in the

following sections and chapters.

Figure 1-2. The BWR System

14

The BWR Reactor Assembly

The BWR reactor assembly consists of the reactor vessel, the core shroud, the top

guide assembly, the core plate assembly, the steam separator and dryer assemblies, the jet

pumps, and the core components. The core components include the control rods and the

fuel. An illustration of the reactor assembly can be seen in Figure 1-3 below.

Figure 1-3. BWR Reactor Vessel Assembly [7]

15

The reactor vessel is a pressure vessel that is made of low alloy steel with the

interior coated with stainless steel to prevent corrosion. It is mounted on a skirt that is

bolted to a concrete pedestal, which is part of the reactor building foundation. The

material composition of the vessel is critical since it is exposed to a neutron flux

throughout its lifetime. The reactor vessel has a removable head, which is necessary for

refueling. The head closure seal consists of two concentric O-rings. The vessel and its

internal and external attachments are designed to withstand combined loads [7].

The core shroud is a barrier located between the pressure vessel and the core. The

shroud is made out of stainless steel and is cylindrical in shape. The main purpose of the

core shroud is to separate the downward flow (consisting of the main feed water and

recirculating water) that proceeds to the recirculation loops (containing recirculation

pumps) from the upward flow in the core. The shroud has a peripheral shelf that is

welded to the pressure vessel itself. The shroud structure also supports the steam

separators and jet pump system. The jet pumps penetrate the shelf of the shroud and eject

the water from the recirculation loops to the bottom of the core [7].

The steam separator assembly and the steam dryer assembly are both used to

improve the quality of the steam before it enters the turbine. The steam separators are

located above the discharge plenum region of the core. They have no moving parts and

are made of stainless steel. When wet steam enters the separators it passes through three

stages, each stage containing parts that put a spin on the steam. Centrifugal forces

separate the water from the steam and the water exits from the lower end of each stage.

When the steam exits the steam separators, it enters the steam dryers. The steam dryers

have many wavy metal plates or vanes that the steam passes through. The moisture

16

collects on these plates and drips down through a system of drains to the pool of water

surrounding the separators [7].

The cruciform control rods in a BWR are an operations feature and a safety feature

in the reactor. The control rods enter from the bottom of the reactor since the steam

separators and dryers are at the top of the reactor. They are inserted and withdrawn by

the hydraulic control rod drive system, consisting of locking piston-type drive

mechanisms [7]. The control rods are made of a boron carbide material. Boron is a

neutron absorber and is used to control the fission chain reaction. If neutrons are

absorbed in the boron, they will not go on to cause fission reactions in uranium-235, and

this will reduce the eigenvalue and power in the reactor. Everywhere that there is a group

of four fuel bundles, which is called a fuel module, there is a cruciform control rod. An

illustration of a fuel module is shown in Figure 1-4 and is shown in more detail in Figure

1-5 and Figure 1-6. There are a few fuel bundles on the outside of the core that are not

part of a fuel module and do not interact with a control rod. An arrangement of a typical

BWR core and a description of the control rod grouping pattern can both be seen in the

cross-sectional view shown in Figure 1-4. The grouping pattern is necessary because

control rods are separated into different banks, which are labeled A1, A2, B1, and B2.

These banks or groups of control rods are inserted and withdrawn in alternating order

throughout the cycle. Also, Figure 1-4 shows in-core monitor locations. Looking at the

four quadrants, it can be seen that the in-core monitor locations are not symmetric

throughout the core. The core is usually designed to have one quarter symmetry, so

having the monitor locations in different locations in each of the quarter cores mimics

having the core monitors in all of the locations in the core. The instrumentation locations

contain local power range neutron flux monitors (LPRMs), which are fixed in-core

17

fission chambers that provide continuous monitoring. Also, a guide tube in each in-core

instrumentation position is used for the traversing in-core probes (TIPs). The TIPs

measure the flux at different axial positions in the core, and are used for both normalizing

LPRM gain readings and to correct the calculated thermal margin predictions. TIP

measurements are taken several times throughout the cycle.

Figure 1-4. A. Cross-Sectional View of BWR Core [7], B. Control Rod Banks

The fuel bundles in the BWR core are made up of fuel rods, tie rods, water rods,

spacer grids, tie plates, and a surrounding metal rectangular can. The fuel rods are

pressure vessels made of a Zircaloy cladding tube filled with UO2 cylindrical pellets.

