Control Rods - Nuclear Community
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Operator Generic Fundamentals Reactor Theory - Control Rods © Copyright 2014 Operator Generic Fundamentals 2 Control Rods Introduction • Excess fuel (kexcess): – More than minimum for a critical mass – Enough fuel to run for entire fuel cycle – A means of reactor control must be provided to balance the excess reactivity and allow for plant operation • PWRs use: – Control rods – Chemical shim – Burnable poisons (fixed) © Copyright 2014 Intro Operator Generic Fundamentals 3 Control Rods Introduction • Control rods made of neutron absorbing materials are used to adjust the reactivity of the core. • Control rods can be designed and used for coarse control, fine control, or fast shutdowns. • Control rods are generally employed to compensate for short term reactivity effects due to fission product poisons, etc. – Boron concentration in coolant/moderator used to compensate for long term reactivity changes, such as caused by fuel depletion. © Copyright 2014 Intro Operator Generic Fundamentals 4 Terminal Learning Objectives (TLOs) 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 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. © Copyright 2014 TLOs Operator Generic Fundamentals 5 Enabling Learning Objectives for TLO 1 This section will discuss control rod design and explain the concept of control rod worth in terms of both differential and integral control rod worth and explain how control rod worth varies due to certain core conditions. 1. Explain the effect of control rods on 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 © Copyright 2014 ELOs Operator Generic Fundamentals 6 Enabling Learning Objectives for TLO 1 5. Describe the shape of a typical integral rod worth curve and the reason for the shape 6. Calculate the effect of 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 an absorber material © Copyright 2014 ELOs Operator Generic Fundamentals 7 Control Rod Worth Effect on Reactor Power ELO 1.1 - Explain the effect of control rods on the neutron lifecycle including how control rod design and movement affects reactor power level. Pressurized-water reactors (PWRs) use a combination of control rods and chemical shim (boron) for reactor 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. © Copyright 2014 ELO 1.1 7 Operator Generic Fundamentals 8 Control Rod Worth Effect on Reactor Power • Rods of neutron-absorbing material installed to provide precise, adjustable control of reactivity – Able to be moved into or out of reactor core in small increments • Material used for control rods varies depending on reactor design – Material selected should have good absorption cross-section for neutrons and long lifetime as an absorber (not burn out rapidly) – Typically contain elements such as silver, indium, cadmium, boron, or hafnium © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 9 Control Rod Worth Effect on Reactor Power • Movement of rods affects multiplication factor • Neutron absorber may be: – Boron (in one form or another) – Hafnium – Silver – Indium – Cadmium – Gadolinium – Or a combination • Rods may be constructed in cylindrical shape – Typically used in PWRs • May be formed into sheets or blades arranged in cruciform shape – Typically used in BWRs © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 10 Westinghouse PWR Control Rod • Typical Westinghouse four-loop plant core contains 193 fuel assemblies • Each fuel assembly contains a 17 x 17 fuel array • Core also provided with 53 full-length control rods referred to as rod control cluster assemblies (RCCAs) © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 11 Westinghouse Design • RCCAs each composed of 24 rodlets (fingers) which may contain: – Silver-Indium-Cadmium alloy (Ag-In-Cd) clad in stainless steel – Boron Carbide (B4C) rod tipped with Ag-In-Cd alloy and clad in stainless steel • Shutdown banks – A, B (16 Rods) (C, D, E) • Control banks – A, B, C, D (29 Rods) © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 12 Control Rod Worth Effect on Reactor Power Figure: Typical Westinghouse Rod Control Cluster Assembly © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 13 PWR Control Rods - CE PWR • Core of typical CE System 80 plant has 89 control rods called control element assemblies (CEAs) • CEAs are provided in 3 basic arrangements: – 48 twelve-finger full-length rods (B4C), bottom foot constructed of Ag-In-Cd – 28 four-finger full-length rods – 13 four-finger part-length rods Figure: Typical CE Control Element Assembly © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 14 PWR Control Rods - B&W PWR • CRAs utilize Ag-In-Cd alloy as neutron absorber • APSRAs use Inconel as neutron absorber • Both types of rods are clad with type 304 Stainless Steel Figure: Typical B*W Control Element Assembly © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 15 Advantages of Using B4C in Control Rods • B4C is common boron compound with desirable properties for use in nuclear reactor control rods – Stable in environment presented by core (high temperatures, etc.) – Able to absorb neutrons without forming long lived radionuclides • During manufacture B4C compacted into stainless steel tube in order to form control rod – Leaves room for accumulation of helium, which results from boron capture reaction 10 1 11 π΅+ π→ π΅ 5 0 5 © Copyright 2014 ELO 1.1 ∗ 7 4 → πΏπ + π»π 3 2 Operator Generic Fundamentals Advantages of Using B4C in Control Rods • B4C control rods can absorb ~100 percent of neutrons at energies below ~10 eV • Above 10 eV, neutron absorption probability drops almost linearly • 1/v characteristic Figure: Thermal and Epithermal Neutron Absorption in B4C Control Rods © Copyright 2014 ELO 1.1 Operator Generic Fundamentals Advantages of Using Ag-In-Cd in Control Rods (Westinghouse) • Ag-In-Cd rods absorb most neutrons from thermal energy to approximately 50 eV Figure: Thermal and Epithermal Neutron Absorption in Ag-In-Cd Control Rods © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 18 Advantages of Using Hf • Hf has 5 stable isotopes that are capable of absorbing neutrons 1 1 1 1 176 177 178 179 180 π»π + π → π»π + π → π»π + π → π»π + π → π»π 72 0 72 0 72 0 72 0 72 © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 19 Control Rod Worth Effect on Reactor Power Properties of PWR Control Rod Materials Isotope Abundance Microscopic Cross Section for Thermal Neutrons (σa) Microscopic Cross Neutron Section for Energy Resonant Absorption (σa) B-10 19.9 % 3,837 barns 1,722 barns Ag-107 51.8% 45 barns 630 barns Epithermal average 16.6 eV Ag-109 48.2% 92 barns 12,500 barns 5.1 eV In-113 4.3% 12 barns 310 barns In-115 95.7% 203 barns 30,000 barns Epithermal average 1.46 eV Cd-114 12.2% 20,000 barns 7,200 barns 0.18 eV © Copyright 2014 ELO 1.1 19 Operator Generic Fundamentals 20 Control Rod Worth Effect on Reactor Power Characteristics of Natural Hafnium Isotope Natural Abundance Hf-176 5.2 % Microscopic Cross Section for Neutron Absorption (σa) 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 © Copyright 2014 ELO 1.1 20 Operator Generic Fundamentals 21 Effect of Control Rod on Neutron Cycle • As control rods are withdrawn and inserted, amount of reactivity in the core is changed • Control rods are neutron absorbers ⇒ – Affect ππππ and neutron life cycle ππππ = ππΏπ ππΏπ‘β ππ © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 22 Control Rod Worth Effect on Reactor Power Effects on Six Factor Formula ππππ = ππΏπ ππΏπ‘β ππ • Terms in six factor formula most affected by control rod motion are: πΏπ , πΏπ‘β , π and π • Consider effects on six factor formula as control rods are withdrawn from core © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 23 Effects on Six Factor Formula – πΏπ and πΏπ‘β Control rod withdrawal • Effectively increases size of core for neutron production • As effective core size increases, average neutron must travel farther in order to leak out of core • Neutron leakage decreases resulting in increase in both πΏπ and πΏπ‘β © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 24 Effects on Six Factor Formula – π Control rod withdrawal • Control rods containing silver and indium affect the resonance escape factor by absorbing an epithermal energy neutrons • The resonance escape factor and ππππ increase as the absorber is withdrawn • With fewer resonant absorbers in the core, more neutrons will reach thermal energy and be available to be absorbed in the fuel, resulting in more fissions and power increasing © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 25 Effects