# Units of Fuel Burnup

## Units of Fuel Burnup

There are three different units in common use for describing the state or depletion of the fuel. These units are:

Megawatt-day per Metric Ton of Heavy Metal (unit: MWd/tHM)
In general, megawatt-day is a derived unit of energy. It is used to measure energy produced, especially in power engineering. One megawatt-day is equal to one megawatt of power produced by power plant over a period of one day (megawatts multiplied by the time in days). 1 MWd = 24,000 kWh.

At nuclear power plants there are also gigawatt-days, because it approximately corresponds to energy produced by power plant over a period of one day. This unit (MWd) was also used to derive unit of fuel burnup. The most commonly used measure of fuel burnup is the fission energy release per unit mass of fuel. Therefore fuel burnup of nuclear fuel is normally have units of megawatt-days per metric tonne (MWd/MTU), where tonne refers to a metric ton of uranium metal (sometimes MWd/tU HM as Heavy Metal). In this field, the megawatt-day refers to the thermal power of the reactor, not the fraction which is converted to electricity. For example, for a typical nuclear reactor with a thermal power of 3,000 MWth, about ~1,000 MWe of electrical power is generated in the generator.

For example, a reactor with 100,000 kg of fuel operating at 3000 MWth power level for 1,000 days would have a burnup increase of 30,000 MWd/MTU. As was written, each watt of power production requires about 3.1×1010 fissions per second. In words of fissions, fissioning of about 1 g of U-235 produces about 1 MWd of thermal energy (see: Energy Release per Fission).

Discharged fuel (i.e. after four years of operation) from light water reactors has usually a burnup of 45,000 to 50,000 MWd/tU. This means that about 45 to 50 kg of fissile material per metric ton of nuclear fuel used have been fissioned.

Burnup Fraction - Fission Burnup
Engineers sometimes use fission burnup or the burnup fraction as a useful unit of fuel burnup. This unit expresses the number of fission normalised to the initial number of uranium nuclei (or another fissionable nuclei). Fission burnup is the proportion of heavy nuclei placed in the reactor core that have undergone nuclear fission either directly or after conversion. In general 1% in fission burnup is approximately equal to 10,000 MWd/tU.

Therefore, PWRs, which have an initial load of about 4% of uranium 235 (96% of uranium 238), reach about 4% of burnup fraction.

EFPD - Effective Full Power Day

Commonly used unit, that describes the state of the fuel is the Effective Full Power Day (EFPD). It specifies the burnup of a given fuel assembly by the number of days it has resided in the core while the core was operated at full power. This unit is commonly used especially for cycle burnup description. For example, a typical 18 month fuel cycle requires an excess of reactivity for 500 EFPDs. It means the core must be refueled after 500 days at 100% of rated power, or after 1000 days at 50% of rated power. The relation between EFPD and MWd/tU is:

Neutron Fluence
In nuclear engineering, we have to distinguish between the neutron flux density, the neutron intensity and the neutron fluence.

Neutron fluence, previously referred to as the neutron dose, is defined as the time integral of the neutron flux density, expressed as number of particles (neutrons) per cm2. Neutron fluence is primarily defined for material engineering, but is widely used by reactor engineers as a unit of fuel burnup.

Neutron Fluence and  Fuel Burnup – Neutrons per Kilobarn

Neutron fluence can be used as a measure of fuel burnup as well. Since reaction rate is given by the product RR = Ф . Σ, the rate of burnup is proportional to the neutron flux. The accumulated burnup over a specific period of time (t) is therefore proportional to the product of flux and time (F = Ф . t or F = ∫Фdt). This product is known as the neutron fluence or the total neutron exposure of the fuel. The units of neutron fluence are also neutrons per m2, but, in practice, it is often expressed in neutrons per kilobarn:

1 n/kb = 1025 neutrons per m2

For example, let assume the fuel in PWR, which is irradiated with a flux on the order of 3×1017 neutrons.m-2s-1 for approximately 4 years. The total fluence of discharged fuel is then 4 n/kb.

