{"id":18449,"date":"2018-08-25T12:34:08","date_gmt":"2018-08-25T12:34:08","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=18449"},"modified":"2023-02-03T18:00:13","modified_gmt":"2023-02-03T18:00:13","slug":"fuel-burnup","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/fuel-burnup\/","title":{"rendered":"Fuel Burnup"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">In <a title=\"Nuclear Engineering\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/\">nuclear engineering<\/a>,<strong> fuel burnup<\/strong> (also known as <strong>fuel utilization<\/strong>) measures how much energy is extracted from <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a> and is a measure of fuel depletion.<\/p>\n<p>Fuel burnup of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a> normally has units of megawatt-days per metric tonne (<strong>MWd\/MTU<\/strong>), where tonne refers to a metric ton of uranium metal (sometimes MWd\/tU HM as Heavy Metal). For example &#8211; BU<sub>core<\/sub> = 25 000 MWd\/tHM<\/p>\n<\/div><\/div>\n<p><strong>Fuel burnup<\/strong> (also known as <strong>fuel utilization<\/strong>) measures how much energy is extracted from <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a> and measures fuel depletion in <a title=\"Nuclear Engineering\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/\">nuclear engineering<\/a>. The most commonly defined as the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\">fission energy release<\/a> 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 defines the isotopic composition of irradiated fuel. Since during refueling, every 12 to 18 months, some of the fuel \u2013 usually <strong>one third or one-quarter of the core<\/strong> \u2013 is replaced by <strong>fresh fuel assemblies,<\/strong>\u00a0and <a title=\"Power Distribution in Conventional Reactors\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/power-distribution-conventional-reactors\/\">power distribution<\/a> is not uniform in the core, reactor engineers distinguish between:<\/p>\n<ul>\n<li><strong>Core Burnup<\/strong>. Averaged burnup over entire core (i.e., over all fuel assemblies). For example &#8211; BU<sub>core<\/sub> = 25 000 MWd\/tHM<\/li>\n<li><strong>Fuel Assembly Burnup<\/strong>. Averaged burnup over single assembly \u00a0(i.e., overall fuel pins of a single fuel assembly). For example &#8211; BU<sub>FA<\/sub> = 40 000 MWd\/tHM<\/li>\n<li><strong>Pin Burnup<\/strong>. Averaged burnup over a single fuel pin or fuel rod (overall fuel pellets of a single fuel pin). For example &#8211; BU<sub>pin<\/sub> = 45 000 MWd\/tHM<\/li>\n<li><strong>Local or Fine Mesh Burnup<\/strong>. Burnup significantly varies also within a single fuel pellet. For example, the local burnup at the rim of the UO<sub>2<\/sub> pellet can be 2\u20133 times higher than the average pellet burnup. This local anomaly causes the formation of a structure known as a <strong>High Burnup Structure<\/strong>.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Units of Fuel Burnup<\/h2>\n<p>There are three different units in common use for describing the state or depletion of the fuel. These units are:<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Megawatt-day per Metric Ton of Heavy Metal (unit: MWd\/tHM)<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>megawatt-day<\/strong> is a derived <a title=\"Energy Units \u2013 Conversion\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/energy-units-conversion\/\">unit of energy<\/a>. It is used to measure the <a title=\"What is Energy \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/\">energy<\/a> produced, especially in <strong>power engineering<\/strong>. One megawatt day equals one megawatt of power produced by a power plant for one day (megawatts multiplied by the time in days). <strong>1 MWd = 24,000 kWh<\/strong>.<\/p>\n<p>At <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants, <\/a>there are also gigawatt-days because it approximately corresponds to energy produced by power plants for one day. This unit (MWd) was also used to derive the unit of <strong>fuel burnup<\/strong>. The most commonly used measure of fuel burnup is the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\">fission energy release<\/a> per unit mass of fuel. Therefore fuel burnup of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a> normally has units of megawatt-days per metric tonne (<strong>MWd\/MTU<\/strong>), 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 <a title=\"Reactor Thermal Power\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/reactor-thermal-power\/\">thermal power <\/a>of the reactor, not the fraction which is converted to electricity. For example, for a typical nuclear reactor with thermal power of <strong>3,000 MWth<\/strong>, about <strong>~1,000 MWe<\/strong> of electrical power is generated in the generator.<\/p>\n<p>For example, a reactor with 100,000 kg of fuel operating at a 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\u00d710<sup>10<\/sup> fissions per second. In words of fissions, the fissioning of about 1 g of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">U-235<\/a> produces about 1 MWd of thermal energy (see: <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\">Energy Release per Fission<\/a>).<\/p>\n<p>Discharged fuel (i.e., after four years of operation) from light water reactors usually has 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 has been fissioned.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Burnup Fraction - Fission Burnup<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Engineers sometimes use fission burnup or the burnup fraction as a useful unit of fuel burnup. This unit expresses the number of fission normalized to the initial number of uranium nuclei (or other <a href=\"https:\/\/sitepourvtc.com\/glossary\/fissionable-material\/\">fissionable nuclei<\/a>). 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.<\/p>\n<p>Therefore, <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a>, which have an initial load of about 4% of <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">uranium 235<\/a> (96% of <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\">uranium 238<\/a>), reach about 4% of burnup fraction.