Nuclear Fuel

Nuclear fuel is generally any material that can be ‘burned’ by nuclear fission or fusion to derive nuclear energy. There are many design considerations for the material composition and geometric configuration of the various components comprising a nuclear fuel system. Common nuclear reactors use an enriched uranium and plutonium as a fuel.

Generally, there are two types of nuclear fuel cycles (for PWRs):

  • Uranium fuel cycle. Uses an enriched uranium fuel (~4% of U-235) as a fresh fuel. During the fuel burning, the content of the U-235 decreases and the content of the plutonium increases (up to ~1% of Pu ).
  • Thorium fuel cycle. Uses a thorium – 232 as a fertile material. During the fuel burning, the Th-232 transforms into a fissile  U-233.
VVER-type reactor

VVER-type reactors use a fuel that is characterized by their hexagonal arrangement, but is otherwise of similar length and structure to other PWR fuel assemblies.
Source: www.gidropress.podolsk.ru

Uranium 235 is a fissile isotope and its fission cross-section for thermal neutrons is about 585 barns (for 0.0253 eV neutron). For fast neutrons its fission cross-section is on the order of barns. Most of absorption reactions result in fission reaction, but a minority results in radiative capture forming 236U. The cross-section for radiative capture for thermal neutrons is about 99 barns (for 0.0253 eV neutron). Therefore about 15% of all absorption reactions result in radiative capture of neutron. About 85% of all absorption reactions result in fission.

Uranium absorption reaction

Typically, when uranium 235 nucleus undergoes fission, the nucleus splits into two smaller nuclei (triple fission can also rarely occur), along with a few neutrons (the average is 2.43 neutrons per fission by thermal neutron) and release of energy in the form of heat and gamma rays. The average of the fragment atomic mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 (Krypton) and 137 (Barium). Most of the fission fragments are highly unstable(radioactive) nuclei and undergo further radioactive decays to stabilize itself.

Energy Release per Fission

Energy release per fissionIn general, the nuclear fission results in the release of enormous quantities of energy. The amount of energy depends strongly on the nucleus to be fissioned and also depends strongly on the kinetic energy of an incident neutron. In order to calculate the power of a reactor, it is necessary to be able precisely identify the individual components of this energy. At first, it is important to distinguish between the total energy released and the energy that can be recovered in a reactor.

The total energy released in fission can be calculated from binding energies of initial target nucleus to be fissioned and binding energies of fission products. But not all the total energy can be recovered in a reactor. For example, about 10 MeV is released in the form of neutrinos (in fact antineutrinos). Since the neutrinos are weakly interacting (with extremely low cross-section of any interaction), they do not contribute to the energy that can be recovered in a reactor.

See also: Energy Release from Fission

PWR nuclear fuel assembly

The fuel assembly

The fuel assembly.
Source: www.kernbrennstoff.de

Pressurised water reactors (PWRs) are the most common type of nuclear reactor accounting for two-thirds of current installed nuclear generating capacity worldwide. Most of PWRs use the uranium fuel, which is in the form of uranium dioxide. Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand the uranium dioxide has very high melting point and has well known behavior. The UO2 is pressed into pellets, these pellets are then sintered into the solid.

These pellets are then loaded and encapsulated within a fuel rod (or fuel pin), which is made of zirkonium alloys due to its very low absorbtion cross-section (unlike the stainless steel). The surface of the tube, which covers the pellets, is called fuel cladding. Fuel rods are base element of a fuel assembly.  The fuel rods and the pellets constitute the first barrier in Defence in depth strategy. The first barrier, which retains radioactive material within the fuel and protect the environment.

The collection of fuel rods or elements is called the fuel assembly. The fuel assembly constitute the base element of the nuclear reactor core. The reactor core (PWR type) contains about 157 fuel assemblies (depending on a reactor type). Western PWRs use a square lattice arrangement and assemblies are characterized by the number of rods they contain, typically, 17×17 in current designs. The enrichment of fuel rods is never uniformed. The enrichment is differentiated in radial direction but also in axial direction. This arrangement improves power distribution and improves fuel economy.

