
Крючков Фундаменталс оф Нуцлеар Материалс Пхысицал Протецтион 2011
.pdfoxide fuel. The starting inventory of a 1 GWe reactor is about 100 t of UO2. It generates about 200 kg of plutonium per GWe×year.
Channel-type reactors (RBMK). RBMK reactors using graphite moderator and light-water coolant run on uranium oxide fuel of low enrichment (1.8–2 % 235U). The first core of a 1 GWe reactor contains about 150–180 t of UO 2. It produces approximately 250 kg of plutonium per GWe×year.
The proliferation hazard presented by RBMKs lies in the possibility of channel-by-channel refueling without reactor shutdown.
4. Heavy water CANDU reactors
CANDU reactors are fuelled with natural uranium. The first core of a 1 GWe reactor takes approximately 100 t of UO2. Every year, it will generate 350 kg/GWe.
CANDU reactors operate under conditions of continuous refueling carried out without reactor shutdown. This can pose certain difficulties for inspecting the way primary fuel is used and secondary fuel accumulated.
5. Fast breeder reactors
Fast reactors run on uranium oxide fuel of medium enrichment (15–25 % 235U). The inventory of a 1 GWe reactor is 10–15 t, wh ich means that the
core contains 2–3 t of 235U. It generates plutonium at a rate of about 1500 kg/(GWe×year) in an open fuel cycle. If the fuel cycle is closed, about 80 % of plutonium will be recycled, and its net output will approach 250 kg/(GWe)×year.
Natural NM mining and primary processing
High chemical activity of uranium and thorium explains why they occur in nature only in chemical compounds. All in all, about 200 uranium and thorium minerals were discovered.
The known rich uranium deposits are relatively scarce. The total uranium reserves in the Earth crust are estimated at 1014 t, with another ~ 4×109 t found in the water of seas and oceans (3.3 mg/m3 on the average).
Ore varies in uranium content, appearing as:
·very rich ore: more than 1 % of U;
·rich ore: 0.5–1 % of U;
·medium-grade ore: 0.25–0.5 % of U;
·run-of-mine ore: 0.09–0.25 % of U;
·lean ore: less than 0.09 % of U.
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Generally, mined ore contains about 0.1 % of uranium – these are lean and run-of-mine ores.
Uranium reserves are estimated by two cost criteria as:
∙cheap uranium, costing under $ 80 per 1 kg U3O8; and
∙expensive uranium, costing over $ 80 per 1 kg U3O8.
The threshold value of $ 80 per 1 kg U3O8 was adopted at the time when it marked the border of NPP competitiveness against coal-fired plants.
More than 80 % of proven and probable uranium reserves are found in 8 countries of America (USA, Canada, Brazil), Australia and Africa (SAR, Niger, Angola, Namibia). Two countries, namely, Canada and Australia, produce over 50 % of globally mined uranium. The CIS accounts for about 15 % of the world’s resources. The annual uranium output is not large enough to meet the requirements of global nuclear power. The deficit is offset by using reserves, waste processing, and recycling.
There are four methods of uranium production, i.e.:
∙underground mining;
∙quarrying;
∙in-situ leaching;
∙recovery from seawater.
The stage of ore mining is followed by its hydrometallurgical processing. Uranium can be extracted owing to high solubility of uranium oxides in acid and alkaline solutions.
Hydrometallurgical processing results in dry concentrate of uranium oxides (mainly, U3O8). The concentrate will contain all the uranium found before in the ore, as well as impurities (with 95–9 6 % accounted for by uranium oxides and 4–5 % by impurities). The impuri ties, which have to be removed from the concentrate, include powerful neutron absorbers: B, Cd, Hf and rare-earth elements (Eu, Gd, Sm).
The next stage is uranium concentrate purification using a refining process.
The most common method is refining by extraction, with tributylphosphate (TBP) serving as an extracting agent. The TBP density (0.973 g/cm3) is slightly lower than that of water. To reduce its viscosity, TBP is dissolved in neutral organic compounds. An important property of TBP is its capability of selectively extracting uranium compounds. Uranyl nitrate UO2(NO3)2 is extracted by this agent from a mixture 104 times more efficiently than are impurities.