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>EFPD - Effective Full Power Day<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_18453\" aria-describedby=\"caption-attachment-18453\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Boron-fuel-burnup.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18453\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Boron-fuel-burnup-300x215.png\" alt=\"boron concentration vs. cycle burnup - PWR\" width=\"300\" height=\"215\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Boron-fuel-burnup-300x214.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Boron-fuel-burnup.png 493w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-18453\" class=\"wp-caption-text\">boron concentration vs. cycle burnup &#8211; PWR<\/figcaption><\/figure>\n<p>A commonly used unit that describes the state of the fuel is the <strong>Effective Full Power Day<\/strong> (<strong>EFPD<\/strong>). 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 <strong>cycle burnup<\/strong> 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% rated power or after 1000 days at 50% rated power. The relation between EFPD and MWd\/tU is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Unit-of-Burnup-EFPD.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18452\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Unit-of-Burnup-EFPD.png\" alt=\"Unit of Burnup - EFPD\" width=\"479\" height=\"173\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Unit-of-Burnup-EFPD.png 479w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Unit-of-Burnup-EFPD-300x108.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Neutron Fluence<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In nuclear engineering, we have to distinguish between the<a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\"><strong> neutron flux density<\/strong><\/a>, the <a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\"><strong>neutron intensity<\/strong><\/a>, and the<strong> neutron fluence.<\/strong><\/p>\n<p><strong>Neutron fluence<\/strong>, previously referred to as the <strong>neutron dose<\/strong>, is defined as the <strong>time integral<\/strong> of the <strong>neutron flux density<\/strong>, expressed as the number of particles (neutrons) per cm<sup>2<\/sup>. Neutron fluence is primarily defined for <a title=\"Materials for Nuclear Engineering\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/\">material engineering<\/a>\u00a0but is widely used by reactor engineers as a unit of fuel burnup.<\/p>\n<p><strong>Neutron Fluence and \u00a0Fuel Burnup &#8211; Neutrons per Kilobarn<\/strong><\/p>\n<p>Neutron fluence can be used to measure fuel burnup since the reaction rate is given by the product <strong>RR = \u0424 . \u03a3<\/strong>, the rate of burnup is proportional to the neutron flux. The accumulated burnup over a specific period (t) is therefore proportional to the product of flux and time (<strong>F = \u0424 . t<\/strong> or <strong>F = \u222b\u0424dt<\/strong>). 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 m<sup>2<\/sup>, but, in practice, it is often expressed in <strong>neutrons per kilobarn<\/strong>:<\/p>\n<p>1 n\/kb = 10<sup>25<\/sup> neutrons per m<sup>2<\/sup><\/p>\n<p>For example, let assume the fuel in PWR, which is irradiated with flux on the order of 3&#215;10<sup>17<\/sup> neutrons.m<sup>-2<\/sup>s<sup>-1<\/sup> for approximately 4 years. The total fluence of discharged fuel is then 4 n\/kb.<\/p>\n<p><strong>Neutron Fluence and Irradiation Embrittlement<\/strong><\/p>\n<p>During the nuclear power plant operation, the material of the <a title=\"Reactor Pressure Vessel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/reactor-pressure-vessel\/\">reactor pressure vessel<\/a> and the material of other reactor internals are exposed to <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron radiation<\/a> (especially to fast neutrons), which results in <strong>localized embrittlement<\/strong> of the steel welds in the area of the reactor core. <strong>Irradiation embrittlement<\/strong> can lead to loss of fracture toughness. Typically, the low alloy reactor pressure vessel steels are ferritic steels that exhibit the classic <strong>ductile-to-brittle transition<\/strong> behavior with decreasing temperature. This transitional temperature is of the highest importance during plant heat up.<\/p>\n<p>Failure modes:<\/p>\n<ul>\n<li>Low toughness region: Main failure mode is the <strong>brittle fracture<\/strong> (transgranular cleavage). In brittle fracture, no apparent plastic deformation takes place before fracture. Cracks propagate rapidly.<\/li>\n<li>High toughness region: Main failure mode is the <strong>ductile fracture<\/strong> (shear fracture). In ductile fracture, extensive plastic deformation (necking) occurs before fracture. Ductile fracture is better than brittle fracture because there is slow propagation and an absorption of a large amount of energy before fracture.<\/li>\n<\/ul>\n<p>Neutron irradiation tends to <strong>increase the temperature<\/strong> (<strong>ductile-to-brittle transition temperature<\/strong>) at which this transition occurs and tends to decrease the ductile toughness.<\/p>\n<p>Since the <strong>reactor pressure vessel<\/strong> is considered <strong>irreplaceable<\/strong>, neutron irradiation embrittlement of pressure vessel steels is a key issue in the long-term assessment of structural integrity for life attainment and extension programs.<\/p>\n<p>Radiation damage is produced when neutrons of sufficient energy displace atoms (especially in steels at operating temperatures 260 &#8211; 300\u00b0C) 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. To minimize such material degradation type and structure of the <strong>steel must be appropriately selected<\/strong>. Today it is known that the susceptibility of reactor pressure vessel steels is strongly affected (negatively) by the presence of copper, nickel, and phosphorus.<\/p>\n<p>To minimize neutron fluence:<\/p>\n<ul>\n<li><a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\"><strong>Radial neutron reflectors<\/strong><\/a> are installed around the reactor core. Neutron reflectors reduce neutron leakage, and therefore they reduce the neutron fluence on a reactor pressure vessel.