The pellets are inserted into the cladding tube, which is then sealed and pressurized with

helium. The pressurization prevents the tubes from collapsing when in the high pressure

environment of the reactor. The tie rods are fuel rods that are screwed into the lower tie

18

plate and attached to the upper tie plate to hold the bundle together during refueling. The

water rods are diagonally adjacent empty rods in the center of the fuel bundle that allow

water to pass through. In between the tie plates there are several spacer grids which serve

to keep the fuel rods separated, and additionally to cause some turbulence in the flow for

increased heat exchange. The fuel rods, tie rods, and water rods, supported by spacer

girds and upper and lower tie plates, are arranged into a square array. The original fuel

bundles in commercial General Electric (GE) BWRs had a 7x7 array of fuel rods.

Currently the newest fuel bundles are up to a 10x10 array of fuel rods. This increase in

fuel rods was accomplished by decreasing fuel rod diameter, while keeping the actual

size of the fuel bundle constant. The increased fuel rod design adds a significant amount

of surface area for increased heat exchange [7]. Illustrations of fuel modules are shown

in Figures 1-5 and 1-6. Figure 1-5 shows a cross-sectional view of a fuel module of the

old 8x8 fuel assemblies, and Figure 1-6 shows a three dimensional view of a fuel module.

Figure 1-5. Cross-Sectional View of BWR Fuel Module [7]

19

Figure 1-6. BWR Fuel Assemblies and Control Rod Module

The fuel rods in the BWR fuel bundle can be either standard, contain gadolinium,

or be part-length. The enrichment of the fuel rods in a BWR fuel bundle is varied

radially, which can be seen in Figure 1-7. In the figure, each cell represents a fuel rod

except for the middle adjacent large cells, which represent two water rods. The water

rods have a much larger diameter than fuel rods, and are empty to allow for water to pass

through. The values in each white cell and the top values in each gray cell represent the

enrichment of the fuel rod in weight percent. The bottom values in each gray cell

represent the concentration of gadolinium in the fuel rod in weight percent. The cells

20

labeled “E” represent fuel rods that are empty or have no fuel in that zone, these rods then

become designated by “V” in a higher zone, which stands for vanished or partial length

rods. This figure only shows a single axial zone in a fuel bundle. There are several

different axial zones within the fuel bundle. The different axial zones are necessary

because of the part-length rods and other axial variations. A more detailed illustration of

a fuel bundle, with all of the zones included can be seen in Figure 4-4.

A B C D E F G H J K

1 1.60 2.00 3.20 3.60 3.95 4.40 3.95 3.60 3.20 2.40

2 2.00 E 3.60 E 3.95 4.407.00 E 4.40 E 3.60

3 3.20 3.60 4.90 4.90 4.40 4.90 4.90 4.90 4.407.00 4.40

4 3.60 E 4.90 4.906.00 4.90 WR - 4.90 E 4.90

5 3.95 3.95 4.40 4.90 E - - 4.907.00 4.90 4.90

6 4.40 4.407.00 4.90 WR - E 4.90 4.904.906.00 4.90

7 3.95 E 4.90 - - 4.90 4.90 4.906.00 E 4.90

8 3.60 4.40 4.90 4.90 4.907.00 4.904.906.00 4.90

4.407.00 4.90

9 3.20 E 4.407.00 E 4.904.906.00 E

4.407.00 E 4.40

10 2.40 3.60 4.40 4.90 4.90 4.90 4.90 4.90 4.40 3.60

Figure 1-7. Cross-Sectional View of BWR Fuel Bundle

In BWR fuel bundles, the fuel rods on the outer edge need special consideration.

For example, row 1 and column A are sides of the fuel bundle that both face the blades of

the cruciform control rod and are exposed to a higher volume of moderator when the

control rod is withdrawn. These outer edge fuel rods have lower enrichments because of

their location. If a control rod is inserted during beginning of cycle (BOC), it is shielding

these outside fuel rods from thermal neutrons, causing a decreased amount of fission.