on Six Factor Formula - π • Effect of control rod motion on f is greater than that on πΏπ , πΏπ‘β and π Equation for f accounts for absorption of neutrons in other core materials, including control rods: π= ππ’ππ + π ππ’ππ π ππππ ππππ‘πππ ππππ + + π π ππ‘βππ π • As control rod is removed, its macroscopic cross section for ππππ‘πππ ππππ absorption ( ) decreases π ↑π= © Copyright 2014 ππ’ππ + π ππππ + π ELO 1.1 ππ’ππ π ππππ‘πππ ππππ ↓+ π ππ‘βππ π Operator Generic Fundamentals 26 Effects on Six Factor Formula - π • • • • Control rod withdrawal at power Macroscopic cross section for absorption is decreased - π Greater number of neutrons absorbed by fuel ππππ has increased, positive reactivity added • Reactor power increases temporarily • Moderator and fuel temperature increase, adding negative reactivity • Without a change in steam demand, power will remain constant at a higher moderator and fuel temperature © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 27 Effects on Six Factor Formula - π • • • • Control rod inserted at power Macroscopic cross section for absorption is increased - π Fewer neutrons available for absorption in fuel ππππ decreased and negative reactivity added • Reactor power decreases temporarily • Moderator and fuel temperature decrease, adding positive reactivity • Without a change in steam demand, power will remain constant at a lower moderator and fuel temperature © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 28 Control Rod Worth Effect on Reactor Power Reactor Trip • Ability to rapidly insert negative reactivity into the core 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 means of inserting large amount of negative reactivity very quickly to attain rapid shutdown. • Reactor trip (or scram) is the rapid insertion of all control rods to fully inserted position. This action inserts a large amount of negative reactivity into the core in a very short time, driving the reactor subcritical. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 29 Control Rod Worth Effect on Reactor Power 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. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 30 Control Rod Worth Effect on Reactor Power 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 min 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. Correct answer is D. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 31 Control Rod Worth Effect on Reactor Power 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. Correct answer is ANSWER DD. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 32 Control Rod Worth ELO 1.2 - Describe the term control rod worth. This section discusses how control rod worth varies by core location and variations in neutron flux profiles. 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. © Copyright 2014 ELO 1.2 32 Operator Generic Fundamentals 33 Control Rod Effectiveness Control Rod Worth (CRW) Effectiveness of specific control rod in absorbing neutrons • As control rod is moved, core characteristics change primarily in region near tip of control rod • Only a small region of core near tip of the rod is affected by rod motion ⇒ amount of reactivity inserted into core is determined by conditions in this region Effect of Neutron Flux on CRW • If neutron flux in area near tip of particular rod is large ⇒ larger fraction of neutrons have chance of being absorbed • Reactivity change due to motion of this particular control rod will be greatest when tip of rod is moving through region of core experiencing greatest neutron flux © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 34 Control Rod Effectiveness If reactor has only one control rod, rod should be placed in center of reactor core for maximum effectiveness or worth Numerous control rods are required - excess reactivity Figure: Effect of Control Rod on Radial Flux Distribution © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 35 Control Rod Effectiveness If additional rods are added the most effective location to place them would be in location where flux is maximum Figure: Effect of Control Rod on Radial Flux Distribution © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 36 Effect of Rod Location on CRW • “Relative importance” of neutrons near tip of control rod also determines CRW – Neutrons produced near edge of core more likely to leak out of core – less important – Neutrons thermalized in region of core with high poison or low fuel concentration likely to be captured by poison – less important • Neutrons most likely to cause fission are those born near center of core, in regions of low poison concentration and high fuel concentration • Reactivity changes are largest when tip of control rod moves through regions where neutrons relatively important to chain reaction • Neutron flux tends to be greater in same areas of core where importance of neutrons is greater © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 37 Control Rod Worth 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: 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. 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. 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. 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. Correct answer is A. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 38 Differential and Integral CRW ELO 1.3 - Define the following terms: a. Differential rod worth, b. Integral rod worth Figure: Differential Rod Worth for Banked Control Rods © Copyright 2014 ELO 1.3 Figure: Integral Rod Worth Curve Referenced to Bottom and Top of Core 38 Operator Generic Fundamentals 39 Differential and Integral CRW • Graph depicts integral control rod worth over full range of withdrawal • Integral rod worth (IRW) - the reactivity inserted by moving a control rod from a reference position to any other rod height • Reactors operate with control rods completely withdrawn, so the top of the core is normally the reference and the control rods add negative reactivity as they are inserted from the reference position Figure: Integral Control Rod Worth © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 40 Differential and Integral CRW • Slope of integral rod worth curve is the rate of a reactivity addition at that control rod position • Plot of slope of integral rod worth curve results in the differential control rod worth (DRW) • As rod approaches center of core its effect becomes greater, DRW is greater Figure: Integral Control Rod Worth © Copyright 2014 ELO 1.3 40 Operator Generic Fundamentals 41 Differential Rod Worth • Differential Control Rod Worth - reactivity change per unit movement of a control rod • Since control rods move vertically, control rod position is referred to as rod height βπ π·π π = βπ» • Units: pcm (%Δk/k)/inch, step or % withdrawn © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 42 Differential Rod Worth • DRW depends on relative flux near control rod’s tip, relative importance of neutrons near control rod tip and control rod itself ππ‘ππ π·π π = πΆ π πππ£π π·π π = differential control rod worth πΆ = constant based on control rod size, shape and material ππ‘ππ = neutron flux near control rod tip πππ£π =average neutron flux in core π = flux importance factor • In most reactors, flux importance factor is proportional to local flux: ππ‘ππ π∝ πππ£π © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 43 Differential and Integral CRW ππ‘ππ π·π π = πΆ π πππ£π In most reactors, importance factor is directly proportional to local relative flux: Where: ππ‘ππ π∝ πππ£π π·π π = differential control rod worth πΆ = constant based on control rod size, shape, and neutronabsorbing material ππ‘ππ = neutron flux near control rod tip πππ£π = average neutron flux in core π = importance factor © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 44 Differential and Integral CRW • Therefore, DRW is proportional to the square of local relative flux, as shown in the following equations: ππ‘ππ ππ‘ππ π·π π = πΆ πππ£π πππ£π 2 ππ‘ππ π·π π ∝ πππ£π © Copyright 2014 ELO 1.3 Operator Generic Fundamentals Solution 45 Differential and Integral CRW 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 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? © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 48 Differential and Integral CRW Knowledge Check – NRC Bank 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 1 x 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 Correct answer is D. