Revision 1
December 2014
Control Rods
Student Guide
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Table of Contents
INTRODUCTION .................................................................................................................. 1
TLO 1 CONTROL ROD WORTH CONCEPTS ......................................................................... 3
Overview ........................................................................................................................ 3
ELO 1.1 Control Rod Worth Effect on Reactor Power .................................................. 4
ELO 1.2 Control Rod Worth Definition....................................................................... 14
ELO 1.3 Differential and Integral Control Rod Worth ................................................ 17
ELO 1.4 Differential Control Rod Worth Characteristics ............................................ 20
ELO 1.5 Integral Control Rod Worth Characteristics .................................................. 24
ELO 1.6 Control Rod Position Effects ......................................................................... 27
ELO 1.7 Core Parameters Impact on Control Rod Worth ........................................... 33
TLO 1 Summary........................................................................................................... 42
TLO 2 PLANT OPERATION AND IMPACT OF CONTROL ROD POSITIONING ........................ 44
Overview ...................................................................................................................... 44
ELO 2.1 Core Power Distribution ................................................................................ 44
ELO 2.2 Control Rod Operation Considerations ......................................................... 48
ELO 2.3 Power Peaking and Hot Channels ................................................................. 54
ELO 2.4 Quadrant Power Tilt Ratio Effects ................................................................ 57
ELO 2.5 Calculating Quadrant Power Tilt Ratio ......................................................... 61
ELO 2.6 Reactor Operator Responsibilities ................................................................. 64
TLO 2 Summary........................................................................................................... 67
CONTROL RODS SUMMARY ............................................................................................. 68
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Control Rods
Revision History
Revision
Date
Version
Number
Purpose for Revision
Performed
By
11/6/2014
0
New Module
OGF Team
12/10/2014
1
Added signature of OGF
Working Group Chair
OGF Team
Introduction
For a reactor to operate at any appreciable power level, it must contain more
fuel than required to reach critical mass. This excess fuel is necessary for
overcoming temperature effects, fission-product buildup, and fuel depletion.
A supercritical assembly of fissionable material (i.e., one that is larger than
the minimum critical mass) requires some method to control the chain
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1
reaction. The power would rise at a rate determined by the degree of
supercriticality until temperature effects within the reactor halted the power
rise. For highly supercritical reactors, these temperature effects may not
occur in time to prevent fuel damage.
A reactor-control mechanism must give the operator the means to shut the
plant down, vary the steady-state power level, and ensure that no fuel
damage will occur due to excessive power generation.
Pressurized-water reactors (PWRs) use a combination of control rods and
chemical shim (boron) for reactor control. Boiling-water reactors (BWRs)
also use control rods, but do not use boron for normal reactivity control.
The chemical shim consists of boric acid dissolved in the reactor coolant
system and is used for slow changes in core reactivity and to ensure the
reactor is adequately shut down. Operators use the control rods to bring the
reactor critical and control the power ascension; control rods are essentially
fully withdrawn at full power. Operators use the control rods mainly for
control of fast-changing reactivity transients, power changes, and reactor
trips. Control rods can provide coarse control, fine control, or fast
shutdowns. Reactors include control rods to compensate for short-term
reactivity effects due to fission product poisons, etc. This lesson describes
the uses of control rods and their relationship to core power production.
Control Rods Importance
The understanding of the nuclear effects of control rod motion is essential,
as this is the operator's first and fastest method of reactivity control.
Knowledge of how to use the rod control system to control reactivity, shape
power distribution, and ensure core protection is a key part of "Operator
Fundamentals." There have been several major events resulting in fuel
damage and even death caused by the improper operation of the rod control
system.
Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of 80 percent
or higher on the following Terminal Learning Objectives (TLOs):
1. Explain the concept of control rod worth and how it is affected by
control rod design and changes in core parameters.
2. Explain how control rods affect plant operation and the core power
distribution.
2
Rev 1
TLO 1 Control Rod Worth Concepts
Overview
Understanding how to position control rods to make reactivity changes is a
fundamental knowledge and skill required by a reactor operator. However,
the movement of control rods does not always result in the same reactivity
change due to varying core conditions. The operator must understand how
the design of the control rods and changing core conditions affect the
control rod worth and why this occurs. This section covers how the control
rods are constructed, how they affect reactivity, and how changing core
conditions affect the worth of the control rods.
Control Rod Worth Importance
Precise reactivity control is an "Operator Fundamentals" expectation. An
operator cannot accomplish precise reactivity control without understanding
the design features of the control rods, and how the existing core conditions
affect the effectiveness or worth of the control rods before they are moved.
This will ensure the plant responds as anticipated and minimizes the
negative effects of control rod motion. A good reactor operator is always
capable of predicting the final plant conditions before making any control
rod changes.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Explain the effect of control rods on the neutron lifecycle including
how control rod design and movement affects reactor power level.
2. Describe the term control rod worth.
3. Define the following terms:
a. Differential rod worth
b. Integral rod worth
4. Describe the shape of a typical differential control rod worth curve
and the reason for the shape.
5. Describe the shape of a typical integral rod worth curve and the
reason for the shape.
6. Calculate the effect that control rod position in the core and grouping
control rods has on differential rod worth.
7. Explain how control rod worth is affected by the following core
conditions:
a. Moderator temperature
b. Poison concentration
c. Reactor power level
d. Presence of additional control rods (rod shadowing
e. Boron concentration
f. Neutron spectrum hardening
g. Control rod design and absorber material
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3
ELO 1.1 Control Rod Worth Effect on Reactor Power
Effect of Control Rods on the Neutron Lifecycle Introduction
Reactors contain control rods made of neutron-absorbing materials that
operators use to adjust the reactivity of the core. Each vendor for
commercial nuclear plants has a different design for the control rods used in
their plants. Control rods are the fastest method of changing core reactivity.
Since they change reactivity, they must affect the neutron lifecycle. This
section will discuss how the design and motion of the control rods changes
the neutron life cycle.
Control Rod Design and Construction
Control rods are movable assemblies of neutron-absorbing material that
operators position to control the reactor. Since they absorb neutrons, any
movement of the rods affects the effective multiplication factor (keff) of the
system. An operator can move these control rods into or out of the reactor
core to provide precise, adjustable control of reactivity. The control rods
typically contain elements such as silver, indium, cadmium, boron, or
hafnium as the absorber material.
The material used for the control rods varies depending on reactor design.
Generally, the material selected should have a good absorption crosssection for neutrons and a long lifetime as an absorber (i.e., it should not
burn out rapidly).
Control Rod Shapes
Manufacturers construct control rods in various shapes, depending on the
reactor. Rods may be cylindrical in shape, such as those typically used in a
PWR, or they may be sheets or blades arranged in a cruciform shape, such
as the control rods typically used in a BWR. The cylindrical-shaped control
rods fit inside of the guide tubes within the fuel assembly matrix. The
BWR blades (cruciforms) fit in the gaps between four fuel assemblies.
PWR Control Rods
Generally, the number, design, and arrangement of control rods in a
commercial PWR are unique to the reactor's manufacturer. One of the three
companies listed below designed and manufactured most of the commercial
nuclear power plants in operation in the U.S.:
 Westinghouse
 Combustion Engineering (CE)
 Babcock & Wilcox (B&W)
Westinghouse PWR
In a typical four-loop Westinghouse plant, the core contains 193 fuel
assemblies, each assembly containing a 17 x 17 fuel array. The core also
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Rev 1
contains 53 full-length control rods referred to as rod control cluster
assemblies (RCCAs).
Each RCCA in a 17 x 17 fuel assembly contains 24 individual absorber
rods, or rodlets (fingers). The figure below shows a top view and side view
of a typical RCCA.
Figure: Typical Westinghouse Rod Control Cluster Assembly
Two- and three-loop Westinghouse plants typically contain 33 and 45
RCCAs respectively. The RCCA individual absorber rods in a
Westinghouse plant are composed of a silver-indium-cadmium alloy (AgIn-Cd) rod clad in stainless steel.
Note that in the recent past, some Westinghouse-designed plants used
hafnium control rods clad in stainless steel. Problems with control rod
swelling at these plants led to discontinued use of hafnium control rods.
Combustion Engineering PWR
The core of a typical CE System 80 plant has 89 control rods called control
element assemblies (CEAs). The CEAs are available in three basic
arrangements:
 48 twelve-finger full-length rods
 28 four-finger full-length rods
 13 four-finger partial-length rods
The full-length rodlets are comprised of 150 inches of boron carbide (B4C)
pellets inside Inconel tubes. The partial length rodlets are comprised of a
combination of solid Inconel, a floodable Inconel tube, and B4C pellets.
Some CE designs include silver-indium-cadmium alloy (Ag-In-Cd) tips on
the end sections of certain control absorber rodlets. For these rodlets, the
Rev 1
5
bottom 12 inches is comprised of the Ag-In-Cd alloy. The following figure
shows a side view of a CE control element assembly.
Figure: Typical CE Control Element Assembly
Babcock & Wilcox PWR
A typical B&W plant has 60 control rods, referred to as control rod
assemblies (CRAs), 8 axial power shaping rod assemblies (APSRAs), and
40 burnable poison rod assemblies (BPRAs). Each type of assembly
contains 16 rodlets.
The CRAs utilize a silver-indium-cadmium (Ag-In-Cd) alloy as the neutron
absorber, whereas the APSRAs use Inconel as the neutron absorber. Both
types of rods are clad with stainless steel. The following figure shows a top
view and a side view of a typical CRA.
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Rev 1
Figure: Typical B&W Control Rod Assembly
Advantages of Using Boron Carbide in Control Rods
Boron carbide (B4C) is a common boron compound with several desirable
properties for use in nuclear reactor control rods. In particular, it is stable in
the environment presented by the core of a nuclear reactor (for example,
high temperatures) and it has the ability to absorb neutrons without forming
long-lived radionuclides.
Natural boron is composed of approximately 20 percent boron-10 and
approximately 80 percent boron-11. Boron-10 readily absorbs thermal
neutrons and is therefore the isotope of interest where reactor control is
concerned. In many isotopes like boron-10, the cross-section for neutron
absorption decreases almost linearly with the increase in neutron kinetic
energy. Because of this inverse relationship between the kinetic energy of
the neutron and the microscopic absorption cross-section of the isotope, we
refer to isotopes like boron-10 as 1/v absorbers.
During manufacturing, boron-carbide powder is compacted into a stainless
steel tube to form a control rod. This leaves room for the accumulation of
helium, which results from the boron capture reaction shown in the equation
below.
10
1
11 ∗ 7
4
𝐵 + 𝑛 → ( 𝐵) → 𝐿𝑖 + 𝐻𝑒
5
0
5
3
2
Rev 1
7
Boron is used in control rods because of its high thermal neutron crosssection (σa = 3,837 barns at 0.025 eV). Boron also exhibits a large crosssection for absorption of neutrons in the lower epithermal-energy region.
Epithermal means "above thermal" and refers to that neutron energy region
involving neutrons that are slowing down (i.e., becoming thermalized) in a
reactor.
The boron carbide control rods can absorb almost 100 percent of the
neutrons in a reactor whose energies range from thermal (approximately
0.05 eV at 550°F) up to about 10 eV in the epithermal spectrum. As shown
in figure below, the neutron absorption probability for a boron carbide
control rod drops almost linearly as the kinetic energy of the neutron
increases. As the velocity of an incident neutron increases, the crosssection for the boron absorption reaction shown below (n,) decreases
approximately linearly. This characteristic of boron carbide provides for
effective neutron absorption over a broad range of neutron energies.
Because the control rods in a thermal nuclear reactor encounter a greater
concentration of thermal neutrons (greater than fast or epithermal neutrons),
these control rods are frequently considered thermal neutron absorbers.
Figure: Thermal and Epithermal Neutron Absorption in B4C Control Rods
Advantages of Using Hf and Ag-In-Cd in Control Rods
The hafnium (Hf) or silver-indium-cadmium alloy (Ag-In-Cd) control rods
used by Westinghouse and B&W PWRs have large absorption crosssections for thermal neutrons (Cd and Hf) and/or epithermal neutrons (Ag,
In, Hf).
Silver-indium-cadmium rods are excellent neutron absorbers over a large
energy range. The silver-indium-cadmium rods absorb essentially all
neutrons from thermal energy to approximately 50 eV, as shown in the
figure below.
8
Rev 1
Figure: Thermal and Epithermal Neutron Absorption in Ag-In-Cd Control
Rods
Properties of PWR Control Rod Materials
The following table shows the nuclide cross-sections for neutron absorbers
in both boron-carbide and silver-indium-cadmium control rods used in
PWRs.
