Corresponding author: Evgeny G. Kulikov (egkulikov@mephi.ru)
Academic editor: Yury Korovin
Increasing fuel burnup is one of the important areas of nuclear power development. Currently, the most common type of lightwater reactors is characterized by burnup ratios of about 5%, i.e., only a small fraction of fuel is used to generate electricity. The paper considers the possibility of a significant increase in fuel burnup due by introducing protactinium and neptunium into the fuel composition. The chains of nuclide transformations starting with protactinium and neptunium are characterized by a gradual improvement in the multiplying properties, which ensures increased fuel burnup. At the same time, a situation may be observed when the multiplying properties of a fuel composition are improved during the campaign, which indicates that at a certain point in time the accumulation rate of fissile nuclides from protactinium and neptunium exceeds the accumulation rate of fission products. While protactinium is hardly accessible in sufficient quantities, neptunium is contained in spent nuclear fuel, a significant amount of which is stored in onsite facilities. Therefore, from a practical perspective, the introduction of neptunium into fuel compositions seems to be more preferable. The novelty of the work is the analysis of the effects of protactinium and neptunium on the reactivity coefficients during fuel campaigns. The calculations were carried out for a VVER1000 type reactor using the SCALE6.2 software package.
Modern lightwater reactors have fuel burnup ratios of about 5%. Thanks to new fuel technologies and, in particular, to the use of advanced burnup absorbers, it is possible to achieve 6% burnup.
Increasing fuel burnup is necessary to:
– improve the economy of the nuclear fuel cycle by reducing the volume of fresh and spent nuclear fuel;
– reduce the number of fuel reloads; and
– reduce the likelihood of switching fissile material from spent fuel to nonenergy targets (
To increase fuel burnup, we shall consider the possibility of introducing protactinium and neptunium into fuel compositions. This issue was previously studied in (
We consider the unit cell of a VVER1000 reactor: its parameters are presented in Table
VVER100 unit cell parameters (
Parameter  Value 

Fuel density, g/cm^{3}  10.7 
Fuel inner/outer radius, cm  0.115/0.375 
FE cladding inner/outer radius, cm  0.386/0.4582 
Cladding/central tube material  Zr (1% Nb, 0.03% Hf) 
Cladding density, g/cm^{3}  6.45 
Central tube inner/outer radius, cm  0.45/0.515 
FE array pitch, cm  1.275 
Moderator density, g/cm^{3}  0.71 
Fuel temperature, K  966 
Cladding temperature, K  630 
Moderator temperature, K  578 
All the subsequent burnuprelated calculations are made for an equivalent cell by means of the SCALE6.2 software package, a widely used set of modeling and simulation tools for performing neutronphysical calculations (SCALE,
As a result of radiative neutron capture reactions on protactinium and neptunium, moderately fissile isotopes of uranium232 and plutonium238 are accumulated, leading to the accumulation of wellfissile isotopes of uranium233 and plutonium239 (Table
Neutron fission/capture crosssections at a heat spot and the number of neutrons per fission event (







Fertile  ^{238}U  1.7×10^{–5}  2.7  2.32 
^{232}Th  5.4×10^{–5}  7.3  1.89  
^{231}Pa  0.023  202  2.09  
^{237}Np  0.020  178  2.62  
Fissile  ^{233}U  531  45  2.48 
^{235}U  585  99  2.43  
^{239}Pu  747  271  2.87  
^{232}U  77  75  3.12 
According to its neutronphysical properties, ^{237}Np is a raw nuclide. Neptunium has large capture crosssections in both the thermal and resonance regions. The thermal neutroncapture crosssection of ^{237}Np is 178 barn, and the fission crosssection is 0.020 barn (see Table
A chain of nuclide transformations starting with neptunium (
Figure
The effect of neptunium on the neutron multiplication factor in the process of fuel burnup: 1) conventional uranium fuel (4.4% of ^{235}U + 95.6% of ^{238}U); 2) introducing 1% of neptunium (4.4% of ^{235}U + 94.6% of ^{238}U + 1% of ^{237}Np); 3) introducing 2% of neptunium (4.4% of ^{235}U + 93.6% of ^{238}U + 2% of ^{237}Np); 4) introducing a large amount of neptunium (35% of ^{235}U + 65% of ^{237}Np).
