Design of Nuclear Reactor Protection Systems:
Lessons from Fukushima
by
Christopher Michael Fennell Petty
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Dr. Ernesto Guitierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
May 2012
© Copyright 2012
by
Christopher Petty
All Rights Reserved
ii
CONTENTS
Design of Nuclear Reactor Protection Systems: Lessons from Fukushima ....................... i
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
LIST OF EQUATIONS ................................................................................................... vii
LIST OF EXAMPLES .................................................................................................... viii
NOMENCLATURE ......................................................................................................... ix
GLOSSARY .................................................................................................................... xii
ACKNOWLEDGMENT ................................................................................................ xiv
ABSTRACT .................................................................................................................... xv
1. Introduction / Background ........................................................................................... 1
1.1
Nuclear Physics .................................................................................................. 2
1.1.1
Elements & Isotopes .............................................................................. 2
1.1.2
Mass Defect & Binding Energy ............................................................. 2
1.1.3
Nuclear Force ......................................................................................... 4
1.1.4
Coulomb Force ....................................................................................... 4
1.1.5
Nuclear Stability..................................................................................... 5
1.2
Uranium.............................................................................................................. 8
1.3
Nuclear Reactions .............................................................................................. 9
1.3.1
Fission .................................................................................................... 9
1.3.2
Moderation ........................................................................................... 10
1.3.3
Fission Energy Release ........................................................................ 12
1.3.4
Reactor Coolant .................................................................................... 16
2. Theory / Methodology ............................................................................................... 17
2.1
Nuclear Reactors .............................................................................................. 17
2.2
Boiling Water Reactors .................................................................................... 17
2.3
Pressurized Water Reactors.............................................................................. 23
iii
2.4
2.5
Nuclear Reactor Protection Systems ................................................................ 29
2.4.1
Pressure Protection ............................................................................... 29
2.4.2
Thermal Protection ............................................................................... 32
2011 Japan Catastrophic Earthquake and Tsunami ......................................... 35
2.5.1
Fukushima Daiichi Nuclear Power Plant Accident .............................. 35
2.5.2
Pressure Protection System Failure ...................................................... 35
2.5.3
Thermal Protection System Failure ...................................................... 37
3. Discussion .................................................................................................................. 38
3.1
3.2
3.3
Pressure Relief Valves ..................................................................................... 38
3.1.1
Pilot-Actuated Pressure Relief Valves Description ............................. 38
3.1.2
Pressure Relief Valve Size Determination ........................................... 41
3.1.3
Pressure Relief Valves Setpoint Determination ................................... 41
Operational Power History & Decay Heat ....................................................... 45
3.2.1
Operational Power History................................................................... 45
3.2.2
Radioactive Decay ............................................................................... 45
3.2.3
Decay Heat Generation ........................................................................ 46
3.2.4
Decay Heat Calculation........................................................................ 48
3.2.5
Decay Heat Removal............................................................................ 56
Passive Decay Heat Removal........................................................................... 57
3.3.1
Natural Circulation ............................................................................... 58
4. Conclusions................................................................................................................ 60
5. References.................................................................................................................. 61
iv
LIST OF TABLES
Table 1 - Calculated Binding Energies ............................................................................ 13
Table 2 - Fission Radiation and Released Particles ......................................................... 14
Table 3 - Average Energy from Uranium-235 Fission .................................................... 15
Table 4 - Relief Valve Setpoint Calculation .................................................................... 44
Table 5 - Coefficients for thermal fission of U235, Pu239, Pu241 and fast fission of U238.. 52
Table 6 - Power Fractions for Fission of U235, Pu239, U238and Pu241 ............................... 52
Table 7 - Calculated Decay Heat versus Time ................................................................ 54
v
LIST OF FIGURES
Figure 1-1- Proton to Neutron Ratio .................................................................................. 5
Figure 1-2 - Binding Energy per Nucleon versus Mass Number ...................................... 6
Figure 1-3 - Nuclear Fission .............................................................................................. 9
Figure 1-4 - Neutron Cross-Sections for Fission of Uranium and Plutonium ................. 12
Figure 2-1 - Boiling Water Reactor Systems Overview .................................................. 18
Figure 2-2 - Main Steam System Overview .................................................................... 20
Figure 2-3 - Typical Main Steam Isolation Valve ........................................................... 20
Figure 2-4 - Internals of a BWR Reactor Vessel ............................................................. 22
Figure 2-5 - Pressurized Water Reactor Systems Overview ........................................... 24
Figure 2-6 - Internals of a PWR Reactor Vessel ............................................................. 28
Figure 2-7 - Typical Pressure Relief Valve ..................................................................... 30
Figure 2-8 - PWR Primary Relief System ....................................................................... 31
Figure 2-9 - PWR Secondary Relief System ................................................................... 31
Figure 2-10 - BWR Emergency Core Cooling System ................................................... 32
Figure 2-11 - Fukushima Containment Buildings for Reactor Units 1 - 4 ...................... 36
Figure 3-1- Unitized Pilot Relief Valve........................................................................... 40
Figure 3-2 - Separated Pilot Relief Valve........................................................................ 40
Figure 3-3 - Uranium 238 Radioactive Decay Chain ...................................................... 46
Figure 3-4 - Overview Calculated Decay Heat Versus Time .......................................... 55
Figure 3-5 - Residual Heat Removal System .................................................................. 56
vi
LIST OF EQUATIONS
Equation [1] – Mass Defect ............................................................................................... 3
Equation [2] – Coulomb’s Force1 ...................................................................................... 4
Equation [3] – Change of Binding Energy ...................................................................... 13
Equation [4] – Theoretical Decay Heat ........................................................................... 46
Equation [5] – Fissions Per Second ................................................................................. 47
Equation [6] – Decay Heat .............................................................................................. 47
Equation [7] – Immediate Rector Heat Production Rate2 ................................................ 48
Equation [8] – Reactor Decay Heat Production Rate ...................................................... 49
Equation [9] – Combination of Equations 7 & 8 ............................................................. 49
Equation [10] – Decay Heat Production Rate Over Time3 .............................................. 50
Equation [11] – Decay Heat Production Rate at Time Zero ............................................ 50
Equation [12] – Time Dependant Decay Heat Concentration at Equilibrium4 ............... 50
Equation [13] – Total Decay Heat Rate ........................................................................... 51
Equation [14] – Total Decay Heat Rate at Equilibrium .................................................. 51
Equation [15] – Final Decay Heat Production Rate ........................................................ 51
Equation [16] – Decay Heat Production Rate with ANSI/ANS-5.1-2005 Substitutions5 51
1
http://en.wikipedia.org/wiki/Coulomb%27s_law
Glasstone. Page 119.
3
Nichols. Page 69.
4
Ibid.
5
ANSI/ANS-5.12005. Pages 20 – 21.
2
vii
LIST OF EXAMPLES
Example 1 - Mass Defect of Uranium-235.................................................................2
Example 2 - Binding Energy of Uranium-235............................................................3
Example 3 - Amount of Energy Released during Fission of Uranium-235...............13
Example 4 - Theoretical Average Decay Heat...........................................................46
Example 5 - Fissions per Second Calculation…………………………….………...47
Example 6 - Decay Heat of 7% Power.......................................................................47
viii
NOMENCLATURE
σa
absorption microscopic cross section
ABWR
advanced boiling water reactor
α
alpha particle
AC
alternating current
ASME
American Society of Mechanical Engineers
υ̅
antineutrino
A
atomic mass number (number of nucleons)
amu
atomic mass units
Z
atomic number (number of protons)
Tc
average cold leg primary coolant temperature
Th
average hot leg primary coolant temperature
Tave
average overall primary coolant temperature
β-
beta-minus (electron) decay
β+
beta-plus (positron) decay
BE
binding energy
BWR
boiling water reactor
BTU
British Thermal Units
Ni
concentration of the fission products (nuclei/cm3)
UTC
Coordinated Universal Time
F
Coulomb Force
λi
decay constant (sec-1)
Q̇DH
decay heat production rate
Q̇DH,Chains
decay heat production rate from the fission products
(energy/time-cm3)
DHR
decay heat removal
DOE
Department of Energy
ECCS
emergency core cooling system
E
Energy
ε
fast fission factor (~0.32 typically)
ix
fm
femtometer (1.0x10-15 meters)
σf
fission microscopic cross section
γi
fission yield of the fission products (nuclei/fission)
F
fissions
GE
General Electric
IE
immediate energy released per fission, 185.6 MeV
Q̇IH
immediate heat production rate
JST
Japan Standard Time
kW-hr
Kilo-Watt Hour
∑235
𝑇𝐻
macroscopic thermal fission cross section for uranium-235 (cm-1)
m
mass
Δm
mass defect (amu)
me
mass of electron (0.000548597 amu)
matom
mass of nuclide (amu)
mn
mass of nuetron (1.008665 amu)
mp
mass of proton (1.007277 amu)
MeV
Mega-Electron Volt
MWe
Mega-Watt Electric (MWt * 0.33 = MWe)
MWt
Mega-Watt Thermal
υ
neutrino
NRC
Nuclear Regulatory Commission
N/S
Nuclear Ship, commercial ship’s propulsion plant designator
PDHR
passive decay heat removal
q1
point charge 1
q2
point charge 2
PSI
pounds per square inch
PWR
pressurized water reactor
ke
proportionality constant
RCIC
reactor core isolation cooling
Vc
reactor core volume (cm3)
P
reactor power (MWt)
x
RPI
Rensselaer Polytechnic Institute
RHRS
residual heat removal system
σs
scattering microscopic cross section
r
separation distance
c
speed of light
φ2
thermal neutron flux (neutrons/cm2-sec)
tf
time at constant fission rate (forming time)
ts
time after shutdown
Q̇RX
total reactor heat production rate
ED,Chains
useable energy released by each decay of a fission product
decay chain (energy/decay)
V
volume
xi
GLOSSARY
Advanced Boiling Water Reactor (ABWR): is a newer design boiling water reactor.
Usually applied to boiling water reactors designed after 1980.
Boiling Water Reactor (BWR): is a type of light water nuclear reactor used for the
generation of electrical power. In a boiling water reactor, the reactor heats water which
turns to steam and then drives a steam turbine.
Decay Heat: is the heat released as a result of radioactive decay.
Department of Energy (DOE):
is a Cabinet-level department of the United States
government concerned with the United States' policies regarding energy and safety in
handling nuclear material.
Emergency Core Cooling (ECCS): is a series of systems that are designed to safely shut
down a nuclear reactor during accident conditions.
Japan Standard Time (JST): is the standard time zone of Japan, and is 9 hours ahead of
Coordinated Universal Time (UTC).
Nuclear Regulatory Commission (NRC): is an independent agency of the United States
government that was established by the Energy Reorganization Act of 1974 from the
United States Atomic Energy Commission, and was first opened January 19, 1975. The
NRC oversees reactor safety and security, reactor licensing and renewal, radioactive
material safety, and spent fuel management (storage, security, recycling, and disposal).
Passive Decay Heat Removal (PDHR): is a process to removal decay heat without
pumps, power or other support systems.
xii
Pressurized Water Reactor (PWR): is a type of light water nuclear reactor used for the
generation of electrical power. In a pressurized water reactor, the reactor heats highly
pressurized water (primary water) which in turn transfers the heat to an isolated water
loop (secondary water). The secondary water is boiled off during the heat transfer
process to create steam and then drive a steam turbine.
Reactor Core Isolation Cooling (RCIC): is a reactor safety system that can inject high
pressure water into a reactor.
Radioactive Decay: is the process by which an atomic nucleus of an unstable atom loses
energy by emitting ionizing particles.
Residual Heat Removal System (RHRS): is a system used to remove decay heat during
a normal shutdown of the reactor.