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 49 Differential Control Rod Worth Characteristics ELO 1.4 - Describe the shape of a typical differential control rod worth curve and the reason for the shape. Differential rod worth varies greatly from bottom to top of core. At some core heights, the rods have almost no effect while at other heights they have a large effect. To control the reactor precisely, the operator must be able to determine effect on reactivity that movement of control rods will produce. DRW is the amount of reactivity a control rod or group of control rods adds per incremental movement. © Copyright 2014 ELO 1.4 49 Operator Generic Fundamentals 50 Differential Control Rod Worth Characteristics At bottom and top of core, there are few neutrons of low importance, rod movement has little effect ⇒ DRW is small As rod approaches center of core its effect becomes greater, more neutrons with higher portents, DRW is greater © Copyright 2014 Figure: Differential Control Rod Worth ELO 1.4 50 Operator Generic Fundamentals 51 DRW vs. Rod Position in Core • As control rod moves in core, DRW of rod changes • Any change in reactor core which affects axial flux distribution depicted here will affect DRW of the control rods within core Figure: Axial Flux Variation in a Bare Homogenous Core © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 52 DRW vs. Rod Position • Movement of control rods changes axial flux shape ⇒ change DRW • Neutron flux will be depressed in region of core where control rods are inserted • Flux will be greater in unrodded regions • Highest DRW occurs at rod height below core midplane © Copyright 2014 Figure: Shift in Core Axial Neutron Flux due to Control Rod Insertion ELO 1.4 Operator Generic Fundamentals 53 DRW vs. Rod Position in Core • When control rods are near bottom of core, neutron flux will shift back to core midplane • A fully inserted control rod has a uniform affect on the axial flux distribution Figure: Shift in Core Axial Neutron Flux due to Control Rod Insertion © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 54 DRW for Banked Rods • A rod bank is group of control rods which are moved together • Graph shows DRW versus rod height in typical reactor with banked control rods • Similar to an individual DRW curve (for the same reasons) Figure: Differential Rod Worth for Banked Control Rods © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 55 Differential Control Rod Worth Characteristics Sample Question – NRC Bank 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. moderator temperature coefficient decreases, causing decrease competition. C. fuel temperature increases, decreasing neutron absorption in fuel. D. decreased moderator density increases neutron migration length. Correct answer is D. © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 56 Differential Control Rod Worth Characteristics Practice Knowledge Check – NRC Bank 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... A. more negative due to better moderation of neutrons. B. less negative due to shorter neutron migration length. C. more negative due to increased neutron absorption in moderator. D. less negative due to increased resonance absorption of neutrons. Correct answer is B. © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 57 Differential Control Rod Worth Characteristics Knowledge Check – NRC Bank 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 D. Burnable poison distribution Correct answer is B. © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 58 Differential Control Rod Worth Characteristics Knowledge Check – NRC Bank 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.) 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 the core. D. Shifts away from the top and bottom toward the center of the core. Correct answer is B. © Copyright 2014 ELO 1.4 Operator Generic Fundamentals 59 Integral Control Rod Worth Characteristics ELO 1.5 - Describe the shape of a typical integral control rod worth curve and the reason for the shape Total reactivity effect of moving rods from one position to another is termed IRW. Knowledge of the total amount of reactivity added by rod motion is essential for calculating core reactivity balances, estimating critical rod positions, and predicting the effect of a proposed rod position change. © Copyright 2014 ELO 1.5 59 Operator Generic Fundamentals 60 Integral Rod Worth • Reactivity inserted by moving control rod from reference position to any other rod height is called IRW at that height • IRW at given withdrawal is summation of all DRW’s up to point of withdrawal • IRW is also area under DRW curve at any given withdrawal position Figure: Integral Rod Worth Curve © Copyright 2014 ELO 1.5 Operator Generic Fundamentals 61 Integral Rod Worth • Reference position for control rods is selected for convenience and may be All Rods In (ARI) or ARO position • Control rods are normally ARO ⇒ top of core is normally selected as reference (0) position for control rod movement Figure: Integral Rod Worth Curve © Copyright 2014 ELO 1.5 Operator Generic Fundamentals 62 Integral Rod Worth Figure: Integral Rod Worth Curves Referenced to Bottom and Top of Core βπ = πΌπ π − πΌπ πππππ‘πππ © Copyright 2014 ELO 1.5 62 Operator Generic Fundamentals 63 Integral Rod Worth Typical DRW and IRW curves for Westinghouse commercial nuclear reactor for Cycle 1 at BOL and hot zero power (HZP) conditions Figure: IRW and DRW Curves for Westinghouse Plant at HZP © Copyright 2014 ELO 1.5 Operator Generic Fundamentals 64 Integral Control Rod Worth Characteristics Example Problem – NRC Bank The total amount of reactivity added by a control rod position change 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. Correct answer is C. © Copyright 2014 ELO 1.5 Operator Generic Fundamentals 65 Integral Control Rod Worth Characteristics Knowledge Check – NRC Bank 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. Correct answer is C. © Copyright 2014 ELO 1.5 Operator Generic Fundamentals 66 Control Rod Effects (Worth) ELO 1.6 - Calculate the effect control rod position in the core and grouping control rods has on differential rod worth. Knowledge of change in reactivity following the rod motion allows the reactor operator to control evolution by observing that plant responds as predicted. © Copyright 2014 Figure: Rod Worth Curves for Example Problems ELO 1.6 66 Operator Generic Fundamentals 67 Control Rod Effects (Worth) IRW - Example: • Using IRW curve provided, find reactivity inserted by moving the rod from 12 inches withdrawn out to 18 inches withdrawn Figure: Rod Worth Curves for Example Problems © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 68 Control Rod Effects (Worth) IRW - Solution: • The integral rod worth at 12 inches is 40 pcm and the integral rod worth at 18 inches is 80 pcm βπ = ππππππ − πππππ‘πππ βπ = π18 − π12 βπ = 80 πππ − 40 πππ βπ = 40 πππ © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 69 Control Rod Effects (Worth) IRW – Example 2: • Using the differential rod worth curve provided, calculate the reactivity inserted by moving the rod from 10 inches withdrawn to 6 inches withdrawn Figure: Rod Worth Curves for Example Problems © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 70 Control Rod Effects (Worth) IRW – Solution 2: • 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.) Figure: Rod Worth Curves for Example Problems 8 © Copyright 2014 πππ πππ +3 πππβ πππβ 2 4 πππβππ = −22 πππ ELO 1.6 Operator Generic Fundamentals 71 Control Rod Effects (Worth) IRW – Solution 2: • Method 2. Using the central value of rod position at 8 inches yields an average rod worth of 5.5 pcm/inch. Multiplying by the 4 inches of πππ rod travel yields the answer: 5.5 4 πππβππ = −22 πππ πππβ Figure: Rod Worth Curves for Example Problems © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 72 Control Rod Effects (Worth) IRW – Solution 2: • Method 3. Breaking the rod travel total into two parts (10 inches to 8 inches and 8 inches to 6 inches) yields: πππ πππ + 5.5 πππβ πππβ −2 πππβππ = −13.5 πππ 2 πππ πππ 5.5 +3 πππβ πππβ −2 πππβππ = −8.5 πππ 2 −13.5 πππ + −8.5 πππ = −22 πππ 8 The 3 methods resulted in the same calculated reactivity change because for the small amount of rod motion the change in differential rod worth was almost linear. © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 73 Control Rod Effects (Worth) IRW – Example 3: • For the differential rod worth data given, construct differential and integral rod worth curves © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 74 Control Rod Effects (Worth) IRW – Solution 3: • For each interval, pcm/inch must be determined • In first interval (0 inches to 2 inches), 10 pcm is added ⇒ DRW