<\/li>\n<li>Core designers design the <strong>low leakage loading patterns<\/strong>\u00a0in which <strong>fresh fuel assemblies are not situated in the peripheral positions<\/strong> of the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a>.<\/li>\n<\/ul>\n<p>Heating the irradiated steel to a temperature sufficiently above the irradiation temperature can mitigate the embrittlement. At the normal operation of LWRs, the RPV material temperature is far from this temperature. Therefore, when it is required, plant operators must perform <strong>thermal annealing<\/strong> of irradiated reactor pressure vessel material to restore the mechanical properties. The degree of recovery for given steel depends on the time and the temperature at which annealing is performed.<\/p>\n<p>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.<\/div><\/div><\/div>\n<h2>Fuel Depletion &#8211; Isotopic Changes<\/h2>\n<figure id=\"attachment_18460\" aria-describedby=\"caption-attachment-18460\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18460\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes-300x226.png\" alt=\"Fuel Depletion - Isotopic Changes\" width=\"300\" height=\"226\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes-300x226.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes.png 612w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-18460\" class=\"wp-caption-text\">Isotopic changes of 4% uranium-235 fuel as a function of fuel burnup.<\/figcaption><\/figure>\n<p>As a <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">reactor<\/a> is operated at significant power, fuel atoms are constantly consumed, resulting in the <strong>slow depletion<\/strong> of the <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">fuel<\/a>. It must be noted there are also research reactors, which have very low power, and the fuel in these reactors does not change its isotopic composition.<\/p>\n<p>Research reactors with significant thermal power and all power reactors are subjected to significant <strong>isotopic changes<\/strong>. The study of these isotopic changes is known as <strong>long-term kinetics,<\/strong> which describes phenomena that occur over months or even years. The study of phenomena that occur for several hours to a few days, for example, effects of neutron poisons on the reactivity (i.e., <strong>Xenon poisoning<\/strong> or <strong>spatial oscillations<\/strong>), is known as <strong>medium-term kinetics.<\/strong><br \/>\nThis chapter describes the <strong>long-term kinetics <\/strong>of thermal reactors based on the uranium fuel cycle, in which a fuel with a large concentration of <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\">uranium-238 <\/a>is used (e.g., <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a> or <a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\">BWRs<\/a>). Most common reactor fuels are composed of either <a title=\"Natural Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/natural-uranium\/\">natural<\/a> or partially <a title=\"Enriched Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/enriched-uranium\/\">enriched uranium<\/a>. Typically, PWRs use enriched uranium fuel (~4% of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">U-235<\/a>) as fresh fuel. Exposure to neutron flux gradually depletes the uranium-235, decreasing core reactivity (compensated by control rods, chemical shim, or burnable absorbers). The initial fuel load of a new reactor core (so-called first core) is entirely fresh fuel, fuel with no plutonium or fission products present. The contribution of uranium-238 directly to fission is quite small in most thermal reactors. On the other hand, uranium-238 plays a very important role, and this chapter is primarily about this isotope.<\/p>\n<p>See also:\u00a0<a title=\"Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\">Uranium<\/a><\/p>\n<p>See also: <a title=\"Plutonium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/\">Plutonium<\/a><\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Uranium 235<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12060\" aria-describedby=\"caption-attachment-12060\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12060\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12060\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p>is a <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>, and its <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/cross-sections-of-uranium\/\">fission cross-section<\/a> for thermal neutrons is about <strong>585 barns<\/strong> (for 0.0253 eV neutron). For fast neutrons, its fission cross-section is <strong>on the order of barns<\/strong>. Most absorption reactions result in fission reactions, but a minority results in radiative capture forming <sup>236<\/sup>U. The cross-section for radiative capture for thermal neutrons is about <strong>99 barns<\/strong> (for 0.0253 eV neutron). Therefore about 15% of all absorption reactions result in radiative capture of neutrons. About 85% of all absorption reactions result in fission.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12159\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\" alt=\"Uranium absorption reaction\" width=\"775\" height=\"148\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png 775w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction-300x57.png 300w\" sizes=\"(max-width: 775px) 100vw, 775px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Uranium 238<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12062\" aria-describedby=\"caption-attachment-12062\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12062\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238-300x205.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"205\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238-300x205.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238.png 588w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12062\" class=\"wp-caption-text\">Fissile \/ Fertile Material Cross-sections. Uranium 238.