SCRAM: is an operation that shuts down a nuclear reactor. In a reactor, a SCRAM is
achieved by a large insertion of negative reactivity by insertion of the control rods.
xiii
ACKNOWLEDGMENT
The author would like to thank his family, especially his wife Kristen, who has been so
supportive throughout the entire Masters of Engineering in Mechanical Engineering
curriculum. He would also like to thank the faculty of Rensselaer Polytechnic Institute
in Hartford and Groton, for sharing their experience and expertise throughout the
curriculum.
xiv
ABSTRACT
Economic instability in today's world markets have caused the price of traditional fuel
commodities, e.g. crude oil and coal, to rise to record levels. This sharp increase in fuel
prices has forced the general public to demand cheaper power generation alternatives.
Construction of nuclear power plants would alleviate these cost burdens; however in the
light of the crises at: Fukushima, Chernobyl and Three Mile Island, the general public is
concerned about the safety of these plants near their homes and businesses. Despite
recent disasters, nuclear power has the potential to be a safe and reliable way to produce
electrical energy.
These catastrophes have shown the need for robust and reliable reactor protection
systems. Complex reactor protection systems are designed to shutdown and cool down
an operating nuclear reactor in an emergency, to protect the integrity of the reactor
containment. The two most important protection issues are system over pressurization
and fuel element overheating. Reactor protection equipment, such as pressure relief
valves, prevent catastrophic destruction of vital reactor systems by relieving pressure
buildup. Other reactor protection systems, such as passive decay heat removal, prevent
the reactor fuel elements from overheating during the weeks and months of decay heat
generation after the reactor is shutdown.
This engineering project evaluates these
protection systems by: determining the heat load required to be removed by the cooling
systems through decay heat calculation, determining the layout of the cooling systems to
promote passive decay heat removal flow modes, and determining the appropriate relief
valve setpoints of the over pressure protection systems. The analyses of these systems
will include an examination of the lessons learned from the events at the Fukushima
Daiichi nuclear power station in Japan.
xv
1. Introduction / Background
Recent catastrophic events at the Fukushima Daiichi nuclear power station in Japan have
reemphasized the importance of reliable reactor protection systems. The failure of these
systems, caused by two beyond-design-basis events (i.e., earthquake, tsunami), has
increased awareness in the general public regarding the safety of nuclear power plants
around the world. In light of recent disasters, public opinion of nuclear power is that it is
not safe. In reality, complex safety systems are integrated into every reactor design.
Regulatory committees provide specific criteria for the design of the reactor protection
systems to protect against failure for a series of potential, realistic causalities. Design
agencies use these criteria to develop methodologies for implementing reactor safety into
their plant designs. This project evaluates one methodology for designing the reactor
protection systems required for a 1600 MWe Boiling Water Reactor nuclear power plant.
There are three major factors in overall reactor safety: 1. the capability of cooling
systems to remove heat generated during decay of fission daughter products (commonly
known as decay heat removal), 2. the capability of protection systems to relieve high
pressure before a catastrophic failure occurs and 3. redundancy of these safety systems.
The objective of this study was to review how the three major factors in reactor
safety failed in the catastrophic events at the Fukushima Daiichi nuclear power station in
Japan, as well as, reviewing lessons learned to design more robust reactor protection
systems in future nuclear power plants. This report describes design strategies for safer
nuclear power operations and reactor casualty minimization. This report is organized in
the following way: 1. an overview of nuclear power and nuclear plant designs, 2. an
overview of the Fukushima Daiichi nuclear power disaster, 3. an updated approach to
calculations used in determining the: operational power history, decay heat generation,
and pressure relief valve setpoints, and 4. an analytical analysis of the results, utilizing
lessons learned from the Fuskushima Daiichi disaster, to properly size and locate the
reactor protection systems within a reactor plant design.
1
1.1 Nuclear Physics
A review of basic principles of nuclear physics is presented. For further details see
details presented in USNRC Technical Training Center’s Reactor Concepts Manual.
Nuclear power is an unique way to produce heat and thus steam used in turbine
generators to produce electricity.
Nuclear power generation is possible because of
special properties of the nucleus of certain elements.
1.1.1
Elements & Isotopes
All elements, on the periodic table, are described and differentiated by the
number of protons (atomic number) contained within the nucleus of the element (e.g.,
Hydrogen (1 proton), Carbon (6 protons), Uranium (92 protons)). The nucleus of an
element will always contain the same number of protons, but may contain a different
number of neutrons.
Nuclei that are related in this way are called isotopes (e.g.,
Uranium-235 (92 protons, 143 neutrons), Uranium-236 (92 protons, 144 neutrons),
Uranium-238 (92 protons, 146 neutrons)).
1.1.2
Mass Defect & Binding Energy
When examining an isotope, the atomic mass of the isotope never exactly
matches the combined masses of the proton(s) and neutron(s). This difference is called
the mass defect. The mass defect is defined as the missing mass in an isotope. See
Example 1 for the mass defect of uranium-235.
2
Example 1 - Mass Defect of Uranium-235
𝑚𝑎𝑠𝑠 𝑑𝑒𝑓𝑒𝑐𝑡 = ∆𝑚 = [𝑍(𝑚𝑝 + 𝑚𝑒 ) + (𝐴 − 𝑍)𝑚𝑛 ] − 𝑚𝑎𝑡𝑜𝑚
6
[1]
where:
Δm
=
mass defect (amu)
mp
=
mass of proton (1.007277 amu)
me
=
mass of electron (0.000548597 amu)
mn
=
mass of neutron (1.008665 amu)
matom =
mass of nuclide for U235 (235.043924 amu)
Z
=
atomic number (number of protons = 92)
A
=
mass number (number of nucleons = 235)
∆𝑚 = [92(1.007277 + 0.000548597) + (235 − 92)1.008665] − 235.043924
∆𝑚 = 1.915125 𝑎𝑚𝑢
In classical physics, mass defect is not possible, however this phenomenon is explained
through the conservation of energy and Albert Einstein's mass-energy equivalence
equation 𝐸 = 𝑚𝑐 2. The lost mass of the nucleus is converted to energy (commonly
referred to as Binding Energy) when the isotope is formed.
Therefore, binding energy (BE) represents the amount of energy required to split
the nucleus of an atom. See Example 2 for the binding energy for uranium-235.
Example 2 - Binding Energy of Uranium-235
From example 1, the mass defect of uranium-235 is 1.915125 amu.
∆𝑚 = 1.915125 𝑎𝑚𝑢
Since 1 amu = 931.5 MeV
931.5 𝑀𝑒𝑉
𝐵𝑖𝑛𝑑𝑖𝑛𝑔𝐸𝑛𝑒𝑟𝑔𝑦 = 𝐵𝐸 = ∆𝑚 (
)
𝑎𝑚𝑢
𝐵𝐸 = 1.915125 ∗ 931.5
𝐵𝐸 = 1783.94 𝑀𝑒𝑉
6
Department of Energy. www.ne.doe.gov/
3
1.1.3
Nuclear Force
Certain elements have a stable nucleus because of the presence of the nuclear
force. In the nucleus of an isotope, there is a collection of closely packed protons and
neutrons. The protons (with like charges), in close proximity to each other, exert large
repulsive electrostatic forces. This repulsion should cause the nucleus to fly apart.
However, the nuclear force, at short distances, and allows the nuclei to remain intact.
The nuclear force is defined as the interaction force that holds the nucleons in a nucleus
together.
The nuclear force is powerfully attractive between nucleons at distances between
1 and 2 femtometers (fm) (1.0 x 10−15 meters and 2.0 x 10−15 meters), but rapidly
decreases to insignificance at distances beyond about 2.5 fm. At very short distances of
less than 0.7 fm, the nuclear force becomes repulsive, and is therefore responsible for the
physical size of nuclei. This phenomenon results in a minimum separation distance
between the nucleons.
1.1.4
Coulomb Force
The protons in a nucleus attach to each other via the nuclear force, and at the
same time they repel each other with a large repulsive electrostatic force, the Coulomb
force. The Coulomb force is governed by Coulomb's law. Coulomb's law is a law of
physics describing the electrostatic interaction between electrically charged particles.
The law states that electrical charges of the same sign have a force that is repulsive; on
the other hand, the electrical charges of opposite signs have a force that is attractive.
The magnitude and sign of the electrostatic force between two idealized point charges
(q1) and (q2), is given by:
𝑭 = 𝒌𝒆
𝒒𝟏 𝒒 𝟐
𝒓𝟐
where:
F
ke
r
q1
q2
=
=
=
=
=
Coulomb Force
proportionality constant
separation distance
point charge 1
point charge 2
4
[2]
1.1.5
Nuclear Stability
Figure 1-1 is a plot of the number of protons versus the number neutrons, with all
stable isotopes high-lighted in the "belt of stability". Note that light nuclei are the most
stable if they contain equal numbers of protons and neutrons. Furthermore, heavy nuclei
are more stable if the number of neutrons exceeds the number of protons. We can
understand this by recognizing that as the number of protons increases, the strength of
the Coulomb force increases, which tends to break the nucleus apart. As a result, more
neutrons are needed to keep the nucleus stable, since the neutrons experience only
attractive nuclear forces. Eventually, the repulsive forces between protons cannot be
compensated for by the addition of more neutrons; this occurs when the number of
protons ≈ 83. Elements that contain more than 83 protons do not have stable nuclei.
Figure 1-1- Proton to Neutron Ratio7
7
http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Nuclear-Stability-748.html
5
The stability of an isotope can be determined by the summation of all the forces
(binding energy) per nucleon. The total binding energy of an isotope increases as the
number of particles in the nucleus increases. However, the rate of the binding energy
increase is not uniform with the rate of number of particle increase, resulting in a
variation in the amount of binding energy associated with each nucleon within the
nucleus. This variation in the binding energy per nucleon (BE/A) is easily seen among
different nuclei when the average BE/A is plotted versus atomic mass number (A), as
shown in Figure 1-2. It is apparent from Figure 1-2 that the most stable isotope is iron56 (Fe56). (Located at the top of the curve.)
Figure 1-2 - Binding Energy per Nucleon versus Mass Number8
8
http://www.euronuclear.org/info/encyclopedia/bindingenergy.htm
6
Because iron-56 is the most stable isotope, other isotopes will undergo
radioactive decay to become iron-56; essentially becoming more stable. Isotopes that
are larger and heavier than iron-56 will fission to become stable; likewise, isotopes that
are smaller and lighter than iron-56 will combine, through fusion, to become more
stable. The nuclear force also affects the binding energy of a nucleus and its probability
to decay.
For a small isotope (small A), the nuclear radius is small and each of the isotope
nucleons can interact strongly with other nucleons. Thus, for light nuclei, the BE/A
curve rises rapidly as A increases because the number of interacting nucleon pairs
increases. As mentioned earlier, the nuclear force is strong, but has a very short range of
effect, therefore as the nucleus grows in size, the nuclear forces holding it together
decrease. This is noticeable for heavier nuclei on the BE/A curve where BE/A decreases
gradually as the nuclear radius increases. This is because strong bonds can form only
between the nearest neighboring nucleons.
As the atomic mass number (A) increases further and the nucleus becomes larger
still, a point at which the field of each nucleon cannot reach all the remaining nucleons
occurs, and the nuclear force is saturated. The binding energy per nucleon shows little
change as more nucleons are added.
At this point (A ≈ 70) the nuclear radius
corresponds roughly to the range of the nuclear force. If the nuclear force were the only
phenomenon acting on the nucleus, the value of BE/A would remain constant at its
maximum value as A increases beyond 70. There is another phenomenon, however,
which shifts the maximum in the BE/A curve to A ≈ 60 and results in the gentle
downward slope observed beyond that value.