However, the fuel rods are not being shielded from energetic neutrons, allowing for

energetic neutron absorption by uranium-238, which produces plutonium-239. Later in

the cycle, when the control rods are removed, the fuel rods are exposed to a higher

amount of moderator, while having a high amount of uranium-235 and now also a higher

21

amount of plutonium-239 than the other rods. This combination causes the fission rate in

these rods to be much higher than the surrounding rods, which is an unfavorable

condition. To compensate for this phenomenon, the rods in these outer rows have lower

enrichments. Also, row 10 and column K may have lower enrichments, since these fuel

rods are also surrounded by a higher volume of moderator, which causes an increase in

the amount of fission, especially at BOC.

BWR Cycle Design

The BWR core has many important design parameters. Some of these parameters

are: the moderator to fuel volume ratio, core power density, fuel exposure level, flow

distribution, operating pressure, void content, heat transfer, and cladding stress [7]. Since

each plant is unique, the design of the cycle depends on the specific plant, and the energy

plan of the utility. The cycle design also depends on the nuclear computer code package

used for the analysis. As a result of the coolant boiling in the core, the BWR is very

complicated to model completely and there is always a bias associated with the code

calculated values. While each code package in use today has the same basic structure and

uses the same principals, each code also uses unique approximations and methods,

therefore having its own bias. Due to the complexity of modeling BWR plants, the bias

of each nuclear code package also depends on the specific plant and even a specific cycle.

Even if the plant was on an equilibrium cycle, where the cycle design is identical from

one cycle to the next, the bias would still vary for that plant due to non-code related

uncertainties further discussed later in this paper. In addition to uncertainties, there are

almost always planned as well as unexpected variations from cycle to cycle, causing an

added change to the bias.

22

The main bias in the nuclear code packages is on the eigenvalue. An example of

what the code calculated eigenvalue may look like is shown if Figure 1-8. While the

code calculates a certain eigenvalue trend, the actual, physical core criticality

(represented by keff) throughout the cycle is maintained at exactly one during steady state

plant operation. Steady state plant operation is maintained during the majority of the

cycle. In order to design a cycle, it is necessary to “guess” what this eigenvalue bias is

going to be, based on previous cycles of the plant or similar plants. This guess of the

eigenvalue trend for the cycle is called the nuclear design basis (NDB). The chosen NDB

is used to normalize the code calculated results to the actual values. Unless the plant is

on a perfect equilibrium cycle, it is not possible to exactly guess the NDB. As mentioned

earlier, even if a plant is put on an equilibrium cycle, the NDB still cannot be determined

exactly due to non code related uncertainties, which are discussed in this thesis.

0.9980.9991.0001.0011.0021.0031.0041.0051.0061.0071.0081.0091.0101.0111.012

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Cycle Exposure MWd/MT

Kef

f

Code Calculated Hot EigenvalueActual Plant Criticality

Figure 1-8. Bias Eigenvalue Trend

The cycle is designed to meet the utilities energy plan, as well as all of the

reactivity and thermal-hydraulic limits that have been determined for that specific plant

and for the fuel used. Once the NDB is determined, the amount of fuel and type of fuel is

23

chosen depending on the utilities energy plan for the cycle. If the NDB is very far off,

then the amount and type of fuel chosen will be incorrect for the planned cycle and other

problems may arise. When a cycle is designed, the fuel amount, type, and position in the

core are determined, as well as operating characteristics like the flow variation and the

control rod patterns throughout the cycle. The amount of flow and the control rod

patterns are specifics of a cycle design and can be modified during the cycle. Each plant

has an on-line core monitoring system that works with the core instrumentation to record

the activity of the plant throughout the cycle. Usually, this core monitoring system

comes from the same nuclear code package as was used to do calculations for the cycle

and, therefore, has the same bias. When it is noticed that the eigenvalue throughout the

cycle is drifting away from the predicted NDB trend, then changes are made in the core

flow and control rod patterns to compensate and keep the core within limits. If

significant adjusting of the control rod patterns and flow occurs in the cycle, the future

cycle being designed also has to be adjusted, therefore, it crucial to predict a good NDB

for the cycle. Also, TIP measurements are done throughout the cycle and are checked

with code calculated values. TIP comparisons can also be used as an indicator of certain

variations in the core. However, if the measured and calculated power shapes are

substantially different, it might also be expected that projected or planned control rod

inventory and eigenvalue may not be achieved because the thermal margins are

sufficiently different than expected. At that point, operational changes from the plan may

be used to take advantage of extra margin or recover margin for continued safety.

There are several limits that are looked at during typical cycle design calculations.