Isotope
Abundance
Microscopic
Cross-Section
for Thermal
Neutron
Absorption
(σa)
Microscopic
Cross-Section
for Resonance
Neutron
Absorption
(σa)
Neutron
Energy
B-10
19.9 %
3,837 barns
1,722 barns
Epithermal
average
Ag-107
51.8%
45 barns
630 barns
16.6 eV
Ag-109
48.2%
92 barns
12,500 barns
5.1 eV
In-113
4.3%
12 barns
310 barns
Epithermal
average
In-115
95.7%
203 barns
30,000 barns
1.46 eV
Cd-114
12.2%
20,000 barns
7,200 barns
0.18 eV
Rev 1
9
The previous table shows that the silver-indium-cadmium combination
provides large microscopic absorption cross-sections for both thermal
neutrons and resonance neutrons.
Hafnium
Some control rods also use hafnium as part of the control rod blade. The
advantage of using hafnium is that when it absorbs a neutron, another stable
isotope of hafnium is formed that still has a high cross-section for
absorption of thermal neutrons. Hafnium has five stable isotopes that are
capable of absorbing neutrons in a successive fashion, as shown in the
reaction below.
176
1
177
1
178
1
179
1
180
𝐻𝑓 + 𝑛 →
𝐻𝑓 + 𝑛 →
𝐻𝑓 + 𝑛 →
𝐻𝑓 + 𝑛 →
𝐻𝑓
0
0
0
0
72
72
72
72
72
Characteristics of Natural Hafnium
The "nonburnable" characteristic of hafnium leads to longer control-rod life.
The following table shows the characteristics of natural hafnium.
Isotope
Natural Abundance
Microscopic Cross-Section for
Neutron Absorption (σa)
Hf-176
5.2%
26 barns
Hf-177
18.6%
373 barns
Hf-178
27.3%
84 barns
Hf-179
13.6%
43 barns
Hf-180
35.1%
13 barns
Resonance-Neutron Absorbers
Another factor in control-rod material selection is that materials that absorb
epithermal (resonance) neutrons are often preferred to those that only have
high thermal-neutron absorption cross-sections. Resonance-neutron
absorbers absorb neutrons in the epithermal-energy range.
The path lengths traveled by epithermal neutrons in a reactor are greater
than those traveled by thermal neutrons, therefore, a resonance absorber will
absorb neutrons that originated farther (on average) from the control rod, as
compared to a pure thermal absorber. This has the effect of making the
zone of influence around a resonance absorber larger than that around a
thermal absorber, which makes it more useful in a control rod.
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Rev 1
Effect of Control Rods on the Neutron Life Cycle
As control rods are positioned (withdrawn and inserted) within the core, the
amount of reactivity in the core is changed. This change in reactivity is a
result of the effects of the control rods' neutron absorbers on the effective
multiplication factor (keff).
Effects on Six-factor Formula
Recall that the six-factor formula yields the effective multiplication factor:
𝑘𝑒𝑓𝑓 = 𝜀𝐿𝑓 𝜌𝐿𝑡ℎ 𝑓𝜂
Withdrawing a control rod assembly removes the rod’s strong neutron
absorbing capability from the active fuel region of the core. Relating the
effects of control rod motion to the six-factor formula explains how this
results in positive reactivity addition to the core. The terms in the six-factor
formula most affected by control rod motion are the non-leakage
probabilities (Lf and Lth), the resonance escape probability (ρ), and the
thermal utilization factor (f).
Effects on Non-leakage Probabilities
Control-rod withdrawal effectively increases the size of the core for neutron
production. As effective core size increases, the average neutron must
travel farther to leak out of the core; therefore, neutron leakage decreases.
This results in an increase in both of the non-leakage probabilities (Lf and
Lth), which increases keff.
Effects on Resonance Escape Probability
The control rods contain absorber material that has a high absorption crosssection for neutrons above the thermal energy level, resulting in the
absorption of epithermal neutrons. This results in a decrease in the
resonance escape probability and a decrease in keff, when the rods are
present in the core. Withdrawing the rods from the core causes absorption
of fewer resonance-energy neutrons, which results in an increase in the
resonance escape probability, and an increase in keff.
Effects on Thermal Utilization Factor
The contribution to the overall change in reactivity from the changes in the
fast and thermal non-leakage terms and the resonance escape probability of
on the six-factor formula, due to control rod withdrawal, is small in
comparison to the change in the thermal utilization factor. The equation for
the thermal utilization factor has a term in it that accounts for absorption of
neutrons in "other" core materials, including control rods. This equation as
written below shows the control-rod contribution to the thermal utilization
factor:
Rev 1
11
∑ 𝑓𝑢𝑒𝑙
𝑎
↓↑ 𝑓 =
𝑓𝑢𝑒𝑙
𝑚𝑜𝑑𝑠
𝑐𝑜𝑛𝑡𝑟𝑜𝑙
𝑟𝑜𝑑𝑠
𝑜𝑡ℎ𝑒𝑟
∑
+∑
+∑
↑↓ + ∑
𝑎
𝑎
𝑎
𝑎
Upon insertion of a control rod into the core (refer to the blue arrows in the
equation above), the atom density of the neutron absorber in the fuel region
increases. This increases the denominator and decreases the overall
fraction; this means that the fuel becomes less competitive in absorbing
thermal neutrons (i.e., f and keff both decrease). Since fewer neutrons are
available to cause fission, we are adding negative reactivity to the core.
This negative reactivity causes reactor power to decrease.
Upon withdrawal of a control rod (refer to the red arrows in the equation
above), the atom density of the neutron absorber in the fuel region
decreases. This decreases the denominator and increases the overall
fraction; this means that the fuel becomes more competitive in absorbing
thermal neutrons (i.e., f and keff both increase). Since the fuel is absorbing
more neutrons, positive reactivity is added into the core. This positive
reactivity addition will cause reactor power to increase.
Increasing the value of the thermal utilization factor means that a greater
number of neutrons are available for absorption by the fuel, which causes an
increase in keff. Since the fuel is absorbing more neutrons, and keff
increases, the core experiences an increase in positive reactivity. This
positive reactivity addition will result in a reactor power increase as control
rods are withdrawn.
As reactor power primarily follows steam demand, the effects of rod motion
on reactor power are only transient in a critical reactor. Without a change in
steam demand, reactor power will return to its original value, keff will return
to unity, and core reactivity will return to zero, due to the inherent reactivity
feedback mechanisms from the fuel and moderator temperature coefficients.
If the rods use silver and indium, rod movement also changes the resonance
escape factor, by adding/removing resonance materials from the core. A
rod insertion causes the resonance escape factor and keff to decrease, while a
rod withdrawal causes both to increase.
Reactor Trip
The ability to insert negative reactivity into the core using control rods is
very important to the safe operation of a nuclear reactor. During reactor
operation, occasions may arise where it is necessary to shut down the
reactor rapidly. Control rods provide a means of inserting a very large
amount of negative reactivity very quickly to attain rapid shutdown.
A reactor trip (or scram) is the rapid insertion of all control rods to their
fully inserted position. This action inserts a large amount of negative
reactivity into the core in a very short time, driving the reactor subcritical.
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Rev 1
Discussion Topic
Describe the change in the boron-10 microscopic neutron absorption
cross-section as the plant progresses from cold shutdown conditions to hot
full-power operation.
Answer
Since boron-10 is a 1/v absorber, the microscopic neutron absorption
cross-section continuously decreases as the plant's temperature is
increased.
Discussion Topic
State two disadvantages of boron control rods, as compared to silverindium-cadmium control rods.
Answer
Boron control rods are not as good at absorbing epithermal neutron
absorbers compared to silver-indium-cadmium rods. When boron absorbs a
neutron, the reaction generates helium gas. This gas has the negative effect
of increasing the internal pressure of the control rod as it absorbs neutrons.
Discussion Topic
What is the advantage of using hafnium control rods?
Answer
When hafnium absorbs a neutron, the resulting isotope also has a good
microscopic absorption cross-section for thermal neutrons, resulting in
longer control rod life (unlike other absorber materials whose isotopes do
not exhibit strong microscopic absorption cross-sections).
Discussion Topic
State an advantage of using a resonance absorber material for the control
rod construction versus a purely thermal absorber material.
Answer
Since neutrons exist at all energy levels within the core, having a control
rod capable of absorbing neutrons of varying energies ensures that the
Rev 1
13
operator will be able to control the core's reactivity at any time in life.
Thermal-neutron energy level increases over core life; by having rods that
can absorb neutrons at higher energies, these rods will still be effective even
at the end of life.
Knowledge Check – NRC Bank
A nuclear reactor is exactly critical below the point of
adding heat (POAH) during a reactor startup at the end of
core life. Control rods are withdrawn for 20 seconds to
establish a 0.5 disintegrations per minute startup rate.
Reactor power will increase...
A.
continuously until control rods are reinserted.
B.
and stabilize at a value slightly below the POAH.
C.
temporarily, then stabilize at the original value.
D.
and stabilize at a value slightly above the POAH.
Knowledge Check – NRC Bank
A nuclear reactor is critical at 50 percent power. Control
rods are inserted a short distance. Assuming that the
main turbine generator load remains constant, actual
reactor power will decrease and then...
A.
stabilize in the source range.
B.
stabilize at a lower value in the power range.
C.
increase and stabilize above the original value.
D.
increase and stabilize at the original value.
ELO 1.2 Control Rod Worth Definition
Introduction
The change in core reactivity from the movement of the control rods is a
variable, but the value is predictable if the reactor operator understands the
location of the control rods in relation to the neutron flux distribution in the
core. This section will discuss how the control rod worth varies by core
location and variations in the neutron flux profiles.
Control Rod Effectiveness
The effectiveness or reactivity worth of a control rod depends largely upon
the value of the neutron flux at the location of the rod, compared to the
average neutron flux. The control rod has a maximum effect or worth, if it
is located where the flux is highest.
14
Rev 1
If a reactor has only one control rod, maximum worth will result upon
insertion of the rod in the center of the reactor core. The following figure
shows the effect of such a rod on the flux distribution.
Figure: Effect of Control Rod on Radial Flux Distribution
If we add additional rods to this simple reactor, the most effective location
to place them would be in a location where the flux is highest, such as the
peaks at point A around the control rod.
Numerous control rods are required for a reactor that has a large amount of
excess reactivity. The exact amount of reactivity that each control rod
inserts depends upon the reactor design.
Control Rod Worth
The effectiveness of a specific control rod in absorbing neutrons is termed
control rod worth (CRW). As a control rod is moved into or out of a reactor
core, the core characteristics change (primarily, in the region near the tip of
the control rod). Since only a small region of the core near the tip of the rod
changes due to rod motion, the amount of reactivity inserted into the core
depends on conditions in this region.
Effect of Neutron Flux on Control Rod Worth
If the neutron flux near the tip of a particular rod is large, a higher
percentage of neutrons have a probability of absorption by that control rod.
The reactivity change due to the motion of this particular control rod will be
greatest when the tip of the rod is moving through the region of the core
with the most neutron flux.
Effect of Control Rod Location on Control Rod Worth
Another factor determining CRW is the relative importance of the neutrons
near the tip of the control rod. Neutrons produced near the edge of the core
are more likely to leak out of core and, therefore, are less likely to cause
fission. Additionally, neutrons thermalized in a region of the core with a
high poison concentration have a higher probability of capture by the poison
and, therefore, are less likely to cause fission.
Rev 1
15
Neutrons near the edge of the core, in regions of high poison concentration,
or in areas with low fuel concentration, are of lesser importance to a
reactor's chain reaction because they are less likely to cause fission in the
first place. The neutrons most likely to cause fission are born near the
center of the reactor's core and in regions of low poison concentration and
high fuel concentration.
Reactivity changes are largest, therefore, when the tip of a control rod
moves through regions where the neutrons produced are relatively
important to the nuclear chain reaction. In most cases, the neutron flux
tends to be greater in the same areas of the core where the importance of the
neutrons is greater.
In general, control rods located near the center of the core tend to produce a
greater reactivity effect, during motion, than those located on the periphery
of the core. For a particular control rod, the amount of reactivity change
produced by motion of the rod tends to be greater, when the tip of the rod is
moving near the center of the core.
Knowledge Check
Control rods near the center of a nuclear reactor’s core
generally have greater control rod worth than control
rods on the periphery of the core because:
16
A.
A larger magnitude of neutron flux is found near the
center of the core and the neutrons produced in the center
of the core are more likely to result in fission.
B.
The control rods located in the center of the core tend to
be longer than the control rods located near the outer
edges of the core and therefore have more area for
neutron absorption.
C.