During the operation of a nuclear power plant, the material of the reactor pressure vessel and the material of other reactor internals are exposed to neutron radiation (especially to fast neutrons), which results in localized embrittlement of the steel and welds in the area of the reactor core. Irradiation embrittlement can lead to loss of fracture toughness. Typically, the low alloy reactor pressure vessel steels are ferritic steels that exhibit the classic ductile-to-brittle transition behaviour with decreasing temperature. This transitional temperature is of the highest importance during plant heatup.

Failure modes:

• Low toughness region: Main failure mode is the brittle fracture (transgranular cleavage). In brittle fracture, no apparent plastic deformation takes place before fracture. Cracks propagate rapidly.
• High toughness region: Main failure mode is the ductile fracture (shear fracture). In ductile fracture, extensive plastic deformation (necking) takes place before fracture. Ductile fracture is better than brittle fracture, because there is slow propagation and an absorption of a large amount energy before fracture.

Neutron irradiation tends to increase the temperature (ductile-to-brittle transition temperature) at which this transition occurs and tends to decrease the ductile toughness.

Since the reactor pressure vessel is considered irreplaceable, neutron irradiation embrittlement of pressure vessel steels is a key issue in the long term assessment of structural integrity for life attainment and extension programmes.

Radiation damage is produced when neutrons of sufficient energy displace atoms (especially in steels at operating temperatures 260 – 300°C) that result in displacement cascades which produce large numbers of defects, both vacancies and interstitials. Although the inside surface of the RPV is exposed to neutrons of varying energies, the higher energy neutrons, those above about 0.5 MeV, produce the bulk of the damage. In order to minimize such material degradation type and structure of the steel must be appropriately selected. Today it is known that the susceptibility of reactor pressure vessel steels is strongly affected (negatively) by the presence of copper, nickel and phosphorus.

To minimize neutron fluence:

• Radial neutron reflectors are installed around the reactor core. Neutron reflectors reduce neutron leakage and therefore they reduce the neutron fluence on a reactor pressure vessel.
• Core designers design the low leakage loading patterns, in which fresh fuel assemblies are not situated in the peripheral positions of the reactor core.

Heating the irradiated steel to a temperature sufficiently above the irradiation temperature can mitigate the embrittlement. At normal operation of LWRs, the RPV material temperature is far from this temperature. Therefore, when it is required, plant operators must perform thermal annealing of irradiated reactor pressure vessel material to restore the mechanical properties. The degree of recovery for a given steel depends on the time and the temperature at which annealing is performed.

See also: Integrity of reactor pressure vessels in nuclear power plants: assessment of irradiation embrittlement effects in reactor pressure vessel steels.  International Atomic Energy Agency, ISBN 978-92-0-101709-3, Vienna, 2009.

## Fuel Burnup

In nuclear engineering, fuel burnup (also known as fuel utilization) is a measure of how much energy is extracted from a nuclear fuel and a measure of fuel depletion. The most commonly defined as the fission energy release per unit mass of fuel in megawatt-days per metric ton of heavy metal of uranium (MWd/tHM), or similar units. Fuel burnup defines energy release as well as it defines isotopic composition of irradiated fuel. Since during refueling, every 12 to 18 months, some of the fuel – usually one third or one quarter of the core – is replaced by a fresh fuel assemblies and power distribution is not uniform in the core, reactor engineers distinguish between:

• Core Burnup. Averaged burnup over entire core (i.e. over all fuel assemblies). For example – BUcore = 25 000 MWd/tHM
• Fuel Assembly Burnup.  Averaged burnup over single assembly  (i.e. over all fuel pins of a single fuel assembly). For example – BUFA = 40 000 MWd/tHM
• Pin Burnup. Averaged burnup over single fuel pin or fuel rod (over all fuel pellets of a single fuel pin). For example – BUpin = 45 000 MWd/tHM
• Local or Fine Mesh Burnup. Burnup significantly varies also within single fuel pellet. For example, the local burnup at the rim of the UO2 pellet can be 2–3 times higher than the average pellet burnup. This local anomaly causes formation of a structure known as High Burnup Structure.

References:
Nuclear and Reactor Physics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.