Thermal-mechanical limits are based on thermal-mechanical, as well as, emergency core

cooling system (ECCS) and loss of coolant accident (LOCA) aspects. There are two

24

thermal-mechanical aspects that are considered. The first is a mechanical aspect that

includes placing a limit on the peak fuel pin power level, which would result in a 1%

plastic strain on the clad. The second is a thermal aspect that includes limiting the power

to prevent centerline melting in the fuel. The ECCS/LOCA aspect is to place a limit on

the power level, which would result in a peak clad temperature of 2200°F during a design

basis LOCA.

There are three major limits that are derived from the aspects mentioned

previously. One limit is the maximum average planar ratio (MAPRAT). The MAPRAT

is the ratio of the maximum average planar linear heat generation rate (MAPLHGR), in

units of the average KW/ft for that lattice, for a particular node divided by the

MAPLHGR limit (ECCS limiting average KW/ft). A second limit is the maximum

fraction of limiting power density (MFLPD). The MFLPD is the most limiting value of

the fraction of limiting power density (FLPD), which is the maximum rod power density

(MRPD) or the peak KW/ft value in a node, divided by the exposure dependant steady

state thermal-mechanical limit. Also, there is the critical power ratio (CPR), which is a

bundle quantity. The minimum critical power ratio (MCPR) is the ratio of the bundle

power required to produce the onset of transition boiling somewhere in the bundle,

divided by the actual bundle average power. The CPRRAT is the ratio of the operating

limit critical power ratio (OLMCPR) divided by the MCPR. The MAPRAT, MFLPD,

and CPRRAT should all be less than one for thermal limits to be met.

25

CHAPTER 2 INTRODUCTION

It is beneficial to have the ability to predict and evaluate changes in bias eigenvalue

trends, thermal margin trends, and TIP bias trends when variations occur in a BWR core

from one cycle to another. Currently the NDB is the predicted cycle eigenvalue bias, as

discussed previously. The NDB prediction is usually based on previous knowledge from

experimental data of the core or related cores, and it involves engineering judgment for

interpreting the available experience base. However, it may be difficult to develop a firm

NDB for an initial core, or when the history data is not fully relevant due to significant

changes in the core characteristics. This problem is amplified by the introduction of new

fuel designs, power up rates, longer operating cycles, changes in operating philosophy,

and operation in regimes without substantial prior experience. For example, BWR plants

are running at increasingly higher capacity factors, with fewer opportunities to

benchmark cold calculation models because outage schedules continue to be minimized.

Since BWR analysis models are quite sensitive to past history, the integral value of the

effect of a perturbation can be larger than expected later in future cycles. Also, if the

previous recorded history of the core is incorrect, the calculated values for the power

distribution can be different than the actual values.

To enable this study a multicycle benchmark model created by Global Nuclear

Fuel–Americas (GNF-A) was used [8]. It is a reference BWR three-dimensional multi-

cycle rodded core simulation model, which includes all basic details that a BWR core

designer requires from an actual operating reactor, i.e. detailed core loading patterns for

26

four cycles, varying operating conditions, rod patterns, and cold critical “measurements”

at BOC, middle of cycle (MOC) and end of cycle (EOC). Since it is not a real cycle,

“measurements” refers to code calculated cold critical values at the various points in the

cycle. Various perturbations in the area of fuel manufacturing and plant measurement

were studied using this model. The effects on hot eigenvalue trend, distributed and local

cold critical predictions, thermal margins, and changes in TIP bias are evaluated in this

study for the transition from the original cycle through a future equilibrium cycle.

Interesting results have been obtained through these efforts, and further investigations

would result in even more insights.

The basis of these studies involves perturbations. The perturbations are done to

evaluate the effects of varying certain input parameters, which are used in cycle

calculations, within realistic uncertainties. These uncertainties are related to

manufacturing, methods, instrument readings, and other possible components. This type

of analysis is useful when considering that typical BWR industry uncertainty on the core

eigenvalue is ± 0.003, which in large plants roughly translates into ± 6 assemblies in a

reload batch (or ± 15 days of operation) [8]. Therefore, it is valuable to minimize the

uncertainties on the eigenvalue trends and other parameters (e.g. thermal margin trends

and TIP bias trends), due to their large impact on financial and safety considerations.

Below are a few figures 2-1, 2-2, and 2-3, which illustrate the financial impact of

incorrectly predicting the eigenvalue. It can be seen that in larger cores each individual

bundle has a smaller effect than in smaller cores. As a result, to correct the problem it

takes more bundles in a larger core and therefore the cost is greater.