<br \/>Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a> is a <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissionable-material\/\">fissionable isotope<\/a> but is not a\u00a0<a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>. <sup>238<\/sup>U cannot undergo a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a> after absorbing a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">thermal neutron<\/a>. On the other hand,\u00a0<sup>238<\/sup>U can be fissioned by fast neutron with energy higher than &gt;1MeV. During the fuel burning, the content of the U-235 continuously decreases, and the content of the plutonium increases (up to ~1% of Pu ). <sup>238<\/sup>U also belongs to the group of <a href=\"http:\/\/sitepourvtc.com\/glossary\/fertile-material\/\">fertile isotopes<\/a>. Radiative capture of a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> leads to the formation of fissile <sup>239<\/sup>Pu and other transuranic elements. This is the way how <sup>238<\/sup>U contributes to the operation of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/what-is-nuclear-reactor\/\">nuclear reactors<\/a> and the production of electricity through this plutonium. For example, at a burnup of 40GWd\/tU, about<strong> 40%<\/strong> of the total energy released comes from bred plutonium. This corresponds to a breeding ratio for this fuel burnup 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 nearly twice what it would otherwise be. 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.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/plutonium.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12213\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/plutonium.png\" alt=\"Equation - Plutonium 239 breeding from Uranium 238\" width=\"456\" height=\"52\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/plutonium.png 456w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/plutonium-300x34.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Plutonium 239<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12064\" aria-describedby=\"caption-attachment-12064\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12064\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239-300x207.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"207\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239-300x207.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239.png 583w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12064\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><strong>Plutonium 239<\/strong><\/a> is a<a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\"> fissile isotope<\/a>, and its fission cross-section for <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">thermal neutrons<\/a> is about <strong>750 barns<\/strong> (for 0.025 eV neutron). <strong>For fast neutrons,<\/strong> its fission cross-section is <strong>on the order of barns<\/strong>. Most of the absorption reactions result in <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reactions<\/a>, but a part of reactions result in radiative capture forming <sup>240<\/sup>Pu. The cross-section for radiative capture for thermal neutrons is about <strong>270 barns<\/strong> (for 0.025 eV neutron). Therefore about <strong>27%<\/strong> of all absorption reactions result in radiative capture of incident neutron. About<strong> 73%<\/strong> of all absorption reactions result in fission.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12392\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png\" alt=\"Plutonium fission vs. radiative capture\" width=\"753\" height=\"132\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png 753w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission-300x53.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Plutonium 241<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12066\" aria-describedby=\"caption-attachment-12066\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_241.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12066\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_241-300x212.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_241-300x212.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_241.png 575w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12066\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Plutonium 241\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-241\/\"><sup>241<\/sup>Pu<\/a> is a <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>, which means <sup>241<\/sup>Pu can undergo a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a> after absorbing a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">thermal neutron<\/a>. <span data-preserver-spaces=\"true\">Moreover, 241Pu also meets the alternative requirement that the amount of neutrons produced by fission of 241Pu (<\/span><strong><span data-preserver-spaces=\"true\">~2.94<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0per one fission by thermal neutron)\u00a0<\/span><strong><span data-preserver-spaces=\"true\">is sufficient to sustain a nuclear fission chain reaction<\/span><\/strong><span data-preserver-spaces=\"true\">.<\/span>\u00a0Its fission <a href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">cross-section<\/a> for thermal neutrons is about <strong>1012 barns<\/strong> (for 0.025 eV neutron). For fast neutrons, its fission cross-section is on the order of barns. Most absorption reactions result in fission reactions, but a part of reactions result in radiative capture forming <sup>242<\/sup>Pu. The cross-section for radiative capture for thermal neutrons is about <strong>363 barns<\/strong> (for 0.025 eV neutron). Therefore about <strong>74%<\/strong> of all absorption reactions result in radiative capture of neutrons. About <strong>26%<\/strong> of all absorption reactions result in fission. <sup>241<\/sup>Pu decays via beta decay into <sup>241<\/sup>Am with a half-life of only <strong>14.3 years<\/strong>. <sup>241<\/sup>Am has relatively high cross-section for radiative capture for thermal neutrons (<strong>~680 barns<\/strong> \u2013 0.025eV). These two phenomena (<strong>decrease in fissile isotope<\/strong> and <strong>increase in neutron absorber<\/strong>) cause a slight decrease in reactivity of irradiated fuel when stored in a spent fuel pool.