equals ≈ 5 pcm/inch • DRW for first interval plotted at center of interval ⇒ 1 inch • Values of pcm/inch are determined for each interval and plotted © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 75 Control Rod Effects (Worth) IRW – Solution 3: Figure: Rod Worth Curves from Example © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 76 Control Rod Effects (Worth) IRW – Solution 3 • To plot IRW, develop a cumulative total of reactivity added after each interval and plot summed reactivity insertion vs. rod position © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 77 Control Rod Effects (Worth) IRW – Solution 3 Figure: Rod Worth Curve from Example 3 © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 78 Control Rod Effects (Worth) • If IRW curve is supplied, a DRW curve can be generated from IRW data – Select convenient interval of rod withdrawal, such as 1 inch or 2 inches – Determine from curve amount of reactivity added for each constant interval of rod withdrawal – Plot this reactivity addition versus rod withdrawal © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 79 Control Rod Effects (Worth) 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. Correct answer is B. © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 80 Control Rod Effects (Worth) Knowledge Check – NRC Bank Integral control rod worth can be described as the change in __________ for a __________ change in rod position. A. B. C. D. reactor power; total reactivity; unit reactor power; unit reactivity; total Correct answer is D. © Copyright 2014 ELO 1.6 Operator Generic Fundamentals 81 Core Parameters Impact on CRW ELO 1.7 - 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 © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 82 Effects of Core Conditions on CRW • Various conditions in core will affect reactivity worth of control rods: – Moderator temperature – Fission product poisons – Soluble boron concentration – Reactor power – Presence of other control rods © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 83 Moderator Temperature Effects • Moderator temperature has significant impact on reactivity worth of control rods Figure: Changes in Control Rod Worth due to Changes in Temperature © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 84 Moderator Temperature Effects • As moderator temperature increases, it becomes less dense • Neutrons able to travel greater distance before interacting with water molecules (greater migration length) • Since neutrons travel greater distance, they have a higher probability of reaching particular control rod • Control rod worth increases due to control rod’s increased sphere of influence © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 85 Moderator Temperature Effects • Rod worth curve over core life at two different temperatures • Both moderator/coolant temperature and core life affect value of control rod worth Figure: Group Rod Worth versus Temperature over Core Life © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 86 Core Life Effects • Effects of core life can be attributed to fuel burnout and fission product poison buildup • Tends shift neutron flux towards the control rods increasing their worth Figure: Group Rod Worth versus Temperature over Core Life © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 87 Neutron Absorber Effects • Most FPP’s and chemical shim (boron) are strong thermal neutron absorbers • Both of these tend to shift neutron flux spectrum to epithermal energy range – Referred to as (flux) spectrum hardening • B4C, hafnium, and silver-indium-cadmium control rods are strong epithermal neutron absorbers ⇒ increased reactivity worth when FPP concentrations are high © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 88 Neutron Absorber Effects • For given temperature, reactivity worth of control rod bank increases with core age. • FPP inventory increases causes the neutron flux average energy to increase (harden) and shift towards the control rods Figure: Bank Control Rod Worth Changes due to Spectrum Hardening © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 89 Neutron Absorber Effects • Xenon is a fission product • Concentrates in the fuel rods • Shifts some of the thermal flux away from the fuel rods into the control rod locations • Plant curves usually have both Xe free and Peak Xe for rod worths – be careful © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 90 Power Level Effects • Although reactivity worth of control rods does not depend on absolute magnitude of flux in core, control rod reactivity worth does change with reactor power level • Change is small and is normally considered to be negligible • Changes in neutron flux profile due to Doppler reactivity effects, changes in moderator temperature, and buildup of FPP’s causes neutron flux distribution to change with reactor power © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 91 Power Level Effects Shifting Flux Distribution Effects • Neutron flux in nuclear reactor tends to move radially outward over core life • As flux moves outward, it tends to interact with greater number of control rods – Usually more control rods located in periphery of core than center Figure: Shift in Radial Neutron Flux Profile over Core Life © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 92 Control Rod Location • Result of shift in radial neutron flux profile toward outer edges of core results in overall increase in CRW over core life. • As radial flux moves outward, it interacts with greater number of control rods, because more control rods located in the periphery of the core. • Figure shows control rod locations as colored blocks, with more rods near periphery than center of core. © Copyright 2014 Figure: Control Rod Location ELO 1.7 Operator Generic Fundamentals 93 Control Rod Effects • Radial thermal neutron flux distribution with respect to average thermal flux with no control rods • Control rod worth is proportional to relative flux squared (or relative power squared) Figure: Radial Thermal Neutron Flux Profile with No Control Rods ππ‘ππ π·π π ∝ πππ£π © Copyright 2014 ELO 1.7 2 Operator Generic Fundamentals 94 Control Rod Effects Rod Shadowing • Sharp drop in thermal neutron flux will occur as one individual control rod assembly enters into thermal neutron flux in reactor core • Inserting one control rod would result in significant power reduction in upper region of core, as shown by thermal flux profile Figure: Control Rod Shadowing Effects on Thermal Flux © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 95 Control Rod Effects Rod Shadowing • When Rod #2 is inserted at position A, reactivity worth of Rod #2 is lower than reactivity worth of Rod #1 because neutron flux has already been depressed by Rod #1 • Positive Rod shadowing Figure: Control Rod Shadowing Effects on Thermal Flux © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 96 Control Rod Effects Rod Shadowing • Rod #2 inserted into core significant distance (Point B) from Rod #1 • Rod #2 has greater reactivity worth as compared to what its reactivity worth would have been without Rod #1 • Negatively Shadowed Figure: Control Rod Shadowing Effects on Thermal Flux © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 97 Control Rod Effects ο¦ (r) ROD # 1 WITHOUT ROD # 2 CONTROL ROD NO. 1 INSERTED Rod Shadowing - Rod Placement to Avoid Shadowing Effects • When Rod #2 inserted into core at position C, has same reactivity worth whether Rod #1 inserted into core or not C A ο¦ (r) WITH CONTROL ROD NO.1 INSERTED B ο¦ AV G Assume Figure: Control two Rod identical Shadowingcontrol Effects rods on Thermal Flux © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 98 Control Rod Effects Grouping of Control Rods • In commercial PWRs, control rods are withdrawn in symmetrical arrays known as rod groups • Overall objective of rod grouping is to maintain flattest possible flux profile across entire volume of core • Tends to minimize rod shadowing effects and reactivity worth of individual control rods – Ratio of local thermal flux to overall core thermal flux squared is approximately equal to 1 © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 99 Effects of Core Conditions on CRW • Radial Effects: Location • Axial Effect: Height • Each Core Quadrant has symmetrically placed control rods for each bank • Blocks of the same color form banks – Shutdown Banks: SA, SB, SC, SD, SE – Control Banks: A, B, C, D Figure: Control Rod Location © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 100 Control Rod Effects Grouping of Control Rods • Control rods are grouped such that individual rods are not located in immediate core vicinity of other rods in group • Spacing between control rods results in neutron flux peaks in area where each control rod has been withdrawn • Neutrons are limited to small area of travel ⇒ movement of any one control rod has little shadowing effect on any of other control rods in same group • Overall objective of rod grouping: – Minimize flux peaking associated with any one control rod – Minimize shadowing of other rods in that group © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 101 Effects of Core Conditions on CRW Knowledge Check 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 _______. 