This effect is a consequence of the
Coulomb force, described in section 1.1.4. As A increases beyond ≈ 60, the mutual
repulsion of the protons in the nucleus opposes the attractive nuclear force and tends to
destabilize the nucleus. The Coulomb force is a powerful over a larger range than the
nuclear force, further destabilizing the nucleus with the addition of more neutrons and
protons. The result is a net decrease in binding energy per nucleon beyond A ≈ 60. This
fundamental understanding of isotope nucleus formation is the reason heavy isotopes are
used for fission.
7
1.2 Uranium
Uranium, a heavy element found abundantly in the earth's crust, is obtained through
milling and enrichment.
Naturally occurring uranium contains various isotopes;
uranium-238, uranium-235 and uranium-234. The majority (99.2745%) of all the atoms
in natural uranium are uranium-238. Most of the remaining natural uranium atoms
(0.72%) are uranium-235, and the remainder (0.0055%) uranium-234. Although all
isotopes of uranium have similar chemical properties, each isotope's nuclear properties
differ significantly. The difference in nuclear properties allows one isotope, uranium235, to be useful for thermal fission. To allow a commercial power reactor to operate
approximately two years before new fuel is required, the fuel must be enriched.
Enriching the uranium fuel increases the number of uranium-235 atoms in a given
volume thus increasing the usefulness of the field.
8
1.3 Nuclear Reactions
1.3.1
Fission
As described in Section 1.2, uranium-235 is used as reactor fuel because of its
nuclear properties. Uranium-235 has a high probability of absorbing a thermal (low
energy) neutron causing fission. Fission occurs because the arrangement of particles in
the nucleus is unstable and allows it to disintegrate easily to become more stable. When
the uranium-235 nucleus absorbs a thermal neutron, it becomes uranium-236.
Uranium-236 is not found in nature and is highly unstable, therefore it quickly
disintegrates into two or more smaller element isotopes; commonly known as daughter
products. See Figure 1-3 for a pictorial description of the fission process. Each time a
fission event occurs and the nucleus is split into daughter products, there is a release of
two or three neutrons and a substantial amount of energy. The energy released from the
fission process is utilized to heat the reactor coolant; while the neutrons released allow
the fission chain reaction to continue.
Figure 1-3 - Nuclear Fission9
The neutrons released by the fission process can be divided into two categories,
prompt neutrons and delayed neutrons. Prompt neutrons constitute 99.35 percent of the
9
http://web.mit.edu/nrl/www/reactor/fission_process.htm
9
total neutrons released. They are released within 10-14 seconds (or less) of the instant of
fission.10 The average lifetime of prompt neutrons is 26 microseconds.
Delayed
neutrons are expelled from the daughter products over a period of several minutes after
fission. The average lifetime of delayed neutrons is between 0.2 seconds and 1 minute.
The presence of delayed neutrons prevents the chain reaction from increasing too rapidly
therefore controlling the fission process.
1.3.2
Moderation
In nuclear fission, moderation plays an important role. During each fission
process, two to three neutrons can be released with high energy (≥ 2 MeV), called fast
neutrons. In order for the chain reaction of fission to continue; a released neutron must
have the proper energy to be absorbed by another uranium-235 nucleus. Uranium-235
undergoes fission more readily when the neutrons are of low energy, called slow
neutrons or thermal neutrons. Thus, for a neutron to be absorbed by uranium-235 it must
slow down or reduce its energy. The process of reducing the energy of a neutron to the
thermal region (~0.00625 MeV) by elastic scattering is referred to as thermalization or
moderation.
The material used for the purpose of thermalizing neutrons is called a moderator.
During the fission process, neutrons are released at different energies depending on
when the neutrons are released, prompt versus delayed. Prompt neutrons born during the
fission process have energies greater than 0.1 MeV with an average energy of 2 MeV.
These high energies are well above the thermal region and require thermalization to be
useful for fission. In contrast, delayed neutron energies are lower than those for the
prompt; with the delayed neutron average energy being approximately 0.4 MeV. These
higher energy neutrons are thermalized through scattering events where they lose some
of their kinetic energy to the surrounding bulk material and coolant.
Elastic and inelastic scattering reactions are the only types of interactions that
cause the neutrons to lose energy without removing them from the fission cycle. Of the
two types of scattering reactions, elastic scattering collisions are the most important
since they occur at all neutron energies.
10
Glasstone. Page 106.
10
The collisions are not possible unless there is an effective moderator in the
reactor core. Effective moderators are classified as mediums that create a large energy
loss per collision. They have large scattering cross sections, and low absorption cross
sections. The maximum energy lost in any single collision increases as the mass of the
target nucleus decreases. This means that light nuclei, for example hydrogen, contribute
more effectively to the slowing down process and are considered effective moderators.
A practical example is a “pool” ball can transfer all of its energy to another “pool” ball
that results in stopping of the first “pool” ball and the movement of the second “pool”
ball. However, on the other hand, a “pool” ball will transfer some of its energy to a
“bowling” ball. This energy transfer may occur without visibly moving the “bowling”
ball.
Moderation allows a neutron to be useful for fission by "increasing" its
absorption cross section. While the physical size of a neutron does not change, the
absorption cross section of the nucleus represents its probability to fission, and changes
with speed and energy. At fast speeds and high energy, a neutron has a large scattering
cross section, σs, and a small absorption cross section, σa; indicating that the neutron has
a higher probability to scatter instead of fission. Likewise, at slow speeds and low
energy a neutron has a large absorption cross section and a small scattering cross
section; indicating that the neutron has a higher probability to be absorbed and fission.
See Figure 1-4.
The absorption cross section decreases faster than the inverse of
velocity (1/V) so it is generally smaller than the scattering cross section at fast energies.
The highest probability of neutrons to induce fission events occurs in the thermal energy
range where the absorption cross section is the highest.
11
Figure 1-4 - Neutron Cross-Sections for Fission of Uranium and Plutonium11
1.3.3
Fission Energy Release
As mentioned in section 1.3.2, neutrons can be released from the fission process
with high amounts of energy. This energy is proportional to the decrease in mass of the
system described in section 1.1.2. The relationship between mass and energy was
explained in section 1.1.2. Therefore the amount of energy released as usable energy
during the fission process, a conservation of mass-energy equation can be analyzed. The
energy released from the system will be equivalent to the difference in binding energy
(BE) between the reactants and the products. See Example 3 for the amount of energy
release during a specific fission event.
11
http://world-nuclear.org/education/phys.htm
12
Example 3 - Amount of Energy Released during Fission of Uranium-235
135
Assumptions: urnaium-235 will fission into Yttrium-98 ( 98
39𝑌 ) and Iodine-135 ( 53𝐼 )
1
0𝑛
+ 235
92𝑈 →
236 ∗
92𝑈
→
98
39𝑌
1
+ 135
53𝐼 + 3( 0𝑛)
Using example 1, we can determine the binding energies:
Table 1 - Calculated Binding Energies
Nuclide
Atomic Mass (amu)
Binding Energy (MeV)
235
92𝑈
235.043924
1783.940
Total Reactants
1783.940
98
39𝑌
97.9222195
832.960
135
53𝐼
134.9100503
1131.993
Total Products
1964.953
∆𝑩𝑬 = ∆𝑩𝑬𝑷𝒓𝒐𝒅𝒖𝒄𝒕𝒔 − ∆𝑩𝑬𝑹𝒆𝒂𝒄𝒕𝒂𝒏𝒕𝒔
[3]
135
235
∆𝐵𝐸 = ( 98
39𝑌 + 53𝐼 ) − 92𝑈
∆𝐵𝐸 = 1964.953 − 1783.940 = 181.013𝑀𝑒𝑉
Example 3 demonstrates the amount of prompt energy that is released from
uranium-235 when the fission products are yttrium-98 and iodine-135. This example,
however, doesn't demonstrate all the energy released during the fission process. Energy
in the form radiation and particles are also released. The radiation released during the
fission can come in different forms. See Table 2 for the types of radiation and released
particles.
13
Table 2 - Fission Radiation and Released Particles12
Particle
Radiation
Type
Symbol
Gamma (Photon)
Gamma
Radiation
γ
Beta-minus
(electron)
Beta-plus
(positron)
Neutrino
Antineutrino
Alpha
12
𝐴
𝑍𝑋
Charge
Mass (amu)
𝐴
𝑍𝑋
0
0
β-
0
−1𝑒
-1
0.000548597
Beta Decay
β+
0
1𝑒
+1
0.000548597
Alpha Decay
υ
υ̅
Α
0
0υ
0
̅
0υ
4
2𝐻𝑒
0
0
+2
0
0
4.002602
Glasstone. Page 330.
14
Notation
Taking into consideration the prompt energy, radiation and particle release, the average
total amount of energy released per fission of one uranium-235 atom is summarized in
Table 3.
Table 3 - Average Energy from Uranium-235 Fission13
Emitted Energy
(MeV)
Instantaneous Energy
Recoverable Energy
(MeV)
Kinetic energy of fission fragments
165.6
165.6
Kinetic energy of fission neutrons
4.8
4.8
Fission gamma rays
7.7
7.7
Neutron capture gamma rays
7.5
7.5
Total instantaneous energy
185.6
185.6
Delayed Energy
13
Kinetic energy of beta particles
7.2
7.2
Delayed neutrons
~0
~0
Fission product decay gamma rays
7.2
7.2
Antineutrinos
10.2
0
Total delayed energy
24.6
14.4
Total energy released per fission
210.2
200.0
Glasstone. Page 17.
15
1.3.4
Reactor Coolant
In a nuclear reactor, the reactor coolant also plays an important role.
As
described in sections 1.3.1 and 1.3.3, the fission process releases thermal energy as part
of the energy conservation process. The medium that removes the thermal energy
generated during the fission process, in a reactor, is called the reactor coolant. The
thermal energy resulting from the fission process establishes a temperature difference
between the reactor fuel elements and the circulating reactor coolant. This temperature
difference results in a transfer of energy from the fuel elements to the reactor coolant.
Along with the fission thermal energy, most of the kinetic energy in the neutron
is transferred directly to the reactor coolant as heat during the thermalization process,
described in section 1.3.2. During the thermalization process, neutron elastic collisions
with hydrogen nuclei dominate the slowing-down process, along with the inelastic
scattering collisions with heavier elements such as zirconium (typically used in fuel
element construction). These elastic and inelastic collisions also generate heat that needs
to be removed by the reactor coolant. This energy is then used to create steam and
ultimately generate electrical power.
16
2. Theory / Methodology
2.1 Nuclear Reactors
Nuclear power plants currently in operation and under design, in the United States, fall
into two main categories: boiling water reactors (BWR) and pressurized water reactors
(PWR). The basic concepts between the two types of plants are similar but the details of
the reactor designs of these reactor types vary drastically. These variations account for
multiple heat transfer loops as well as designs involving different components.
2.2 Boiling Water Reactors
In the United States, BWRs encompass approximately 33 percent of all commercial
nuclear power plants in operation.
There are two operating BWR types, an older
variation BWRs and advanced boiling water reactors (ABWR). BWRs have been in
operation since 1960; with the original BWRs being developed by General Electric (GE)
in the 1950s. The first BWR nuclear power station was Dresden Unit-1 (200 MWe)
commissioned in July 1960. This first BWR was a dual cycle plant like a PWR, as will
be described in section 2.3. However, subsequent designs were modified to adopt a
single direct cycle. The Fukushima Daiichi Nuclear Power station had six separate
BWRs.
