# Void coefficient

In nuclear engineering, the void coefficient (more properly called “void coefficient of reactivity”) is a number that can be used to estimate how much the reactivity of a nuclear reactor changes as voids (typically steam bubbles) form in the reactor moderator or coolant. Reactivity, in the nuclear engineering sense (not to be confused with chemical reactivity), measures the degree of change in neutron multiplication in a reactor core. Reactivity is directly related to the tendency of the reactor core to change power level: if reactivity is positive, the core power tends to increase; if it is negative, the core power tends to decrease; if it is zero, the core power tends to remain stable. The reactivity of the core may be adjusted by the reactor control system in order to obtain a desired power level change (or to keep the same power level). It can be compared to the reaction of an automobile as conditions around it change (for instance, wind intensity and direction or road slope), and therefore the corresponding counter-measure that the driver applies to maintain road speed or execute a desired manoeuvre.

Reactivity is affected by many factors, including coolant/moderator temperature and density, fuel temperature and density, and structural temperature and density. Net reactivity in a reactor is the sum total of all these contributions, of which the void coefficient is but one. Reactors in which either the moderator or the coolant is a liquid typically will have a void coefficient value that is either negative (if the reactor is under-moderated) or positive (if the reactor is over-moderated). Reactors in which neither the moderator nor the coolant is a liquid (e.g., a graphite-moderated, gas-cooled reactor) will have a void coefficient value equal to zero. It is unclear how the definition of 'void' coefficient applies to reactors in which the moderator/coolant is neither liquid nor gas (supercritical water reactor).

## Explanation

Nuclear fission reactors run on nuclear chain reactions, in which each nucleus that undergoes fission releases heat and neutrons. Each neutron may impact another nucleus and cause it to undergo fission. The speed of this neutron affects its probability of causing additional fission, as does the presence of neutron-absorbing material. In particular, slow neutrons are more easily absorbed by fissile nuclei than fast neutrons, so a neutron moderator which slows neutrons will increase the reactivity of a nuclear reactor. On the other hand, a neutron absorber will decrease the reactivity of a nuclear reactor. These two mechanisms are used to control the thermal power output of a nuclear reactor.

In order to keep a nuclear reactor intact and functioning, and to extract useful power from it, a cooling system must be used. Some reactors circulate pressurized water; some use liquid metal, such as sodium, NaK, lead, or mercury; others use gases (see advanced gas-cooled reactor). If the coolant is a liquid, it may boil if the temperature inside the reactor rises. This boiling leads to voids inside the reactor. Voids may also form if coolant is lost from the reactor in some sort of accident (called a loss of coolant accident, which has other dangers). Some reactors operate with the coolant in a constant state of boiling, using the generated vapor to turn turbines.

The coolant liquid may act as a neutron absorber or as a neutron moderator. In either case, the amount of void inside the reactor can affect the reactivity of the reactor. The change in reactivity caused by a change of voids inside the reactor is directly proportional to the void coefficient.

A positive void coefficient means that the reactivity increases as the void content inside the reactor increases due to increased boiling or loss of coolant; for example, if the coolant acts as a neutron absorber. If the void coefficient is large enough and control systems do not respond quickly enough, this can form a positive feedback loop which can quickly boil all the coolant in the reactor. This happened in the RBMK reactor that was destroyed in the Chernobyl disaster.

A negative void coefficient means that the reactivity decreases as the void content inside the reactor increases - but it also means that the reactivity increases if the void content inside the reactor is reduced. In boiling-water reactors with large negative void coefficients, a sudden pressure rise (caused, for example, by unplanned closure of a steamline valve) will result in a sudden decrease in void content: the increased pressure will cause some of the steam bubbles to condense ("collapse"); and the thermal output will possibly increase until it is terminated by safety systems, by increased void formation due to the higher power, or, possibly, by system or component failures that relieve pressure, causing void content to increase and power to decrease. Boiling water reactors are all designed (and required) to handle this type of transient. On the other hand, if a reactor is designed to operate with no voids at all, a large negative void coefficient may serve as a safety system. A loss of coolant in such a reactor decreases the thermal output, but of course heat that is generated is no longer removed, so the temperature could rise (if all other safety systems simultaneously failed).

Thus, a large void coefficient, whether positive or negative, can be either a design issue (requiring more careful, faster-acting control systems) or a desired quality depending on reactor design. Gas-cooled reactors do not have issues with voids forming.

## Reactor designs

• Boiling water reactors generally have negative void coefficients, and in normal operation the negative void coefficient allows reactor power to be adjusted by changing the rate of water flow through the core. However, the negative void coefficient can cause an unplanned reactor power increase in events (such as sudden closure of a steamline valve) where the reactor pressure is suddenly increased. In addition, the negative void coefficient can result in power oscillations in the event of a sudden reduction in core flow, such as might be caused by a recirculation pump failure. Boiling water reactors are designed to ensure that the rate of pressure rise from a sudden steamline valve closure is limited to acceptable values, and they include multiple safety systems designed to ensure that any sudden reactor power increases or unstable power oscillations are terminated before fuel or piping damage can occur.
• Pressurized water reactors operate with a relatively small amount of voids, and the water serves as both moderator and coolant. Thus a large negative void coefficient ensures that if the water boils or is lost the power output will drop.
• CANDU reactors have positive void coefficients that are small enough that the control systems can easily respond to boiling coolant before the reactor reaches dangerous temperatures (see References).
• RBMK reactors, such as the reactors at Chernobyl, have a dangerously high positive void coefficient. This allowed the reactor to run on unenriched uranium and to require no heavy water, saving costs (also, unlike the other main power design, VVER, RBMKs were dual use,[1] able to produce weapons-grade plutonium). Before the Chernobyl accident these reactors had a positive void coefficient of 4.7 beta and after the accident that was lowered to 0.7 beta. This was done so all RBMK reactors could resume safe operation and produce much needed power for the then USSR and its satellites.
• Fast breeder reactors do not use moderators, since they run on fast neutrons, but the coolant (often lead or sodium) may serve as a neutron absorber and reflector. For this reason they have a positive void coefficient.
• Magnox reactors, advanced gas-cooled reactors and pebble bed reactors are gas-cooled and so void coefficients are not an issue. In fact, some can be designed so that total loss of coolant does not cause core meltdown even in the absence of active control systems. As with any reactor design, loss of coolant is only one of many possible failures that could potentially lead to an accident. In case of accidental ingress of liquid water into the core of pebble bed reactors, a positive void coefficient may occur.[2]

## Notes

1. ^ Prelas, Mark A.; Peck, Michael (2016-04-07). "Nonproliferation Issues For Weapons of Mass Destruction". Google Books. p. 89. Retrieved 2016-04-20.
2. ^ See chapter 5.1.4

## References

• Chernobyl - A Canadian Perspective - A brochure describing nuclear reactors in general and the RBMK design in particular, focusing on the safety differences between them and CANDU reactors. Published by Atomic Energy of Canada Ltd. (AECL), designer of the CANDU reactor.
• J.J. Whitlock, Why do CANDU reactors have a "positive void coefficient"? - An explanation published on The Canadian Nuclear FAQ, a website of "frequently-asked questions" and answers about Canadian nuclear technology.
• J.J. Whitlock, How do CANDU reactors meet high safety standards, despite having a "positive void coefficient"? - An explanation published on The Canadian Nuclear FAQ, a website of "frequently-asked questions" and answers about Canadian nuclear technology.