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 Correct answer is A. © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 102 Effects of Core Conditions on CRW 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... A. more negative due to better moderation of neutrons. B. less negative due to shorter neutron migration length. C. more negative due to increased neutron absorption in the moderator. D. less negative due to increased resonance absorption of neutrons. Correct answer is B. © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 103 Effects of Core Conditions on CRW Knowledge Check – NRC Bank Differential rod worth will become most negative if reactor coolant system (RCS) temperature is __________ and RCS boron concentration is __________. A. increased; decreased B. decreased; decreased C. increased; increased D. decreased; increased Correct answer is A. © Copyright 2014 ELO 1.7 Operator Generic Fundamentals 104 TLO 1.0 Summary Review Use Class Discussion and selected Knowledge Check questions to review ELO’s 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 (πΏπ and πΏπ‘β ), the resonance escape probability (π) and the thermal utilization factor (π) 2. Describe the term control rod worth • Effect of neutron flux on control rod worth • Effect of control rod location on control rod worth © Copyright 2014 TLO 1 Operator Generic Fundamentals 105 TLO 1.0 Summary Review 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. Describe shape of a typical differential control rod worth curve and the reason for the shape • Typical differential rod worth curve has a bell shape. • Has very low values at top and bottom of core and a maximum value at the center of the core • Curve has this shape because rod worth is related to neutron flux, and flux is highest in the center of the core © Copyright 2014 TLO 1 Operator Generic Fundamentals 106 TLO 1.0 Summary Review 5. 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. Calculate the effect that control rod position in the core and grouping control rods has on differential rod worth 7. Core parameters impact on control rod worth • Moderator Temperature (Temp Up – CRW Down) • Fission product and Soluble boron poisons (FPP Up – CRW Up) • Reactor power (Rx PWR Up - CRW Up Slightly) • Presence of other control rods (per IG depends on relative location) • Absorber material used in the control rods (high absorption cross section for epithermal neutrons) © Copyright 2014 TLO 1 Operator Generic Fundamentals 107 TLO 1.0 Summary Review 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. © Copyright 2014 TLO 1 Operator Generic Fundamentals 108 Control Rods – TLO 1.0 Summary Review 5. Describe the shape of a typical integral rod worth curve and the reason for the shape. 6. Calculate the effect 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 © Copyright 2014 TLO 1 Operator Generic Fundamentals 109 Plant Operation and Control Rod Impact TLO 2 - Explain how control rods affect plant operation and the core power distribution. This section will explain the concept of control rod worth in terms of both differential and integral control rod worth and explain how control rod worth varies due to certain conditions. The operator must understand potential adverse effects of control rod movement and minimize these effects by maintaining control rods within established operating limits, thereby preventing core damage. © Copyright 2014 TLO 2 109 Operator Generic Fundamentals 110 Plant Operation and Control Rod Impact • Explain how control rods affect core power distribution. • Describe the following control rod operational considerations including: – Flux shaping – Bank overlap – Bank sequencing – Rod insertion limits – Reactor scram/trip – Power peaking and hot channel factors • Describe power peaking and hot channel factors. • Define quadrant power tilt (symmetric offset) ratio (QPTR) and explain the long range effects of operating with a high QPTR. • Given appropriate data, calculate QPTR. • Describe the nuclear reactor operator’s responsibilities with regard to control rods. © Copyright 2014 TLO 2 Operator Generic Fundamentals 111 Core Power Distribution ELO 2.1 - Explain how control rods affect core power distribution. The flux shape in the core has a direct effect on CRW. ROD # 1 ROD # 2 Control rod position has a direct effect on the flux shape. C A These differences in flux shapes affect CRW and core power distribution; operators must understand effects to control reactor. © Copyright 2014 ο¦ (r) WITHOUT CONTROL ROD NO. 1 INSERTED B ο¦ AVG ο¦ (r) WITH CONTROL ROD NO.1 INSERTED ELO 2.1 111 Operator Generic Fundamentals 112 Effects on Core Power Distribution • Each reactor has certain core volume and certain number of square feet of heat transfer surface • If reactor could be operated in ideal manner (flat flux profile), all portions of core would be producing equal amounts of power • Fuel would be burned uniformly, core size would be minimized, and costs associated with fuel would be minimal • Unfortunately, there are unavoidable factors associated with core design and operation which make it impossible to achieve perfectly uniform power distribution across core © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 113 Bare (Unreflected) Reactor • Simple homogenous uncontrolled reactor surrounded by vacuum • Neutrons born near edge of core have greater probability of leaking out compared to neutron born near core center • Power density within core drops off significantly in any direction outward from core’s center • Most reactor cores approximate right circular cylinder • Radial and axial power distribution approximate a cosine shape Figure: Neutron Flux Profile © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 114 Effects on Core Power Distribution Reflected Reactor • In reality, bare homogenous reactors do not exist • Role of reflector on operation of homogenous core must be considered • Reflector is material that is present in or near reactor, which reflects neutrons back into core • In commercial PWR, water in downcomer region and in bottom and top of core act as reflectors © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 115 Effects on Core Power Distribution Reflected Reactor • Two effects in regard to flux distribution: – Scatters some thermal neutrons back into fuel – Moderates some fast neutrons that leaked from core – Both effects tend to increase neutron flux at edges of core which tends to flatten neutron flux distribution across core Figure: Neutron Flux Profile © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 116 Effects on Core Power Distribution Heterogeneous Reactor • Just as there are no real reactors which are bare, there are also no real reactors which are homogenous • Commercial PWRs are heterogeneous, meaning fuel, control rods, moderator, coolant, etc. contained within core are separate entities and are not uniformly mixed • Although neutron flux distribution in heterogeneous reactor tends to be similar in shape to homogeneous reactor, radial shape would be rougher due to discontinuities caused by separation of moderator and fuel © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 117 Effects on Core Power Distribution Heterogeneous Reactor • In heterogeneous reactor most thermal neutrons produced in moderator but are absorbed before reaching center of fuel rod • Results in flux depression in each rod and corresponding flux peak in water gaps between fuel rods Figure: Distortion of Radial Neutron Flux in Heterogeneous Core © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 118 Effects on Core Power Distribution Heterogeneous Reactor • Axial flux in heterogeneous reactor is also disturbed by presence of control rods in core Figure: Shift in Core Axial Neutron Flux due to Control Rod Insertion © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 119 Core Power Distribution 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. Correct