The control rods located near the center of the core tend
to move faster than control rods located near the outer
edges of the core and therefore can affect neutron flux
levels more quickly.
D.
Control rod motion near the center of the core results in
greater moderator displacement as compared to control
rod motion on the periphery of the core, making fewer
thermal neutrons available for fission.
Rev 1
ELO 1.3 Differential and Integral Control Rod Worth
Differential and Integral Control Rod Worth Introduction
This section introduces two terms pertaining to control rod worth.
Differential rod worth (DRW) is the instantaneous rate of reactivity addition
and integral rod worth (IRW) is total reactivity addition for a given rod
movement. To make a controlled power change or compensate for
changing fission-product-poison concentrations, the operator not only needs
to know the total amount of reactivity needed, but must also determine the
rate at which this reactivity is to be added. It is important to understand
how the present plant conditions could raise or lower the value of CRW,
because the control rods do not always have the same worth each time they
move.
Integral and Differential Control Rod Worth
Personnel determine control rod worth experimentally, and typically
perform this determination periodically, during low-power physics testing.
For example, personnel withdraw a control rod in small increments, such as
0.5 inch, and determine the change in reactivity after each increment of
withdrawal. Plotting the resulting reactivity added versus rod position
yields a graph similar to the one shown in the figure below, which depicts
the IRW over the full range of rod withdrawal.
The IRW at a given amount of withdrawal (i.e., the area under the curve,
from the bottom of the core up to withdrawal position) is the total reactivity
worth of the rod at that point. The total reactivity added, when moving a
rod from an intermediate position (such as X1, in the figure below) to
another position (e.g., X2), is equivalent to the area under the curve between
those positions.
Figure: Integral Control Rod Worth
Rev 1
17
The instantaneous slope of the above curve (i.e., ∆ρ/∆X) is the amount of
reactivity inserted per unit of withdrawal at a given location. This slope is
greatest when the control rod is at the core midplane, since that is the area
of greatest neutron flux; hence, the amount of change in neutron absorption
is greatest in this area.
The slope of the IRW curve at any given point is the rate of change of rod
worth (i.e., the DRW) for that rod position. The figure below shows a plot
of the slope of the IRW curve, termed the DRW curve.
Figure: Differential Control Rod Worth
In the areas near the top and bottom of the core (where there are fewer
neutrons, due to leakage), rod movement adds little reactivity; hence, the
rate of change in rod worth (i.e., the DRW) is small in these areas. As the
rod approaches the center of the core (where the neutron flux is highest), it
has a greater effect on reactivity, and the change in rod worth per inch of
withdrawal is higher. At the core midplane, the DRW is greatest.
Differential Rod Worth
Differential control rod worth is the reactivity change per unit movement of
a control rod (i.e., the change in reactivity resulting from a unit change of
control rod position). Since control rods move vertically, many refer to
control rod position as rod height. For a commercial nuclear reactor, the
number of inches moved or the number of steps taken by the control rod’s
lifting mechanism usually provides a measure of control rod position.
The equation below defines differential rod worth:
𝐷𝑅𝑊 =
∆𝜌
∆𝐻
Where:
DRW = differential control rod worth
Δρ = reactivity change
ΔH = change in control rod height
Typical units of DRW include ρ, Δk/k, or pcm per inch, step, or %
withdrawn (e.g., ρ/step, Δk/k/inch, pcm/%).
18
Rev 1
The DRW depends on the relative flux near the control rod's tip, the relative
importance of the neutrons near the tip, and the control rod itself.
𝜙𝑡𝑖𝑝
𝐷𝑅𝑊 = 𝐶 (
)𝜓
𝜙𝑎𝑣𝑔
Where:
DRW = differential control rod worth
C = constant based on control rod size, shape, and neutron-absorbing
material
ϕtip = neutron flux near control rod tip
ϕavg = average neutron flux in core
ψ = importance factor
In most reactors, importance factor is directly proportional to local relative
flux:
𝜓∝
𝜙𝑡𝑖𝑝
𝜙𝑎𝑣𝑔
Therefore, DRW is proportional to the square of the local relative flux, as
shown in the following equations:
𝜙𝑡𝑖𝑝
𝜙𝑡𝑖𝑝
𝐷𝑅𝑊 = 𝐶 (
)(
)
𝜙𝑎𝑣𝑔 𝜙𝑎𝑣𝑔
2
𝜙𝑡𝑖𝑝
𝐷𝑅𝑊 ∝ (
)
𝜙𝑎𝑣𝑔
Discussion Topic
With the plant at the beginning of a new cycle (BOL) and at 50 percent
power, describe how a hypothetical control rod's worth varies as it
progresses from full out to full in.
Answer
With the plant at 50 percent power at BOL, the axial flux shape should be
shifted towards the bottom half of the core, due to inserted rods. As the
hypothetical control rod begins to insert, it moves through a low local flux
region, which results in a low CRW. As the rod continues to insert, the
local neutron flux increases, until it reaches a maximum below core
midplane; hence, the CRW would increase, until reaching this maximum
neutron flux. Continuing to insert the control rod will result in a
continually decreasing CRW, until the rod reaches the bottom of the core.
Practice:
The average neutron flux in a reactor is 1.2 x 1012 n/cm2-sec. By what
factor does a control rod’s differential worth change as it moves from a
Rev 1
19
region with a flux of 2.2 x 1012 n/cm2-sec to a region with a flux of 1.5 x
1012 n/cm2-sec?
Knowledge Check
NRC Example Question
A control rod is positioned in a nuclear reactor with the
following neutron flux parameters: core average thermal
neutron flux = 1 x 1012 neutrons/cm2-sec.
Control rod tip neutron flux = 5 x 1012 neutrons/cm2-sec.
If the control rod is slightly withdrawn such that the tip
of the control rod is located in a neutron flux of 1013
neutrons/cm2-sec, then the differential control rod worth
will increase by a factor of _______. (Assume the
average flux is constant.)
A. 0.5
B. 1.4
C. 2.0
D. 4.0
ANSWER: D Since the neutron flux at the rod tip went
up by a factor of 2, the total worth increased by 22 or by a
factor of 4.
A.
0.5
B.
1.4
C.
2.0
D.
4.0
ELO 1.4 Differential Control Rod Worth Characteristics
Differential Control Rod Worth Introduction
Differential rod worth varies greatly from the bottom to the top of the core.
At some core heights, the rods have almost no effect on the neutron
population while at other heights they have a large effect. To control the
reactor precisely, the reactor operator must be able to determine the effect
on reactivity that each movement of control rods will produce. This section
will relate the control rod worth to its location in the core.
Differential Control Rod Worth Definition
The DRW is the amount of reactivity a control rod or group of control rods
adds per incremental movement. The CRW is directly related to the
neutron flux at the tip of the control rod compared to the average neutron
flux. Depending upon the control rod's location within the core, the local
flux at the control rod tip can be much higher or much lower than the
average flux, which results in a large variance in the DRW.
20
Rev 1
Differential Control Rod Worth Example
As a control rod moves, the differential worth of the rod changes. The
neutron flux in a bare homogeneous core is greatest near the core midplane.
The figure below shows this axial flux variation.
Figure: Axial Flux Variation in a Bare Homogenous Core
Based upon the above figure, DRW will be the greatest near the core
midplane and lowest near the top and bottom of the core, due to the
variation in the neutron flux. Any change that affects the axial flux
distribution would also affect the DRW.
The movement of the control rods changes the axial flux shape and,
therefore, the shape of the DRW curve. Neutron flux is depressed in the
region of the core where control rods are present and is greater in regions
where there are no control rods (i.e., where control rods have been
withdrawn).
Axial neutron flux distribution shifts as control rods move into or out of the
core. The figure below shows the axial neutron flux shift from core
midplane to near the core bottom, as personnel insert a control rod bank
from the top to the middle of the core.
Rev 1
21
Figure: Shift in Core Axial Neutron Flux due to Control Rod Insertion
When the control rods are near the bottom of the core (i.e. fully inserted),
the neutron flux peak will shift back to the core midplane. Since the fully
inserted rods are a uniformly distributed poison (in the vertical dimension),
the axial flux distribution will return to its original shape.
Differential Rod Worth for Banked Rods
A rod bank is a group of control rods that move together. The figure below
shows a graph of DRW versus rod height, for a typical reactor with banked
control rods.
Figure: Differential Rod Worth for Banked Control Rods
As can be seen in the above figure, the DRW for a group of rods is similar
to that for an individual rod; i.e., group DRW is greatest near the core
midplane and least near the top and bottom of the core.
22
Rev 1
Sample Question: (QID: P856)
During normal full power operation, the differential control rod worth is
less negative at the top and bottom of the core compared to the center
regions due to the effects of:
A. reactor coolant boron concentration
B. neutron flux distribution
C. xenon concentration
D. fuel temperature distribution
Due to increased neutron flux leakage at the top and bottom of the core the
local flux at the tip of the control rod is less than it is towards the center of
the core. The correct answer is B.
Sample Question:
As moderator temperature increases, the differential rod worth becomes
more negative because:
A. decreased moderator density causes more neutron leakage out of the
core
B. the moderator temperature coefficient decreases, causing decreased
neutron competition
C. fuel temperature increases, decreasing neutron absorption in fuel
D. decreased moderator density increases neutron migration length.
An increased moderator temperature increases the space between moderator
molecules becoming less dense. The neutrons are able to travel farther
without interaction due to this density change and are more likely to reach a
control rod increasing the control rod effect on the core. The correct answer
is D.
Rev 1
23
Discussion Topic
With the plant at the beginning of a new cycle (BOL) and at 50 percent
power, describe how a control rod's worth varies as a bank of eight rods
are inserted from full out to full in.
Answer
With the plant at power at BOL, the axial flux shape should be shifted
towards the bottom half of the core. Therefore, as the control rods begin
to insert they are moving through a low local flux region resulting in a
low control rod worth. As the rods continue to insert, the local neutron
flux increases until it reaches a maximum somewhere below core
midplane. Therefore, the control rods' worth would continue to increase
until reaching this maximum neutron flux height in the core. Continuing
to insert the control rods further will result in their worth decreasing until
it is minimal again at the bottom of the core. Since all the rods in a bank
are moved at the same time, you can discuss bank differential rod worth
the same way you can discuss an individual control rod's worth.
Knowledge Check – NRC Bank QID: P655
Which one of the following parameters typically has the
greatest influence on the shape of a differential rod worth
curve?
A.
Core radial neutron flux distribution
B.
Core axial neutron flux distribution
C.
Core xenon distribution
D.
Burnable poison distribution
ELO 1.5 Integral Control Rod Worth Characteristics
Integral Control Rod Worth Introduction
As the control rods move, the core experiences increased reactivity with
each increment of rod motion; the DRW provides a numerical measure of
this incremental addition. The total reactivity effect of moving the rods
from one position to another is termed the IRW. A knowledge of the total
amount of reactivity added by a given rod motion is essential for calculating
core reactivity balances, estimating critical rod positions, and predicting the
effect of a proposed rod position change.
Integral Control Rod Worth Definition
The reactivity inserted by moving a control rod from an initial position
(e.g., fully inserted) to another rod height is the IRW at that height. The
24
Rev 1
IRW at a given rod position is the integration (or summation) of all the
DRWs up to that point of withdrawal; mathematically, this is equivalent to
the area under the differential rod worth DRW curve up to a given
withdrawal position. The same concepts apply to any change in control rod
height (i.e., between any initial and final positions).
Integral Control Rod Worth Example
A reactor operator may select the reference position for control rods for
convenience, and the reference position may be the fully inserted or fully
withdrawn position. In most commercial nuclear reactors, the control rods
are fully withdrawn at 100 percent power; hence, many operators select the
top of the core as the reference position for control rod movement.
Withdrawing control rods adds positive reactivity to the reactor core. In
this case, the IRW is zero at zero steps (i.e., rods fully inserted) and
increases with withdrawal of the control rods from the core.
Conversely, inserting control rods from the fully withdrawn position adds
negative reactivity to the core. In this case, the IRW is zero when the rods
are fully withdrawn and becomes more negative with insertion of the
control rods into the core. The figure below is a graph of the IRW curve
and its corresponding DRW curves for a typical three-bank design.
The figure below displays the two standard methods of denoting IRW;
either as positive reactivity added to core, or as negative reactivity removed
from core. The units for measuring rod bank height may be percent, inches,
or steps withdrawn.
