# Nuclear Breeding

## Nuclear Fuel Breeding

All commercial light water reactors contain 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 the 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), 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.

Effect of Fuel Temperature on Nuclear Breeding
In LWRs, the fuel temperature influences the rate of nuclear breeding (the breeding ratio). In principle, the increase in 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 the formation of unstable nuclei with higher neutron number. Such unstable nuclei undergo a nuclear decay, which may lead to the formation of other fissile nuclei. This process is also called 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 absorber 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 the fuel cycle). In other words, it is better to capture the neutron (lower 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) 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 pellet volume. 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. System parameters in steam generators directly give the core inlet temperature. When steam generators are operated at approximately 6.0MPa, the saturation temperature is equal to 275.6 °C. Since there must always be 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 a 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 additional absorbers must be inserted inside the core to lower the reactor power.  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 economical to use due to a quicker drop-off in reactivity through cycle life.
Plutonium 239 breeding

Neutron capture may also be used to create fissile 239Pu from 238U, 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.

Uranium 233 breeding

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.

Thorium 232. Comparison of total fission cross-section and cross-section for radiative capture.

## Conversion Factor – Breeding Ratio

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

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

If we use a simplified model, which includes only uranium and plutonium-239, the conversion factor is:

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