answer is A, C, D, and E. © Copyright 2014 ELO 2.1 Operator Generic Fundamentals 120 Control Rod Operation Considerations ELO 2.2 - Describe the following control rod operational considerations including: a. b. c. d. e. f. Flux shaping Bank overlap Bank sequencing Rod insertion limits Reactor scram/trip Power peaking and hot channel factors This section describes how operating control rods influence flux shaping, and problems that arise when using rods in this manner. © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 121 Flux Shaping • Flux Shaping - method of control rod operation used to control radial and axial neutron flux distribution in reactor • Goals of Flux Shaping: – Minimization of localized power peaking – Control of control rod worth to minimize fuel burnout problems and optimize fuel depletion • Flux shaping accomplished by establishing specific pattern of control rod withdrawal and insertion - Rod Sequence - employed during reactor operation – Designed to control reactor’s core radial power distribution • Rod sequence established by grouping individual control rods into rod banks • Withdrawal of rod banks performed in specific sequence in order to maintain “bank overlap” © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 122 Bank Overlap • To expedite core reactivity changes with minimum rod movement, control rods are operated in symmetrically arranged banks of control rods • Typical four-loop Westinghouse commercial PWR has four control banks and four or five shutdown banks – Shutdown banks are always fully withdrawn during reactor operations – Control banks are operated at various core heights in order to maintain reactor critical © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 123 Bank Overlap • Control banks are operated with certain amount of overlap (Bank Overlap) • Before one control bank is fully withdrawn, another control bank will begin to move off core bottom • Amount of overlap between control rod banks depends on reactor design and is varied from cycle to cycle by changing the all rods out position – Core Operating Limits Report © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 124 Bank Overlap Example 1 • Westinghouse-designed reactor plant: • ARO = 228 and Bank Overlap set at 114 steps – Control bank A withdrawn from 0 to 228 steps (ARO position for this cycle) – When control bank A reaches 114 steps, control bank B begins to move outward – When control bank A reaches 228 steps - control bank B is at 114 steps, control bank C begins to move out to overlap the last 114 steps of bank B, control bank A stops at 228 – The same overlap occurs between control bank C and control bank D © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 125 Bank Overlap Example 2 • Westinghouse-designed reactor plant: • ARO = 230 and Bank Overlap set at 115 steps – Control bank A withdrawn from 0 to 230 steps – When control bank A reaches 115 steps, control bank B begins to move outward – When control bank A reaches 230 steps - control bank B is at 115 steps, control bank C begins to move out of the core to overlap the last 115 steps of bank B, control bank A stops at 230 steps © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 126 Bank Overlap • Bank overlap provides for more uniform differential control rod worth and more uniform axial neutron flux distribution within core during control rod movement • Non-uniform axial flux distribution could result in abnormally high power peaks in core, and fuel damage • Uniform differential control rod worth ensures that rod motion always produces a change in reactivity Figure: Effect of Bank Overlap on Differential Rod Worth © Copyright 2014 ELO 2.2 Figure: Effect of Bank Overlap on Integral Rod Worth Operator Generic Fundamentals 127 Rod Insertion Limits (RILs) • Reactor design may allow control rods to be positioned axially at any height in the core • Procedurally, control rods must be above a specified height during reactor operations • Height is Rod Insertion Limit (Technical Specifications) © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 128 Rod Insertion Limits • Rod insertion limits are designed to: – Minimize consequences of ejected rod accident – Guarantee sufficient shutdown margin from given power level – Produce an axial flux distribution which prevents high local peak power levels Figure: Rod Insertion Limits for a Westinghouse PWR © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 129 Rod Ejection • Maintaining control rods high in core prevents ejected control rod from inserting excessive positive reactivity into core that could result in local fuel damage – Rod ejection will result in a small-break loss-of-coolant-accident (SBLOCA), due to rupture of control rod drive housing © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 130 Rod Insertion Limits Shutdown Margin • When the reactor trips, positive reactivity actually added to core by the fuel and moderator temperature decreasing to HZP values: – Power Defect (FTC and MTC) – Moderator/coolant temperature decrease below HZP average coolant temperature (due to cooldown from continued steam demand) will add additional positive reactivity • RILs ensure control rods have sufficient negative reactivity to shutdown reactor from given power level with sufficient shutdown margin to maintain reactor in safe shutdown condition • The operator routinely monitors the control rods to be above the RILs to ensure adequate Shut Down Margin exists © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 131 Rod Insertion Limits Axial Flux Distribution • If control rods are inserted too far into the core, power production in top of core will be suppressed, resulting in corresponding increase in power production in bottom of core • Higher power in bottom of core could result in abnormally high fuel temperatures and fuel damage © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 132 Rod Insertion Limits Axial Flux Difference (AFD) • ΔΦ or ΔI - difference in power production between the upper and lower half of the core as indicated by the delta between the power range upper and lower detectors • Power Range detectors are Ion Chambers and produce a current (I) output proportional to neutron Φ Figure: Upper and Lower Power Range Neutron Detector Locations © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 133 Rod Insertion Limits Axial Flux Distribution - Axial Flux Difference • Difference is also proportional to difference in axial neutron flux between upper and lower halves of core: βπ· = π·π‘ππ − π·πππ‘π‘ππ • For detectors, change in flux can be equated to change in the ion chamber detector current: βπ· = π·π‘ππ − π·πππ‘π‘ππ © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 134 Rod Insertion Limits Axial Flux Distribution - Axial Flux Difference • AFD must be maintained in specified band during reactor operation to ensure more uniform axial flux distribution across core ⇒ preventing high peak power in either top or bottom of core (Technical Specifications) – High peak power results in high fission product concentration in that location – Decay heat generated by fission products could overheat fuel during loss of coolant accident • Control rod position used to maintain AFD within allowed operating range during reactor operations • Under most operating conditions, AFD limitation more restrictive than rod insertion limits © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 135 Control Rod Operation Considerations Knowledge Check - NRC Bank Why are the control rod insertion limits power dependent? A. Power defect increases as power increases. B. Control rod worth decreases as power increases. C. Doppler (fuel temperature) coefficient decreases as power increases. D. Equilibrium core xenon-135 negative reactivity increases as power increases. Correct answer is A. © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 136 Control Rod Operation Considerations Knowledge Check – NRC Bank Control rod insertion limits ensure that control rods will be more withdrawn as reactor power ____________ to compensate for the change in ____________. A. increases; xenon reactivity B. decreases; xenon reactivity C. increases; power defect D. decreases; power defect Correct answer is C. © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 137 Control Rod Operation Considerations Knowledge Check – NRC Bank 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. To increase control rod worth by peaking the thermal neutron flux at the top of the reactor core Correct answer is A. © Copyright 2014 ELO 2.2 Operator Generic