BWRs utilize light water (normal H20 as opposed to “heavy” water commonly
known as deuterium) as the reactor coolant and moderator to generate electricity by
directly boiling the light water in a reactor core to make steam that is delivered to a
turbine generator to produce electricity. A BWR and ABWR nuclear power plant
consists of: a nuclear reactor, a reactor coolant recirculation system, main steam system,
condensate system, feed system, turbine equipment, generator equipment and other
important secondary systems (e.g., purification, sampling) and equipment. Along with
the reactor operational systems, engineered safety features including: pressure protection
system, emergency core cooling system, reactor core isolation cooling, containment
cooling system and injection system is provided for emergency operations. See Figure
2-1 for a systems overview of a typical BWR.
17
Figure 2-1 - Boiling Water Reactor Systems Overview14
14
http://www.ge-energy.com/
18
A BWR provides cooling to the reactor and generates steam with utilizing a
single loop system called the reactor coolant recirculation system. The reactor coolant
recirculation system circulates subcooled water for neutron moderation and for removal
of the heat generated in the core. The heat transfer in the reactor core, from the fuel
elements to the reactor coolant, generates steam inside the reactor vessel and supplies the
steam to the main steam system. The main steam system transports the steam from the
reactor vessel to the electrical generation turbines. Once all the steam energy is used the
steam is condensed back to liquid. This water is supplied to the condensate and feed
systems which direct the water back to the reactor vessel for the heat transfer cycle to be
repeated.
The reactor coolant recirculation system is located inside the primary
containment and is divided into multiple units; with the exact number depending on the
size of the reactor, with a common reactor vessel. The principal components of each
unit are a steam separator and reactor coolant recirculation pump(s); typically between
two and four units per reactor. Water discharged by the reactor coolant recirculation
system passes through the reactor core which heats the water to a mixture of water and
steam. The steam-water mixture is discharged by the reactor to risers. The risers convey
the steam-water mixture to the steam separators which separate and dry the steam. The
steam separators dry the steam, aka increase the quality, and remove residual moisture;
which is fed back to the reactor for reuse.
The main steam system transports the dry and saturated steam from the steam
separators to the main turbines to produce electrical power, see Figure 2-2 for a detailed
main steam system overview. The number of main steam headers depends on size of the
reactor; typically between two and five main steam headers per reactor. The main steam
system originates at the steam outlets of the steam separator and passes through the
primary containment into the turbine building. The system consists of the necessary
piping, valves, and instrumentation required to transport steam from the steam separators
to the inlet of the main electrical turbines. A set of primary containment isolation valves
are located on either side of the containment boundary for isolation of the reactor, see
Figure 2-3. These isolation valves, see Figure 2-3, isolate the reactor and primary
containment from the manned spaces in an emergency or during maintenance evolutions.
19
Figure 2-2 - Main Steam System Overview15
Figure 2-3 - Typical Main Steam Isolation Valve16
15
16
http://www.ge-energy.com/
Ibid.
20
Once the steam has expelled all of its energy in the turbines, its temperature and pressure
are reduced. Spent, low-pressure steam exits the turbines and enters the condenser
where it flows over tubes cooled by water. As the remainder of the energy is removed
from the steam, by cooling in the turbine condensers, a liquid called condensate is
formed. The condensate system then transports the deaerated condensate from the
condenser hot well to the reactor feed pumps for return to the reactor coolant
recirculation system. Each condensate system, one for each main steam header and
turbine generator, consists of condensate pumps connected to the condenser hot well,
associated valves and a recirculation line. The condensate pumps increase the pressure
of the water to approximately half the required pressure and then discharges it into a
common header. The condensate header directs the condensate to the reactor feed
system, specifically the reactor feed pump suction header.
The reactor feed system completes the heat transfer cycle by transporting the
water from the condensate system back to the reactor vessel. The reactor feed system
completes the pressure increase of the water to a pressure that is greater than reactor
operating pressure. This water enters the reactor pressure vessel through feed nozzles
high on the vessel, well above the top of the fuel assemblies but below the water level to
prevent splashing and causing a thermal shock on the feed nozzle piping. The feed
water is pumped into the reactor pressure vessel after going through feed water heaters
to raise its temperature; so the reactor vessel is not thermally shocked by "cold" feed
water. Without these heaters and proper feed piping placement, the shock to the system
could cause brittle fracture cracks and/or failures. The feed water enters the reactor
vessel in the downcomer region and combines with excess water exiting the steam
separators. The feed water then flows down the downcomer region and goes through
either jet pumps or reactor coolant pumps that provide additional pumping power. The
water, now called reactor coolant again, makes a 180 degree turn and moves up through
the lower core plate into the core where the fuel elements heat the water and restart the
process. See Figure 2–4 for the internals of BWR reactor vessel.
21
Figure 2-4 - Internals of a BWR Reactor Vessel17
17
http://www.euronuclear.org/e-news/e-news-18/HP-BWR.htm
22
2.3 Pressurized Water Reactors
In the United States, pressurized water reactors (PWR) encompass the majority of
commercial nuclear power plants. A PWR is considerably different than a BWR in its
heat transfer and steam generation location details.
These details add complexity
through multiple loops and components. In the US, PWRs were originally designed at
the Oak Ridge National Laboratory for use as a nuclear submarine power plant. The
remaining designs were conducted by Westinghouse's Bettis Atomic Power Laboratory.
The first purely commercial nuclear power plant was a PWR built at Shippingport
Atomic Power Station and went critical on December 2, 1957.
A PWR is fundamentally different than a BWR because a PWR is designed to
preclude boiling in the reactor vessel. In a PWR heat is removed from the reactor and
steam is generated utilizing a two loop system configuration, called the primary and
secondary loops; see Figure 2-5. The primary loop system removes the heat generated
by the fission process by circulating reactor coolant and transfers that thermal energy to
the secondary loop; via the steam generator. The purpose of the secondary loop system
is to: "cool" the primary loop, generate steam, transport the steam to the turbine
generators and resupply makeup water to the steam generator. The steam generated in
the steam generator is transported to the main turbine building to rotate the main
electrical turbines and generate electricity. Once all the steam energy is expelled, the
steam is condensed. The condensed water is fed to the condensate and feed systems to
raise the water's pressure and direct it back to the steam generator for the heat transfer
cycle to repeat.
The primary system is a pressurized, enclosed loop that removes heat from the
reactor core and prevents boiling in the reactor vessel. The primary system in a PWR is
maintained at high temperatures (≥400°F) and high pressure (≥1500 psia). Boiling in the
primary system is prevented because heat generated from fission in the reactor fuel could
cause excessive temperatures and distorting or melting of core components if not
properly removed.
These problems would occur due to the steam heat transfer
properties being less effective than liquid water heat transfer properties. The primary
system obtains its required operating pressure by electrically heating a tank of water, the
23
Figure 2-5 - Pressurized Water Reactor Systems Overview18
18
http://aboutnuclearphysics.blogspot.com/2010_07_01_archive.html
24
pressurizer, and raising the temperature of the water in the pressurizer to the saturation
temperature corresponding to the desired primary system pressure. The pressurizer's
temperature is maintained well above reactor coolant temperatures in the reactor so that
boiling occurs in the pressurizer and not in the reactor core.
Reactor coolant is continuously circulated in the primary system loop which
connects the reactor to the steam generator and the steam generator back to the reactor.
"Hot" reactor coolant leaves the reactor, and flows through the hot-leg piping of the
primary loop and enters the steam generator. Inside the steam generator, the reactor
coolant transfers its heat energy to the secondary loop for steam generation. "Cold"
reactor coolant leaving the steam generator, due to the heat energy transfer, flows
through the cold-leg piping and pump(s) of the primary loop and reenters the reactor
vessel, completing the primary heat cycle.
The primary system has a temperature
difference of only approximately 50°F (375°F - 425°F) if the average reactor coolant
temperature is 400°F. This constitutes the "hot" leg having a temperature of 425°F
reactor coolant and the "cold" leg having a temperature of 375°F reactor coolant; for this
example. If the reactor coolant flow rate is reduced or lost and/or reactor coolant liquid
volume is lost, heat generated in, but not removed from the reactor, could result in
excessive temperatures and ultimately damage to the reactor fuel elements.
A main aspect to the primary system is the reactor coolant pressurizing system.
The reactor coolant pressurizing system serves two main purposes: 1. to develop and
maintain the reactor coolant system pressure during operation and 2. to provide a means
of removing non-condensable gases from the primary system so that gas concentrations
are kept within specifications. Although inherent self-regulation of the reactor tends to
keep the average reactor coolant temperature (Tave) constant, the cold-leg temperature
(Tc), and the hot-leg temperature (Th) vary during steam demand transients. These
temperature changes affect the density and, hence, the volume of the primary system.
Changes in reactor coolant volume, in turn, produce pressure changes in a closed system.
The pressurizing system handles these volume changes without requiring the reactor
coolant system to have water added or removed; all while maintaining the system
pressure below the maximum design pressure.
25
The secondary system cycle consists of: the steam generator, a main turbine, a
condenser, a condensate pump, a feed pump, feed heaters and associated piping and
valves. Heat transferred from the reactor coolant to the secondary fluid generates highpressure and low-quality steam. After the steam generator dries the steam, the secondary
system directs the high-pressure high-quality steam that exits the steam generator to the
main turbine generators where the steam's potential energy is changed to kinetic energy
through turbine work. As steam completes work in the turbines, its temperature and
pressure are reduced.
Spent, low-pressure steam exits the turbines and enters the
condenser where it flows over tubes cooled by water. As the remainder of the energy is
removed from the steam, by cooling in the turbine condensers, a liquid called condensate
is formed. To complete the secondary cycle, this condensate is returned to the steam
generator by the combined pressure addition of the condensate and feed pumps. The
condensate pump is designed to operate with a low suction pressure such as that in the
condenser, and protects the feed pump from damage due to cavitation by providing
sufficient pressure at the inlet to the feed pump. The feed pump completes the heat
transfer cycle by increasing the pressure of the secondary coolant above the steam
generator operating pressure and returning the fluid to the steam generator for reuse.
The primary purpose of the steam generating system is to transfer heat from the
reactor coolant to secondary water. The region above the tube sheet and outside the Utubes in the generator is the secondary side. In this region, heat is transferred through
the U-tubes from the reactor coolant to the secondary water. The combined action of
heat transferred from the reactor coolant and the colder water returned by the feed
system establishes an internal circulation of secondary water.
As secondary water is heated by the U-tubes, its temperature increases, its
density decreases, and it rises up through the tube bundle region. When its temperature
reaches saturation temperature, it begins to boil, forming a mixture of steam and liquid
water. This mixture flows upward into the riser region above the U-tubes. The internal
steam generator structure guides the upward-flowing steam-water mixture toward the
moisture separators in the upper part of the steam generator. The moisture separators
reduce the quality of the steam and permit dry saturated steam to exit the steam
26
generator through the steam nozzle, into the main steam system, while returning
saturated liquid to the downcomer region.
The main steam, condensate and feed systems function exactly the same way as
the boiling water reactor's main steam, condensate and feed systems perform. The main
steam system transports the dry and saturated steam from the steam separators to the
main electrical turbines to produce electrical power. The condensate system transports
the deaerated condensate from the condenser hot well to the feed pumps. The reactor
feed system transports the condensate from the condensate system to the steam
generator. The final destination of the feed water is the only difference between the
PWR system (steam generator) and BWR system (reactor vessel).
27
Figure 2-6 - Internals of a PWR Reactor Vessel19
19
http://www.nrc.gov/reading-rm/basic-ref/teachers/04.pdf
28
2.4 Nuclear Reactor Protection Systems
Robust reactor protection systems are common to both types of nuclear reactor plants. A
reactor protection system is a set of nuclear safety components in a nuclear power plant
designed to protect and/or safely shutdown the reactor while preventing the release of
radioactive materials. In a nuclear power plant, protection systems are broken down into
two main categories; pressure protection and thermal protection.