The left graph (A) has the reference for rod worth at the bottom of the core,
while the right graph (B) has the reference at the top of the core. In either
case, the equation below yields the reactivity change resulting from any rod
motion:
∆𝜌 = 𝐼𝑅𝑊𝑓𝑖𝑛𝑎𝑙 − 𝐼𝑅𝑊𝑖𝑛𝑖𝑡𝑖𝑎𝑙
Figure: Integral Rod Worth Curves Referenced to
Bottom and Top of Core
The figure below shows a typical differential and integral rod worth curves
for a Westinghouse commercial nuclear reactor for Cycle 1 fuel loading at
the beginning of core life (BOL) and hot zero power (HZP) conditions.
Rev 1
25
Some manufacturers present control rod curves for hot full power (HFP), so
be extra careful when you are using the curve book to ensure or that you are
using the correct curve for the given plant conditions.
The acronym for cold zero power (CZP), describes conditions where the
coolant temperature is below 200°F.
Figure: IRW and DRW Curves for Westinghouse Plant at HZP
Example:
The total amount of reactivity added by changing control rod position from
a reference height to any other rod height is called:
A. differential rod worth
B. shutdown reactivity
C. integral rod worth
D. reference reactivity
The integral rod worth is zero at zero steps and will increase as rods are
withdrawn from the core. Many commercial reactors operate with all of the
control rods withdrawn completely; so many operators select the top of the
core as the reference. As the control rods enter the core from the reference
position, they add negative reactivity to the core. The integral rod worth is
26
Rev 1
zero when rods are fully withdrawn; inserting the rods causes rod worth to
become more negative. The integral rod worth is the total reactivity added
(positive or negative) from one reference point in core to another point
within the core. The correct answer is C.
Knowledge Check
Which one of the following expresses the relationship
between differential rod worth (DRW) and integral rod
worth (IRW)?
A.
IRW is the slope of the DRW curve.
B.
IRW is the inverse of the DRW curve.
C.
IRW is the sum of the DRWs between the initial and
final control rod positions.
D.
IRW is the sum of the DRWs of all control rods at a
specific control rod position.
ELO 1.6 Control Rod Position Effects
Introduction
We have discussed control rod worth only in terms of magnitude and
polarity. Using developed and supplied rod worth curves, we will calculate
the reactivity addition for various rod movements. This is an important
concept, as the reactor operator must be able to perform calculations of
reactivity additions from rod motion before he or she begins to move rods.
The knowledge of the increase in reactivity following the rod motion allows
the reactor operator to control the evolution by observing that the plant
responded as he or she had predicted. This is a required "Operator
Fundamentals" ability.
Integral and Differential Control Rod Worth Examples
The following exercises will reinforce the concepts of integral and
differential rod worth.
Example 1:
Using the integral rod worth curve provided in the figure below, find the
reactivity inserted by moving the rod from 12 inches withdrawn out to 18
inches withdrawn.
Rev 1
27
Figure: Rod Worth Curves for Example Problems
Solution:
The integral rod worth at 12 inches is 40 pcm and the integral rod worth at
18 inches is 80 pcm.
∆𝜌 = 𝜌𝑓𝑖𝑛𝑎𝑙 − 𝜌𝑖𝑛𝑖𝑡𝑖𝑎𝑙
∆𝜌 = 𝜌18 − 𝜌12
∆𝜌 = 80 𝑝𝑐𝑚 − 40 𝑝𝑐𝑚
∆𝜌 = 40 𝑝𝑐𝑚
Example 2:
Using the above provided in differential rod worth curve, calculate the
reactivity inserted by moving the rod from 10 inches withdrawn to 6 inches
withdrawn.
Solution:
The solution is the area under the curve for the given interval. The answers
obtained in the following approximation may vary slightly depending upon
the degree of approximation.
Method 1. Treating the range from 10 inches to 6 inches as a trapezoid, that
is, taking the end values of pcm/inch and multiplying their average by the 4
inches moved, yields the following. (This is negative because the rod was
inserted).
𝑝𝑐𝑚
𝑝𝑐𝑚
8
+3
𝑖𝑛𝑐ℎ
𝑖𝑛𝑐ℎ
(
) (4 𝑖𝑛𝑐ℎ𝑒𝑠) = −22 𝑝𝑐𝑚
2
Method 2. Using the central value of rod position at 8 inches yields an
average rod worth equal to 5.5 pcm/inch. Multiplying by the 4 inches of
rod travel yields the answer:
𝑝𝑐𝑚
(5.5
) (4 𝑖𝑛𝑐ℎ𝑒𝑠) = −22 𝑝𝑐𝑚
𝑖𝑛𝑐ℎ
28
Rev 1
Method 3. Breaking the rod travel total into two parts (10 inches to 8
inches and 8 inches to 6 inches) yields:
𝑝𝑐𝑚
𝑝𝑐𝑚
8
+ 5.5
𝑖𝑛𝑐ℎ
𝑖𝑛𝑐ℎ
(
) (−2 𝑖𝑛𝑐ℎ𝑒𝑠) = −13.5 𝑝𝑐𝑚
2
𝑝𝑐𝑚
𝑝𝑐𝑚
5.5
+3
𝑖𝑛𝑐ℎ
𝑖𝑛𝑐ℎ
(
) (−2 𝑖𝑛𝑐ℎ𝑒𝑠) = −8.5 𝑝𝑐𝑚
2
(−13.5 𝑝𝑐𝑚) + (−8.5 𝑝𝑐𝑚) = −22 𝑝𝑐𝑚
In this example, the various approximations used did not cause any
difference because the problem deals with a section of the curve with an
approximately constant slope. To obtain the value over the interval
between 8 inches and 20 inches, however, would require the use of several
subintervals (as in the last approximation) to obtain an accurate answer.
Example 3:
For the differential rod worth data given below, construct differential and
integral rod worth curves.
Interval (inches)
Reactivity Inserted (pcm)
1.
0 to 2
10
2.
2 to 4
20
3.
4 to 6
40
4.
6 to 8
60
5.
8 to 10
60
6.
10 to 12
40
7.
12 to 14
20
8.
14 to 16
10
Solution for differential rod worth:
For each interval, the number of pcm/inch must be determined. For
example, in the first interval (0 inches to 2 inches), 10 pcm is added.
Therefore, the differential rod worth equals an average 5 pcm/inch. We will
plot this value of differential rod worth at the center of each interval. The
center of the interval 0 inches to 2 inches is 1 inch. The table below lists
the values of pcm/inch for each interval.
Rev 1
29
DIFFERENTIAL ROD WORTH
Interval Center
pcm/inch
1.
1
5
2.
3
10
3.
5
20
4.
7
30
5.
9
30
6.
11
20
7.
13
10
8.
15
5
Solution for integral rod worth:
To plot the integral rod worth, merely develop a cumulative total of the
reactivity added after each interval, as listed in the table below.
INTEGRAL ROD WORTH
Interval Endpoint
Summed Reactivity (pcm)
2
10
4
30
6
70
8
130
10
190
12
230
14
250
16
260
Using the values in the two tables developed above, we plot the values of
pcm/inch for each interval in the differential rod worth figure shown below
left, and the cumulative total of the reactivity added after each interval in
the integral rod worth figure shown below right.
30
Rev 1
Figure: Rod Worth Curves from Example
Given an integral rod worth curve, you can generate a differential rod worth
curve from the integral rod worth data. Select a convenient interval of rod
withdrawal, such as 1 inch or 2 inches. Then, determine from the curve the
amount of reactivity added for each equal interval of rod withdrawal. A
plot of this reactivity addition versus rod withdrawal represents differential
rod worth.
Examples
1. Consider a control rod in a nuclear reactor with the following neutron
flux parameters:
Core average thermal neutron flux = 1012 neutrons/cm2-sec
Control rod tip neutron flux = 5 x 1012 neutrons/cm2-sec
If the control rod is slightly withdrawn such that the tip of the control
rod is located in a neutron flux of 1013 neutrons/cm2-sec, then the
differential control rod worth will increase by a factor of _______.
(Assume the average flux is constant.)
A. 0.5
B. 1.4
C. 2.0
D. 4.0
The DRW is proportional to the square of the local relative flux. The
reactivity worth at the tip of a control rod is proportional to the square
of the surrounding neutron flux. The increase in neutron flux at tip
from 5x1012 up to 1x1013, which is an increase by a factor of two,
produces a DRW increase by a factor of four. The correct answer is
D.
2. Which one of the following parameters typically has the greatest
effect on the shape of a differential rod worth curve?
A. Core radial neutron flux distribution
B. Core axial neutron flux distribution
C. Core xenon distribution
Rev 1
31
D. Burnable poison distribution
Differential rod worth is the change in reactivity resulting from a unit
of change of rod position. Because the differential rod worth is the
change in reactivity resulting from a unit change of rod position, how
the axial flux at one rod height differs from another rod height will
greatly affect it. The control rods all move in an axial position so that
every movement of rods has an effect on axial flux distribution. The
correct answer is B.
Knowledge Check – NRC Bank
During normal full power operation, the differential
control rod worth is less negative at the top and bottom
of the core compared to the center regions due to the
effects of...
A.
reactor coolant boron concentration.
B.
neutron flux distribution.
C.
xenon concentration.
D.
fuel temperature distribution.
Knowledge Check – NRC Bank
Integral control rod worth can be described as the change
in __________ for a __________ change in rod position.
A.
reactor power; total
B.
reactivity; unit
C.
reactor power; unit
D.
reactivity; total
Knowledge Check
Which one of the following expresses the relationship
between differential rod worth (DRW) and integral rod
worth (IRW)?
32
A.
DRW is the area under the IRW curve at a given rod
position.
B.
DRW is the slope of the IRW curve at a given rod
position.
C.
DRW is the IRW at a given rod position.
D.
DRW is the square root of the IRW at a given rod
position.
Rev 1
ELO 1.7 Core Parameters Impact on Control Rod Worth
Effects of Core Conditions on Control Rod Worth Introduction
We have learned that control rod worth is not constant depending on certain
core conditions. We have examined the relationship between the control
rods axial location and its worth. In this section, we will learn about other
core parameters that change the worth of the control rods independent of
their axial location. The effects of these conditions on control rod worth are
not always intuitive and therefore require a good depth of knowledge to
understand.
Effects of Core Conditions on Control Rod Worth Fact Details
Various conditions in a nuclear reactor core will affect the reactivity worth
of the control rods. The following characteristics are among those that will
affect control rod worth:






Moderator temperature
Fission product poisons
Soluble boron concentration
Reactor power
Presence of other control rods
Absorber material used in the control rods
Moderator Temperature Effects
As the moderator/coolant temperature increases, it becomes less dense. At
this lower density, neutrons are able to travel a greater distance before
interacting with water molecules. Since neutrons travel a greater distance,
they have a higher probability of reaching a particular control rod as shown
in the figure below.
Figure: Changes in Control Rod Worth due to Changes in Temperature
As the moderator/coolant temperature increases, the control rod worth
increases due to the control rod's increased sphere of influence. The
decrease in moderator density with temperature is not linear and therefore
has a larger decrease in density at higher temperatures resulting in a larger
change in control rod worth with temperature.
The figure below shows a rod worth curve for a specific plant showing
changes in reactivity worth of a particular control rod bank over core life at
Rev 1
33
two different temperatures. This shows that both moderator/coolant
temperature and core life affect the value of control rod worth. The
following sections will discuss the effects of core life.
Figure: Group Rod Worth versus Temperature over Core Life
Fission Products Poisons Effects
Most fission products poisons and chemical shim (boron) are strong thermal
neutron absorbers. High concentrations of boron or xenon in the core tend
to reduce the thermal neutron flux. Both of these neutron poisons shift the
spectrum of the neutron flux energy to the epithermal range. This
phenomenon is spectrum hardening.
Since hafnium and silver-indium-cadmium control rods are strong
epithermal neutron absorbers, they have increased rod worth when fission
product poisons or chemical shim concentrations are high. The B4C
absorption cross-section is large (up to ~10 eV), but drops off quickly above
that and is no longer a strong absorber.
Soluble Boron Concentration
The figure below shows that for a given temperature, the reactivity worth of
the control rod bank increases with core age as fission product poison
inventory increases. As the core ages, the boron concentration continuously
decreases, which results in an increase in control rod worth as the boron no
longer competes as strongly for the thermal neutrons.
34
Rev 1
Figure: Bank Control Rod Worth Changes due to Spectrum Hardening
Power Level Effects
Although the reactivity worth of the control rods in a reactor does not
depend on the absolute magnitude of flux in the core, control rod reactivity
worth does change with reactor power level. This reactivity change is
small; normally, it is negligible.
The changes in neutron flux profile due to Doppler reactivity effects,
changes in moderator temperature, and buildup of fission product poisons
causes the neutron flux distribution to change with reactor power. The
shifting neutron flux distribution and the spectrum hardening effect caused
by the buildup of fission product poisons combine to cause control rod
reactivity worth to increase as reactor power increases. These two effects
may be considered individually.
