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BLD-NUCL84-02 · Lesson 6 · 22 clock hours · demo

Control Rods, Chemical Shim, and Reactivity Control Systems

Objective. Students will describe how control rods and boron chemical shim (PWR) or control rods alone (BWR) are used to control reactor power and shutdown margin, and identify the reactivity worth concepts involved.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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Control Rods, Chemical Shim, and Reactivity Control Systems

Reactivity control is at the heart of safe nuclear plant operation. Reactivity (symbol ρ) is the measure of how far a reactor is from a critical, self-sustaining chain reaction. When reactivity is positive the chain reaction is accelerating; when negative it is slowing down; at zero the reactor is exactly critical and power is steady. Two primary tools keep reactivity under precise control: control rods and, in pressurized water reactors (PWRs), chemical shim (boric acid dissolved in the coolant).

Control Rods

Control rods are assemblies of neutron-absorbing material — commonly hafnium, silver-indium-cadmium alloy, or boron carbide — that can be inserted into or withdrawn from the reactor core. When inserted, they absorb neutrons that would otherwise sustain fission, reducing reactivity. When withdrawn, more neutrons are available for fission and reactivity rises.

The reactivity worth of a control rod describes how much reactivity it adds or removes. Total worth is the total reactivity change from fully withdrawn to fully inserted. Differential worth is the reactivity change per unit of rod travel (e.g., per inch or per step). Because neutron flux is not uniform across the core — it peaks at the center and falls off toward the edges — a rod absorbs more neutrons when it is near the core midplane than when it is near the top or bottom. This produces the characteristic S-shaped (sigmoidal) differential worth curve: differential worth is low when the rod tip is at the top or bottom of the core and reaches its maximum when the rod tip is at the core midplane.

This shape has a direct safety implication. If an operator withdraws a rod rapidly while its tip is at the midplane, the reactivity insertion rate is at its highest. Plant procedures and automatic rod withdrawal limiters are designed to prevent uncontrolled positive reactivity additions — a condition that, if unchecked, can lead to a reactivity accident.

Integral worth is the cumulative reactivity added from full insertion to any given position. It is the area under the differential worth curve up to that point.

Chemical Shim — PWR Only

In a PWR, boric acid (H₃BO₃) is dissolved in the reactor coolant (the primary loop water). Boron-10 is a strong neutron absorber. Increasing boron concentration (measured in parts per million, ppm) adds negative reactivity; decreasing it (dilution with unborated water) adds positive reactivity. This is called chemical shim because it trims reactivity over the long term rather than providing rapid control.

Chemical shim is used to compensate for slow reactivity changes such as:

Because adjusting boron concentration is a deliberate, relatively slow process involving pumps and mixing time, it is not used for rapid power maneuvers or emergency shutdown. Control rods fulfill those roles.

Shutdown Margin

Shutdown margin (SDM) is the amount of negative reactivity that would exist in the reactor — with all control rods fully inserted and credited absorbers in place — beyond what is needed to reach and stay subcritical. Regulations require a minimum SDM at all times. In a PWR, the boron concentration must be high enough to ensure SDM is met even if the most reactive rod is assumed to be stuck out (the "stuck rod" criterion). Verifying adequate SDM before any mode change is a fundamental operator responsibility and a key exam topic.

BWR Reactivity Control

Boiling water reactors (BWRs) do not use soluble boron for normal power control. Instead, BWRs rely on control rods (entering from the bottom of the core) and on coolant void fraction — the amount of steam bubbles in the core. More steam means fewer moderating water molecules, which reduces reactivity (a strong negative feedback). BWR operators adjust power by moving control rods and by changing recirculation flow rate, which alters the void fraction. Emergency boration systems exist in BWRs but are not part of normal operation.

Safety Considerations

All work near reactor controls falls under strict procedural and regulatory controls:

Key Takeaway

Control rods provide rapid, precise reactivity control in both PWRs and BWRs. Chemical shim provides long-term reactivity management in PWRs by adjusting boron concentration. Together — and within the bounds of strict procedural controls — they keep the reactor operating safely, maintain adequate shutdown margin, and allow operators to respond to changing plant conditions.

Key terms10

Reactivity (ρ)A measure of the departure of a reactor from criticality; positive reactivity means the chain reaction is increasing, negative means it is decreasing, and zero means the reactor is exactly critical.
Control Rod WorthThe amount of reactivity a control rod (or group of rods) adds or removes; total worth is full-travel reactivity change; differential worth is reactivity change per unit of rod travel at a given position.
Differential Worth CurveAn S-shaped (sigmoidal) curve showing how much reactivity is added or removed per unit of rod travel at each core position; maximum differential worth occurs when the rod tip is at the core midplane where neutron flux is highest.
Chemical ShimThe use of boric acid dissolved in PWR primary coolant to trim reactivity; increasing boron concentration (ppm) adds negative reactivity, while dilution adds positive reactivity.
Shutdown Margin (SDM)The minimum amount of negative reactivity by which a reactor is subcritical, or would be subcritical, with all rods fully inserted and the most reactive rod assumed stuck in the fully withdrawn position.
Boron Concentration (ppm)The mass of boric acid solute per million parts of primary coolant by weight; used to quantify chemical shim level in PWR operations.
Void FractionThe proportion of steam bubbles versus liquid water in the BWR core; higher void fraction reduces neutron moderation and lowers reactivity, providing an inherent negative feedback.
Reactor PeriodThe time (in seconds) for reactor power to change by a factor of e (~2.718); a short positive period means rapidly rising power and requires immediate operator or automatic action.
Integral Rod WorthThe cumulative reactivity change from full rod insertion to a given rod position; represented graphically as the area under the differential worth curve up to that position.
Stuck Rod CriterionA regulatory requirement that shutdown margin be demonstrated with the assumption that the single most reactive control rod remains fully withdrawn and does not insert during a shutdown.