The pressure
protection systems have the responsibility to protect the reactor and various systems'
pressure integrity. The thermal protection systems have the responsibility to keep the
reactor fuel elements covered at all times and, when necessary, reduce the temperature of
the reactor coolant to a safe and stable temperature.
There are three major factors in overall reactor protection design:
1. Capability of the pressure protection systems to relieve high pressure before a
catastrophic failure occurs,
2. Capability of the thermal protection systems to remove heat generated during decay of
fission daughter products (commonly known as decay heat removal) and,
3. Redundancy of these safety systems to prevent any single point failures.
These major factors directly affect the design of the nuclear power plants.
2.4.1
Pressure Protection
The purpose of a pressure relief system is to prevent the plant pressure from
exceeding the design system pressure. This is accomplished by discharging liquid or
steam through a relief valve when the pressure exceeds the relief valve's set pressure.
See Figure 2-7 for a typical nuclear power plant relief valve. The consequences of
excessive pressure can include leakage through pressure boundaries in valves, distorting
and/or weakening of system components, and in the worst case, rupture of the system's
pressure boundary. A rupture of a pressure boundary could potentially release fission
products and radioactivity to the primary containment or to the environment in extreme
cases.
29
Figure 2-7 - Typical Pressure Relief Valve20
In a BWR, there is only one set of relief valves required to protect the reactor
pressure vessel due to the simplicity of having a single direct steam generation cycle, see
Figure 2–2. In a PWR however, there are multiple relief valves sets required. A set of
relief valves protect the over pressurization of the primary loop, usually installed in the
pressurizer, and a set of relief valves to protect the secondary loop, usually installed near
the steam generator in the main steam piping. See Figures 2–8 and 2–9.
In both reactor designs there are multiple relief valves for redundancy. Every
high pressure system in a reactor design must account for ASME codes and catastrophes,
specifically the possibility of a relief valve failing to open. If reactor plant designs did
not have redundancy and a single relief valve failed to open, with no other means of
relieving the pressure; the chances of a pressure boundary rupturing would dramatically
increase. Also, while multiple relief valves provide valuable backup protection, their set
pressure must differ enough to prevent two from lifting simultaneously and reducing
20
http://www.process-safety-design.com/safely-relief-valves.html
30
pressure too rapidly. Properly addressing over pressure protection will be addressed in
Section 3.
Figure 2-8 - PWR Primary Relief System21
Figure 2-9 - PWR Secondary Relief System22
21
22
http://www.nrc.gov/reading-rm/basic-ref/teachers/04.pdf
Ibid.
31
2.4.2
Thermal Protection
The purpose of the emergency core cooling system (ECCS) is to provide the
capability to remove design decay heat from the reactor when normal reactor cooling is
unavailable. Other reactor protection systems, e.g., SCRAM, stop the chain reaction of
fission. The ECCS is responsible for removing heat generated during the fissions and
decays of the daughter fission products after the reactor plant is shutdown. The quantity
of decay heat required to be removed will be discussed in section 3.2. There are two
types of emergency core cooling; electrically powered and passive. See Figure 2-10.
Figure 2-10 - BWR Emergency Core Cooling System23
23
http://www.ge-energy.com/
32
In a BWR and PWR there are multiple emergency core cooling systems; one
high pressure core cooling system, one intermediate pressure injection system, cold-leg
accumulators, and a low pressure core injection (reflooder) system (see Figure 2–10).
These emergency safety systems are not nuclear plant type specific; they are mandated
by the regulating governing agencies, Department of Energy (DOE) and Nuclear
Regulatory Commission (NRC) and ASME codes. All of these systems are completely
independent and redundant divisions of safety systems. The emergency systems are
mechanically separated and have no cross connections to prevent one failure from
destroying all the ECCS. These systems are also electronically separated so that each
division has access to redundant sources of AC power and, for added safety, its own
dedicated emergency diesel generator. Each system division is located in a different
quadrant of the reactor building, separated by fire walls for redundancy reasons. A fire,
flood or loss of power which disables one division has no effect on the capability of the
other systems. Finally, each division contains both a high and low pressure system and
each system has its own dedicated heat exchanger to control core cooling and remove
decay heat.
The high pressure injection system uses special dedicated pumps to deliver this
water to the reactor vessel. Upon receipt of an emergency actuation signal, the system
will automatically realign to take water from the refueling water storage tank and pump
it into the reactor coolant system. The high pressure injection system is designed to
provide water to the core during emergencies in which reactor coolant system pressure
remains relatively high (such as small break in the reactor coolant system, steam break
accidents, and leaks of reactor coolant through a steam generator tube to the secondary
side).
The intermediate pressure injection system is also designed for emergencies in
which the primary pressure stays relatively high, such as small to intermediate size
primary breaks. Upon an emergency start signal, the intermediate pressure injection
system pumps will take water from the refueling water storage tank and pump it into the
reactor coolant system.
The cold leg accumulators do not require electrical power to operate. These
tanks contain large amounts of borated water with a pressurized nitrogen gas bubble in
33
the top. If the pressure of the primary system drops below the pressure of cold leg
accumulators, the nitrogen will force the borated water out of the tank and into the
reactor coolant system. These tanks are designed to provide water to the reactor coolant
system during emergencies in which the pressure of the primary drops very rapidly, such
as large primary breaks.
The low pressure injection system (also known as residual heat removal) is
designed to inject water from the refueling water storage tank into the reactor coolant
system during large breaks, which would cause a very low reactor coolant system
pressure. In addition, the residual heat removal system has a feature that allows it to
take water from the containment sump, pump it through the residual heat removal
system heat exchanger for cooling, and then send the cooled water back to the reactor for
core cooling. This is the method of cooling that will be used when the refueling water
storage tank goes empty after a large primary system break. This is called the long term
core cooling or recirculation mode.
In an event where there is a station blackout or total loss of all AC power, one of
the high pressure systems, the reactor core isolation cooling (RCIC) system, is powered
by steam provided by the reactor. The RCIC is provided to inject the condensed water
of residual heat removal system or condensate storage tank water, etc. into the reactor
core with a steam turbine-driven pump. As long as steam is available, the RCIC is able
to utilize it for use in the high pressure injection pump.
When there is an event that causes a plant and electric casualty, a passive
emergency cooling system is needed. In both a BWR and PWR, the reactor cooling
utilizing the passive emergency cooling system must be independent of electrical power.
Therefore, it is designed to use natural circulation produced by a thermal driving head.
A thermal driving head is a difference in pressure caused by a temperature difference
and thus a density difference between two columns of water. The warmer water, less
dense water tends to flow upward, while cooler, denser water tends to flow downward
by gravity. The pressure difference caused by this phenomenon allows flow in the
reactor coolant system without a recirculation pump assistance. Passive decay heat
removal will be described in detail in section 3.3.
34
2.5 2011 Japan Catastrophic Earthquake and Tsunami
On Friday March 11, 2011, a magnitude 9.0 earthquake hit off the coast of Japan at
14:46 Japan Standard Time (JST).
The earthquake occurred with the epicenter
approximately 43 miles east of the Oshika Peninsula of Tohoku and the hypocenter at an
underwater depth of approximately 20 miles.
It was the most powerful known
earthquake ever to have hit Japan, and one of the five most powerful earthquakes in the
world since modern record-keeping began in 1900. The earthquake triggered powerful
tsunami waves that reached heights of up to 133 feet in Miyako in Tōhoku's Iwate
Prefecture, and which, in the Sendai area, travelled up to 6 miles inland.24
2.5.1
Fukushima Daiichi Nuclear Power Plant Accident
Prior to the disaster, Fukushima had six operable reactors, three units were
operating (units 1, 2 and 3) and three units were shut down for planned maintenance
(units 4, 5, and 6). After the earthquake occurred, reactor protection safety measures
automatically shutdown, e.g., SCRAMed, the three operating reactors. As the reactor
operators were completing the post SCRAM procedures on the reactors, the tsunami
struck the Fukushima Daiichi nuclear power plant operating stations approximately 30 to
60 minutes following the earthquake. This catastrophic event started a series of events
and failures that led to a loss of all primary and backup electrical power systems. This
loss of all electrical power, known as a complete station blackout, resulted in the three
operating reactors becoming uncontrollable with respect to reactor core cooling. At the
Fukushima Daiichi plant, substantial fuel damage and core meltdowns have occurred in
units 1, 2 and 3. These meltdowns led to explosions in units 1, 2, 3 and 4.
2.5.2
Pressure Protection System Failure
Events from Fukushima highlight the important use of pressure relief valves.
The pressure relief valves worked the way they should work. Unfortunately, the
discharge of the valves was directed to an undesirable location, within the secondary
containment building. Because of the meltdown occurring in the core, the fuel element
coating, zirconium, was heating up and releasing hydrogen gas into the pressure vessel.
24
http://en.wikipedia.org/wiki/2011_T%C5%8Dhoku_earthquake_and_tsunami
35
Zircaloy, undergoes an exothermal chemical reaction with water at high temperatures,
causing a release of hydrogen gas. When the relief valves were manually operated to
vent the steam out, hydrogen gas also escaped into the containment building. Once the
hydrogen found an ignition source, the containment building exploded destroying the
second containment. See Figure 2–11 showing the exploded secondary containment
buildings; Unit 1, Unit 3 and Unit 4.
The lesson learned from this catastrophe, related to pressure relief, is to direct the
pressure relief discharge to an explosion proof, radiological controlled area. If the plants
in Fukushima were designed in this manner, the primary containment and secondary
containment building would not have failed due to an explosion. This could have
prevented (or minimized) the release of radiation and contaminants from the building;
which would have resulted in minimizing the environmental damage and personnel
radiation exposure. Since the primary and secondary containments failed, the high
levels of radiation and contamination being released slowed the emergency responder
actions due to the high exposure concerns. This problem resulted in a delay of restarting
reactor cooling and thus caused more reactor damage from failure to remove decay heat.
Unit 4
Unit 2
Unit 3
Unit 1
Figure 2-11 - Fukushima Containment Buildings for Reactor Units 1 - 425
25
Ragheb, M. Page 67
36
2.5.3
Thermal Protection System Failure
The catastrophe at Fukushima occurred because the reactor operators were
unable to remove the decay heat from the reactors. After the earthquake occurred, the
reactors were SCRAMed to stop the prompt fissions from occurring. RCIC and ECCS
were activated to cool the reactor core. Unfortunately, the tsunami destroyed all primary
and backup AC power sources and internal emergency diesel generators. Once all
power was drained from the final safety backup battery banks, the reactor was left with
only natural circulation cooling utilizing PDHR.
The design of the reactor coolant recirculation system wasn't adequate enough to
maintain natural circulation flow without power. Once natural circulation flow was lost
the decay heat from the reactor core caused a pressure increase. This pressure increase
caused the relief valves lifted causing a loss of reactor coolant. One lesson learned from
this disaster is to design reactor coolant recirculation loops to never lose natural
circulation flow. The second lesson learned is to better protect the last line of defense;
the emergency diesel generators. These generators were placed in pits to prevent fuel
spills from leaking into the environment but the tsunami ended up filing those fuel spill
pits with water and destroying the generators. If the emergency diesel generators were
able to operate, the decay heat generation might have been able to be controlled.
37
3. Discussion
3.1 Pressure Relief Valves
Pressure relief valves are special valves designed in accordance with ASME standards to
protect the integrity of a pressure vessel by relieving abnormally high pressures before a
catastrophic failure occurs. These valves are designed to open automatically whenever
pressure exceeds certain valves and to terminate the discharge automatically when the
pressure decreases below a preset value. There are many types of pressure relief valves
depending on the system requirements. Most nuclear power plants use pilot-actuated
relief valves for their protection.