Shifting Flux Distribution Effects
In general, the radial neutron flux in a nuclear reactor tends to move
outward over the life of the reactor core (BOL to EOL), as shown in the
figure below.
Rev 1
35
Figure: Shift in Radial Neutron Flux Profile over Core Life
Control Rod Location
The result of this shift in the radial neutron flux profile toward the outer
edges of the core results in an overall increase in control rod worth over
core life. As the radial flux moves outward, it interacts with a greater
number of control rods, because there are usually more control rods located
in the periphery of the core. The figure below shows control rod locations
as colored blocks, with more rods near the periphery than near the center of
the core. Blocks of same color form a group or bank of rods.
Figure: Control Rod Location
36
Rev 1
Control Rod Effects
The figure below shows radial thermal neutron flux distribution with
respect to average thermal flux with no control rods.
Figure: Radial Thermal Neutron Flux Profile with No Control Rods
The presence of a control rod will result in a disturbance in the radial flux
profile. The area of the rod tip will depress thermal flux levels around the
tip and local flux peaks will form radially around the control rod.
Rod Shadowing
Recall that control rod worth is proportional to the relative flux squared (or
relative power squared):
2
𝜙𝑡𝑖𝑝
𝐷𝑅𝑊 ∝ (
)
𝜙𝑎𝑣𝑔
Because the magnitude of the radial thermal neutron flux is not constant
across the core, the worth of a control rod can vary depending upon its
relative radial location. The presence of control rods will affect the
reactivity worth of other control rods. Rod shadowing is the term for
reactivity worth change due to the presence of other control rods.
Control Rod Shadowing Effects on Thermal Flux
The figure below shows the effect on thermal neutron flux near a particular
control rod before and after control rod insertion.
Rev 1
37
Figure: Control Rod Shadowing Effects on Thermal Flux
The figure above shows the shift in thermal neutron flux before and after
insertion of one control rod into the core. Inserting one control rod will
result in significant power reduction in that region of core as the inserted
rod forces the neutron flux away from the rod.
Rod shadowing is the process by which the movement of an individual
control rod results in a neutron flux increase or decrease in the vicinity of
one or more other control rods resulting in a change in the reactivity worth
of the affected rod(s).
If we insert a second control rod (No. 2) at position A, the reactivity worth
of the second rod is lower than the reactivity worth of the first rod (No. 1)
because the presence of the first control rod already depressed the neutron
flux. This is an example of rod shadowing.
Figure: Control Rod Shadowing Effects on Thermal Flux
You can think of shadowing in the following way: upon inserting an
adjacent control rod, the second rod has less worth because of the lower
local flux profile created by the insertion of the first rod. The power
38
Rev 1
reduction caused by inserting the second rod is also less than the power
reduction caused by inserting the first rod. In this case, the first rod
“shadows” the second rod.
In general, one control rod is capable of shadowing another control rod if it
is within one neutron thermal diffusion length of the other rod.
Shadowing can increase or decrease the worth of the adjacent control rod
depending on the existing core conditions, specifically the ratio of local to
average neutron flux. Inserting a second control rod at position A results in
a decrease in the worth of the second rod. This is a positive shadowing
because the presence of the first control rod makes the reactivity worth of
the second control rod less negative (more positive).
In order to counteract the decrease in neutron flux upon insertion of control
rod No. 1 and maintain a constant reactor power level, the neutron flux must
increase in some other region of the core. This creates peaks in the radial
neutron flux profile and changes the reactivity of other control rods,
depending upon their position.
If we insert a second control rod (No. 2) at position B, control rod No. 2
will have a higher reactivity worth compared to what its reactivity worth
would have been without the first control rod (No. 1). This is due to the
increase in the neutron flux profile created by the insertion of the first rod
(No. 1).
In this case, the second control rod (No. 2) is termed negatively shadowed.
This effect is termed negative shadowing because the presence of the first
control rod has increased the negative reactivity worth of the second control
rod.
When the second control rod (No. 2) is inserted into the core in position C it
has the same reactivity worth whether control rod (No. 1) is inserted or not.
This is because in position C the neutron flux profile is the same (same
point on both flux curves) with or without the first control rod inserted. In
this case, no rod shadowing takes place.
Grouping of Control Rods
In commercial PWRs, operators move control rods in symmetrical arrays
known as rod banks (groups). In Westinghouse plants, each bank is divided
into two smaller groups that move separately but stay within one step of the
other rods in that bank. In this text, we use the terms bank and group
interchangeably, but the terms may mean something different from one
vendor to another. The overall objective of rod banking or grouping is to
maintain the flattest possible radial flux profile across the entire volume of
the core; this tends to minimize the effects of rod shadowing. BWRs do not
group their control rods; operators move each rod separately guided by a
rod sequence program.
Rev 1
39
The figure below shows control rod banks as separate colors. Normally,
two criteria determine which rods form a bank. The individual control rods
in a bank are not located close to the other control rods in the bank, and are
symmetrically located throughout the four quadrants of the core.
Figure: Control Rod Location
This arrangement results in separation of individual control rods in a bank
by a large number of control rods in other banks. As rod withdrawal begins
for the first control rod groups to be withdrawn during a reactor startup, the
first groups of control rods are normally pulled continuously from their fullin to their full-out position. These are the shutdown banks of control rods.
They are normally withdrawn to provide a means of negative reactivity
insertion before the dilution of the plant or withdrawal of other control rods
to bring the reactor critical.
The withdrawal of a control rod results in neutron flux peaks in the location
of each withdrawn control rod. Neutrons are limited to a small area of
travel, so movement of any single control rod has little shadowing effect on
any of the other control rods in the same group.
As the startup progresses, operators withdraw subsequent rod banks, and the
average core neutron flux increases. This tends to couple the core together
such that each additional rod bank has a larger effect on the core-wide flux
profile resulting in increased values of rod worth. At some point in the
startup sequence, the operator slows rod withdrawal to ensure that the
reactor operator remains in control of the added reactivity.
The largest impact on neutron flux will occur in the rod withdrawal
location. The peak flux in that particular area of core could be significantly
higher than in other areas of the core, depending upon the distance that the
rod moves.
40
Rev 1
The overall objective of rod grouping is to minimize the flux peaking
associated with any single control rod within a particular group and to
minimize the shadowing of other rods in that group.
Discussion Topic
A nuclear reactor startup is in progress from a cold shutdown condition.
During the RCS heatup phase of the startup, control rod differential
reactivity worth (Δk/k per inch insertion) becomes _______ negative; and
during the complete withdrawal of the initial bank of control rods, control
rod differential reactivity worth becomes _______.
Answer
A. more; more negative and then less negative
B. more; less negative and then more negative
C. less; more negative during the entire withdrawal
D. less; less negative during the entire withdrawal
Explain your answer.
Knowledge Check
Which one of the following expresses the relationship
between differential rod worth (DRW) and integral rod
worth (IRW)?
A.
DRW is the area under the IRW curve at a given rod
position.
B.
DRW is the slope of the IRW curve at a given rod
position.
C.
DRW is the IRW at a given rod position.
D.
DRW is the square root of the IRW at a given rod
position.
Knowledge Check
With a nuclear power plant operating normally at full
power, a 5°F decrease in moderator temperature will
cause the differential control rod worth to become...
Rev 1
A.
more negative due to better moderation of neutrons.
B.
less negative due to shorter neutron migration length.
41
C.
more negative due to increased neutron absorption in the
moderator.
D.
less negative due to increased resonance absorption of
neutrons.
TLO 1 Summary
During this lesson, you learned about control rods: their construction,
materials, how control rods affect reactivity, and how changes in core
conditions affect control rod worth. The listing below provides a summary
of sections in this TLO.
1. Control rod worth effect on reactor power
 Control rod design and construction: materials and manufacturers
 Material characteristics
 The terms in the six-factor formula most affected by control rod
motion are the nonleakage probabilities (Lf and Lth), the resonance
escape probability (ρ) and the thermal utilization factor (f).
o Control rod withdrawal results in an increase in the resonant
escape probabilities.
o Control rod withdrawal increases the value of the thermal
utilization factor.
o Since 𝑘𝑒𝑓𝑓 = 𝜀𝐿𝑓 𝜌𝐿𝑡ℎ 𝑓𝜂, withdrawing control rods increases
the core reactivity.
2. Describe the term control rod worth
 Effect of neutron flux on control rod worth
 Effect of control rod location on control rod worth
3. Differential and integral rod worth
 Differential rod worth: the reactivity change per unit movement of
a control rod
 Integral rod worth: the total reactivity worth of the control rod at a
particular degree of withdrawal from the core
4. Differential control rod worth characteristics
 Describe the shape of a typical differential control rod worth curve
and the reason for the shape.
The typical differential control rod worth curve has a bell shape.
It has very low values at the top and bottom of the core and a
maximum value at the center of the core.
The curve has this shape because rod worth is related to neutron flux,
and flux is highest in the center of the core.
5. Integral control rod worth
 Describe the shape of a typical integral rod worth curve and the
reason for the shape.
The typical integral control rod worth curve has an "S" shape.
It has a relatively flat slope at the top and bottom of the core and a
maximum slope at the center of the core.
6. Control rod position effects on integral and differential control rod
worth
7. Core parameters impact on control rod worth
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Rev 1
 Moderator temperature: As the moderator temperature increases its
density decreases, allowing neutrons to travel further between
collisions, which increases the sphere of a control rod’s influence
and raises the control rod’s worth.
 Poison concentration: As fission product poisons increase, they
tend to absorb more thermal neutrons hardening the neutron energy
spectrum, which tends to make the control rod worth increases
because the rods use epithermal neutron absorbers.
 Reactor power level: As power level is increased, the fuel
temperature also increases, which results in shifting the neutron
flux towards the control rods and increasing their worth slightly.
 Presence of additional control rods (rod shadowing): The presence
of other control rods may increase or decrease the neutron flux
local to another control rod. If the local neutron flux has been
increased, the presence of the first control rod causes the second
control rod’s worth to be greater.
 Boron concentration: The presence of boron hardens the neutron
spectrum, which increases control rod worth.
 Neutron spectrum hardening: The shifting of the average neutron
energy to higher values results in the control rod's worth increasing
since the rods contain material that has high cross-sections for
absorption of epithermal neutrons.
 Control rod design and absorber material: The choice of absorber
material will determine how most of the above changes affect the
control rod's worth; for the discussions in this chapter and to
answer the NRC questions we must assume that the control rods
use absorber material with high cross-sections for absorption of
epithermal neutrons.
Now that you have completed this lesson, you should be able to do the
following:
1. Explain the effect of control rods on the neutron lifecycle including
how control rod design and movement affects reactor power level.
2. Describe the term control rod worth.
3. Define the following terms:
a. Differential rod worth
b. Integral rod worth
4. Describe the shape of a typical differential control rod worth curve
and the reason for the shape.
5. Describe the shape of a typical integral rod worth curve and the reason
for the shape.
6. Calculate the effect that control rod position in the core and grouping
control rods has on differential rod worth.
7. Explain how control rod worth is affected by the following core
conditions:
a. Moderator temperature
b. Poison concentration
c. Reactor power level
d. Presence of additional control rods (rod shadowing)
Rev 1
43
e. Boron concentration
f. Neutron spectrum hardening
g. Control rod design and absorber material
TLO 2 Plant Operation and Impact of Control Rod
Positioning
Overview
We have learned how certain core conditions affect the worth of a control
rod. We will now learn how control rod positioning affects certain core
operating parameters. Inserting or withdrawing control rods has an
immediate and observable effect on the axial flux distribution and a smaller,
less obvious effect on the radial flux distribution. Under some operating
conditions, the flux shape distortions caused by control rods may increase
temperatures to the core thermal operating limits.
The reactor operator must understand the potential adverse effects of control
rod movement and minimize these effects by maintaining the control rods
within the established operating limits, thereby preventing core damage.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Explain how control rods affect core power distribution.
2. Describe the following control rod operational considerations
including:
a. Flux shaping
b. Bank overlap
c. Bank sequencing
d. Rod insertion limits
e. Reactor scram/trip
f. Power peaking and hot channel factors
3. Describe power peaking and hot channel factors.
4. Define quadrant power tilt (symmetric offset) ratio (QPTR) and
explain the long-range effects of operating with a high QPTR.
5. Given appropriate data, calculate the quadrant power tilt ratio
(QPTR).
6. Discuss the nuclear reactor operator’s responsibilities with regard to
control rods.