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Isotopic enrichment of uranium
The chief material of nuclear power is enriched uranium, which contains more fissionable 235U than its natural variety does.
Uranium enrichment may be conceptually sketched as follows. The feed material is natural uranium, with its quantity in the formula below represented by F and enrichment in 235U by XF. As a result, two materials arise: 1) uranium enriched in 235U (product), its quantity denoted by P and
enrichment in 235U, by XP; and 2) uranium depleted of 235U (waste) found in an amount of W and enriched in 235U as XW.
Then, the NM balance is described by two equations:
·F = P + W for the uranium mass balance and
·XF × F = XP × P + XW × W for the 235U isotope balance.
These two equations in three unknowns (F, P, W) can be rearranged to have two equations in two unknowns (F/P, W/P):
F/P = 1 + W/P;
XF × F/P = XP + XW × W/P.
By solving this system, it is possible to find:
a) the rate of natural uranium consumption per unit of product
F/P = (XP – X W)/(XF – X W);
b) the rate of waste generation per unit of product
W/P = (XP – X F)/(XF – X W);
c) the product-to-feed material ratio q:
F = P + W = q × F + (1 – q) × F; q = P/F = (XF – X W)/(XP – X W).
We shall introduce the concept of relative concentration of isotope 235U in a binary mixture (235U,238U), appearing in the input as R = XF /(1 – XF); in
the product output as R¢ = XP /(1 – XP); and in the waste output as R¢¢ = XW /(1 – XW). Then:
the separation factor for the enriched fraction is:
a = R¢/R = [XP /(1 – XP)]/[XF /(1 – XF)]; 33
the separation factor for the depleted fraction is:
β = R/ R′′ = [XF /(1 – XF)]/[XW /(1 – XW)];
enrichment factor: ε′ = α – 1; depletion factor: ε′′ = β – 1;
total enrichment factor for one stage :
ε = ε′ + ε′′.
Table 2.3 presents some data descriptive of enrichment processes in terms of separation factors and power consumption.
Table 2.3
Separation factors and power consumption specific to enrichment processes
Enrichment |
Separation factor, |
Power |
process |
α |
consumption, |
|
|
kWh/SWU |
Electromagnetic separation |
No data |
4000 |
Gas diffusion |
1.0043 |
2300–2600 |
Gas centrifugation |
1,25 |
100–300 |
Separation nozzle |
1,025 |
3000–3500 |
Laser techniques |
3–15 |
10–50 |
Chemical techniques |
1.0025 |
400–700 |
Gas diffusion and gas centrifugation are the two NFC methods most extensively used on a commercial scale. Both of them rely on the difference in mass between molecules of a gaseous uranium compound (UF6).
Uranium hexafluoride UF6 is often used as a starting material in uranium enrichment. This compound has a number of attractive properties:
∙natural fluorine contains only one stable isotope, namely, 19F;
∙uranium hexafluoride can appear as a solid, liquid or gas at moderate temperatures and pressures;
∙uranium hexafluoride can pass from a solid to a gaseous state and back, skipping the liquid phase.
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One of the shortcomings of uranium hexafluoride is its high chemical activity. It reacts with air and steam, giving rise to uranium tetrafluoride UF4 (powder), which deposits in process circuits. That is why circuits and containers should be made leak-tight, should be desiccated and degreased. Ni, Al, Mg, Cu and their alloys as well as teflon show resistance when exposed to UF6.
Uranium oxide conversion to uranium hexafluoride. For isotopic enrichment, the concentrate of U3O8 has to be turned into UF6. This can be done in a two-step process. First, a reaction with fluorine gas yields uranyl fluoride UO2F2:
U3O8 + 3F2 → 3UO2F2 + O2 at 350–370 оС,
whereupon uranium hexafluoride is formed by a reaction of uranyl fluoride with fluorine at a lower temperature of 270 оС:
UO2F2 + 2F2 → UF6 + O2.
A single-stage process (flame method of direct fluorination) can only take place with excess fluorine and at much higher temperatures (900–1000 оС):
U3O8 + 9F2 → 3UF6 + 4O2 .