With a small addition of ^{237}Np (the second and third fuel compositions), the initial neutron multiplication factor decreases relative to conventional uranium fuel, and achievable burnup is small, which indicates that the accumulation potential of fissile plutonium isotopes does not have time to be realized. At the same time, in the case of using a fuel composition containing 35% of ^{237}Np instead of 35% of ^{238}U, burnup reaches 82 GW∙d/t and the neutron multiplication factor remains close to unity throughout the campaign. This is explained by the fact that, as a result of the capture of ^{237}Np neutrons, ^{238}Pu and ^{239}Pu are formed, i.e., fissile materials that support the fission chain reaction for a long time. In addition, ^{237}Np is characterized by a larger neutroncapture crosssection in the thermal region as compared to that of ^{238}U, which leads to the efficient formation of fissile ^{238}Pu and ^{239}Pu isotopes.
According to the neutronphysical characteristics, protactinium is close to neptunium: its capture crosssection in the thermal region is 202 barn (see Table
A chain of nuclide transformations starting with thorium (
Figure
The effect of protactinium on the neutron multiplication factor in the process of fuel burning: 1) conventional uranium fuel (4.4% of ^{235}U + 95.6% of ^{238}U); 2) fuel composition containing 11% of ^{235}U + 83% of ^{238}U + 6% ^{231}Pa; 3) fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Pa; 4) fuel composition containing 26% of ^{235}U + 54% of ^{238}U + 20% of ^{231}Pa; 5) complete substitution of ^{238}U for ^{231}Pa (44% of ^{235}U + 56% of ^{231}Pa).
As we can see in the figure, the introduction of protactinium in the fuel composition leads to a decreased initial reactivity margin and higher fuel burnup. If ^{238}U is completely substituted for ^{231}Pa (fuel composition containing 44% of^{235}U + 56% of ^{231}Pa), burnup reaches 624 GW∙d/t, while the neutron multiplication factor remains practically unchanged throughout the campaign and is small. For a VVER1000 reactor, this campaign lasts about 40 years.
These results are explained by the following two circumstances. First, the capture of ^{231}Pa neutrons leads to the sequential formation of moderately fissile ^{232}U and wellfissile ^{233}U, which support the fission chain reaction. Second, ^{231}Pa is characterized by a larger neutroncapture crosssection in the thermal region as compared to that of ^{238}U, which leads to the efficient formation of fissile ^{232}U and ^{233}U nuclides.
Reactivity control plays an important role in ensuring the safety of nuclear reactors (Safety of Nuclear Power Reactors). Let us consider the reactivity coefficients in the fuel and coolant temperatures for the case of fuel compositions doped by protactinium and neptunium. Compared to the initial value, the temperature of the reactivity coefficient increased by 100 K when it was estimated with regard to the fuel temperature and by 47 K when it was estimated with regard to the coolant temperature. Since the calculations consider the unit cell of a VVER1000 reactor, the reactivity is determined through the infinite neutron multiplication factor (
Changes in the fuel temperature coefficient of reactivity during the campaign of fuel campaign containing 44% of ^{235}U + 56% of ^{231}Ра are shown in Fig.
Changes in the fuel temperature coefficient of reactivity during the campaign of fuel containing 44% of ^{235}U + 56% of ^{231}Ра.
Negative fuel temperature coefficients of reactivity are favorable because they make the reactor selfregulating. As we can see in the figure, the fuel temperature coefficient of reactivity for the fuel composition containing 44% of ^{235}U + 56% of ^{231}Ра at a certain point of the campaign takes a positive value. This does not meet safety the requirements. Before burnup reaches 266 GW∙d/t (~ 18 years for a VVER1000 reactor), the fuel temperature reactivity coefficient remains negative, and then it becomes positive until burnup reaches 592 GW∙d/t (~ 39 years for a VVER1000 reactor), then it decreases and again remains negative until the end of the campaign.
Thus, it is necessary to determine a fuel composition containing protactinium which will be characterized by a negative fuel temperature coefficient of reactivity throughout the campaign. By means of calculation, it was found that the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Ра is characterized by negative reactivity coefficients in the fuel and coolant temperatures throughout the campaign (Fig.
Changes in the reactivity coefficients for the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Ра during the campaign: 1) fuel temperature coefficient of reactivity; 2) coolant temperature coefficient of reactivity.