27

020406080

100120140160

200 250 300 350 400 450 500 550 600 650 700 750 800

Core Size (# of Bundles)

MW

d/M

T pe

r Bun

dle

Figure 2-1. Energy per Bundle as a Function of Number of Bundles in BWR Core

012345678

200 250 300 350 400 450 500 550 600 650 700 750 800

Core Size (# of Bundles)

Cha

nge

in #

of B

undl

es fo

r0.

003

Erro

r in

Eig

enva

lue

Figure 2-2. Change in the Number of Bundles Needed for a 0.003 Error in Eigenvalue

0200,000400,000600,000800,000

1,000,0001,200,0001,400,0001,600,0001,800,0002,000,000

200 250 300 350 400 450 500 550 600 650 700 750 800Core Size (# of Bundles)

Dol

lars

($)

Figure 2-3. Change in the Total Fuel Cost for 0.003 Error in Eigenvalue (BWR)

28

The initial task in this analysis was to provide information on the sensitivity of the

core to the chosen perturbations as a function of exposure. The resulting information

may be applied in new model development activities for assessment of model changes on

core simulation results. Additionally, the results of this study can assist in the

identification of likely causes for the occasional irregularities observed in core tracking.

Even if the lattice physics and core simulator codes were consistent in the past for the

evaluation of a particular core, there is no absolute guarantee that the existing trends will

continue. The ability to predict or analyze the changes in these trends is important. For

example, it can provide assistance in more accurately predicting the NDB eigenvalue bias

trends. Also, if the NDB trend does not agree with the actual trend during the cycle, this

analysis provides a basis to suggest what unrecognized variations might be present, or

might have occurred in the core.

29

CHAPTER 3 METHODS

There are various perturbation parameters that were considered in this study. Plant

measurement perturbation that were done include core flow, core pressure, core inlet

temperature, and core power variations. The fuel manufacturing perturbations that were

done include variations in burnable poison concentration, enrichment, pellet density,

cladding dimensions, and in channel dimensions. In addition to varying these

parameters, the reference multicycle created by GNF-A can also be used in the future to

study perturbations in core and fuel behavior; such as, variations in the fission product

model, Xenon model, depletion model (slope of depletion), gadolinium burnout, control

rod depletion, control rod design, impact of different types of spacers, impact of plenum

regions at bottom / top / middle of the bundle, impact of the use of hot dimensions, and

impact of TIP modeling. Studies of the perturbations in physics assumptions will also be

possible with this multicycle mode; for example, variations in core axial leakage, core

radial leakage, distribution of flows to bundles, calculation of axial void fraction, control

rod axial worths, modeling vs. not modeling of spacers, axially varying control rods, and

crud build-up. In the future, studies of the effects of varying all these parameters will

assist in the development of a diagnostic tool.

The analysis was performed using the current standard GNF-A analysis package

and the reference multicycle created in a previous study by GNF-A [8]. The analysis

package included the TGBLA06 lattice-physics code and the PANAC11 core-simulator

code. TGBLA06 performs the thermal neutron spectra calculation by a leakage-

30

dependent integral transport method, and it performs a resonance integral calculation for

each resonant nuclide using an approximate one-dimensional geometry. PANAC11 uses

a nuclear diffusion model that is an improved 11/2-group physics or quasi-two group

method, which uses spectral mismatch constants to modify the nodal powers and

boundary condition constants to take into account the core leakage [9,10]. Even though

other BWR code packages have different biases and give different results, all codes

should show similar changes in the overall characteristic trending for a given

perturbation.

The way the reference multicycle was used can be analyzed in several different

manners. Throughout most of the project, the multicycle was considered to be the

calculated prediction for a plant, and each variation case was considered as the measured

plant data. This method allowed for a controlled experiment where effects from

individual perturbations could be evaluated. A comparable real life scenario may be that

all of the reload bundles are manufactured to a slightly higher enrichment, while the cycle

calculations are based on the fuel being within specifications. As a result, the online

monitoring system might then track a different eigenvalue trend than predicted. When

comparing this real life situation with this study, the calculated cycle would correspond to

the reference base case and the online monitoring system values would correspond to the

perturbed case. In order to simplify the calculation process used for TIP comparisons, the

interpretation is opposite; the base or reference case in this study would correspond to the

measured case (from the online monitoring system) and the higher enriched core is

considered as the calculated core.