Russian VVER-type reactors use a fuel that is characterized by their hexagonal arrangement, but is otherwise of similar length and structure to other PWR fuel assemblies.

A PWR fuel assemblies stand between four and five metres high,are about 20 cm across and weighs about half a tonne. The assemblies have vacant rod positions for control rods or in-core instrumentation. Control rods, in-core instrumentation, neutron source, or a test segment can be vertically inserted into a vacant tube called the guide thimble.

nuclear fuel assembly

The nuclear fuel assembly with the rod cluster control assembly.
Source: www.world-nuclear.org

A PWR fuel assembly comprises a bottom nozzle into which rods are fixed through the lattice and to finish the whole assembly it is ended by a top nozzle. There are spacing grids between these nozzles. These grids ensure an exact guiding of the fuel rods. The bottom and top nozzles are heavily constructed as they provide much of the mechanical support for the fuel assembly structure.

An 1100 MWe (3300 MWth) nuclear core may contain 157 fuel assemblies composed of over 45,000 fuel rods and some 15 million fuel pellets. Generally, a common fuel assembly contain energy for approximately 4 years of operation at full power. Once loaded, fuel stays in the core for 4 years depending on the design of the operating cycle. During these 4 years the reactor core have to be refueled. During refueling, every 12 to 18 months, some of the fuel – usually one third or one quarter of the core – is removed to spent fuel pool, while the remainder is rearranged to a location in the core better suited to its remaining level of enrichment. The removed fuel (one third or one quarter of the core, i.e. 40 assemblies) has to be replaced by a fresh fuel assemblies.

Typical PWR fuel assembly consist of:

  • Fuel rods. Fuel rods contain the fuel and burnable poisons.
  • Top nozzle. Provides the mechanical support for the fuel assembly structure.
  • Bottom nozzle. Provides the mechanical support for the fuel assembly structure.
  • Spacing grid. Ensures an exact guiding of the fuel rods.
  • Guide thimble tube. Vacant tube for control rods or in-core instrumentation.

Nuclear Fuel

Nuclear reactor, Rector core, Fuel loading pattern, Fuel assembly, Fuel rod, Fuel pellet

The temperature in an operating reactor varies from point to point within the system. As a consequence, there is always one fuel rod and one local volume, that are hotterthan all the rest. In order to limit these hot places the peak power limits must be introduced. The peak power limits are associated with a boiling crisis and with the conditions which could cause fuel pellet melt. However, metallurgical considerations place an upper limits on the temperature of the fuel cladding and the fuel pellet. Above these temperatures there is a danger that the fuel may be damaged. One of the major objectives in the design of a nuclear reactors is to provide for the removal of the heat produced at the desired power level, while assuring that the maximum fuel temperature and the maximum cladding temperature are always below these predetermined values.

See also: Heat Equation

Nuclear Fuel - Temperatures

Nuclear Fuel Breeding

All commercial light water reactors contains both fissile and fertile materials. For example, most PWRs use low enriched uranium fuel with enrichment of 235U up to 5%. Therefore more than 95% of content of fresh fuel is fertile isotope 238U. During fuel burnup the fertile materials (conversion of 238U to fissile 239Pu known as fuel breeding) partially replace fissile 235U, thus permitting the power reactor to operate longer before the amount of fissile material decreases to the point where reactor criticality is no longer manageable.

The fuel breeding in the fuel cycle of all commercial light water reactors plays a significant role. In recent years, the commercial power industry has been emphasizing high-burnup fuels (up to 60 – 70 GWd/tU), which are typically enriched to higher percentages of 235U (up to 5%). As burnup increases, a higher percentage of the total power produced in a reactor is due to the fuel bred inside the reactor.