Fundamentals 138 Power Peaking and Hot Channels ELO 2.3 - Describe power peaking and hot channel factors. The redistribution of the neutron flux from its design values results in regions of high power production in the core. These peak regions result in higher fuel and moderator temperatures that operators must control to equalize fuel burn up and prevent local fuel damage. © Copyright 2014 ELO 2.3 138 Operator Generic Fundamentals 139 Power Peaking and Hot Channels • The presence of control rods results in neutron flux profiles that have higher peaks and valleys then occur when the rods are fully withdrawn. • Ratio of Φmax /Φavg often referred to as - Hot Channel Factor • Hot Channel Factors are simply Peak / Average values for a given parameter such as enthalpy or heat flux. • Hot channel factors will be covered in more detail in another chapter. • Hot channel factors greater than 1.0 indicate that core flux profile is peaked. • Since core power distribution is proportional to thermal neutron flux distribution, high hot channel factor would indicate that high local power densities exist in reactor core. • Maximum local power density in the core is expressed in terms of total core peaking factor. © Copyright 2014 ELO 2.3 Operator Generic Fundamentals 140 Hot Channel Factor and Power Peaking • The highest power peaking factor should be located under the maximum radial flux and at the height of the maximum axial flux. • Total Core Peaking Factor – product of radial and axial peaking factors. © Copyright 2014 ELO 2.3 Operator Generic Fundamentals 141 Hot Channel Factor and Power Peaking • 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, maximum local power density is limited by reactor operating and design specifications. • Reactor operators should maintain reactor within specifications for Quadrant Power Tilt Ratio and ΔΦ at all times in order to ensure Hot Channel Factor and Power Peaking limitations are not exceeded. © Copyright 2014 ELO 2.3 Operator Generic Fundamentals 142 Power Peaking and Hot Channels Knowledge Checks – NRC Bank 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. Correct answer is B. © Copyright 2014 ELO 2.3 Operator Generic Fundamentals 143 Power Peaking and Hot Channels Knowledge Checks - NRC Bank A nuclear reactor is operating at 85% 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%) a single center control rod to the effects of dropping (full insertion) the same control rod? 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. Correct answer is B. © Copyright 2014 ELO 2.3 Operator Generic Fundamentals 144 Quadrant Power Tilt Ratio Effects ELO 2.4 - Describe Quadrant Power Tilt Ratio (QPTR) and effects of operating with a high QPTR. • Control rods normally moved in banks with symmetrically located rods in each quadrant of core. • At 100% power, control rods at full out position, each core quadrant should be producing ~ 25 percent of total power. • Neutron flux or power tilt exists if one quadrant producing more or less than 25 percent total power. © Copyright 2014 ELO 2.4 Figure: Location of Excore Power Range Detectors for Typical PWR Core 144 Operator Generic Fundamentals 145 Quadrant Power Tilt Ratio Effects Technical Specification Definition QPTR - Shall be the ratio of the maximum upper excore detector calibrated output to the average of the upper excore detector calibrated outputs, OR Ratio of the maximum lower excore detector calibrated output to the average of the lower excore detector calibrated outputs, whichever is greater. © Copyright 2014 ELO 2.4 Figure: Upper and Lower Power Range Neutron Detector Locations Operator Generic Fundamentals 146 Effects of Control Rods on Reactor Operations • QPTR - used to monitor radial neutron flux distribution in reactor core (Tech Spec) – Based on the amount of deviation between individual channels and average radial flux – Monitored for upper and lower detectors – Sometimes called azimuthal power tilt or symmetric offset © Copyright 2014 ELO 2.4 Figure: Location of Excore Power Range Detectors for Typical PWR Core Operator Generic Fundamentals 147 Rod Insertion Limits Quadrant Power Tilt Ratio • When QPTR = 1 - radial neutron flux distribution is uniform, indicating even radial power production throughout each quadrant of the core • When radial power production is not uniform (QPTR > 1), reactor power or neutron flux is “tilted” – Results in uneven fuel burnup and high local peak power levels, if severe or long lasting can result in fuel damage – Technical Specification limit is 1.02 • To prevent flux tilting, control rods are operated in symmetrical bank configurations, with each individual control rod’s height within specified tolerance as compared to height of entire bank (Technical Specifications) • If a single control rod becomes misaligned from its bank it will affect the radial and possibly the axial power distribution © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 148 Rod Insertion Limits Quadrant Power Tilt Ratio • Partially inserted control rod - high QPTR in the upper half of the core with little affect on the QPTR in the lower half of the core. – Partially inserted control rod will also cause AFD to become more negative by forcing power production towards the bottom of the core. • Fully inserted control rod - high QPTR’s in both the upper and lower half of the core. – Fully inserted control rod has little or no affect on AFD since a fully inserted control rod homogenously affects the entire height of the core. © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 149 Quadrant Power Tilt Ratio Effects Knowledge Check – NRC Bank Consider a nuclear reactor core with four quadrants: A, B, C, and D. The reactor is operating at steady state 90% 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%. 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. Correct answer is D. © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 150 Quadrant Power Tilt Ratio Effects Knowledge Check – NRC Bank 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. Departure from nucleate boiling ratio is within design limits. Correct answer is B. © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 151 Quadrant Power Tilt Ratio Effects 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? 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 core. Correct answer is D. © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 152 Quadrant Power Tilt Ratio Effects 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. Correct answer is A. © Copyright 2014 ELO 2.4 Operator Generic Fundamentals 153 Calculating Quadrant Power Tilt Ratio ELO 2.5 - Given appropriate data, Calculate quadrant power tilt ratio (QPTR) Magnitude of the power tilt must be calculated to determine if operational or technical specification limits have been exceeded. Figure: Upper and Lower Power Range Neutron Detector Locations © Copyright 2014 ELO 2.5 153 Operator Generic Fundamentals 154 Calculating Quadrant Power Tilt Ratio QPTR it is calculated using the excore power range detector current values. Example: Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Upper Detector micro-amps 249 248 246 249 Lower Detector micro-amps 251 253 255 247 © Copyright 2014 ELO 2.5 Operator Generic Fundamentals 155 Calculating Quadrant Power Tilt Ratio QPTR can be found using power levels or detector current values. This example uses detector current values. • 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 – The average of the 4 lower detectors is 254 micro-amps • 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: © Copyright 2014 ELO 2.5 Operator Generic Fundamentals 156 Calculating Quadrant Power Tilt Ratio Quadrant 1 249/248 = 1.004 UPPER DETECTORS Quadrant 2 Quadrant 3 248/248 246/248 = 1.000 = 0.992 Quadrant 4 249/248 = 1.004 Quadrant 1 251/254 = 0.988 LOWER DETECTORS Quadrant 2 Quadrant 3 253/254 255/254 = 0.996 = 1.004 Quadrant 4 257/254 = 1.012 © Copyright 2014 ELO 2.5 Operator Generic Fundamentals 157 Calculating Quadrant Power Tilt Ratio • 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. • Action is to restore the power tilt to within acceptable limits or reduce reactor power to minimize the effects of the power tilt. © Copyright 2014 ELO 2.5 Operator Generic Fundamentals 158 Reactor Operator Responsibilities ELO 2.6 - Discuss the nuclear reactor operator’s responsibilities with regard to control rods. Control rods provide the operator with 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. © Copyright 2014 ELO 2.6 158 Operator Generic Fundamentals 159 Reactor Operator Responsibilities Operator Responsibilities