31

In this study the results of selected perturbations are discussed. First there is a

summary of results for perturbations made on plant measurement parameters, and in the

chapter after there is a summary of results for perturbations made on fuel manufacturing

parameters. Even though all cases are shown in the summary tables, detailed plots are

shown only for selected high impact perturbations. While reviewing these results, it is

important to realize that these are extreme cases, which have a low probability of

occurring. However, it is also important to note that each perturbation case only focuses

on one parameter, when realistically multiple situations may occur in the core and even if

they are individually less drastic, it is possible that their effects are additive or they can

cancel each other.

When perturbations are made in the fuel manufacturing aspect of this study, they

are introduced with the fresh reload bundles. In most cases the perturbation is introduced

into all four cycles. As a result of the reload being about one third of the fuel in the core,

the core of Cycle N consists of about one third of the reference/perturbed bundles, the

core of Cycle N+1 consists of about two thirds of those bundles, and the cores of Cycles

N+2 and N+3 consist almost entirely of those bundles, eventually to an approximate

equilibrium cycle.

32

CHAPTER 4 REFERENCE MULTICYCLE

Cycle Characteristics

As mentioned earlier, the reference multicycle described in this chapter was created

by GNF-A in a previous study [8]. The core of the reference multicycle is a 764

assembly General Electric BWR/4 plant, utilizing two year cycles in a control-cell-core

loading, with ~37% batch fraction. There is one GE14 (10x10) fuel assembly type loaded

as fresh fuel in all the cycles. Cycle N is the beginning cycle in the study. Although cycle

N is a starting cycle from an existing core, the reload assemblies and the core loadings do

not reflect the actual operation of any operating BWR, but were constructed to provide

some insights on the sensitivity to the methods of variability in the actual data for this

mode of operation. It is recognized that the sensitivities for a two-year, high-energy

cycle using GNF 10x10 fuel may or may not have any relationship to the sensitivities that

would be seen for an annual cycle operation of a BWR, not loaded with similar fuel or

not of the same size. Additional studies would be needed to make that generalization.

Some of the input and output characteristics to describe the reference multicycle are

shown in Table 4-1 and Figures 4-1 through 4-3. In Table 4-1, the parameters that are

described as rated, refers to their status when the plant is at 100% flow and 100% power.

The values of the cycle describing parameters are typical of a large BWR core, but are set

up to approach an equilibrium cycle, which is not typical of actual operating plants.

Additional plots and tables that further describe each cycle of the reference multicycle

model are provided in Appendix A.

33

Table 4-1. General Cycle Parameters

Figure 4-1 and Figure 4-2 illustrate thermal margin trends, and power and flow

maps for the multicycle analysis. Vertical lines separate each of the cycles, which are

labeled as N, N+1, N+2, and N+3. The cumulative exposure for all four cycles is used as

the parameter for the x-axis. Except where noted, for the purpose of the analysis, the

references cycle values represent the base case predicted or calculated cycle parameters

throughout this study. To make the reference case somewhat realistic, characteristics

such as power coast downs are incorporated. Both the power coast downs and percentage

of core flow can be seen in Figure 4-2.

Figure 4-1. Thermal Margins for Cycles N to N+3

Cycle

Rated Power MWt

Exposure MWd/MT,

Rated

Full Cycle Exposure MWd/MT

Total Cycle Days

Outage Days

Operating Days

Core Weight

MT MWD Rated

MWD EOC

N 3514 16535 18133 728 20 708 135.15 2234674 2450693N+1 3514 15763 17913 728 20 708 136.93 2158432 2452764N+2 3514 16204 17913 728 20 708 136.95 2219197 2453194N+3 3514 16480 17913 728 20 708 137.03 2258240 2454609

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75Cumulative Exposure GWd/ST

Ther

mal

Mar

gin

MAPRAT CPRRATMFLPD

N N+1 N+2 N+3

34

Figure 4-2. Reactor Power and Core Flow for Cycles N to N+3

Figure 4-3 illustrates the shapes of the resulting BOC and EOC core average axial

relative power, and axial average exposure for Cycle N+3, which is considered to be

close to an equilibrium cycle. From the plot it can be seen that both at BOC and EOC the

exposure distribution is relatively flat, which the power distribution is bottom peaked at

BOC and top peaked at EOC. This plot is normalized, and to obtain the actual values,

there is a multiplier in the legend for each parameter.