<\/div><\/div><\/div>\n<h2>Nuclear Transmutation<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/Plutonium-breeding.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-12356\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/Plutonium-breeding-300x225.png\" alt=\"plutonium breeding\" width=\"300\" height=\"225\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/Plutonium-breeding-300x225.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/Plutonium-breeding.png 960w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>In physics,\u00a0<strong>nuclear transmutation<\/strong> is the conversion of one chemical element or an isotope into another. In nuclear engineering, also nuclear reactors cause artificial transmutation by exposing elements to neutrons produced by fission. In nuclear reactors, the most important phenomenon is the transmutation of fertile isotopes (e.g., uranium 238) into fissile isotopes (e.g., plutonium 239). The process of transmutation of fertile materials to fissile materials is referred to as <strong>fuel breeding<\/strong>.<\/p>\n<p>Fertile materials are not capable of undergoing\u00a0<a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a>\u00a0after absorbing thermal (<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">slow or low energy<\/a>)\u00a0<a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a>s, and these materials are not capable of sustaining a <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\">nuclear fission chain reaction<\/a>. There are two basic fertile materials: <strong><a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a>\u00a0and<\/strong>\u00a0<strong><sup>232<\/sup>Th.<\/strong><\/p>\n<p><strong><a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\"><sup>233<\/sup>U<\/a>\u00a0breeding:<\/strong><\/p>\n<p><img class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=n%2B_%7B90%7D%5E%7B232%7D%5Ctextrm%7BTh%7D%20%20%7B%5Crightarrow%7D%20_%7B90%7D%5E%7B232%7D%5Ctextrm%7BTh%7D%2B%5Cgamma%20%5Crightarrow%20%20_%7B91%7D%5E%7B233%7D%5Ctextrm%7BPa%7D%20%5Crightarrow%20%20_%7B92%7D%5E%7B233%7D%5Ctextrm%7BU%7D\" alt=\"n+_{90}^{232}\\textrm{Th} {\\rightarrow} _{90}^{232}\\textrm{Th}+\\gamma \\rightarrow _{91}^{233}\\textrm{Pa} \\rightarrow _{92}^{233}\\textrm{U}\" align=\"absmiddle\" \/><\/p>\n<p><strong><sup>232<\/sup>Th<\/strong> is the predominant isotope of natural thorium. If this\u00a0<strong>fertile material<\/strong>\u00a0is loaded in the\u00a0<a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">nuclear reactor<\/a>, the nuclei of\u00a0<strong><sup>232<\/sup>Th<\/strong>\u00a0absorb a neutron and become nuclei of\u00a0<strong><sup>233<\/sup>Th<\/strong>. The half-life of <strong><sup>233<\/sup>Th<\/strong>\u00a0is approximately\u00a0<strong>21.8 minutes<\/strong>. <strong><sup>233<\/sup>Th<\/strong>\u00a0decays (negative beta decay) to\u00a0<strong><sup>233<\/sup>Pa<\/strong>\u00a0(protactinium), whose half-life is\u00a0<strong>26.97 days<\/strong>. <strong><sup>233<\/sup>Pa<\/strong>\u00a0decays (negative beta decay) \u00a0to\u00a0<strong><sup>233<\/sup>U<\/strong>, a <strong>very good fissile material<\/strong>. On the other hand, proposed reactor designs must attempt to physically isolate the protactinium from further neutron capture before beta decay can occur.<\/p>\n<p><strong><sup>239<\/sup>Pu breeding:<\/strong><\/p>\n<p><strong><strong>\u00a0<img class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=n%2B_%7B92%7D%5E%7B238%7D%5Ctextrm%7BU%7D%20%20%7B%5Crightarrow%7D%20_%7B92%7D%5E%7B239%7D%5Ctextrm%7BU%7D%2B%5Cgamma%20%5Crightarrow%20%20_%7B93%7D%5E%7B239%7D%5Ctextrm%7BNp%7D%20%5Crightarrow%20%20_%7B94%7D%5E%7B239%7D%5Ctextrm%7BPu%7D\" alt=\"n+_{92}^{238}\\textrm{U} {\\rightarrow} _{92}^{239}\\textrm{U}+\\gamma \\rightarrow _{93}^{239}\\textrm{Np} \\rightarrow _{94}^{239}\\textrm{Pu}\" align=\"absmiddle\" \/><\/strong><\/strong><strong><strong>\u00a0<\/strong><\/strong><\/p>\n<p>Neutron capture may also be used to create fissile\u00a0<a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><strong><sup>239<\/sup>Pu<\/strong><\/a>\u00a0from\u00a0<strong><sup>238<\/sup>U<\/strong>, the dominant constituent of naturally occurring uranium (99.28%). Absorption of a neutron in the <strong><sup>238<\/sup>U<\/strong>\u00a0nucleus yields\u00a0<strong><sup>239<\/sup>U<\/strong>. The half-life of <strong><sup>239<\/sup>U<\/strong>\u00a0is approximately\u00a0<strong>23.5 minutes<\/strong>. <strong><sup>239<\/sup>U\u00a0<\/strong>decays (negative beta decay) to\u00a0<strong><sup>239<\/sup>Np<\/strong>\u00a0(neptunium), whose half-life is\u00a0<strong>2.36 days<\/strong>. <strong><sup>239<\/sup>Np<\/strong>\u00a0decays (negative beta decay) \u00a0to\u00a0<strong><sup>239<\/sup>Pu.<\/strong><\/p>\n<p>Transmutation of transuranium elements (i.e., the chemical elements with atomic numbers greater than 92 ) such as the isotopes of plutonium can help solve some problems posed by the management of radioactive waste by reducing the proportion of long-lived isotopes it contains.<\/p>\n<h2>Evolution Equations<\/h2>\n<p>The same evolution of isotopic changes is usually modeled mathematically a set of differential equations known as <strong>evolution equations<\/strong>. These equations describe the rate of burnup of U-235, the rate of buildup of Pu-239, production of Pu-240 and Pu-241, the buildup of neutron-absorbing fission products and the overall rate of reactivity change in the reactor due to the changing composition of the fuel. The evolution equation can be constructed for each isotope. For example:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Evolution-Equations.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18461\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Evolution-Equations.png\" alt=\"Evolution Equations\" width=\"241\" height=\"201\" \/><\/a><\/p>\n<p>Special reference: W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/p>\n<p>Special reference: Paul Reuss, Neutron Physics, EDP Sciences, 2008, ISBN: 2759800415.<\/p>\n<h2>Isotopic Changes &#8211; Summary<\/h2>\n<figure id=\"attachment_18460\" aria-describedby=\"caption-attachment-18460\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18460\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes-300x226.png\" alt=\"Fuel Depletion - Isotopic Changes\" width=\"300\" height=\"226\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes-300x226.