{"id":18518,"date":"2018-09-01T16:39:29","date_gmt":"2018-09-01T16:39:29","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=18518"},"modified":"2023-02-06T15:00:54","modified_gmt":"2023-02-06T15:00:54","slug":"conversion-factor-breeding-ratio","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/conversion-factor-breeding-ratio\/","title":{"rendered":"Conversion Factor – Breeding Ratio"},"content":{"rendered":"
<\/div>\n

Nuclear Fuel Breeding<\/h2>\n

Fuel breeding <\/strong>or fuel conversion<\/strong> plays a significant role in the fuel cycle of all commercial power reactors. During fuel burnup, the fertile materials (conversion of 238<\/sup><\/strong>U<\/strong> to fissile 239<\/sup><\/strong>Pu<\/strong><\/a> known as fuel breeding<\/strong>) partially replace fissile 235<\/sup><\/strong>U<\/strong>, 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.<\/p>\n

It must be added natural uranium<\/strong> primarily consists of isotope 238<\/sup>U<\/a> (99.28%). All commercial light water reactors contain both fissile<\/a> and fertile materials<\/a>. For example, most PWRs <\/a>use low enriched uranium fuel with enrichment of 235<\/sup><\/strong>U<\/strong><\/a> up to 5%. Therefore more than 95% of the content of fresh fuel is fertile isotope 238<\/sup><\/strong>U<\/strong><\/a>.<\/p>\n

There is potential to increase the recoverable energy content from the world’s uranium and thorium resources by almost two orders of magnitude by converting the fertile isotopes<\/a> uranium-238 and thorium-232 into fissile isotopes<\/a>.<\/p>\n

<\/span>Plutonium 239 breeding<\/div>
\u00a0\"n+_{92}^{238}\\textrm{U}<\/strong>\u00a0<\/strong>\n

Neutron capture may also be used to create fissile 239<\/sup>Pu<\/strong>\u00a0from 238<\/sup>U<\/strong>, the dominant constituent of naturally occurring uranium (99.28%). Absorption of a neutron in the 238<\/sup>U<\/strong>\u00a0nucleus yields 239<\/sup>U<\/strong>. The half-life of 239<\/sup>U<\/strong>\u00a0is approximately 23.5 minutes<\/strong>. 239<\/sup>U\u00a0<\/strong>decays (negative beta decay) to 239<\/sup>Np<\/strong>\u00a0(neptunium), whose half-life is 2.36 days<\/strong>. 239<\/sup>Np<\/strong>\u00a0decays (negative beta decay) \u00a0to 239<\/sup>Pu.<\/strong><\/p><\/div><\/div>

<\/span>Uranium 233 breeding<\/div>
\"n+_{90}^{232}\\textrm{Th}\n

232<\/sup>Th<\/strong> is the predominant isotope of natural thorium. If this fertile material<\/strong> is loaded in the nuclear reactor<\/a>, the nuclei of 232<\/sup>Th<\/strong>\u00a0absorb a neutron and become nuclei of 233<\/sup>Th<\/strong>. The half-life of 233<\/sup>Th<\/strong>\u00a0is approximately 21.8 minutes<\/strong>. 233<\/sup>Th<\/strong>\u00a0decays (negative beta decay) to 233<\/sup>Pa<\/strong>\u00a0(protactinium), whose half-life is 26.97 days<\/strong>. 233<\/sup>Pa<\/strong>\u00a0decays (negative beta decay) \u00a0to 233<\/sup>U<\/strong><\/a>, which is a 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><\/div><\/div><\/div>

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Conversion Factor – Breeding Ratio<\/h2>\n

A quantity that characterizes this conversion of fertile into fissile material<\/strong> is known as the conversion factor<\/strong>. The conversion factor<\/strong>\u00a0is defined as the ratio of fissile material created<\/strong> to fissile material consumed<\/strong> either by fission or absorption. If the ratio is greater than one, it is often referred to as the breeding ratio<\/strong>, for then the reactor is creating more fissile material than it is consuming.<\/p><\/div><\/div>

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Comparison of cross-sections<\/h2>\n

Source: JANIS (Java-based nuclear information software) \u00a0http:\/\/www.oecd-nea.org\/janis\/<\/a><\/strong><\/p>\n

\"Fissile<\/a>
Fissile \/ Fertile Material Cross-sections. Uranium 238.
Source: JANIS (Java-based nuclear information software)
http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n
<\/div>\n
\"Fissile<\/a>
Source: JANIS (Java-based nuclear information software)
http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<\/div><\/div>
\"Conversion<\/a>\n

When C is unity, one new atom is produced per one atom consumed. It seems fertile material can be converted in the reactor indefinitely without adding new fuel. Still, the content of fertile uranium 238 decreases in real reactors, and fission products<\/a> with significant absorption cross-section accumulate in the fuel as fuel burnup increases.<\/p>\n

If we use a simplified model, which includes only uranium and plutonium-239, the conversion factor\u00a0is:<\/p>\n

\"Conversion<\/a><\/p>\n

This equation indicates that increased fuel enrichment results in a decreased value of C(0), the initial conversion factor<\/strong>. As the content of fissile material decreases with fuel burnup<\/a>, the conversion factor\u00a0increases. As this happens an increasing fraction of the fission comes from plutonium.<\/p><\/div><\/div>

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Conversion Factor and Excess of Neutrons<\/h2>\n
\"Reproduction<\/a>
Reproduction factor as a function of the uranium enrichment<\/figcaption><\/figure>\n

