Void coefficient

Void coefficient

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In nuclear engineering
Nuclear engineering
Nuclear engineering is the branch of engineering concerned with the application of the breakdown as well as the fusion of atomic nuclei and/or the application of other sub-atomic physics, based on the principles of nuclear physics...

, 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
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...

 changes as voids (typically steam bubbles) form in the reactor moderator
Neutron moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

 or coolant
Coolant
A coolant is a fluid which flows through a device to prevent its overheating, transferring the heat produced by the device to other devices that use or dissipate it. An ideal coolant has high thermal capacity, low viscosity, is low-cost, non-toxic, and chemically inert, neither causing nor...

. Reactivity, in the nuclear engineering sense (not to be confused with chemical reactivity), measures the degree of change in neutron multiplication
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...

 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
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, 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.

Explanation


Nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

 reactors run on nuclear chain reaction
Chain reaction
A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events....

s, in which each nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 that undergoes fission releases heat and neutrons. Each neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 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
Neutron moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

 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
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...

, such as sodium
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

, NaK
NaK
NaK, or sodium-potassium alloy, an alloy, of potassium , and sodium , is usually liquid at room temperature. Various commercial grades are available. NaK is highly reactive with water and may catch fire when exposed to air, so must be handled with special precautions...

, lead
Lead
Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

, or mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

; others use gases (see advanced gas-cooled reactor
Advanced gas-cooled reactor
An advanced gas-cooled reactor is a type of nuclear reactor. These are the second generation of British gas-cooled reactors, using graphite as the neutron moderator and carbon dioxide as coolant...

). 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
Loss of coolant
A loss-of-coolant accident is a mode of failure for a nuclear reactor; if not managed effectively, the results of a LOCA could result in reactor core damage...

 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
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

 loop which can quickly boil all the coolant in the reactor. This happened in the Chernobyl disaster
Chernobyl disaster
The Chernobyl disaster was a nuclear accident that occurred on 26 April 1986 at the Chernobyl Nuclear Power Plant in Ukraine , which was under the direct jurisdiction of the central authorities in Moscow...

. The construction of reactors with a positive void coefficient is illegal in the United States.

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, too large a void coefficient of either sign can be a design issue and may require more careful, faster-acting control systems. Gas-cooled reactors do not have issues with voids forming.

Reactor designs

  • Boiling water reactor
    Boiling water reactor
    The boiling water reactor is a type of light water nuclear reactor used for the generation of electrical power. It is the second most common type of electricity-generating nuclear reactor after the pressurized water reactor , also a type of light water nuclear reactor...

    s 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 reactor
    Pressurized water reactor
    Pressurized water reactors constitute a large majority of all western nuclear power plants and are one of three types of light water reactor , the other types being boiling water reactors and supercritical water reactors...

    s operate with no voids at all, 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
    RBMK
    RBMK is an initialism for the Russian reaktor bolshoy moshchnosti kanalniy which means "High Power Channel-type Reactor", and describes a class of graphite-moderated nuclear power reactor which was built in the Soviet Union. The RBMK reactor was the type involved in the Chernobyl disaster...

     reactors, such as the reactors at Chernobyl, have a dangerously high positive void coefficient. This was necessary for the reactor to run on unenriched uranium
    Uranium
    Uranium is a silvery-white metallic chemical element in the actinide series of the periodic table, with atomic number 92. It is assigned the chemical symbol U. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons...

     and to require no heavy water
    Heavy water
    Heavy water is water highly enriched in the hydrogen isotope deuterium; e.g., heavy water used in CANDU reactors is 99.75% enriched by hydrogen atom-fraction...

    . 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 operating 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
    Lead
    Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

     or sodium
    Sodium
    Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

    ) may serve as a neutron absorber and reflector.
  • Magnox
    Magnox
    Magnox is a now obsolete type of nuclear power reactor which was designed and is still in use in the United Kingdom, and was exported to other countries, both as a power plant, and, when operated accordingly, as a producer of plutonium for nuclear weapons...

     reactors, advanced gas-cooled reactor
    Advanced gas-cooled reactor
    An advanced gas-cooled reactor is a type of nuclear reactor. These are the second generation of British gas-cooled reactors, using graphite as the neutron moderator and carbon dioxide as coolant...

    s and pebble bed reactor
    Pebble bed reactor
    The pebble bed reactor is a graphite-moderated, gas-cooled, nuclear reactor. It is a type of very high temperature reactor , one of the six classes of nuclear reactors in the Generation IV initiative...

    s 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.

See also

  • Chernobyl accident - occurred when an RBMK-1000 reactor overheated; its large positive void coefficient is thought to have been a factor.
  • Neutron moderator
    Neutron moderator
    In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

  • Nuclear physics
    Nuclear physics
    Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

  • Nuclear reactor
    Nuclear reactor
    A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...