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Fuel-Depletion-Isotopic-Changes.png 612w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-18460\" class=\"wp-caption-text\">Isotopic changes of 4% uranium-235 fuel as a function of fuel burnup.<\/figcaption><\/figure>\n<p>In summary, it can be seen for fuel burnup of 40 GWd\/tU:<\/p>\n<ul>\n<li>Approximately 3 &#8211; 4% of the heavy nuclei are fissioned.<\/li>\n<li>About two-thirds of these fissions come directly from uranium 235, and the other third comes from plutonium produced from uranium 238. The contribution significantly increases as the fuel burnup increases.<\/li>\n<li>The removed fuel (<strong>spent nuclear fuel<\/strong>) still contains about <strong>96% reusable material<\/strong>. It must be removed due to decreasing <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/four-factor-formula-infinite-multiplication-factor\/\"><strong>k<\/strong><strong><sub>inf<\/sub><\/strong> <\/a>of an assembly, or in other words, it must be removed due to accumulation of fission products with significant absorption cross-section.<\/li>\n<li>Discharged fuel contains about 0.8% of plutonium and about 1% of uranium 235. It must be noted there is a significant content (about 0.5%) of uranium 236, which is neither a <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>\u00a0nor a <a href=\"http:\/\/sitepourvtc.com\/glossary\/fertile-material\/\">fertile isotope<\/a>.<\/li>\n<\/ul>\n<h2>Neutron Poisons &#8211; Reactor Poisoning<\/h2>\n<figure id=\"attachment_11611\" aria-describedby=\"caption-attachment-11611\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield.png\"><img loading=\"lazy\" class=\"size-medium wp-image-11611\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-300x240.png\" alt=\"Fission fragment yields\" width=\"300\" height=\"240\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-300x240.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-147x118.png 147w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield.png 350w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-11611\" class=\"wp-caption-text\">Fission fragment yield for different nuclei. The most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).<\/figcaption><\/figure>\n<p>Nuclear <strong>fission fragments<\/strong> are the fragments left after a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">nucleus fissions<\/a>. The average of the fragment 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 these fission fragments are <strong>highly unstable<\/strong> (radioactive) and undergo further <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/\">radioactive decays<\/a> to <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/nuclear-stability\/\">stabilize themselves<\/a>.<\/p>\n<p>Plenty of isotopes, usually neutron-rich isotopes, are produced by fission. Many of the resulting fission products have measurable thermal absorption cross-sections. Fission products are of concern in reactors primarily because they become parasitic absorbers of neutrons and result in long-term sources of heat (so-called decay heat). Their buildup in the reactor tends to reduce the multiplication factor. For that reason, these nuclei are known as <strong>neutron poisons<\/strong>.<\/p>\n<p>Each poison\u2019s significance depends on the <strong>yield<\/strong>, <strong>decay rates,<\/strong> and <strong>absorption cross-section<\/strong>. Equilibrium is eventually reached during reactor operation if a radioisotope is produced constantly. After several half-lives, the rate of decay will equal the production rate. Most fission products have a low absorption cross-section, but there are very important exceptions. These isotopes are described in the following table.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18462\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons.png\" alt=\"Table of Neutron Poisons\" width=\"388\" height=\"279\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons.png 388w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons-300x216.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/a><\/p>\n<p>As can be seen, most of these isotopes are stable, and some undergo decay. From this point of view, we distinguish between <strong>neutron poisons<\/strong>, which causes <strong>reactor poisoning,<\/strong> and neutron poisons, which cause <strong>reactor slagging<\/strong>.<\/p>\n<p>The isotope with a short half-life (e.g., xenon-135) is known as reactor poison, while the isotope that is long-lived or even stable is known as reactor slag. The neutron-absorbing fission products <strong>xenon-135<\/strong> and<strong> samarium-149<\/strong> have particular operational importance.<\/p>\n<p>Their concentrations can change quickly, producing major changes in neutron absorption on a relatively short time scale. Because these two fission product poisons remove neutrons from the reactor, they will impact the thermal utilization factor and thus <a title=\"Six Factor Formula \u2013 Effective Multiplication Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/six-factor-formula-effective-multiplication-factor\/\">k<sub>eff<\/sub>\u00a0<\/a>and <a title=\"Reactivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity\/\">reactivity<\/a>. The importance of xenon-135 and samarium-149 is so high that they will be discussed separately.<\/p>\n<p>It must be noted that neutron-absorbing materials, also called neutron poisons, are intentionally inserted into some types of reactors to lower the high reactivity of their initial fresh fuel load. Some of these poisons deplete as they absorb neutrons during reactor operation, while others remain relatively constant.<\/p>\n<h2>Reactor Slagging &#8211; Reactor Slag<\/h2>\n<p>As was written, an isotope long-lived or even stable is known as <strong>reactor slag<\/strong>. The <strong>accumulation<\/strong> of these parasitic absorbers is known as <strong>reactor slagging<\/strong> and determines the lifetime of nuclear fuel in a reactor. Their buildup causes (together with a decrease in fissile material) a continuous decrease in core reactivity.