Figure 4-3. Normalized Axial Core Parameters for Cycle N+3

75

80

85

90

95

100

105

110

115

120

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75Cumulative Exposure GWd/MT

Pow

er (%

) / F

low

(%)

% Flow % Power

N N+1 N+2 N+3

00.10.20.30.40.50.60.70.80.9

11.1

1 5 9 13 17 21 25Axial Node

Nor

mal

ized

Val

ue

BOC Relative Power (Actual x1.451) EOC Relative Power (Actual x1.451)BOC Averave Exposure (Actual x40542.5) EOC Averave Exposure (Actual x40542.5)

Bottom Top

35

Reference Bundle

The reference bundle is a GE14 10x10 fuel bundle as shown in Figure 4-4 below.

Figure 4-4. Reference Bundle Lattice Enrichments and Gadolinium Concentrations

Enrichment: 4.063 wt% U-235 Legend: enrichment(wt% U-235); Gadolinia(wt% Gd2O3); WR = water rod; V = vanished rod; E = empty rod

6 A B C D E F G H J K 5 A B C D E F G H J K1 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 1 1.60 2.00 3.20 3.60 3.95 4.40 3.95 3.60 3.20 2.402 0.71 V 0.71 V 0.71 E V 0.71 V 0.71 2 2.00 V 3.60 V 3.95 4.40 7.00 V 4.40 V 3.603 0.71 0.71 E 0.71 0.71 0.71 0.71 0.71 E 0.71 3 3.20 3.60 4.90 4.90 4.40 4.90 4.90 4.90 4.407.00 4.404 0.71 V 0.71 E 0.71 WR - 0.71 V 0.71 4 3.60 V 4.90 4.90

6.004.90 WR - 4.90 V 4.90

5 0.71 0.71 0.71 0.71 V - - E 0.71 0.71 5 3.95 3.95 4.40 4.90 V - - 4.907.00 4.90 4.906 0.71 E 0.71 WR - V 0.71 0.71 E 0.71 6 4.40 4.407.00 4.90 WR - V 4.90 4.90

4.906.00 4.90

7 0.71 V 0.71 - - 0.71 0.71 E V 0.71 7 3.95 V 4.90 - - 4.90 4.90 4.906.00

V 4.90

8 0.71 0.71 0.71 0.71 E 0.71 E 0.71 E 0.71 8 3.60 4.40 4.90 4.90 4.90 7.00 4.90

4.90 6.00 4.90

4.407.00

4.90

9 0.71 V E V 0.71 E V E V 0.71 9 3.20 V 4.407.00 V 4.90 4.90 6.00 V

4.407.00

V 4.40

10 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 10 2.40 3.60 4.40 4.90 4.90 4.90 4.90 4.90 4.40 3.60

4 A B C D E F G H J K 3 A B C D E F G H J K1 1.60 2.00 3.20 3.60 3.95 4.40 3.95 3.60 3.20 2.40 1 1.60 2.00 3.20 3.60 3.95 4.40 3.95 3.60 3.20 2.402 2.00 E 3.60 E 3.95 4.40

7.00E 4.40 E 3.60 2 2.00 2.80 3.60 4.90 3.95 4.40

7.00 4.90 4.40 4.40 3.603 3.20 3.60 4.90 4.90 4.40 4.90 4.90 4.90 4.407.00 4.40 3 3.20 3.60 4.90 4.90 4.40 4.90 4.90 4.90

4.407.00

4.40

4 3.60 E 4.90 4.90 6.00 4.90 WR - 4.90 E 4.90 4 3.60 4.90 4.904.906.00

4.90 WR - 4.90 4.90 4.905 3.95 3.95 4.40 4.90 E - - 4.907.00 4.90 4.90 5 3.95 3.95 4.40 4.90 4.90 - -

4.907.00

4.90 4.90

6 4.40 4.40 7.00 4.90 WR - E 4.90 4.904.906.00 4.90 6 4.40

4.407.00 4.90 WR - 4.90 4.90 4.90

4.906.00 4.90

7 3.95 E 4.90 - - 4.90 4.90 4.906.00 E 4.90 7 3.95 4.90 4.90 - - 4.90 4.90 4.906.00

4.90 4.90