In LWRs, the fuel temperature influences the rate of nuclear breeding (the breeding ratio). In principle, the increase is the fuel temperature affects primarily the resonance escape probability, which is connected with the phenomenon usually known as the Doppler broadening (primarily 238U).  The impact of this resonance capture reaction  on the neutron balance is evident, the neutron is lost and this effect decreases the effective multiplication factor. On the other hand, this capture leads to formation of unstable nuclei with higher neutron number. Such unstable nuclei undergo a nuclear decay, which may lead to formation of another fissile nuclei. This process is also referred to as the nuclear transmutation and is responsible for new fuel breeding in nuclear reactors.

From this point of view, the neutron is utilized much more effectively when captured by 238U than when captured by absorbator, because the effective multiplication factor must in every state equal to 1 (Note that in PWRs the boric acid is used to compensate an excess of reactivity of reactor core along thefuel cycle). In other words it is better to capture the neutron (lower an excess of reactivity) by 238U, rather than by 10B nuclei.

At HFP (hot full power) state, the fuel temperature is directly given by:

  • Local linear heat rate (W/cm), which is given by neutron flux distribution. See also: Power Distribution
  • Fuel-cladding gap. As the fuel burnup increases the fuel-cladding gap reduces. This reduction is caused by the swelling of the fuel pellets and cladding creep. Fuel pellets swelling occurs because fission gases cause the pellet to swell resulting in a larger volume of the pellet. At the same time, the cladding is distorted by outside pressure (known as the cladding creep). These two effects result in direct fuel-cladding contact (e.g. at burnup of 25 GWd/tU). The direct fuel-cladding contact causes a significant reduction in fuel temperature profile, because the overall thermal conductivity increases due to conductive heat transfer.
  • Core inlet temperature. Core inlet temperature is directly given by system parameters in steam generators. When steam generators are operated at approximately 6.0MPa, it means the saturation temperature is equal to 275.6 °C. Since there must be always ΔT (~15°C) between the primary circuit and the secondary circuit, the reactor coolant (in the cold leg)have about 290.6°C (at HFP) at the inlet of the core. As the system pressure increases, the core inlet temperature must also increase. This increase causes slight increase in fuel temperature.

It can be summarized, the fuel breeding is lower, when the reactor is operated at lower power levels. Note that, in order to lower the reactor power, additional absorbators must be inserted inside the core.  The fuel breeding is higher  (e.g. 1 EFPD surplus), when the core inlet temperature of the reactor coolant is higher (e.g. 1°C for 300 EFPDs). It must be added, the inlet temperature is limited and it cannot be changed arbitrarily.

At a burnup of 30 GWd/tU (gigawatt-days per metric ton of uranium), about 30% of the total energy released comes from bred plutonium. At 40 GWd/tU, that percentage increases to about forty percent. This corresponds to a breeding ratio for these reactors of about 0.4 to 0.5. That means, about half of the fissile fuel in these reactors is bred there. This effect extends the cycle length for such fuels to sometimes nearly twice what it would be otherwise. MOX fuel has a smaller breeding effect than 235U fuel and is thus more challenging and slightly less economic to use due to a quicker drop off in reactivity through cycle life.
 n+_{92}^{238}\textrm{U}  {\rightarrow} _{92}^{239}\textrm{U}+\gamma \rightarrow  _{93}^{239}\textrm{Np} \rightarrow  _{94}^{239}\textrm{Pu} 

Neutron capture may also be used to create fissile 239Pu from 238U, which is the dominant constituent of naturally occurring uranium (99.28%). Absorption of a neutron in the 238U nucleus yields 239U. The half-life of 239U is approximately 23.5 minutes. 239decays (negative beta decay) to 239Np (neptunium), whose half-life is 2.36 days. 239Np decays (negative beta decay)  to 239Pu.

n+_{90}^{232}\textrm{Th}  {\rightarrow} _{90}^{232}\textrm{Th}+\gamma \rightarrow  _{91}^{233}\textrm{Pa} \rightarrow  _{92}^{233}\textrm{U}

232Th is the predominant isotope of natural thorium. If this fertile material is loaded in the nuclear reactor, the nuclei of 232Th absorb a neutron and become nuclei of 233Th. The half-life of 233Th is approximately 21.8 minutes. 233Th decays (negative beta decay) to 233Pa (protactinium), whose half-life is 26.97 days. 233Pa decays (negative beta decay)  to 233U, that is very good fissile material. On the other hand proposed reactor designs must attempt to physically isolate the protactinium from further neutron capture before beta decay can occur.