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-18462\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons-300x216.png\" alt=\"Table of Neutron Poisons\" width=\"300\" height=\"216\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons-300x216.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Table-of-Neutron-Poisons.png 388w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>Samarium 149 belongs to this group of isotopes, but its importance is so high that it is usually discussed separately. As can be seen from the table, there are numerous other fission products that, due to their concentration and thermal neutron absorption cross-section, have a poisoning effect on reactor operation. Other fission products with relatively high absorption cross-sections include <sup>83<\/sup>Kr, <sup>95<\/sup>Mo, <sup>143<\/sup>Nd, <sup>147<\/sup>Pm. Individually, they are of little consequence but taken together, and they have a significant effect. These are often characterized as lumped fission product poisons.<\/p>\n<p>As was written, for fuel burnup of 40 GWd\/tU, approximately 3 &#8211; 4% of the heavy nuclei are fissioned. The discharged fuel (<strong>spent nuclear fuel<\/strong>) still contains about <strong>96% reusable material<\/strong>. It must be removed due to decreasing <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/four-factor-formula-infinite-multiplication-factor\/\"><strong>k<\/strong><strong><sub>inf<\/sub><\/strong> <\/a>of an assembly or in or in other words, and it must be removed due to:<\/p>\n<ul>\n<li>accumulation of fission products with significant absorption cross-section.<\/li>\n<li>decrease in fissile material<\/li>\n<\/ul>\n<p>This is the reason why some nuclear power plant operators use reprocessed fuel to replace fresh uranium fuel partially. Nuclear reprocessing is the technology that was developed to chemically separate and recover fissionable material from spent nuclear fuel as well as to remove these isotopes with significant absorption cross-section.<\/p>\n<h2>Effect of Fuel Depletion on the Power Distribution<\/h2>\n<p>During the operation of a reactor, the amount of <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\"><strong>fissile material<\/strong><\/a> contained in the fuel assembly constantly decreases; therefore, the assembly <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/four-factor-formula-infinite-multiplication-factor\/\"><strong>k<\/strong><strong><sub>inf<\/sub><\/strong><\/a> constantly decreases. During fuel depletion, the decrease of the assembly <strong>k<\/strong><strong><sub>inf <\/sub><\/strong>will be greatest where the <strong>power is greatest<\/strong>. The <strong>differences<\/strong> in <strong>k<\/strong><strong><sub>inf<\/sub><\/strong> between fresh fuel assemblies and high-burnup assemblies decreases. Therefore during cycle depletion, this process will cause the <strong>power to shift<\/strong> away from regions with the highest <strong>k<\/strong><strong><sub>inf<\/sub><\/strong><strong>. <\/strong>This process also depends on the use of burnable absorbers, which disrupt the first assumption about the constantly decreasing assembly <strong>k<\/strong><strong><sub>inf<\/sub><\/strong><strong>.<\/strong><\/p>\n<h2>Effect of Fuel Depletion on Delayed Neutrons<\/h2>\n<p>In LWRs, the <a title=\"Delayed Neutrons Fraction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/delayed-neutrons-fraction\/\">delayed neutron fraction<\/a> <strong>decreases with fuel burnup<\/strong>. This is due to isotopic changes in the fuel. It is simple, and fresh uranium fuel contains only <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> as the <a href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile material<\/a>, meanwhile during fuel burnup, the importance of fission of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><sup>239<\/sup>Pu<\/a> increases (in some cases up to 50%). Since <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><sup>239<\/sup>Pu<\/a> produces significantly <strong>less delayed neutrons <\/strong>(0.0021 vs. 0.0064), the resultant <strong>core delayed neutron fraction<\/strong> of a multiplying system <strong>decreases<\/strong> (the weighted average of the constituent delayed neutron fractions). It follows then that the amount of reactivity insertion needed to produce a given reactor period decreases with the burnup of the fuel. This is also the reason why the neutron spectrum in the core <strong>becomes harder with fuel burnup<\/strong>.<\/p>\n<p><strong>\u03b2<\/strong><strong><sub>core<\/sub><\/strong><strong>= \u2211 P<\/strong><strong><sub>i<\/sub><\/strong><strong>.\u03b2<\/strong><strong><sub>i<\/sub><\/strong><\/p>\n<p>where P<sub>i<\/sub> is the fraction of power generated by isotope i.<\/p>\n<h2>Reactivity Effects of Fuel Burnup<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/infinite-multiplication-factor-nuclear-fuel.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-18466\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/infinite-multiplication-factor-nuclear-fuel-300x244.png\" alt=\"infinite multiplication factor - nuclear fuel\" width=\"300\" height=\"244\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/infinite-multiplication-factor-nuclear-fuel-300x244.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/infinite-multiplication-factor-nuclear-fuel.png 597w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>\u2191burnup <\/strong><strong>\u21d2<\/strong><strong> \u2193k<\/strong><strong><sub>eff<\/sub><\/strong><strong> = \u2193\u03b7 \u00a0.\u03b5.p. \u00a0\u2193f \u00a0. \u00a0\u2191\u2193P<\/strong><strong><sub>f<\/sub><\/strong><strong>. \u00a0\u2191\u2193P<\/strong><strong><sub>t<\/sub><\/strong><\/p>\n<p>It is hard to describe the effects of fuel burnup on the six-factor formula, and it must be noted<strong> that criticality must be maintained for a long period<\/strong>. Therefore all the negative effects must be compensated by increasing the thermal utilization factor (boron dilution or compensating rods withdrawal).