Production of uranium hexafluoride from uranium dioxide (UO2) is achieved by using another two-step process. First, UO2 reacts with hydrofluoric acid (HF) at 500–600 оС to form uranium tetrafluoride (UF4):
UO2 + 4HF → UF4 + 2H2O, whereupon UF4 reacts with fluorine at 400 оС:
UF4 +F2 = UF6.
1. Uranium enrichment by gas diffusion (GD)
The enrichment GD technology is based on different speeds of thermal motion of heavy and light molecules, and on the ease with which the latter go through thin porous partitions.
In a mixture of two gases with the same temperature, light and heavy molecules have the same average kinetic energy:
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mL × VL2 = mH × VH2 ,
while the average speed of light molecules is higher than that of heavy ones:
VL = VH × (mH/mL)1/2.
An ideal separation factor, a0, for a mixture of two gases diffusing through a porous partition, is:
a0 =(mH/mL)1/2 » 1 + Dm/2mL.
For uranium hexafluorides 235UF6 and 238UF6 (mL = 349, mH = 352), the separation factor a0 is equal to the enrichment factor e0:
a0 = 1,0043; e0 = a0 – 1 = 0,0043.
The free path of molecules should be larger than the typical size of pores, so that such molecules could interact mostly with pores in a partition, rather than with one another. The free path of molecules is inversely related to pressure. For UF6, the free path at 1 atm. is 1 mm, and at 1 mm Hg makes 700 mm. Fabrication of partitions with pores measured in microns is a fairly complicated task, which requires a low operation pressure.
Partitions should be:
·thin (fractions of millimeter);
·strong (to withstand a pressure drop of ~ 0.3 atm.);
·corrosion-resistant in the atmosphere of UF6. Partitions with micron-sized pores are made of:
·sintered aluminum and nickel oxide powder;
·sintered nickel powder;
·aluminum with pores produced by electric etching;
·teflon.
The uranium GD–enrichment factor at one stage is sm all (1.0043), wherefore the gas flow has to be repeatedly passed through many enrichment stages. A series of GD stages forms a cascade.
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2. Uranium enrichment in gas centrifuges (GC)
It is assumed that a tube rotating at an angular speed of w contains a mixture of gases with molecular weights of М1 and М2. Their molecules are exposed to centrifugal forces proportional to the mass and radius:
F1,2 = M1,2 × w2 × r.
Gas pressure rises steeply from the center to the periphery:
P1,2 = P0 × exp(M1,2×w2×r2/2RT) ~ exp(a × V 2).
The heavy fraction subjected to the higher pressure is driven to the GC periphery, while the light fraction collects in its central part.
The separation factor in a GC is:
a = exp(DM×w2×r02/2RT) = exp(DM × V(r0)2/2RT); e = a – 1 » DM × V(r0)2/2RT.
Calculations suggest that the following enrichment factors can be provided by gas centrifugation as a function of rotation speed:
e= 0.068 at V = 330 m/s;
e= 0.098 at V = 400 m/s;
e= 0,152 at V = 500 m/s.
Centrifuges are manufactured from the following materials:
·aluminum alloys (for speeds V £ 350 m/s);
·titanium alloys (for speeds V £ 450 m/s);
·alloyed steels (for speeds V £ 500 m/s);
·graphite-reinforced fiber-glass plastics (for V = 500–700 m/s).
3. Separating nozzle
This method essentially relies on different behavior of uranium isotopes in a centrifugal force field. Uranium hexafluoride is fed into a highly curved nozzle where centrifugal forces cause spatial separation of light and heavy isotopes.
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The advantage of this method over GC lies in the absence of rotating components, but the small size of separation slots (a fraction of a millimeter) calls for precision assembly. The uranium enrichment factor for the separating nozzle is e¢ = 0.025.
4. Laser methods
Laser methods of uranium separation are based on the difference in the arrangement of excited energy levels of electrons in atoms of 238U and 235U, which is made possible by use of a monochromatic laser. Excitation of electron shells leads to selective intensification of physical or chemical processes (intensified ionization of excited atoms or intensified dissociation of excited molecules). The conditions for laser-based enrichment include:
1.Presence of an excited electron level unique to one isotope. This level should be sufficiently far removed from other spectrum lines and from lines of other isotopes.