During reactor operations, operator is responsible for safe operation of reactor at all times 1. Ensure control rods are operated with proper bank overlap • Differential control rod worth is more constant 2. Ensure control rods remain above rod insertion limits • Adequate shutdown margin • The adverse effects of control rod insertion on power distribution is minimized • Minimizes the amount of positive reactivity that could be added from a rod ejection accident © Copyright 2014 ELO 2.6 Operator Generic Fundamentals 160 Reactor Operator Responsibilities Operator Responsibilities 3. Ensure axial flux difference (ΔI) is maintained within allowed operating range by proper positioning of control rods • Fuel will be more evenly burned axially throughout the cycle • The potential for a xenon oscillation is reduced 4. Ensure all control rods are maintained within specified tolerance • Radial power distribution is not adversely affected 5. Ensure rod speed is correct for plant conditions • Reactivity control © Copyright 2014 ELO 2.6 Operator Generic Fundamentals 161 Reactor Operator Responsibilities Rod Speeds • The following considerations apply to control rod speed: – Control rod insertion rates on a scram are designed to be sufficient to protect the reactor against damage in all transients – Minimum rod motion speed is based on control rods being able to move rapidly enough to compensate for the most rapid rate at which positive reactivity is expected to build within the reactor – xenon burnout at full power – Maximum rod speed is based on reducing the severity of a continuous rod withdrawal casualty © Copyright 2014 ELO 2.6 Operator Generic Fundamentals 162 Reactor Operator Responsibilities Knowledge Check The main reason for designing and operating a nuclear reactor with a flattened neutron flux distribution is to... A. provide even burnup of control rods. B. provide reduce neutron leakage from the core. C. allow a higher average power density. D. provide more accurate nuclear power indication. Correct answer is C. © Copyright 2014 ELO 2.6 Operator Generic Fundamentals 163 Reactor Operator Responsibilities Knowledge Check What is a purpose of control rod bank overlap? A. Provides a more uniform differential rod worth and axial flux distribution. B. Provides a more uniform 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. Correct answer is A. © Copyright 2014 ELO 2.6 Operator Generic Fundamentals 164 Control Rods TLO 2 Summary 1. Control rods affects on core power distribution • 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. © Copyright 2014 TLO 2 Operator Generic Fundamentals 165 Control Rods TLO 2 Summary 2. Control rod operation considerations (continued) • 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 control rods above rod insertion limits during plant operations. Rod insertion limits vary, and increase as power increases to ensure 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. • Axial flux distribution – if rods inserted too far in core, suppresses power production at top of core. increases power production at bottom of core. © Copyright 2014 TLO 2 Operator Generic Fundamentals 166 Control Rods TLO 2 Summary 2. Control rod operation considerations (continued) • Axial flux difference (AFD)- is proportional to the difference in neutron flux between upper and lower halves of core, and may be expressed as βΦ = Φ top – Φ bottom. • Rod ejection – Maintaining 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. 3. Power Peaking and Hot Channel Factors • 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 Φmax /Φavg is referred to as a hot channel or peaking factor. • Total core peaking factor is a product of the radial and axial peaking factors. © Copyright 2014 TLO 2 Operator Generic Fundamentals 167 Control Rods TLO 2 Summary 4. Quadrant Power Tilt Ratio • Used to monitor the radial neutron flux distribution in a reactor's core. • 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. 5. Calculating Quadrant Power Tilt Ratio • Operators must calculate the magnitude of the power tilt to determine if technical specification limits have been exceeded. 6. Reactor Operator Responsibilities - Reactor operator is responsible for safe operation of the reactor at all times. The reactor operator’s responsibilities for control rod operations are: • Operate controls rods with proper bank overlap. © Copyright 2014 TLO 2 Operator Generic Fundamentals 168 Control Rods TLO 2 Summary 6. Reactor Operator Responsibilities (continued) • Maintain control rods above rod insertion limits. • Properly position control rods to maintain axial flux difference (ΔI) within the allowed operating range. • Maintain all control rods within the specified tolerance. • Move control rods at the proper speed. © Copyright 2014 TLO 2 Operator Generic Fundamentals 169 Control Rods TLO 2 Summary 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 © Copyright 2014 TLO 2 Operator Generic Fundamentals 170 Control Rods TLO 2 Summary 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. © Copyright 2014 TLO 2 Operator Generic Fundamentals 171 Review Question 1 • Reactor power was ramped from 80 percent power to 100 percent power over 4 hours. • The 100 percent conditions are as follows: – RCS boron concentration: 580 ppm The 80 percent conditions were as follows: – Control rod position: 130 inches – Reactor coolant system (RCS) boron concentration: 600 ppm – RCS average temperature: 580°F – Control rod position: 110 inches – Power coefficient: -0.03% Δk/k/% – RCS average temperature: 575°F – Moderator temperature coefficient: -0.02% Δk/k/°F – Differential boron worth: -0.01% Δk/k/ppm © Copyright 2014 Summary Operator Generic Fundamentals 172 Review Question 1 Given the above reactivity coefficient/worth values, and neglecting changes in fission product poison reactivity, what is the differential control rod worth? A. -0.02% Δk/k/inch B. -0.025% Δk/k/inch C. -0.04% Δk/k/inch D. -0.05% Δk/k/inch Correct answer is A. © Copyright 2014 Summary Operator Generic Fundamentals 173 Module Review Question Knowledge Check – NRC Bank A nuclear reactor is operating at equilibrium full power when a single control rod fully inserts (from the fully withdrawn position). Reactor power is returned to full power with the control rod still fully inserted. Compared to the initial axial neutron flux shape, the current flux shape will have a _______________. A. minor distortion, because a fully inserted control rod has zero reactivity worth B. minor distortion, because the fully inserted control rod is an axially uniform poison C. major distortion, because the upper and lower core halves are loosely coupled D. major distortion, because power production along the length of the rod drastically decreases Correct answer is B. © Copyright 2014 Summary Operator Generic Fundamentals 174 Module Review Question Knowledge Check – NTC Bank The purposes of using control rod bank overlap are to... A. provide a more uniform axial power distribution and to provide a more uniform differential rod worth. B. provide a more uniform differential rod worth and to provide a more uniform radial power distribution. C. provide a more uniform radial power distribution and to maintain individual and group rod position indicators within allowable tolerances. D. maintain individual and group rod position indicators within allowable tolerances and to provide a more uniform axial power distribution. Correct answer is A. © Copyright 2014 Summary Operator Generic Fundamentals 175 Control Rods Module Summary • This module presented the nuclear effects of control rod motion. – 1st and fastest method of reactivity control. – Used to bring reactor critical, control power ascension. – Essentially fully withdrawn at full power. • Operators use control rods mainly for control of fast-changing reactivity transients, power changes, and reactor trips. • TLO 1 covered control rod construction and materials, how control rods affect reactivity, and how changes in core conditions affect control rod worth. Differential and integral control rod worth were reviewed, including shapes of curves in the core, and the effect of control rod position on rod worth. © Copyright 2014 Summary Operator Generic Fundamentals 176 Control Rods Module Summary • TLO 2 covered 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. • 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 © Copyright 2014 Summary Operator Generic Fundamentals 177 Control Rods Module 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. © Copyright 2014 Summary Operator Generic Fundamentals