<\/p>\n<p>See more: <a title=\"Operational factors that affect the multiplication in PWRs\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/operational-factors\/\">Operational factors that affect the multiplication<\/a><\/p>\n<h2>Neutron Flux Effects of Fuel Burnup<\/h2>\n<p>In a power reactor<strong> over a relatively short period<\/strong> (days or weeks), the atomic number density of the fuel atoms remains relatively constant. Therefore, the <strong>average neutron flux remains constant <\/strong>in this short period\u00a0when the reactor is operated at a constant power level. On the other hand, the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/atomic-number-density\/\">atomic number densities <\/a>of fissile isotopes for months decrease due to the fuel burnup, and the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/macroscopic-cross-section\/\">macroscopic cross-sections<\/a> decrease. Note that the thermal power is determined by reaction rate (<strong>RR = \u0424 . \u03a3<\/strong>), in which <strong>\u03a3 <\/strong>is continuously decreasing. This result is slow<strong> to increase the neutron flux<\/strong> to keep the desired power level.<\/p>\n<h2>LWR with High Burnup Fuel<\/h2>\n<p>Current<a title=\"LWR \u2013 Light Water Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/lwr-light-water-reactor\/\"> light water reactors<\/a> are typically designed to achieve burnup of about <strong>50 GWd\/tU<\/strong>. With newer fuel technology, and particularly the use of advanced <a title=\"Burnable Absorbers \u2013 Burnable Poisons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/burnable-absorbers-burnable-poisons\/\">burnable absorbers<\/a>, these same reactors can achieve up to 60 GWd\/tU. Some studies show that soon, even with the present enrichment limit (5 wt %), fuel burnup could be extended near to 70 MWd\/kg. Further increase in fuel burnup is impossible without the relaxation of the present enrichment limit (5%).<\/p>\n<p>As can be seen, there has been a clear trend over the last decades toward increasing fuel burnup in light water reactors. In nuclear power plants, high fuel burnup is desirable for:<\/p>\n<ul>\n<li>Reducing the number of fresh nuclear fuel assemblies required and thus reducing spent nuclear fuel assemblies generated. Both aspects lead to improvements in the economics of the fuel cycle.<\/li>\n<li>Reducing the duration of refueling outage.<\/li>\n<li>High burnup results in a lower mass of spent fuel discharged per unit of electricity generated, reducing spent fuel handling and transportation.<\/li>\n<li>A benefit (crucial aspect for some operators) is that loading the \u201chigh\u201d burnup assemblies in the periphery reduces the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\">neutron flux <\/a>on the pressure vessel.<\/li>\n<li>Reducing the potential for diversion of fissile material from spent fuel for non-peaceful.<\/li>\n<\/ul>\n<p>On the other hand, some signals increasing burnup above 50 or 60 GWd\/tU leads to significant engineering challenges, and even it does not necessarily have to lead to economic benefits.<\/p>\n<p>See also: Etienne Parent. Nuclear Fuel Cycles for Mid-Century Deployment. MIT. 2009.<\/p>\n<p>Higher burnup fuels require higher initial enrichment to sustain reactivity. Since the number of separative work units (SWUs) is not a linear enrichment function, it is more expensive to enrich higher enrichments. For instance, to produce one kilogram of uranium enriched to:<\/p>\n<ul>\n<li>5% U-235 requires 8.9 SWU if the tails assay is 0.20%<\/li>\n<li>4% U-235 requires 6.3 SWU if the tails assay is 0.20%<\/li>\n<\/ul>\n<p>But there are also operational aspects of high burnup fuels that are associated especially with the reliability of such fuel. The main concerns associated with high burnup of fuels are:<\/p>\n<ul>\n<li>Increased burnup places additional demands on fuel cladding, which must withstand the reactor environment for a longer period.<\/li>\n<li>The longer residence in the reactor requires a higher corrosion resistance.<\/li>\n<li>Higher burnup leads to a higher accumulation of ga搜索引擎优化us fission products inside the fuel pin resulting in a significant increase in internal pressure.<\/li>\n<li>Higher burnup leads to increased radiation-induced growth, leading to undesirable changes in core geometry (fuel assembly bow or fuel rod bow). FA bow can result in an increased control rods drop time due to friction between the control rod and bowed guide tubes.<\/li>\n<li>These factors must be considered because they can lead to a decrease in operational reliability.<\/li>\n<li>High burnup fuel generates a smaller fuel volume for the reprocessing but more specific activity.<\/li>\n<\/ul>\n<p>Strategic management and decision-making regarding the middle part of nuclear fuel cycles is a very specific problem of power engineering. Such evaluation must also contain nuclear calculations and business-economic evaluation; thus, they cannot be carried out separately. Detailed nuclear calculations are necessary because they can exclude many promising strategies. On the other hand, they do not provide any information about benefits or costs. Strategic decision-making must be carried out based on business-economic evaluations.<\/p>\n<p>Special reference: Technical and economic limits to fuel burnup extension, Proceedings of a Technical Committee meeting, IAEA, 11\/2009<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Reactor Operation<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Fuel burnup (also known as fuel utilization) measures how much energy is extracted from nuclear fuel and measures fuel depletion in nuclear engineering. 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 &#8230; <a title=\"Fuel Burnup\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/fuel-burnup\/\" aria-label=\"More on Fuel Burnup\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":18314,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18449"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=18449"}],"version-history":[{"count":6,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18449\/revisions"}],"predecessor-version":[{"id":37041,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18449\/revisions\/37041"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18314"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=18449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}