2.Availability of a laser tuned to an appropriate radiation frequency.
3.Existence of processes separating excited atoms and molecules.
Laser-based enrichment of uranium vapors. This enrichment method consists of the following stages:
·evaporation of U atoms in vacuum (an electron beam knocks out U vapors from the U–Re alloy);
·irradiation by a xenon laser with ensuing selective excitation of 235U atoms;
·irradiation by a krypton laser with ensuing selective ionization of excited 235U atoms;
·collection of ionized 235U atoms on a charged plate.
Laser-based enrichment of UF6 molecules. This process has three stages:
·cooling of the UF6 + H2 mixture to 30 К for the UF6 molecules to be mostly in an unexcited state;
·irradiation by an infrared laser with ensuing selective excitation of 235UF6 molecules;
·irradiation by an ultraviolet laser with ensuing selective dissociation of excited molecules:
2 × 235UF6 * ® 2 × 235UF5 + F2.
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White powder of 235UF5 (“laser snow”) precipitates from the gas mixture.
The enrichment factor of laser methods is as high as 3 to 15. They offer a possibility to use the waste of GD plants (containing 0.2–0,3 % of U) for recovery of uranium suitable for light water power reactors.
5. Chemical enrichment methods
Chemical methods depend on different stability of isotopes in compounds. A contact between chemical compounds of one element with different valences leads to isotope exchange. Thus, boron can be enriched in isotope 10B via an isotope exchange reaction:
BF3 + BF3O(CH3)2 ® 11BF3 + 10BF3O(CH3)2 ,
in which 10B builds up in the organic phase.
Heavy water generation results from an isotope exchange reaction between light water and hydrogen sulfide:
H2O + HDS ® HDO + H2S,
with deuterium accumulating in the water phase.
The USA and Japan are developing a uranium enrichment process involving UF6 and NOUF6 as contacting compounds. This is essentially oxidation–reduction chromatography achieved by alte rnation of oxidation reactions (addition of oxygen gas) and reduction reactions (addition of
hydrogen gas). In this case it is possible to separate compounds including ions of UO2++(with 6-valent 235U) and U4+(with 4-valent 238U). The
experimentally obtained separation factors reached 1.08 and power consumption proved to be up to 150 KWh/SWU.
6. Plasma method
This method is based on the effect of ion cyclotron resonance.
Charged particles (ions) moving about in a magnetostatic field experience the action of a force
F = q × [V × B],
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causing them to spiral about magnetic field lines. The orbital radius is found from the following equation:
F = q × V × B = mV 2/R ;
R = m× V /(q × B) = (2m × E)1/2/(q × B),
while the rotation frequency w = V/R = q × B/m is the ion cyclotron frequency (ICF).
If a variable electric field is applied, with its frequency equal to the ICF of a specific isotope, this will be the only isotope to take up the field energy. A higher energy of ions of a certain isotope will increase the radius of its rotation about magnetic field lines. It is then possible to separate ions of different isotopes and to accumulate ions of 235U and 238U selectively on appropriately arranged collectors.
Uranium enrichment technologies viewed in the context of non-proliferation of nuclear weapons
Gas diffusion:
a)technically sophisticated process;
b)high power requirements (2300–2600 kWh/SWU); one GD facility in the USA consumes about 5 GWe;
c)relatively low enrichment factor (e¢ = 0.0043);
d)unlikely secret construction of a GD facility.
Gas centrifugation:
a)technically sophisticated process;
b)low power requirements (100–300 kWh/SWU) and hig h enrichment
factor (e¢= 0.2–0.3) make this technology hazardous from the viewpoint of non-proliferation.
Separating nozzle:
a)less sophisticated than GD and GC processes;
b)low enrichment factor (e¢ = 0.025) and high power requirements (3000 kWh/SWU) make this method a lesser proliferation hazard as compared with GD and GC processes.
Laser methods:
a)the highest enrichment factor (e¢ = 3–15) and the lowest energy requirements (10–50 kWh/SWU);
b)the most sophisticated process; the most promising enrichment technology and the most hazardous process from the non-proliferation point of view.
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