Worked examples4

1. A PWR operator needs to compensate for a reactivity change of +200 pcm by adding boric acid. The instructor-provided simplified boron worth is 10 pcm per ppm of boron added. What increase in boron concentration (ppm) is needed?
  1. Identify the reactivity to be compensated: +200 pcm (positive reactivity must be offset by negative reactivity from added boron).
  2. Identify the boron differential worth: 10 pcm per ppm (adding 1 ppm of boron removes 10 pcm of reactivity).
  3. Divide the required reactivity compensation by the boron worth per ppm: 200 pcm ÷ 10 pcm/ppm = 20 ppm.
  4. Confirm units: the result is in ppm of boron concentration increase, which matches the question.
Answer: The boron concentration must be increased by 20 ppm.
2. Using the same simplified boron worth of 10 pcm/ppm, how much reactivity (in pcm) is added if the operator dilutes the primary coolant, reducing boron concentration by 35 ppm?
  1. Identify the change in boron concentration: −35 ppm (dilution removes boron).
  2. Recall that removing boron reduces neutron absorption, so reactivity increases (positive reactivity is added).
  3. Multiply the magnitude of concentration change by the boron worth: 35 ppm × 10 pcm/ppm = 350 pcm.
  4. Assign the correct sign: because boron is being removed, the reactivity change is +350 pcm (positive — core becomes less subcritical or more supercritical).
Answer: +350 pcm of positive reactivity is added to the core.
3. A control rod group has a total worth of 1,000 pcm over 200 steps of travel. On average, what is the differential worth per step? In what region of the core would the actual differential worth be highest?
  1. Calculate average differential worth: Total worth ÷ Total steps = 1,000 pcm ÷ 200 steps = 5 pcm/step.
  2. Note that this is an average value; actual differential worth varies with axial position.
  3. Recall that neutron flux peaks at the core midplane. Rod absorption is proportional to local neutron flux.
  4. Therefore the actual differential worth is highest when the rod tip is at or near the core midplane, and lower when the rod tip is near the top or bottom of the core.
Answer: Average differential worth is 5 pcm/step. Actual differential worth is greatest at the core midplane.
4. A reactor has a required shutdown margin of 1,300 pcm. The total worth of all control rods (with the highest-worth rod stuck out) is 4,500 pcm. Xenon and other negative reactivity feedbacks add 800 pcm of negative reactivity. What is the calculated shutdown margin, and does it meet the requirement?
  1. Total negative reactivity available = rod worth (with stuck rod) + other negative reactivity = 4,500 pcm + 800 pcm = 5,300 pcm.
  2. The reactor starts from a critical condition, requiring 0 net reactivity to be critical; the SDM is the negative reactivity beyond that needed to reach subcritical, so SDM = total negative reactivity available = 5,300 pcm.
  3. Compare to requirement: 5,300 pcm > 1,300 pcm required.
  4. Conclusion: the shutdown margin is met with substantial margin.
Answer: Calculated SDM is 5,300 pcm, which exceeds the 1,300 pcm requirement. The SDM requirement is met.

The math in this lesson1

Learners divide reactivity in pcm by boron worth per ppm to find the boron change.
6.RP.3
In class: Instructor demonstration using a simplified reactor physics simulator (PC-based IAEA PCTRAN or equivalent free-access educational tool): instructor inserts and withdraws control rods while students observe power, period, and temperature response, recording observations in a structured data table. · Boron dilution/addition calculation exercise: students calculate the approximate change in boron concentration (in ppm) needed to compensate a given reactivity change (instructor-provided simplified worth data), reinforcing the chemical shim concept used in PWR operation. · Control rod worth curve sketching: students sketch a typical S-shaped control rod differential worth curve from given data points, label the region of maximum differential worth (rod at core midplane), and explain in writing why rod position matters for reactivity insertion rate.
Materials: PC-based reactor simulator (IAEA PCTRAN or equivalent educational tool), printed control rod worth data table, graph paper, scientific calculators, generic PWR/BWR training manuals
Check: Lab data table reviewed by instructor: all observations correctly recorded and all three boron calculations within 10% of instructor answer. Students must correctly interpret one simulator transient in writing. Pass mark 80%.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Reactor Physics / NRC Non-Licensed Operator Prep
1. Why does the differential worth curve of a control rod have an S-shape (sigmoidal profile)?
Reactor Operations / NRC Non-Licensed Operator Prep
2. In a PWR, what is the primary purpose of chemical shim (dissolved boron)?
Reactor Physics Calculations / NUCP Uniform Curriculum
3. Using a simplified boron worth of 10 pcm/ppm, how many ppm of boron must be added to compensate +150 pcm of positive reactivity?
Reactor Safety / NRC Reactor Operator License Prep
4. What is shutdown margin (SDM)?
Reactor Operations / NRC Non-Licensed Operator Prep
5. How do BWR operators primarily control reactor power during normal operations?
Reactor Operations & Safety / NRC Reactor Operator License Prep
6. An operator is withdrawing a control rod bank and notices the reactor period is becoming very short and positive. What should the operator do first?
Reactor Physics / NUCP Uniform Curriculum
7. Which of the following best describes 'integral rod worth' at a given rod position?
Workplace Safety / OSHA 10
8. Before a technician performs maintenance on a control rod drive mechanism pump, what safety program must be applied to protect against unexpected energization?
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