As we can see in the figure, the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Ра has a negative fuel temperature coefficient of reactivity throughout the campaign and is characterized by burnup of 178 GW∙d/t. The coolant temperature coefficient of reactivity for the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Ра also remains negative throughout the campaign. Thus, the safety requirements put a limit on the maximum protactinium content, making it impossible to achieve ultrahigh burnup, as shown in the previous section of this paper. At the same time, burnup at the level of 178 GW∙d/t is several times higher than the value characterizing conventional uranium fuel.
Let us consider the reactivity coefficients for the fuel composition containing neptunium (35% of ^{235}U + 65% of ^{237}Np). The fuel temperature coefficient of reactivity is negative, whereas the coolant temperature coefficient of reactivity takes positive values throughout the campaign, which does not meet the safety requirements (Fig.
Changes in the reactivity coefficients forf the fuel composition containing 35% of ^{235}U + 65% of ^{237}Np during the campaign: 1) fuel temperature coefficient of reactivity; 2) coolant temperature coefficient of reactivity.
By means of calculation, it was found that the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{237}Np has negative reactivity coefficients in the fuel and coolant temperatures throughout the campaign (Fig.
Changes in the reactivity coefficients for the fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{237}Np during the campaign: 1) fuel temperature coefficient of reactivity; 2) coolant temperature coefficient of reactivity.
Thus, the safety requirements that provide negative values of reactivity coefficients throughout the entire fuel campaign, nullify the potential of neptunium in terms of increasing fuel burnup – the achievable value is 46 GW∙d/t, which is comparable to conventional uranium fuel for VVER1000 reactors.
Currently, the IAEA estimates that spent nuclear fuel contains about 165 tons of neptunium worldwide (Status and Trends 2018). If we rely on the proposed fuel compositions with high neptunium contents, then these resources for loading a single VVER1000 will be enough for only a few decades. Therefore, there is no question of largescale nuclear power generation involving neptunium.
And since protactinium is practically absent in nature, the question arises of its production in significant quantities. There are two methods applicable for this purpose. The first method is to irradiate ^{230}Th available in uranium ores in power reactors. The disadvantage of this method is the low content of ^{230}Th in uranium ore only 16 g/t. At the current level of uranium production in the world (approximately 50,000 t/y), this means that it is possible to produce less than a ton of protactinium per year; however, this option was successfully used in the USA in the 50s and 60s of the 20^{th} century.
The second method is to irradiate ^{232}Th with highenergy thermonuclear neutrons in a blanket of a hybrid thermonuclear reactor. The rate of protactinium production in the thorium blanket of such a reactor is about 1 kg/t/y. The authors evaluated the possibility of producing protactinium in a thorium blanket surrounding an ITER thermonuclear reactor (thermonuclear power of 500 MW): it amounts up to 800 kg of protactinium per year.
In conclusion, it should be noted that, due to their limited reserves, the use of protactinium and neptunium will apparently be more attractive in smallscale power generation: at NPPs for remote areas, at floating NPPs or as a power sources in spaceships.
Fuel compositions containing protactinium and neptunium are characterized by increased burnup. In addition, protactinium is preferable to neptunium due to the best neutronphysical characteristics of ^{232}U and ^{233}U formed from protactinium as compared with the neutronphysical characteristics of ^{238}Pu and ^{239}Pu formed from neptunium.
The introduction of protactinium into fuel compositions ensures ultrahigh burnup (624 GW∙d/t) and a low neutron multiplication factor throughout the campaign; however, fuel with significant contents of protactinium is characterized by positive fuel temperature coefficients of reactivity.
The fuel composition containing 16% of ^{235}U + 74% of ^{238}U + 10% of ^{231}Ра is characterized by negative reactivity coefficients for the fuel and coolant temperatures throughout the campaign. The achievable burnup value in this case is 178 GW∙d/t, and the campaign is ~ 12 years (for a VVER1000 reactor). The production of protactinium is possible in hybrid fusion reactors (
The introduction of neptunium into fuel compositions ensures high burnup (82 GW∙d/t), but fuel with significant contents of neptunium is characterized by positive coolant temperature coefficients of reactivity.
To ensure negative reactivity coefficients throughout the campaign, the content of neptunium in the fuel must be reduced to such an extent that its potential to increase burnup is nullified, i.e., up to 46 GW∙d/t, which is comparable to conventional uranium fuel for VVER1000 reactors.
The study was supported by Competitiveness Growth Program of the NRNU MEPhI.
* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2020, n. 1, pp. 26–36