ELO 2.1 Core Power Distribution
Introduction
In this section, we will examine how the neutron flux profile in a reflected
(real) core varies from that of the non-reflected (theoretical) core. The flux
shape within the core has a direct effect on the worth of a control rod and
the control rod position has a direct effect on the flux shape. These
44
Rev 1
differences in flux shapes affect control rod worth and core power
distribution; operators must understand these effects to control a reactor.
Each individual nuclear reactor has a certain core volume and a certain
number of square feet of heat transfer surface. If it were possible to operate
a reactor in an ideal manner, all portions of the core would be producing
equal amounts of power at the maximum rate allowed by core material heat
transfer limits. Under these ideal conditions, the fuel burn in the core would
be uniform, core size would be minimal, and the costs associated with the
fuel would be minimal.
Core design and operation include a number of unavoidable factors that
make it impossible to achieve a perfectly flat power distribution across the
core. The following sections discuss these factors.
Bare (Unreflected) Reactor
Consider a very simple homogenous uncontrolled reactor surrounded by a
vacuum. This example is termed a bare (unreflected) reactor and the figure
below shows this on the left hand side.
Figure: Neutron Flux Profiles for Bare and Reflected Reactor
In this type of reactor, the power density within the core drops off
significantly in any direction outward from the core's center. This happens
because neutrons born near the edge of the reactor have a far greater
probability of leaking out of the core as compared to a neutron born near the
center of the core. Since leakage removes neutrons from the neutron life
cycle and those leaked neutrons are no longer available to cause fission, the
fission rate or power production rate is depressed along the edges of the
core, and consequently increases toward the center of the core.
Most reactor cores approximate a right circular cylinder. The horizontal
dimension from one side to the other (across the radius of the core) is the
core's radial dimension. The vertical dimension from the top to the bottom
Rev 1
45
of the (along the vertical axis) is referred to as the core's axial dimension.
In the design of the core the radial and axial dimensions are approximately
equal (12ft x 12ft).
In the simple bare reactor described above, at any particular elevation
(height) within the core, the power distribution would look like the positive
half of a cosine curve in radial dimension. Similarly, the power distribution
in the axial dimension would also approximate the same shape.
This idealized distribution is referred to as a cosine distribution, and would
be similar to the axial and radial flux curves for the bare reactor shown in
the above figure, since the thermal neutron flux distribution in a reactor is
directly proportional to the power distribution. The only difference between
these two shapes is a result of the existence of thermal neutrons outside the
core, which do not result in fissions. Therefore, power distribution drops
abruptly to zero at the edge of the core, whereas the neutron distribution
outside the core gradually falls to zero.
Reflected Reactor
In reality, bare homogenous reactors do not exist, because all reactors
include items that act as neutron reflectors. Therefore, it is necessary to
consider the role of a reflector on the operation of a homogenous core. A
reflector is a material present in or near the reactor, which reflects neutrons
back into the reactor core. In a typical commercial PWR, the coolant
downcomer region and the moderator in the bottom and top of the core act
as reflectors.
The right hand side of the figure above also shows the radial and axial
neutron flux profiles for a homogenous reactor equipped with a reflector.
The reflector produces two effects concerning flux distribution:
 It scatters some of the thermal neutrons that have leaked from the core
back into fuel regions.
 It moderates some of the fast neutrons that leaked from the core. Fast
neutrons cause damage to the core barrel. Minimizing fast neutron
impingement on the reactor vessel is important to ensure a long life
for the reactor vessel.
 Moderation of fast neutrons produces an increase of thermal neutrons
just outside the core.
 Reflector peak is the term given to this increase of thermal neutrons.
 Many of these "peak" neutrons reenter the core.
Both of the above-described effects tend to increase the neutron flux at the
edges of the core compared to what flux levels would be without a reflector.
The addition of a reflector to the bare homogenous reactor tends to flatten
the neutron flux distribution across the core, as shown in the right side of
the figure above.
46
Rev 1
Heterogeneous Reactor
Just as there are no real bare reactors, there are no real homogenous
reactors. Commercial reactors are heterogeneous, meaning that the fuel,
control rods, moderator, coolant, etc. contained within the core are separate
entities and are not uniformly mixed within the core.
Although the neutron flux distribution in a heterogeneous reactor tends to
be similar to the modified cosine shape described above, the radial shape
exhibits roughness due to discontinuities caused by the separation of the
moderator and the fuel.
In a heterogeneous reactor, the moderator produces most thermal neutrons
but they are absorbed before they reach the center of the fuel rod. This
results in a flux depression in each rod and a corresponding flux peak in the
water gaps between the fuel rods. Therefore, instead of a smooth flux
distribution like the one described for a homogenous core, the
heterogeneous core has radial distribution similar to the distribution shown
in the figure below.
Figure: Distortion of Radial Neutron Flux in Heterogeneous Core
The presence of control rods in the core disturbs the axial flux in a
heterogeneous reactor. The previous TLO showed this effect.
Rev 1
47
Knowledge Check
Choose all the answers that are a benefit of using a
reflector around the core...
A.
flatter neutron flux profile.
B.
fewer control rods required.
C.
longer life of the reactor vessel.
D.
higher power production near the core peripheral.
E.
higher control rod worth near the edges of the core.
ELO 2.2 Control Rod Operation Considerations
Introduction
This section describes how operating control rods influence flux shaping,
and some problems that arise when using the rods in this manner.
Normally, operators position control rods as far out of the core as possible
to prevent any adverse effects on the designed axial and radial flux profiles.
It is important to consider several factors when placing control rods in the
core, and deciding how to operate the control rods for a particular reactor
design. Among these factors are:






Flux shaping
Bank overlap and sequencing
Rod insertion limits
Axial flux difference
Quadrant power tilt ratio
Rod speed
Flux Shaping
Flux shaping is a method of control rod operation used to control the radial
and axial neutron flux distribution. This minimizes fuel burnout problems
and optimizes fuel depletion by reducing local power peaking and
controlling control rod worth.
Operators accomplish flux shaping by establishing a specific pattern of
control rod withdrawal and insertion referred to as a rod sequence, which
they employ during reactor operation. The specific rod sequence in a PWR
controls the radial power distribution. Flattening the neutron flux
distribution allows a higher average power density.
Grouping individual control rods into rod banks and establishing a sequence
for each bank accomplishes the goals described above. Operators withdraw
these rod banks in a specific sequence and in specific amounts in order to
maintain what is known as bank overlap.
48
Rev 1
Bank Overlap
It is possible to move each control rod individually, however, a single
control rod's reactivity worth will not produce adequate reactor control
response without large, time-consuming rod movement. To expedite core
reactivity changes with minimum rod movement, operators move control
rods in symmetrically arranged groups (banks) of control rods.
A typical Westinghouse commercial nuclear reactor has four control banks
and two to five shutdown banks. During reactor startup and operation,
operators fully withdraw the shutdown banks, but they move the control
banks to various core heights to maintain the reactor critical. The shutdown
banks do not utilize bank overlap but are withdrawn completely one bank at
a time.
Both CE and B&W reactors identify a specified number of rod groups, for
example, seven groups, distributed between shutdown and control or
regulating groups to accomplish these same shutdown and control
functions.
Operators move these control banks, or groups, with a certain amount of
overlap. Before one control bank or group is fully withdrawn, another
control bank or group will begin to move off the bottom of the core. This
method of rod withdrawal is termed bank overlap. The amount of overlap
between control rod groups depends on reactor design considerations;
manufacturers will designate overlap as some fraction of control rod height.
In a Westinghouse plant, the control rods may be withdrawn to 230 steps
(physical limitation) although operators normally stop them at some height
prior to this to ensure the rodlets stay in the guide tubes and have a small
amount of worth (bite) when moved. For this example, we have set 228
steps as the all rods out (ARO) position and selected 114 steps (~50
percent) of bank overlap. The ARO position and the bank overlap is
changed periodically to prevent the tips of the control rodlets from vibrating
against the same location in the control rod guide tubes which has resulted
in mechanical fretting failure of the control rod rodlets.
For this example of bank overlap for a Westinghouse-designed reactor
plant, it would occur as follows:
 First, control bank A is withdrawn from 0 to 228 steps.
 When control bank A reaches 114 steps, control bank B automatically
begins to move out of the core.
 When control bank A reaches 228 steps and control bank B is at 114
steps, control bank A automatically stops moving and control bank C
automatically begins to move out of the core.
 This arrangement results in the last 114 steps of control bank A being
overlapped with the first 114 steps of control bank B. Control bank C
overlaps the last 114 steps of control bank B and control bank D
overlaps the last 114 steps of control bank C.
Rev 1
49
Bank or group overlap provides for a more uniform differential control rod
worth and axial neutron flux distribution within the core during control rod
movement. A non-uniform axial flux distribution could result in
abnormally high power peaks in core, and fuel damage. A uniform
differential control rod worth ensures that rod motion always produces a
change in reactivity. If differential control rod worth is zero or very small
(e.g., control rod at top or bottom of core), no reactivity is added when the
control rods are moved. This is undesirable since control rods must add
reactivity immediately during an accident or transient.
The figures below illustrate the effect of overlapping control rod banks on
differential and integral rod worth curves.
Figure: Effect of Bank Overlap on Differential Rod Worth
Figure: Effect of Bank Overlap on Integral Rod Worth
Rod Insertion Limits
Although the design of a reactor may allow control rods to be positioned
axially anywhere in core, procedures are written to maintain control rods
50
Rev 1
above a specified height during reactor operations. The rod insertion limit
(RIL) is the term for this height.
For example, during operation of a Westinghouse PWR, operators must
maintain control rods above the rod insertion limit lines shown on the figure
below. As reactor power increases, so does the required RIL. Technical
specifications provide the rod height versus power graph. Each step
measures 5/8 inch, therefore 230 steps (top of core) correspond to a rod
height of about 12 feet.
Figure: Rod Insertion Limits for a Westinghouse PWR
The design of RILs minimize the consequences of an ejected rod accident,
guarantee sufficient shutdown margin from any given power level, and
produce an axial flux distribution that prevents high local peak power levels
within the core.
Rod Ejection
Maintaining control rods high in the core while the reactor is at power
prevents an ejected control rod from inserting an excessive amount of
positive reactivity. With control rods high in the core, the amount of
reactivity inserted by a rod ejection should be small enough to prevent fuel
damage or an excessive power spike. A control rod ejected from low in the
core has the potential to add enough positive reactivity instantaneously to
cause local fuel damage from a rapid power spike. A rod ejection also
results in a small-break loss-of-coolant-accident (SBLOCA), due to the
rupture of the associated control rod drive housing.
Shut Down Margin
When a reactor trips (or power is reduced), positive reactivity is added by
the power defect as the fuel and moderator temperatures decrease to hot
Rev 1
51
zero power (HZP) conditions. Operators can add additional positive
reactivity if temperature decreases below the HZP value.
Rod insertion limits ensure that the control rods are withdrawn far enough
for any power level to have sufficient negative reactivity to overcome the
power defect's positive reactivity to shut down and maintain the reactor in a
safe shutdown condition with sufficient shutdown margin.
Axial Flux Distribution
If an operator inserts a reactor's control rods too far into the core, this
suppresses power production in the top of the core, resulting in a
corresponding increase in power production in the bottom of the core. The
higher power in bottom of core could result in abnormally high fuel
temperatures, which could result in fuel damage.
Axial Flux Difference (AFD)
The axial flux difference (ΔΦ or ΔI) is the difference in power level
(currents, ΔI) between power range detectors (located external to the core)
monitoring the upper and lower halves of core. The figure below shows
relative locations for the upper and lower detectors.
Figure: Upper and Lower Power Range Neutron Detector Locations
This power difference is proportional to the difference in neutron flux
between upper and lower halves of core, expressed as:
∆𝛷 = 𝛷𝑡𝑜𝑝 − 𝛷𝑏𝑜𝑡𝑡𝑜𝑚
We can equate the change in flux to a change in detector current since the
detectors are ion chambers and produce a usable current output:
𝛥𝐼 = 𝐼𝑡𝑜𝑝 − 𝐼𝑏𝑜𝑡𝑡𝑜𝑚
To ensure a more uniform axial flux distribution across the core and prevent
high peak power in either the top or the bottom of the core, operators must
maintain the axial flux difference in a specified band during reactor
operation. A high peak power results in a high fission product
52
Rev 1
concentration in that location. The decay heat generated by these fission
products could overheat fuel during a loss of coolant accident.
Discussion Topic
Explain what bank overlap means and list a benefit that it produces.
Answer
Bank overlap results in the last approximately 50 percent of a control
bank’s travel being overlapped with the first 50 percent of the next
sequenced bank movement. Bank, or group, overlap provides for a more
uniform differential control rod worth and a more consistent axial neutron
flux distribution within the core during control rod movement.