The role of the reproduction factor<\/a>, \u03b7<\/strong>, is evident. The rate of transmutation<\/a> of fertile-to-fissile isotopes depends on the number of neutrons more than those needed to maintain the chain fission reaction<\/a> that is available. For conversion to occur, it is necessary that \u03b7 <\/strong>must be greater than unity. Almost all reactors<\/a> operate, at least to some extent, as converters. For fuel breeding to occur, it is necessary that \u03b7 <\/strong>must be greater than 2. One neutron to sustain a chain reaction<\/strong> and one or more neutrons on average must be absorbed in fuel and must produce another fissile atom for natural uranium<\/strong><\/a> in the thermal reactor, \u03b7 = 1.34<\/strong>. As a result of the ratios of the microscopic cross-sections<\/a>, \u03b7 increases <\/strong>strongly in the region of low enrichment fuels<\/strong>. This dependency is shown in the picture. It can be seen there is a limit value about \u03b7 = 2.08<\/strong>.<\/p><\/div><\/div>\n

\n
<\/span>Table of reproduction factors<\/div>
\"Thermal<\/a><\/div><\/div><\/div>\n
<\/div>\n
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The fertile-to-fissile conversion characteristics depend on the fuel cycle and the neutron energy spectrum<\/a>. For a thermal neutron spectrum<\/strong> (E < 1 eV) and the uranium fuel cycle<\/strong>, fuel breeding (C>1) is not feasible, although \u03b7 <\/strong>for both isotopes is greater than 2. <\/strong>This is due to the fact \u03b7 <\/strong>is not large enough to compensate for the neutron leakage<\/a> and its parasitic capture.<\/p>\n

The situation is considerably better for a thermal neutron spectrum<\/strong> (E < 1 eV) and the thorium fuel cycle<\/strong>. Due to the very low capture-to-fission ratio<\/strong><\/a>, the reproduction factor for uranium 233<\/a> is about \u03b7 = <\/strong>2.25. <\/strong>From this point of view, is thorium fuel cycle is promising, and a thermal reactor of this type could successfully be made to breed.<\/p>\n

For a fast neutron spectrum, there are differences in both the number of neutrons<\/strong> produced per one fission and, of course, in the capture-to-fission ratio, which is lower for fast reactors<\/strong>. The number of neutrons produced per one fission is also higher in fast reactors than in thermal reactors. These two features are important in the neutron economy<\/strong> and contribute to the fact that fast reactors have a large excess of neutrons<\/strong> in the core. The superior neutron economy of a fast neutron reactor makes it possible to build a reactor that, after its initial fuel charge of plutonium, requires only natural (or even depleted) uranium feedstock as input to its fuel cycle. Russian BN-350 liquid-metal-cooled reactor was operated with a breeding ratio of over 1.2.<\/p><\/div><\/div>

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Conversion Factor for LWRs<\/h2>\n

All commercial light water reactors<\/a> breed fuel, but they have low breeding ratios. In recent years, the commercial power industry has emphasized high-burnup fuels<\/strong><\/a> (up to 60 \u2013 70 GWd\/tU), typically enriched to higher percentages of U-235 (up to 5%). As burnup<\/a> increases, a higher percentage of the total power produced in a reactor is due to the fuel bred inside the reactor.<\/p>\n

At a burnup of 30 GWd\/tU<\/strong> (gigawatt-days per metric ton of uranium), about 30%<\/strong> of the total energy released comes from bred plutonium. At 40 GWd\/tU<\/strong>, that percentage increases to about forty percent<\/strong>. This corresponds to a breeding ratio for these reactors of about 0.4 to 0.5<\/strong>. Light water reactors with higher fuel burnup (up to 60 GWd\/tU) have a conversion ratio of approximately 0.6. 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<\/strong> has a smaller breeding effect than 235<\/sup><\/strong>U<\/strong> fuel and is thus more challenging and slightly less economical to use due to a quick drop-off in reactivity through cycle life.<\/p>\n

See also: High Burnup Fuel<\/a><\/p><\/div><\/div>

\u00a0
<\/span>Effect of Fuel Temperature on Nuclear Breeding<\/div>
In LWRs, the fuel temperature influences the rate of nuclear breeding (the breeding ratio). In principle, the increase in the fuel temperature affects primarily\u00a0the resonance escape probability<\/strong><\/a>, which is connected with the phenomenon usually known as the Doppler broadening<\/a>\u00a0<\/strong>(primarily 238U<\/a>). The impact of this resonance capture reaction<\/strong><\/a>\u00a0on the neutron balance<\/strong> is evident, the neutron is lost, and this effect decreases the effective\u00a0multiplication factor<\/strong><\/a>. On the other hand, this capture leads to the formation of unstable nuclei with higher neutron numbers. Such unstable nuclei undergo a nuclear decay, leading to the formation of other fissile nuclei<\/strong>. This process is also called\u00a0nuclear transmutation<\/strong> and is responsible for new fuel breeding<\/a> in nuclear reactors<\/a>.\n

From this point of view, the neutron is utilized much more effectively when captured by\u00a0238U<\/a> than when captured by the absorber because the effective multiplication factor must in every state equal to 1 (Note that in PWRs<\/a>,\u00a0the\u00a0boric acid is used to compensate an excess of reactivity of reactor core<\/a> along the fuel cycle). In other words, it is better to capture the neutron (lower excess of reactivity) by 238U rather than by 10B nuclei.<\/p>\n

At HFP (hot full power) state, the fuel temperature is directly given by:<\/p>\n