3.1.1
Pilot-Actuated Pressure Relief Valves Description
A pilot-actuated relief valve is made up of two sections: a main section and a
pilot section. In the unitized pilot-actuated relief valve, the two sections are coupled
directly to each other, see Figure 3–1. In de-coupled pilot-actuated relief valve design,
the main section and the pilot section are separate units connected by a length of pipe,
see Figure 3–2. The main section is a hydraulically operated reverse-seated globe valve.
Use of a reverse seated globe valve allows the reactor plant pressure to help keep the
valve tightly shut. The valve stem extends through the seat port and connects to an
actuating piston in the valve body. A helical compression spring in the valve body holds
the valve stem disc in the shut position.
The pilot section contains its own valve disc, seat, valve stem and a spring
bellows assembly. The pilot disc is held shut by differential pressure acting on the disc
and (at low pressure) by a force exerted by a stretched bellows. The lower end of the
bellows is anchored to the pilot valve body; the upper free end is capped and is
mechanically attached to the pilot valve stem. The capped bellows assembly prevents
inlet pressure from entering the pilot valve upper bonnet.
The differential pressure established across the bellows actuates the main section
of the valve via flow from the pilot section as follows. System pressure, introduced to
the bellows via the sensing port, internally pressurizes the bellows and tends to extend
the bellows linearly.
As system pressure increase and approaches the established
38
pressure relief setting, the extending bellows mechanically unseats the pilot valve disc
and allows steam or water to flow into the actuating piston chamber of the main valve
section. System pressure then acts on the main valve actuating piston, forcing the piston
downward and overcoming both the force of the main relief spring and the system
pressure acting under the disc of the main valve. This action fully opens the relief valve
and permits steam or water to discharge and relieve the overpressure condition. Relief
valve pressure settings are adjusted by varying the normal position of the pilot valve
stem to require more or less bellows travel before engaging the pilot valve disc. For
relief valves, system pressure must increase above the relief setpoint before the designed
flow rate is achieved. The difference between the pressure at the design steam flow or
design water flow is achieved and the relief setpoint is called accumulation.
As system pressure decrease, the pilot bellows contracts and system pressure
reseats the pilot disc. When flow from the pilot valve is shut off, pressure in the main
valve piston chamber discharges at a controlled rate to the outlet side of the valve
through specially designed piston orifices and via space around the piston rings. As the
piston chamber pressure decreases, the spring force, assisted by system pressure, reseats
the main valve. The difference between the relief setpoint and the pressure at which the
relief reseats is called blowdown. If the plant pressure again exceeds the pilot valve
setting, the lifting action is automatically repeated.
39
Figure 3-1- Unitized Pilot Relief Valve26
Figure 3-2 - Separated Pilot Relief Valve27
26
27
http://www.patentgenius.com/image/6318406-2.html
http://www.separation-process.com/pilot-operated-relief-valves.html
40
3.1.2
Pressure Relief Valve Size Determination
Pressure relief valve sizing criteria is controlled by ASME pressure vessel code
section III, subsection NC. Pressure relief valve sizing is completed once the majority of
the reactor coolant recirculation system has been finalized. The size of the relief valve is
dependent on the volumetric flow rate required to protect the plant. A reactor plant
designer must determine the pressure relief volumetric flow rate from the total volume of
the specific system and from a determination of rate in which the pressure will increase
in the system. Once the fastest pressure increase situation is determined, this becomes
the most limiting protection operation. The relief valve size must accommodate this
limit case, with margin, to assure that there is not a failure.
3.1.3
Pressure Relief Valves Setpoint Determination
As described in section 2.4.1.1, multiple relief valves are employed to ensure
protection even when one has failed. While multiple relief valves provide backup
protection from single valve failure, their set pressures must differ enough to prevent the
multiple relief valves from lifting simultaneously and reducing pressure too rapidly. To
prevent multiple pressure relief valves from lifting simultaneously, the set pressures are
staggered. To accomplish this, there is a PSI margin built into the relief valve set point
determination criteria. Also, the valve with the lowest set pressure must not lift during
normal operational transients, and the valve with the highest set pressure must not allow
pressure to exceed the system design pressure. Using design guidance from ASME
pressure vessel code section III, subsection NC to determine the proper setting of a relief
valve, the following must be taken into account: 1. the system normal operating pressure
(NOP), 2. the maximum design transient, 3. instrumentation error, 4. relief valve setpoint
tolerance and 5. maximum design pressure of the system.
Once a NOP of a system is determined, the maximum design pressure is set to
150% of the NOP. In a 1600 MWe BWR nuclear power plant, the reactor coolant
recirculation system is typically operated around 800 PSIG. With this knowledge, the
maximum design pressure can be determined: 800 PSIG * 150% = 1200 PSIG. Once the
NOP has been set, reactor plant designers determine all the operational and pressure
changes, commonly called transients that the reactor plant will go through. A design
41
transient is a temporary increase or decrease in pressure (and/or temperature) that occurs
as a result of other changes occurring in the plant. For example, if the reactor was
operating at 100% power and then decreased to 50% power, there would be a transient
that would cause a sudden rise in temperature and pressure in the reactor. Once the
reactor power reaches 50% power, the reactor will eventually return to a stable pressure
and temperature and the transient is complete. Because there are a large amount of
possible changes within the core, a 12.5% margin in pressure is assumed (for this
project) to account for the worse case high pressure transient; 800 PSIG * 112.5% = 925
PSIG. The exact transient margin would be calculated to determine if 12.5% was a
conservative assumption.
If a relief valve was to lift below 925 PSIG, a normal
operational change in the reactor could potentially cause the first relief valve to lift. To
prevent this from occurring, the first relief valve lift pressure is designed to lift above
this maximum transient with some margin (assume 25 PSI) to account for instrument
error and prevent relief valve cycling.
After the relief valve size is determined and a specific valve is chosen, using
methods described in section 3.1.2, the relief valve setpoint tolerance is obtained.
Manufactures can not guarantee a relief valve will lift at an exact pressure due to
manufacturing / machining differences thus a range of relief valve set pressures are
given. Upon review of a few relief valve manufacturing component data sheets, a 100
PSI relief valve setpoint tolerance is common; ± 50 PSI.
For this example, the first relief valve would be set at 1000 PSIG ± 50 PSI. This
would account for relief valve worse case low opening pressure of 950 PSIG (925 PSIG
to account for the maximum transient and 25 PSI margin). The second relief valve
would be set at 1105 PSIG ± 50 PSI. The second relief valve set pressure would give a 5
PSI margin to prevent both relief valves from opening simultaneously (worse case high
opening of first pressure relief valve at 1050 PSIG (1000 PSIG + 50 PSI) and worse case
low opening of the second pressure relief valve at 1055 PSIG (1105 PSIG - 50 PSI)).
The final margin band to incorporate in the pressure relief system design is above
the second relief valve setpoint and below the maximum design pressure. A reactor
plant designer would not want the second relief valve to lift at exactly the maximum
design pressure.
If a relief valve was set at the maximum design pressure, a
42
manufacturing error / defect or a localized material fatigue issue could cause the pressure
vessel to rupture before the second relief valve lifts. A margin (assume 45 PSI) assures
the second relief valve will lift before a catastrophic failure occurs in the pressure vessel.
See Table 4 for a breakdown of the relief valve setpoints.
43
Table 4 - Relief Valve Setpoint Calculation
PSIG
1200
1155 – 1200
1105 – 1155
1105
1055 – 1105
1050 – 1055
1000 – 1050
1000
950 – 1000
925 – 950
800 – 925
800
%
Above
NOP
Tolerance Description
50%
Setpoint
1200 PSIG - Design Pressure
(45 PSI) Margin to Design Pressure
(50 PSI) Upper Tolerance Band of 2nd Relief Valve
38.125%
1105 PSIG - 2nd Relief Valve Setpoint
25%
1000 PSIG - 1st Relief Valve Setpoint
(50 PSI) Lower Tolerance Band of 2nd Relief Valve
(5 PSI) Margin to Prevent Simultaneous Valve Lifts
(50 PSI) Upper Tolerance Band of 1st Relief Valve
(50 PSI) Lower Tolerance Band of 1st Relief Valve
(25 PSI) Margin to Prevent Unnecessary Lifting
(125 PSI) Margin to Account for Maximum Design Transient
12.5%
800 PSIG - Normal Operating Pressure (NOP)
44
3.2 Operational Power History & Decay Heat
3.2.1
Operational Power History
Operational power history is a calculation that summarizes the operating power
history of a reactor plant. This calculation is dependent on the reactor power history (i.e.
0% - 100%) and time the reactor spent at each power level.
For this project, an
operational power history of 100% power for 10,000 hours is assumed for calculations
described later. Since every reactor plant has a different power rating, operates at
different power levels, and spends different lengths of time at a particular power level;
the operational power histories per plant vary drastically. The operational power history
and power rating directly influences the amount of decay heat generated in the reactor.
For commercial power plants, the operational power histories are relatively close
in comparison to similar reactor power size plants because the power companies'
ultimate goal is for the plant to be operating at 100 percent power all year. In a perfect
scenario, all the commercial plants of the same power rating would operate at 100%
power all the time, thus they would have the exact same operational power history and
the same amount of decay heat. However, in contrast, ships (ex. nuclear powered cargo
ship N/S Savannah) and research reactors (ex. RPI research reactor) have operational
power histories that vary dramatically due to a constant change in reactor power and
operating history; thus creating different operational power histories and decay heat
generation profiles.
3.2.2
Radioactive Decay
Radioactive decay or radioactivity is the phenomenon of an unstable atom or
nucleus becoming more stable through the spontaneous emission of radiation. This
radiation can be in the form of emitted particles such as alpha or beta particles or
electromagnetic emissions such as gamma rays or x-rays. The decay of radioactive
isotopes occurs in a random manner, and the precise time at which a single nucleus will
decay can't be determined.
The fundamental nature of radioactivity is that it is a
statistical process that can be described as a probability that the atoms or nuclei of a
45
substance will undergo a spontaneous transmutation. See Figure 3–3 for a uranium-238
decay chain.
𝟐𝟑𝟖
𝟗𝟐𝐔
→𝛂 →
𝟐𝟑𝟒
𝟗𝟎𝐓𝐡
→𝛃 →
𝟐𝟐𝟔
𝟖𝟖𝐑𝐚
→𝛂 →
𝟐𝟐𝟐
𝟖𝟔𝐑𝐧
→𝛂 →
𝟐𝟏𝟒
𝟖𝟒𝐏𝐨
→𝛂 →
𝟐𝟏𝟎
𝟖𝟐𝐏𝐛
→𝛃 →
𝟐𝟑𝟒
𝟗𝟏𝐏𝐚
𝟐𝟏𝟖
𝟖𝟒𝐏𝐨
𝟐𝟏𝟎
𝟖𝟑𝐁𝐢
→𝛃 →
→𝛂 →
→𝛃 →
𝟐𝟑𝟒
𝟗𝟐𝐔
→𝛂 →
𝟐𝟏𝟒
𝟖𝟐𝐏𝐛
𝟐𝟏𝟎
𝟖𝟒𝐏𝐨
𝟐𝟑𝟎
𝟗𝟎𝐓𝐡
→𝛃 →
→𝛂 →
→𝛂
𝟐𝟏𝟒
𝟖𝟑𝐁𝐢
𝟐𝟎𝟔
𝟖𝟐𝐏𝐛
→𝛃
(𝐬𝐭𝐚𝐛𝐥𝐞)
Figure 3-3 - Uranium 238 Radioactive Decay Chain
α = alpha decay
β = beta decay
*Note - All information in Uranium-238 decay chain was obtained from the chart of
isotopes.