Discussion Topic
What does a -2 AFD mean?
Answer
AFD is the current in the upper detector minus the current in the lower
detector therefore a negative AFD means the lower half of the core
produces more power. Specifically, -2 AFD means that the lower half of
the core produces 51 percent of the power and the upper half of the core
produces 49 percent of the power.
Discussion Topic
List and explain the three bases for the rod insertion limits.
Answer
Minimize the consequences of an ejected rod accident, guarantee sufficient
shutdown margin from any given power level, and produce an axial flux
distribution that prevents high local peak power levels within the core.
Knowledge Check
Why are the control rod insertion limits power
dependent?
Rev 1
A.
Power defect increases as power increases.
B.
Control rod worth decreases as power increases.
53
C.
Doppler (fuel temperature) coefficient decreases as
power increases.
D.
Equilibrium core xenon-135 negative reactivity increases
as power increases.
Knowledge Check
After a control rod is fully inserted (from the fully
withdrawn position), the effect on the axial flux shape is
minimal. This is because...
A.
the differential rod worth is constant along the length of
the control rod.
B.
the fully inserted control rod is an axially uniform
poison.
C.
a control rod only has reactivity worth if it is moving.
D.
a variable poison distribution exists throughout the length
of the control rod.
ELO 2.3 Power Peaking and Hot Channels
Introduction
The redistribution of the neutron flux from its design values results in
regions of high power production. These peak regions result in higher fuel
and moderator temperatures that operators must control to equalize fuel
burnup and prevent local fuel damage.
Power Peaking and Hot Channel Factors
Since the radial and axial power distributions are not flat, there will always
be areas where the local power is greater than the average power. This ratio
of Φmax /Φavg is often referred to as a hot channel or peaking factor. The
core location with the Φmax /Φavg is located periodically using the provided
incore instrumentation and it must be determined to be within allowable
operational limits.
Hot channel factors greater than 1.0 indicate that the core flux profile is
peaked. Since core power distribution is proportional to the thermal
neutron flux distribution, a high hot channel factor would indicate that high
local power densities exist in reactor core.
We express the maximum local power density in the core in terms of total
core peaking factor. This total core peaking factor is a product of the radial
and axial peaking factors. These two factors are the peak to average flux
ratios for their respective flux profiles.
54
Rev 1
The hot channel factors account for variations in core power density due to
fuel burnup, control rods, non-uniform fuel loading, voids, water gaps, etc.
In order to prevent fuel melting or fuel cladding degradation, the maximum
local power density is limited by reactor operating and design
specifications.
Discussion Topic
List two negative effects of having a high peaking or hot channel factors.
Answer
High peaking or hot channel factors result in uneven fuel burnup, which
increases the operating costs. They result in regions of high fission
products that could prevent adequate core cooling following an accident.
They result in localized, high fuel cladding and moderator temperatures that
could approach or exceed core thermal operating limits. They result in
areas of high buildup of fission product poison, which could result in xenon
oscillations.
Knowledge Check
A comparison of the heat flux in the hottest coolant
channel to the average heat flux in the core describes...
A.
a core correction calibration factor.
B.
a hot channel/peaking factor.
C.
a heat flux normalizing factor.
D.
an axial/radial flux deviation factor. The hot channel or
peaking factor is the combination of axial and radial
peaking factors that are used to ensure no localized
power peaking could result in damage to the fuel.
Knowledge Check
A nuclear reactor has been taken critical following a
refueling outage and is currently at the point of adding
heat during a normal reactor startup. Which one of the
following describes the axial power distribution in the
core as power is increased to 10 percent by control rod
withdrawal? (Neglect reactivity effects of reactor
coolant temperature change.)
Rev 1
A.
Shifts toward the bottom of the core.
B.
Shifts toward the top of the core.
C.
Shifts away from the center toward the top and bottom of
55
the core.
D.
Shifts away from the top and bottom toward the center of
the core. The control rods have a large effect on AFD.
As the control rods are withdrawn, the neutron flux will
shift upward and will continue until all rods are fully
withdrawn. As power is increased that Delta T across the
core increases which will shift the power back towards
the bottom of the core.
Knowledge Check
A nuclear reactor is operating at 75 percent power with
all control rods fully withdrawn. Assuming reactor
power does not change, which one of the following
compares the effects of dropping (full insertion) a single
center control rod to the effects of partially inserting (50
percent) the same control rod?
A.
A dropped rod causes a smaller change in axial power
distribution.
B.
A dropped rod causes a smaller change in radial power
distribution.
C.
A dropped rod causes a smaller change in shutdown
margin.
D.
A dropped rod causes a greater change in shutdown
margin. The partially inserted rod would cause larger
flux suppression in the upper portion of the core whereas
the dropped rod is evenly distributed throughout the core.
Knowledge Check
A nuclear reactor is operating at 85 percent power with
all control rods fully withdrawn. Assuming reactor
power does not change, which one of the following
compares the effects of partially inserting (50 percent) a
single center control rod to the effects of dropping (full
insertion) the same control rod?
56
A.
A partially inserted rod causes a smaller change in axial
power distribution.
B.
A partially inserted rod causes a smaller change in radial
power distribution.
C.
A partially inserted rod causes a greater change in
shutdown margin.
D.
A partially inserted rod causes a smaller change in
shutdown margin. The control rod insertion will change
Rev 1
the shape of the reactor neutron flux and the partially
inserted rod would have a greater influence on the upper
portion of the core. The dropped rod would affect the
flux throughout the core therefore the radial flux is
affected less by a partially inserted rod.
ELO 2.4 Quadrant Power Tilt Ratio Effects
Introduction
The presence of control rods distorts both the radial and axial neutron flux
profile. To minimize these effects, operators normally keep control rods
fully withdrawn and move them in banks that contain symmetrically located
control rods in each quadrant of the core. This rod grouping results in equal
effects in each quadrant of the core. At 100 percent power with the control
rods at the full out position, each core quadrant should be producing
approximately 25 percent of the total power. A neutron flux or power tilt
exists if one quadrant is producing more or less than its 25 percent share of
the total power.
Quadrant Power Tilt Ratio
Operators use the quadrant power tilt ratio (QPTR) to monitor the radial
neutron flux distribution in a reactor's core. The figure below illustrates the
location of neutron detectors used to determine the QPTR. The core is
designed to produce an equal percentage of power in each of the four
quadrants by symmetrically loading the fuel, poisons, and the placement of
the control rods in each bank.
Figure: Location of Excore Power Range Detectors for Typical PWR Core
Definition
Technical specifications define the quadrant power tilt ratio as:
Rev 1
57
"QPTR shall be the ratio of the maximum upper excore detector calibrated
output to the average of the upper excore detector calibrated outputs, or the
ratio of the maximum lower excore detector calibrated output to the average
of the lower excore detector calibrated outputs, whichever is greater".
To meet this technical specification, operators must calculate QPTR for
both the upper and lower half of the core to locate the maximum QPTR.
Operators monitor each core quadrant by a power range ion chamber that
consists of two detectors, one positioned to monitor the upper half of the
core, and one positioned to monitor the lower half of the core, as depicted in
the figure below. These ion chambers produce a micro-amp current output
that operators can use in the calculation of QPTR.
Figure: Upper and Lower Power Range Neutron Detector Locations
When the QPTR is equal to one, the core's radial neutron flux distribution is
uniform, indicating an even radial power production throughout the core.
When radial power production is not uniform (QPTR not equal to one),
reactor power or neutron flux is termed "tilted". A tilted flux results in
uneven fuel burnup, and high local peak power levels that could result in
fuel damage.
To prevent flux tilting, operators move control rods in symmetrical bank
configurations, with each individual control rod's height limited to a
specified tolerance as compared to the height of the entire bank.
The reactor design largely determines the radial neutron flux profile, and the
profile will normally follow the shape predicted by the design engineers
throughout the fuel cycle. However, improper operation of the control rods
can greatly affect this flux profile. If an operator inserts a control rod into
the core, neutron flux will decrease around the area of the control rod and
increase in other areas of the core. This results in lower power production
in the core quadrant where the rod is inserted and higher power productions
in the other quadrants.
58
Rev 1
If the operator partially inserted the control rod, the upper half of the core
would see a greater effect than the lower half of the core. A partially
inserted rod will also affect AFD in that quadrant by pushing more power
towards the bottom of the core resulting in a more negative AFD near the
partially inserted control rod.
If the operator inserts the control rod fully, there will be an even greater
decrease in power in that quadrant, resulting in higher power increases in
the other quadrants (higher QPTR). In this case, the effect on AFD would
be minimal since a fully inserted control rod acts as a homogenous poison
from the bottom to the top of the core. It is important to understand the
radial and axial power changes that occur if you move a single control rod
or fail to maintain the rod within its bank limits. An increase in QPTR can
indicate a control rod failure such as a misaligned rod, dropped rod, or
dropped rodlets. Depending on the change in AFD, the operator can
determine if the rod is partially or fully inserted. Both situations have
occurred in the industry.
Discussion Topic
Describe the effects on the radial and axial power distribution if a control
rod drops 50 steps into the core while at 100 percent power.
Answer
A partially inserted control rod would decrease the power in that quadrant
the rod is located in in the upper half of the core. This would result in a
high QPTR for the upper power range detectors, and a tilted radial power
distribution. A partially inserted control rod results in a power reduction in
the area of the rod insertion causing power to be pushed down away from
the rod resulting in a more negative AFD meaning more power is being
produced in the lower half of the core.
Knowledge Check
Which one of the following describes why most of the
power is produced in the lower half of a nuclear reactor
core that has been operating at 100 percent power for
several weeks with all control rods withdrawn at the
beginning of core life?
Rev 1
A.
Xenon concentration is lower in the lower half of the
core.
B.
The moderator to fuel ratio is lower in the lower half of
the core.
C.
The fuel loading in the lower half of the core contains a
higher U-235 enrichment.
D.
The moderator temperature coefficient of reactivity is
adding less negative reactivity in the lower half of the
59
core. The average temperature of the moderator water is
colder at the bottom of the core, which provides better
neutron moderation. With more neutrons in the lower
portion of the core a higher flux level develops and
therefore higher power level. As the moderator flows up
along the fuel assembly, the temperature raises thereby
reducing moderation leading to a lower neutron flux
level where the moderator is hotter, reducing power
level.
Knowledge Check
A nuclear reactor is operating at 75 percent power in the
middle of a fuel cycle. Which one of the following
actions will cause the greatest shift in reactor power
distribution toward the top of the core? (Assume control
rods remain fully withdrawn.)
A.
Decrease reactor power by 25 percent.
B.
Decrease reactor coolant boron concentration by 10 ppm.
C.
Decrease average reactor coolant temperature by 5°F.
D.
Decrease reactor coolant system operating pressure by 15
psia. By decreasing reactor power without changing rod
position causes the flux to shift upward in the core. The
xenon concentration in the lower portion of the core
would be initially higher than the top of the core. When
power was reduced, the xenon concentration would tend
to force power higher in the core.
Knowledge Check
If core quadrant power distribution (sometimes referred
as quadrant power tilt or azimuthal tilt) is maintained
within design limits, which one of the following
conditions is most likely?
A.
Axial power distribution is within design limits.
B.
Radial power distribution is within design limits.
C.
Nuclear instrumentation is indicating within design
accuracy.
D.
Core quadrant power distribution within the design limits
the radial power distribution is ensured to be within
design limits.
Knowledge Check
Consider a nuclear reactor core with four quadrants: A,
60
Rev 1
B, C, and D. The reactor is operating at steady state 90
percent power when a fully withdrawn control rod in
quadrant C drops to the bottom of the core. Assume that
no operator actions are taken and reactor power stabilizes
at 88 percent. How are the maximum upper and lower
core power tilt values (sometimes called quadrant power
tilt ratio or azimuthal power tilt) affected by the dropped
rod?
A.
Upper core value decreases while lower core value
increases.
B.
Upper core value increases while lower core value
decreases.
C.
Both upper and lower core values decrease.
D.
Both upper and lower core values increase. The dropped
rod will affect the radial neutron flux distribution making
it no longer uniform in shape. The rod will affect both
upper and lower regions of the core.
ELO 2.5 Calculating Quadrant Power Tilt Ratio
Quadrant Power Tilt Ratio Calculation Introduction
Previous sections described the effects of control rod misalignment on axial
and radial power distribution. It is not enough to identify abnormal power
distributions, but the magnitude of the power tilt must be calculated to
determine if operational or technical specification limits have been
exceeded. To calculate QPTR (symmetric offset) follow the steps in the
table below.
