Control rod assembly for VVER reactor. Absorber – boron carbide
Source: www.gidropress.podolsk.ru/files/proceedings
/mntk2011/documents/mntk2011-108.pdf

Control rods are an important safety system of nuclear reactors. Their prompt action and prompt response of the reactor is indispencable. Control rods are used for maintaining the desired state of fission reactions within a nuclear reactor (i.e. subcritical state, critical state, power changes) They constitute a key component of an emergency shutdown system (SCRAM).

Control rods are rods, plates, or tubes containing a neutron absorbing material (material with high absorbtion cross-section for thermal neutron) such as boron, hafnium, cadmium, etc., used to control the power of a nuclear reactor. By absorbing neutrons, a control rod prevents the neutrons from causing further fissions.

Control rods usually constitute cluster control rod assemblies (PWR) and are inserted into guide thimbles within a nuclear fuel assembly. The absorbing material (e.g. pellets of Boron Carbide) is protected by the cladding usually made of stainless steel. They are grouped into groups (banks) and the movement occurs usually by the groups (banks). Typical total number of clusters is 70. This number is limited especially by number of penetrations of the reactor pressure vessel head.

A control rod is removed from or inserted into the reactor core in order to increase or decrease the reactivity of the reactor (increase or decrease the neutron flux). By the changes of the reactivity the changes of neutron power are performed. This in turn affects the thermal power of the reactor, the amount of steam produced, and hence the electricity generated.

In PWRs they are inserted from above, with the control rod drive mechanisms being mounted on the reactor pressure vessel head. Due to the necessity of a steam dryer above the core of a boiling water reactor, this design requires insertion of the control rods from underneath the core.

## Control Rods usage

• Reactor startup.
• Control of the reactor and power maneuvering.
• Axial offset control.
• Reactor shutdown.
• Emergency shutdown – SCRAM.

## Grey control rods

Some nuclear power plants use load following. These plants have the capability to make power maneuvering between 30% and 100% of rated power, with a slope up to 5% of rated power per minute. They can respond very quickly to the grid requirements. In order to fulfill these requirements without introducing a large perturbation of the power distribution, special control rods have to be used. These control rods are called “grey” control rods. Grey control rods use a grey neutron absorber, which absorbs less neutrons than a “black” absorber.  Consequently, they cause smaller depressions in the neutron flux and power in the vicinity of the rod.

#### Boron as the neutron absorber

Natural boron consists primarily of two stable isotopes, 11B (80.1%) and  10B (19.9%). In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope  10B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope  11B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

Boron 10. Comparison of total cross-section and cross-section for (n,alpha) reactions.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Moreover, isotope 10B has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements becomes very small at high energies as in the case of cadmium. The cross-section of 10B decreases monotonically with energy. For fast neutrons its cross-section is on the order of barns.

Boron as the neutron absorber has another positive property. The reaction products (after a neutron absorption), helium and lithium, are stable isotopes. Therefore there are minimal problems with decay heating of control rods or burnable absorbers used in the reactor core.

On the other hand production of helium may lead to significant increase in pressure (under rod cladding), when used as the absorbing material in control rods. Moreover 10B is the principal source of radioactive tritium in primary circuit of all PWRs (which use boric acid as a chemical shim), because reactions with neutrons can rarely lead to formation of radioactive tritium via:

10B(n,2x alpha)3H                             threshold reaction (~1.2 MeV)

and

10B(n,alpha)7Li(n,n+alpha)3H     threshold reaction (~3 MeV).

#### Cadmium as the neutron absorber

Neutrons of kinetic energy below the cadmium cut-off energy (~0.5 eV) are strongly absorbed by 113-Cd.
Source: JANIS (Java-based nuclear information software) www.oecd-nea.org/janis/

Natural cadmium consists of eight isotopes, 106Cd (1.3%),  108Cd (0.9%), 110Cd (12.5%), 111Cd (12.8%), 112Cd (24.3%), 113Cd (12.2%), 114Cd (28.7%) and 116Cd (7.5%). Two of them are radioactive isotopes with very long half-life (113Cd – 7.7 x 1015 y and 116Cd – 2.9 x 1019 y).