Comparison of cross-sections

Source: JANIS (Java-based nuclear information software)  http://www.oecd-nea.org/janis/ Uranium 238. Comparison of total fission cross-section and cross-section for radiative capture. Uranium 238. Comparison of total fission cross-section and cross-section for radiative capture.
Thorium 232. Comparison of total fission cross-section and cross-section for radiative capture. Thorium 232. Comparison of total fission cross-section and cross-section for radiative capture.

Pu-239 breeding. The uranium nucleus absorbs neutron, thus leads to Pu-239 breeding.

Pu-239 breeding. The uranium nucleus absorbs neutron, thus leads to Pu-239 breeding.

Fuel Consumption – Summary

Consumption of a 3000MWth (~1000MWe) reactor (12-months fuel cycle)

It is an illustrative example, following data do not correspond to any reactor design.

  • Typical reactor may contain about 165 tonnes of fuel (including structural material)
  • Typical reactor may contain about 100 tonnes of enriched uranium (i.e. about 113 tonnes of uranium dioxide).
  • This fuel is loaded within, for example, 157 fuel assemblies composed of over 45,000 fuel rods.
  • A common fuel assembly contain energy for approximately 4 years of operation at full power.
  • Therefore about one quarter of the core is yearly removed to spent fuel pool (i.e. about 40 fuel assemblies), while the remainder is rearranged to a location in the core better suited to its remaining level of enrichment (see Power Distribution).
  • The removed fuel (spent nuclear fuel) still contains about 96% of reusable material (it must be removed due to decreasing kinf of an assembly).
  • Annual natural uranium consumption of this reactor is about 250 tonnes of natural uranium (to produce of about 25 tonnes of enriched uranium).
  • Annual enriched uranium consumption of this reactor is about 25 tonnes of enriched uranium.
  • Annual fissile material consumption of this reactor is about 1 005 kg.
  • Annual matter consumption of this reactor is about 1.051 kg.
  • But it corresponds to about 3 200 000 tons of coal burned in coal-fired power plant per year.

See also: Fuel Consumption

Uranium vs. MOX Fuel – Neutron Flux Difference

Note that, there is a difference between neutron fluxes in the uranium fueled core and the MOX fueled core. The average neutron flux in the first example, in which the neutron flux in a uranium loaded reactor core was calculated, was 3.11 x 1013 neutrons.cm-2.s-1. In comparison with this value, the average neutron flux in 100% MOX fueled core is about 2.6 times lower (1.2 x 1013  neutrons.cm-2.s-1), while the reaction rate remains almost the same. This fact is of importance in the reactor core design and in the design of reactivity control. It is primarily caused by:

  • higher fission cross-section of 239Pu. The fission cross-section is about 750 barns in comparison with 585 barns for 235U.
  • higher energy release per one fission event. In order to generate the same amount energy a MOX core do not require such the neutron flux as a uranium fueled core.
  • larger fissile loading. The main reason is in the larger fissile loading. In MOX fuels, there is relatively high buildup of 240Pu and 242Pu. Due to the relatively lower fission-to-capture ratio, there is higher accumulation of these isotopes, which are parasitic absorbers and that results in a reactivity penalty. In general, the average regeneration factor η is lower for 239Pu fuel than for 235U fuel. Therefore the MOX fuel requires a larger fissile loading to achieve the same initial excess of reactivity at the beginning of the fuel cycle.

The relatively lower average neutron flux is MOX cores has following consequences on reactor core design:

  • Because of the lower neutron flux and the larger thermal absorption cross section for 239Pu, reactivity worth of control rodschemical shim (PWRs) and burnable absorbers is less with MOX fuel.
  • The high fission cross-section of  239Pu and the lower neutron flux lead to greater power peaking in fuel rods that are located near water gaps or when MOX fuel is loaded with uranium fuel together.

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