3.2.3
Decay Heat Generation
Unlike all other forms of electrical power generation, upon shutdown of a nuclear
power plant, the power from the core does not instantaneously stop. This remaining
power is generated when fission products release energy by undergoing radioactive
decay, typically β- decay and γ decay for uranium-235 fission daughter products. This
power is commonly referred to as the decay heat production rate or decay heat.
When a reactor is abruptly shut down by the insertion of the control rods, all of
the prompt energy sources are eliminated because virtually all fissions stop. β- decay
and γ decay, however, do not stop. Reactor thermal output does not drop to zero
immediately after shut down; instead it drops to approximately 7 percent of the preshutdown power and continues to decrease at a slower and slower rate as the fission
fragments β- decay and γ decay to stable daughter products.
See Example 4
demonstrating theoretical decay heat using average fission energy values from Table 3.
Example 4 - Theoretical Average Decay Heat
𝑫𝒆𝒄𝒂𝒚 𝑯𝒆𝒂𝒕 =
𝟕.𝟐𝑴𝒆𝑽(𝜷− )+𝟕.𝟐𝑴𝒆𝑽(𝜸)
𝑬𝒏𝒆𝒓𝒈𝒚⁄
𝟐𝟏𝟎.𝟐 𝑴𝒆𝑽(
𝑭𝒊𝒔𝒔𝒊𝒐𝒏)
46
= 𝟔. 𝟖𝟓% ≈ 𝟕%
[4]
The decay heat production rate is proportional to the number of fission fragments
in the reactor. For example, a reactor which has been operating at full power, in this
case a 1600 MWe (4800 MWt) BWR, for a long time contains approximately 1.62x1020
fissions fragments undergoing β- decay and γ decay each second. See Example 5.
Example 5 - Fissions per Second Calculation
𝑑𝐹
1
= 𝑃 ∗ 𝐼𝐸 ∗
𝑑𝑡
1.6𝑥10−13
𝒅𝑭
𝑾𝒂𝒕𝒕
𝒇𝒊𝒔𝒔𝒊𝒐𝒏
𝟏
𝑴𝒆𝑽
= 𝑷[𝑴𝑾𝒕]𝒙𝟏𝟎𝟔 [
] ∗ 𝑰𝑬 [
]∗
[
]
𝒅𝒕
𝑴𝑾𝒕
𝑴𝒆𝑽
𝟏. 𝟔𝒙𝟏𝟎−𝟏𝟑 𝑱𝒐𝒖𝒍𝒆
=[
𝒇𝒊𝒔𝒔𝒊𝒐𝒏𝒔
] [5]
𝒔𝒆𝒄
𝑑𝐹
1
1
𝑓𝑖𝑠𝑠𝑖𝑜𝑛𝑠
= 4800𝑥106 ∗
∗
= 1.62𝑥1020 [
]
−13
𝑑𝑡
185.6 1.6𝑥10
𝑠𝑒𝑐
Where:
F
=
fissions
P
=
reactor power (MWt)
IE
=
immediate energy released per fission, 185.6 MeV (from Table 3)
All of the β- particles and most of the γ particles are absorbed within the core, causing
the reactor coolant within the reactor vessel to heat up. In a large nuclear power plant,
approximately 7 percent of the power is still a significant amount of heat, see Example 6.
This heat generation is large enough to cause reactor damage if not removed from the
core by the reactor coolant. For this reason, reactor power plant designers are careful to
ensure that sufficient coolant flow can be maintained, even in a shutdown reactor.
Example 6 - Decay Heat of 7% Power
𝑸̇𝑫𝑯 = 𝑸̇𝑹𝑿 ∗ 𝟎. 𝟎𝟕
𝑄̇𝐷𝐻 = 4800𝑀𝑊𝑡 ∗ 0.07 = 336𝑀𝑊𝑡
𝑄̇𝐷𝐻 = 336𝑀𝑊𝑡 ∗
47
3.41214 𝑀𝐵𝑇𝑈
𝑀𝑊𝑡 ∗ 𝐻𝑟
[6]
𝑄̇𝐷𝐻 = 1146.48
3.2.4
𝑀𝐵𝑇𝑈
𝐵𝑇𝑈
= 1.14648 ∗ 109
𝐻𝑟
𝐻𝑟
Decay Heat Calculation
Fission product decay heat (excluding neutron capture) is able to be calculated
using methods and data developed in the American National Standard for Decay Heat
Power Generation, ANSI/ANS-5.1-2005. The procedures described in the standard are
applicable for calculation of decay heat for both irrated PWR and BWR reactor
assemblies. The contribution of fission products to the decay heat power, uncorrected
for neutron capture, is calculated from the individual contributions from fission of the
four major fissionable isotopes in low-enriched uranium fuel: uranium-235 (U235),
plutonium-239 (Pu239), uranium-238 (U238), and plutonium-241 (Pu241).
These four
isotopes account for more than 99 percent of the fissions in a typical fuel. Fission of
other isotopes is considered by treating them as uranium-235, which is conservative for
most cooling times.
The standard also corrects for neutron capture, but it is not
necassary for the scoping of this project.
For a detailed analysis of decay heat
generation, reactor design companies use high performance computers and all the data
from this standard to complete an accurate analysis. The assupmtions and procedure
utlized for this project allow these calculations to become managable, using excel; while
still providing the appropriate amount of accuracy.
To accurately determine the decay heat production rate a detailed calculation
could be considered by reviewing all the decay chains of all fission products versus time.
However due to the extreme complexity of this approach, decay heat can be realistically
predicted with sufficient accuracy by a few-group representation (e.g. 13 groups).
ANSI/ANS-5.1-2005 provides details for 23 groups, however the amount of value added
in the calculation is small. To determine the decay heat production rate, first the heat
generated during the operation of the core (from the β- decay and γ decay), commonly
called immediate heat, must be analyzed. The immediate heat production rate (Q̇IH )
from fission is found using equation 7.
𝑸̇𝑰𝑯 = 𝑰𝑬 ∗ ∫ 𝑽𝒄 ∗ 𝜺 ∗ ∑
48
𝟐𝟑𝟓
𝑻𝑯
𝝋𝟐 𝒅𝑽𝒄
[7]
Where:
ε
=
fast fission factor
∑235
𝑇𝐻
=
macroscopic thermal fission cross section for uranium-235 (cm-1)
φ2
=
thermal neutron flux (neutrons/cm2-sec)
Vc
=
reactor core volume (cm3)
The decay heat production rate (Q̇DH ) is the sum of the contributions due to the decay of
several groups of decay chains. Using ANSI/ANS-5.1-2005, the decay chains that are
consentrated on are: uranium-235, plutonium-239, uranium-238 and plutonium-241.
𝑛
𝑄̇𝐷𝐻 = ∑ 𝑄̇𝐷𝐻,𝐶ℎ𝑎𝑖𝑛𝑠
[8]
𝑖=1
Where:
Q̇DH,Chains
=
decay heat production rate from the fission products decay chains
(energy/time-cm3)
The decay heat production rate from the fission products decay chains is equal to the
energy released by each decay times the decay rate.
𝑄̇𝐷𝐻 = 𝐸𝐷,𝑐ℎ𝑎𝑖𝑛𝑠 ∗ 𝜆 ∫ 𝑁𝑑𝑉𝑐
Where:
ED,chain s
=
useable energy released by each decay of a fission product
decay chain (energy/decay)
λ
=
decay constant (sec-1)
N
=
concentration of the fission products decay chains (nuclei/cm3)
49
[9]
Since the concentration of the fission products (N) is position-dependent, it must be
integrated over the core volume to obtain the total number of fission products in the
core.
The time aspect of the decay heat production rate depends on how the
concentration of the fission products changes. The differential equation describing the
rate of change of N is described in equation 10:
235
𝑑𝑁
= 𝛾𝑖 ∗ 𝜀 ∗ ∑ 𝜑2 − 𝜆 ∗ 𝑁
𝑑𝑡
𝑇𝐻
[10]
Where:
γi
=
fission yield of the fission products (nuclei/fission)
The solution to the differential equation, equation 10, for the initial concentration (time =
0) of fission products is given by equation 11:
𝑁(𝑡) =
𝛾𝑖 ∗ 𝜀 ∗ ∑235
𝑇𝐻 𝜑2
(1 − 𝑒 −𝜆∗𝑡𝑓 )
𝜆
[11]
Where:
tf
=
time at constant fission rate
As shown in the in equation 11, the time dependence of the fission product
concentration, N, is governed by (1 − 𝑒 −𝜆𝑖 ∗𝑡𝑓 ). Once a reactor operates a long time at a
constant power, the fission products concentration will reach equilibrium. This extended
operation at a constant power (and constant fission rate), will reach an equilibrium
concentration given by equation 12:
𝑁𝑒𝑞
𝛾𝑖 ∗ 𝜀 ∗ ∑235
𝑇𝐻 𝜑2
=
𝜆
50
[12]
If you substitute equation 12 into equation 9, the total decay heat rate versus time during
the buildup to equilibrium is given by equation 13:
𝑛
𝑄̇𝐷𝐻 (𝑡𝑓 ) = ∑ 𝐸𝐷,𝐶ℎ𝑎𝑖𝑛𝑠 ∗ 𝜆 ∗ ∫ 𝑉𝑐 ∗ 𝑁𝑖,𝑒𝑞 𝑑𝑉𝑐 (1 − 𝑒 −𝜆𝑖 ∗𝑡𝑓 )
[13]
𝑖=1
and the equilibrium decay heat rate is equation 14:
𝑛
𝑄̇𝐷𝐻 (∞) = ∑ 𝐸𝐷,𝐶ℎ𝑎𝑖𝑛𝑠 ∗ 𝜆 ∗ ∫ 𝑉𝑐 ∗ 𝑁𝑒𝑞 𝑑𝑉𝑐
[14]
𝑖=1
When the reactor is shutdown, the fission products will decay with a time dependence
given by 𝑒 −𝜆𝑖 ∗𝑡𝑠 where ts is the time after shutdown.