Quadrant Power Tilt Ratio Calculation Step-by-Step Table
Step
Action
1.
Using the table below for power range detector currents,
calculate the average upper and lower detector current values.
2.
Divide each quadrant of the upper (lower) detectors current by
the average current of the upper (lower) detectors.
3.
Locate the quadrant with the highest peak to average ratio.
4.
Determine if the location exceeds the technical specification
limit of 1.02, and take appropriate actions if needed.
Rev 1
61
Quadrant Power Tilt Calculation Demonstration
The following table lists the micro-amp current output from each of the four
excore power detectors upper and lower ion chambers. Use this data to
calculate the QPTR.
Quadrant
1
Quadrant
2
Quadrant
3
Quadrant
4
Upper Detector
micro-amps
249
248
246
249
Lower Detector
micro-amps
251
253
255
247
Step 1 - To find QPTR from the information given, first find the average
upper and lower detector current values.
– The average of the 4 upper detectors is 248 micro-amps
(249 + 248 + 246 + 249)
= 248
4
– The average of the 4 lower detectors is 254 micro-amps
251 + 253 + 255 + 247
= 254
4
Step 2 - Divide each quadrant of the upper detectors by the average of the
upper detectors and divide each quadrant of the lower detectors by the
average of the lower detectors:
UPPER DETECTORS
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
249/248
248/248
246/248
249/248
= 1.004
= 1.000
= 0.992
1.004
LOWER DETECTORS
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
251/254
253/254
255/254
257/254
= 0.988
= 0.996
= 1.004
= 1.012
Step 3 – Locate the quadrant with the highest ratio.
The QPTR is the highest value found, which would be 1.012 on the
quadrant 4 lower detector.
Step 4 - Determine if the location exceeds the Technical Specification limit
of 1.02 (or other more restrictive plant operating limits) and take the
appropriate actions to determine the cause of the tilt and what can be done
to reduce it. Not exceeded – no action required
62
Rev 1
If the technical specification limit is exceeded the operator is required to
restore the power tilt to within limits or reduce reactor power to minimize
the effects of the power tilt.
Discussion Topic
Use the following data to calculate the QPTR.
The table lists the micro-amp current output from each of the four excore
power detectors upper and lower ion chambers.
Quadrant
1
Quadrant
2
Quadrant
3
Quadrant
4
Upper Detector
micro-amps
275
268
272
265
Lower Detector
micro-amps
351
359
350
342
Answer
Step 1 - To find QPTR from the information given, first find the average
upper and lower detector current values.
– The average of the 4 upper detectors is 270 micro-amps
275 + 268 + 272 + 265
= 270
4
– The average of the 4 lower detectors is 350.5 micro-amps
351 + 359 + 350 + 342
= 350.5
4
Step 2 - Divide each quadrant of the upper detectors by the average of the
upper detectors and divide each quadrant of the lower detectors by the
average of the lower detectors:
UPPER DETECTORS
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
275/270
268/270
272/270
265/270
= 1.019
= 0.993
= 1.007
0.982
LOWER DETECTORS
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
351/350.5
359/350.5
350/350.5
342/350.5
= 1.001
= 1.024
= 0.998
= 0.976
Step 3 – Locate the quadrant with the highest ratio.
The QPTR is the highest value found, which would be 1.024 on the
Rev 1
63
quadrant 2 lower detector.
Step 4 - Determine if the location exceeds the technical specification limit
of 1.02 (or other more restrictive plant operating limits) and take the
appropriate actions to determine what caused the tilt and what you can do
to reduce it. Yes – determine if caused by control rod misalignment and
recover if possible.
The QPTR exceeds the technical specification limit; the operator must
restore the power tilt to within limits or reduce reactor power to minimize
the effects of the power tilt.
ELO 2.6 Reactor Operator Responsibilities
Introduction
Control rods provide the operator with a method of rapidly changing core
reactivity during plant operations. However, the use of the control rods can
result in undesirable effects on both radial and axial core power distribution.
Operators must operate control rods within specific limitations to minimize
these adverse effects.
Operator Responsibilities
The reactor operator is responsible for the safe operation of the reactor at all
times. The reactor operator’s responsibilities for control rod operations are:
1. Operate control rods with proper bank overlap.
This ensures more constant differential control rod worth and
minimizes the effect on the radial flux profile with movement of the
control banks.
2. Maintain control rods above rod insertion limits.
This ensures adequate shutdown margin, minimizes the adverse
effects of control rod insertion on power distribution, and minimizes
the amount of positive reactivity that a rod ejection accident could
add.
3. Properly position control rods to maintain axial flux difference (ΔI)
within the allowed operating range.
This ensures more even burning of the fuel axially throughout the
cycle. Control rod insertion results in a large shift in power towards
the bottom half of the core resulting in a more negative AFD. This
would result in faster fuel depletion in the lower half of the core and
possible high power-producing regions that could result in fuel
damage in the lower half of the core.
4. Maintain all control rods within the specified tolerance.
This ensures that the presence of control rods does not adversely
affect the radial power distribution (QPTR). This would result in
64
Rev 1
uneven fuel burnup and potential high power producing regions that
could result in fuel damage.
5. Move control rods at the proper speed.
This ensures that the control rods are inserting the correct amount of
reactivity for the current plant conditions.
During normal rod motion, the control rods must be able to move
rapidly enough to compensate for the most rapid rate that the operator
expects the positive reactivity to build in order to provide positive
control.
The burnout of peak xenon while at full power is the transient
normally considered when setting this minimum rod speed. Xenon
burnout is usually the most rapid, non-accident transient expected.
The maximum rod speed is normally limited in order to reduce the
severity of an accident involving the continuous withdrawal of control
rods.
On a scram, the control rod insertion rates are sufficient to protect the
reactor against damage in all transients expected to occur during the
life of the reactor.
Discussion Topic
Describe how the value of differential rod worth would vary if there were
zero bank overlap and why this would be undesirable.
Answer
As a control rod first moves from the full in position, there is very low
neutron flux density and very low or zero differential rod worth. The
differential rod worth increases to a maximum near the core midplane, then
decreases to near zero as the rod moves to the full out position. This results
in a non-uniform axial flux distribution. Bank overlap decreases the flux
variation, smoothing the power distribution in the core. Bank overlap also
increases rod worth and reactivity available for shutdown margin.
Knowledge Check
The main reason for designing and operating a nuclear
reactor with a flattened neutron flux distribution is to...
Rev 1
A.
provide even burnup of control rods.
B.
reduce neutron leakage from the core.
C.
allow a higher average power density.
D.
provide more accurate nuclear power indication. The
farther the reactor is operated away from local power
peaking, the higher the power the reactor can be operated
at. If the local power peaking was too high, the reactor
65
power levels would have to be lowered to ensure fuel
limits are not exceeded.
Knowledge Check
Which one of the following is a reason for neutron flux
shaping in a nuclear reactor core?
A.
To minimize local power peaking by more evenly
distributing the core thermal neutron flux
B.
To reduce thermal neutron leakage by decreasing the
neutron flux at the edge of the reactor core
C.
To reduce the size and number of control rods needed to
ensure the reactor remains subcritical following a reactor
trip
D.
The flux shape is forced to control the radial and axial
neutron flux distribution within the reactor core. By
controlling the resultant flux the local power peaking can
be minimized, thereby ensuring that fuel design limits are
not exceeded.
Knowledge Check
What is a purpose of control rod bank overlap?
66
A.
Provides a more uniform differential rod worth and axial
flux distribution.
B.
Provides a more constant differential rod worth and
allows dampening of xenon-induced flux oscillations.
C.
Ensures that all rods remain within the allowable
tolerance between their individual position indicators and
their group counters, and ensures rod insertion limits are
not exceeded.
D.
Ensures that all rods remain within their allowable
tolerance between individual position indicators and their
group counters, and provides a more uniform axial flux
distribution. Overlapping of control rod banks provides
more even reactivity additions that ensure a more
uniform differential control rod worth and a more
uniform axial neutron flux distribution.
Rev 1
TLO 2 Summary
During this lesson, you learned how control rod positioning affects core
power distribution. Control rods suppress the neutron flux and power
production in the area around their position. This essentially makes the core
power producing volume smaller requiring more power production in the
unrodded volume of the core. Therefore, the flux increases radially around
the core away from the control rods and axially towards the bottom of the
core away from the control rods in the upper region of the core. The listing
below provides a summary of sections in this TLO.
1. Core power distributions defined for unreflected, reflected, and
heterogeneous reactors.
 Commercial reactors are heterogeneous, meaning that the fuel,
control rods, moderator, coolant, etc. contained within the core are
separate entities and are not uniformly mixed within the core.
 Flux shape within the core has a direct effect on the worth of a
control rod
 Control rod position has a direct effect on the flux shape. These
differences in flux shapes affect control rod worth and core power
distribution.
2. Control rod operation considerations
 Flux shaping - A method of control rod operation used to control
the radial and axial neutron flux distribution in a reactor core.
 Bank overlap - Describes a method of operating control rods where
the next sequenced bank of rods begins to move (overlap) during
the last 50 percent of the previous bank’s travel.
 Rod insertion limits – Operators must maintain the control rods
above the rod insertion limits during plant operations. Rod
insertion limits vary, and increase as power increases to ensure
maintaining an adequate shutdown margin. Operating with the rods
withdrawn at a height greater than the rod insertion limit also
minimizes the control rods adverse effect on core power
distribution, and limits the amount of positive reactivity that an
ejected control rod could add during an accident.
 Rod ejection - With control rods high in the core, the amount of
reactivity inserted by a rod ejection should be small enough to
prevent fuel damage or an excessive power spike.
 Shut down margin  Axial flux distribution - if control rods inserted too far in core,
suppresses power production at top of core, increases power
production at bottom of core.
 Axial flux difference – (AFD) is proportional to the difference in
neutron flux between upper and lower halves of core, and may be
expressed as ∆Φ = Φ top – Φ bottom
3. Power peaking and hot channel factors
4. Quadrant power tilt ratio (QPTR) effects
 QPTR - Shall be the ratio of the maximum upper excore detector
calibrated output to the average of the upper excore detector
calibrated outputs, or the ratio of the maximum lower excore
Rev 1
67
detector calibrated output to the average of the lower excore
detector calibrated outputs, whichever is greater.
5. Calculating quadrant power tilt ratio – example calculations
6. Reactor operator responsibilities
 Operate control rods with proper bank overlap.
 Maintain control rods above rod insertion limits.
 Maintain axial flux difference (ΔI) within allowed operating range
by proper positioning of control rods.
 Maintain all control rods within specified tolerance.
 Move control rods at the proper speed.
Now that you have completed this lesson, you should be able to do the
following:
1. Explain how control rods affect core power distribution.
2. Describe the following control rod operational considerations
including:
a. Flux shaping
b. Bank overlap
c. Bank sequencing
d. Rod insertion limits
e. Reactor scram/trip
f. Power peaking and hot channel factors
3. Describe power peaking and hot channel factors.
4. Define quadrant power tilt (symmetric offset) ratio (QPTR) and
explain the long-range effects of operating with a high QPTR.
5. Given appropriate data, calculate QPTR.
6. Discuss the nuclear reactor operator’s responsibilities with regard to
control rods.
Control Rods Summary
Module Summary
This module presented the nuclear effects of control rod motion. This
knowledge is essential, as control rods are the operator's first and fastest
method of reactivity control. Operators use the control rods to bring the
reactor critical and control the power ascension; control rods are essentially
fully withdrawn at full power. Operators use the control rods mainly for
control of fast-changing reactivity transients, power changes, and reactor
trips. Control rods can provide coarse control, fine control, or fast
shutdowns. Reactors include control rods to compensate for short-term
reactivity effects due to fission product poisons, etc.
TLO 1 presented control rod construction and materials, how control rods
affect reactivity, and how changes in core conditions affect control rod
worth. TLO 1 discussed differential and integral control rod worth, the
shapes of those two worth curves in the core, and the effect of control rod
position on rod worth, as well as the effects of various core conditions on
control rod worth.
68
Rev 1
TLO 2 presented how control rods affect core power distribution, and
methods for operators to calculate the effects of moving control rods on the
power conditions in the reactor core. TLO 2 discussed a variety of control
rod position aspects, including flux shaping, bank overlap, bank sequencing,
rod insertion limits, reactor scram/trip, QPTR, and hot channel factors
Summary
Now that you have completed this module, you should be able to
demonstrate mastery of this topic by passing a written exam with a grade of
80 percent or higher on the following TLOs:
1. Explain the concept of control rod worth and how it is affected by
control rod design and changes in core parameters.
2. Explain how control rods affect plant operation and the core power
distribution.
Rev 1
69