In nuclear industry cadmium is commonly used as a thermal neutron absorber due to very high neutron absorption cross-section of 113Cd. 113Cd has specific absorption cross-section. There is a cadmium cut-off energy (Cadmium edge) in the absorption cross-section. Only neutrons of kinetic energy below the cadmium cut-off energy (~0.5 eV) are strongly absorbed by 113Cd. Therefore cadmium is widely used to absorb thermal neutrons in a thermal neutron filters.

### How to control the reactor power?

Reactor criticality. A – a supercritical state; B – a critical state; C – a subcritical state

A thermal power of the reactor is determined by a number of fission reactions per time unit and by remaining decay heat (~tens of MW). During the normal operation of the reactor, the thermal power from fission dominates. The number of fission reactions is determined by the neutron flux in the reactor. A position of control rods directly affects a criticality of the reactor. When the reactor is critical (control rods on a critical position), the power of the reactor and the neutron flux is stable at a given power level. When the reactor is subcritical (control rods below a critical position), the power of the reactor and the neutron flux is exponentially decreasing. When the reactor is supercritical (control rods above a critical position), the power of the reactor and the neutron flux is exponentially increasing. It should be noted this behavior describes “zero power criticality” (i.e. a reactor without reactivity feedbacks, 10E-8% – 1% of rated power).

## Criticality of a Power Reactor

For power reactors at power conditions the reactor can behave differently as a result of the presence of reactivity feedbacks. Power reactors are initially started up from hot standby mode (subcritical state at 0% of rated power) to power operation mode (100% of rated power) by withdrawing control rods and by boron dilution from the primary coolant. During the reactor startup and up to about 1% of rated power, the reactor kinetics is exponential as in zero power reactor. This is due to the fact all temperature reactivity effects are minimal.

On the other hand, during further power increase from about 1% up to 100% of rated power, the temperature reactivity effects play very important role. As the neutron population increases, the fuel and the moderator increase its temperature, which results in decrease in reactivity of the reactor (almost all reactors are designed to have the temperature coefficients negative).

The negative reactivity coefficient acts against the initial positive reactivity insertion and this positive reactivity is offset by negative reactivity from temperature feedbacks. In order to keep the power to be increasing, positive reactivity must be continuously inserted (via control rods or chemical shim). After each reactivity insertion, the reactor power stabilize itself on the power level proportionately to the reactivity inserted.

#### Power increase – from 75% up to 100%

Let assume that the reactor is critical at 75% of rated power and that the plant operator wants to increase power to 100% of rated power. The reactor operator must first bring the reactor supercritical by insertion of a positive reactivity (e.g. by control rod withdrawal or boron dilution). As the thermal power increases, moderator temperature and fuel temperature increase, causing a negative reactivity effect (from the power coefficient) and the reactor returns to the critical condition.

In order to keep the power to be increasing, positive reactivity must be continuously inserted (via control rods or chemical shim). After each reactivity insertion, the reactor power stabilize itself proportionately to the reactivity inserted. The total amount of feedback reactivity that must be offset by control rod withdrawal or boron dilution during the power increase (from ~1% – 100%) is known as the power defect.

Let assume:

• the power coefficient:                 Δρ/Δ% = -20pcm/% of rated power
• differential worth of control rods:    Δρ/Δstep = 10pcm/step
• worth of boric acid:                                      -11pcm/ppm
• desired trend of power decrease:              1% per minute

75% → ↑ 20 steps or ↓ 18 ppm of boric acid within 10 minutes → 85% → next ↑ 20 steps or ↓ 18 ppm within 10 minutes → 95% → final ↑ 10 steps or ↓ 9 ppm within 5 minutes → 100%