Therefore, the decay heat
production rate following shutdown is given by equation 15:
𝑛
𝑄̇𝐷𝐻 (𝑡𝑓 , 𝑡𝑠 ) = ∑ 𝐸𝐷,𝐶ℎ𝑎𝑖𝑛𝑠 ∗ 𝜆 ∗ ∫ 𝑉𝑐 ∗ 𝑁𝑒𝑞 𝑑𝑉𝑐 (1 − 𝑒 −𝜆𝑖 ∗𝑡𝑓 )𝑒 −𝜆𝑖 ∗𝑡𝑠
[15]
𝑖=1
Since most of the variables in the equation above are constant, we can substitute many of
these variables with constants from the ANSI/ANS-5.1-2005 specification to make the
calcuation more managable. Equation 15 then becomes equation 16:
13
𝑄̇𝐷𝐻 (𝑡𝑓 , 𝑡𝑠 ) = ∑
𝑖=1
𝛼𝑖𝑗
(1 − 𝑒 −𝜆𝑖 ∗𝑡𝑓 )𝑒 −𝜆𝑖 ∗𝑡𝑠
𝜆𝑖𝑗 𝑖
51
[16]
Table 5 - Coefficients for thermal fission of U235, Pu239, Pu241 and fast fission of U238
Term
index
j
1
2
3
4
5
6
7
8
9
10
11
12
13
U-235 (thermal)
α1j
λ1j
5.28E-04 2.72E+00
6.86E-01 1.03E+00
4.08E-01 3.14E-01
2.19E-01 1.18E-01
5.77E-02 3.44E-02
2.25E-02 1.18E-02
3.34E-03 3.61E-03
9.37E-04 1.40E-03
8.09E-04 6.26E-04
1.96E-04 1.89E-04
3.26E-05 5.51E-05
7.58E-06 2.10E-05
2.52E-06 9.99E-06
Pu-239 (thermal)
U-238 (fast)
α2j
λ2j
α3j
λ3j
1.65E-01 8.92E+00 3.94E-01 4.34E+00
3.69E-01 6.90E-01 7.46E-01 1.71E+00
2.40E-01 2.36E-01 1.22E+00 6.06E-01
1.03E-01 1.01E-01 5.28E-01 1.94E-01
3.49E-02 3.72E-02 1.48E-01 6.98E-02
2.30E-02 1.43E-02 4.60E-02 1.88E-02
3.91E-03 4.51E-03 1.04E-02 6.13E-03
1.31E-03 1.32E-03 1.70E-03 1.38E-03
7.03E-04 5.35E-04 6.91E-04 5.28E-04
1.43E-04 1.73E-04 1.47E-04 1.61E-04
1.76E-05 4.89E-05 2.40E-05 4.84E-05
7.35E-06 2.02E-05 6.93E-06 1.56E-05
1.77E-06 8.37E-06 6.49E-07 5.36E-06
Pu-241 (thermal)
α4j
λ4j
3.09E-01 2.90E+00
5.44E-01 6.49E-01
4.08E-01 2.56E-01
1.58E-01 8.71E-02
4.16E-02 2.51E-02
1.48E-02 1.33E-02
5.82E-03 6.38E-03
1.95E-03 2.02E-03
9.52E-04 6.29E-04
1.82E-04 1.75E-04
1.53E-05 4.02E-05
4.50E-06 1.53E-05
9.83E-07 7.61E-06
Table 6 - Power Fractions for Fission of U235, Pu239, U238and Pu241
Burnup
5 MWd/KgU
4 % U-235 Enrichment
U-235
Pu-239
U-238
Pu-241
0.808
0.129
0.061
0.002
Since there are not equal amounts of uranium-235, plutonium-239, uranium-238 and
plutonium-241 in the fuel at any one time, a percentage of the elements is assumed in
Table 5. This assumption is of uranium-235 at 4 percent enrichment and 5 MWd/KgU
burned (aka short operating history). Calculation of the fission product decay heat
power requires the fraction of fission power contributed by each of the fissionable
nuclides at each irradiation time step. The fractions are required because each fission
nuclide has a unique decay heat power curve as represented by the coefficients described
in Table 6. For low uranium typically used in power reactors, the initial power comes
mainly from uranium-235 and uranium-238. During irradiation and the depletion of
uranium-235, fission power shifts uranium-235 to the plutonium-239 and plutonium-241
52
isotopes. Using equation 16 and values from Tables 528 and 629, the decay heat versus
time can be calculated for each isotope. Each isotope's values are added together to get a
total energy (MeV) per second per fission result. These values can be adjusted to the
size of the reactor (1600 MWe, 4800 MWt) and operational power history (100% power
for 10,000 hours) to get energy per hour. The results of the calculations are summarized
in Table 7 and graphed in Figures 3–4.
28
29
ANSI/ANS-5.1–2005. Pages 20 - 21
Nichols. Page 19.
53
Table 7 - Calculated Decay Heat versus Time
Decay Heat
Decay Heat
Decay Heat
Decay Heat
Decay Heat
Time
(Seconds after
shutdown)
(Minutes after
shutdown)
(Hours after
shutdown)
(Days after
shutdown)
(Months after
shutdown)
(MBTU/hr)
(MBTU/hr)
(MBTU/hr)
(MBTU/hr)
(MBTU/hr)
0.0001
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
6.0
7.0
8.0
9.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
120.0
1140.17777
1096.92471
1062.27526
1032.42310
1006.45754
983.66103
963.46656
945.42458
929.17693
914.43727
900.97545
877.17600
856.66551
838.68986
822.72279
808.38598
753.29481
714.87020
685.61332
662.00457
642.18694
625.09449
610.06892
596.67657
573.66449
554.46092
538.10156
523.94278
511.52832
500.52209
490.67066
662.00457
573.66449
523.94278
490.67066
466.29932
447.36009
432.02950
419.23951
408.30991
398.78217
382.73856
369.46769
358.07529
348.04433
339.05708
304.22644
279.39351
260.19665
244.65818
231.71756
220.72791
211.25559
202.99165
189.22595
178.16343
169.02205
161.29388
154.63610
148.81021
143.64593
244.65818
189.22595
161.29388
143.64593
131.02682
121.34784
113.60579
107.23549
101.87895
97.29233
89.78461
83.81489
78.88495
74.70275
71.08721
58.33431
50.54007
45.24009
41.36823
38.39913
36.04678
34.13463
32.54932
30.06799
28.20201
26.73137
25.52762
24.51203
23.63424
22.86083
65.11453
46.16239
37.88684
33.14985
30.06799
27.88128
26.22310
24.89935
23.80049
22.86083
21.30764
20.04812
18.98871
18.07759
17.28201
14.42356
12.60864
11.31482
10.32785
9.54493
8.90810
8.38028
7.93562
7.22557
6.67741
6.23380
5.86124
5.53955
5.25626
5.00352
14.33254
10.25585
8.32058
7.17469
6.39945
5.81856
5.35279
4.96399
4.63217
4.34548
3.87718
3.51526
3.23136
3.00515
2.82223
2.26708
1.97638
1.78726
1.65722
1.56148
1.49027
1.43625
1.39418
1.33300
1.28919
1.25437
1.22426
1.19677
1.17094
1.14615
54
Decay Heat (MBTU/hr)
1200
1150
1100
1050
1000
950
900
850
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
50
0
Decay Heat versus Time
Seconds
Minutes
Hours
0
10
20
30
40
50
60
Time
70
80
Figure 3-4 - Overview Calculated Decay Heat Versus Time
55
90
100
110
120
3.2.5
Decay Heat Removal
The decay heat that is created after the nuclear reactor is shutdown is removed
using the normal active decay heat removal system (residual heat removal system
(RHRS)). This system consists of an independent loop, consisting of dedicated heat
exchangers and pumps to cool the reactor coolant and fuel elements. See Figure 3–5 for
a typical decay heat removal system.
Figure 3-5 - Residual Heat Removal System30
30
http://www.nrc.gov/reading-rm/basic-ref/teachers/04.pdf
56
3.3 Passive Decay Heat Removal
Passive decay heat removal (PDHR) is utilized when active decay heat removal,
described in section 3.2.5, is unavailable. If active decay heat removal capability should
be lost, decay heat generation within the core will cause reactor plant temperatures to
increase. PDHR, on the other hand, doesn't require AC power to operate. PDHR uses
natural circulation, described in section 3.3.1, along with ambient heat loses to lower the
temperature in the reactor core. Heat losses from the reactor plant to its surrounding
structures, the primary containment, and adjacent buildings will increase as the plant
temperature increases. Hence, heat losses to ambient will increase as the decay heat
generation rate falls off.
In a BWR, during the first hours of the PDHR operations, the decay heat
generation will exceed the ambient heat loss rate. This thermal energy generation will
be dissipated by the heating and boiling of the reactor coolant. Excess steam pressure
may cause relief valve cycling to dissipate the pressure buildup in the reactor vessel.
Unfortunately this action, while helping to reduce the pressure in the reactor vessel and
main steam system, causes a loss of reactor coolant inventory. This loss of reactor
coolant will allow the creation of more steam within the reactor vessel. Once the steam
bubble becomes large enough to cover the feed water return nozzle, the steam will stop
all flow of makeup water into the reactor vessel. This will cause the water level to
continuously decrease, due to the lack of makeup water, and uncover the fuel elements.
In a PWR, during the first hours of the PDHR operations, the decay heat
generation will also exceed the ambient heat loss rate similar to a BWR. The thermal
energy generation is dissipated by the heating of the primary and secondary plant
systems. First, secondary system water inventory will be lost by boiling off the steam
generator inventory and cause steam generator relief valve cycling. This loss of steam
generator water inventory prolongs the heating of the reactor coolant due to the heat
transfer within the steam generator. This heat transfer increases the probability of
success to cool the plant. Following loss of all steam generator inventory, decay heat
continues to heat the primary coolant and may lift a primary relief valve. The lift of a
primary relief valve will cause a loss of reactor coolant volume and potentially uncover
the fuel elements.
57
In both cases, if the decay heat generation rate exceeds the ambient heat loss rate,
reactor coolant inventory will be lost through a relief valve, the fuel channels could
begin to boil dry, and the fuel could overheat and be damaged. If the reactor decay heat
generation falls below the ambient heat loss rate before the fuel uncovers, the reactor
will cool and the fuel will remain submerged and undamaged.
3.3.1
Natural Circulation
During PDHR operations, natural circulation is important in maintaining reactor
coolant flow. Active DHR requires pumping power, with various pumps called forced
circulation, to move water. Natural circulation, on the other hand, achieves flow without
the use of a mechanical source, e.g., no pump.
If there is little or no flow of the reactor coolant, the temperature will increase
rapidly and the creation of steam would increase. Therefore, a reactor plant is designed
to use natural circulation produced by a thermal driving head. A thermal driving head is
a difference in pressure caused by a temperature difference and thus a density difference
between two columns of water. The warmer water, less dense water tends to flow
upward, while cooler, denser water tends to flow downward by gravity. The pressure
difference caused by this phenomenon allows flow in the reactor coolant system without
a reactor coolant recirculation pump assistance.
In reactor plants, natural circulation in the coolant loops may be lost by 1. steam
voiding of a high point or 2. cold trapping in the reactor coolant recirculation loops low
points.
In a PWR, steam voiding can occur as the pressurizer cools off and depressurizes
and the plant reaches saturation. Once saturated plant conditions exist, the bubble in the
pressurizer can transfer into the reactor vessel and reactor plant and interrupt liquid flow.
In a BWR, steam voiding can occur when the steam bubble stops all make-up water
from entering the vessel, thus interrupting fluid flow. This casualty will reduce ambient
losses since the steam is less effective heat transfer properties than liquid-filled piping.
Cold trapping can occur when a portion of the loop piping experiences some
localized cooling. At some point, the flow may stop if the plant lacks sufficient thermal
driving head to push out the column of cooler, denser water that has formed. This can
58
reduce ambient losses by isolating the vessel from a portion of the reactor coolant
recirculation loop heat transfer surfaces.
59
4. Conclusions
Events at the Fukushima Daiichi nuclear power station in Japan have reemphasized the
importance of reliable reactor protection systems. While design requirements were
complex and robust, in a post Fukushima era, reactor plant designs must account for
many new scenarios that were deemed improbable in the past designs. The probability
and severity of the design basis accidents, analyzed in the future design process, will
increase due to the recent nuclear plant accidents as well as the increase in major natural
disasters around the world. These new analyses will help improve the robustness of the
reactor plant safety requirements.
The reactor plant safety requirements are, and will continue to be, stringent
because personnel and environmental safety is paramount. The recent events have
brought skepticism to the general public about the safety posture of all current plants. In
order to prove to the general public that nuclear power is safe and have them remain
tolerant of nuclear power plant risks, the safety posture of every plant must be proven to
be undeniably safe.
Using correct pressure relief protection sizing and setpoint determinations,
described in section 3.1, and updated decay heat generation values, described in section
3.2 and shown in Figure 3–4, and; new nuclear power plant concepts can be designed
with robust integrity. Applying the natural circulation criteria and PDHR concepts,
described in section 3.3, to the reactor plant design will also help improve the safety
posture of the future reactor plants while reducing their dependence on outside AC
power.
Incorporating the design guidance described in this project and applying the
lessons learned from Fukushima, future nuclear power plants will be better equipped to
handle major natural disasters while minimizing the damage of the reactor.
This
improved design information will ease the public's worry about the chances of another
catastrophic disaster like Fukushima occurring near their homes and businesses.
60
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Massachusetts Institute of Technology Nuclear Reactor Laboratory.
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62