There is currently a consensus among the scientific and engineering community regarding the solution to the problem of minor actinides (MAs) formed in the process of nuclear power operation: MAs need to be converted to fission products during burnup in power reactors. Fast neutron reactors (BN, BREST) and molten salt reactors (MSR) are considered largely to this end. Despite the advantages of using fast reactors, there are no currently power unit designs with BN or BREST reactors available for commercial operation. The possibility of using VVER reactors for this purpose is rarely covered in scientific literature, despite the fact that the technology of light water reactors has long been mastered, and preparing a VVER-based MA burner reactor is technically simpler than on the basis of a pilot commercial BN technology or BREST or MSR reactors at different R&D stages. In the previously published first part of the study by Kazansky and Karpovich 2022, the fuel cycle for VVER reactors was investigated: minor actinides obtained during reactor operation were extracted from spent nuclear fuel and added to fresh fuel for the same reactor. It has been found that implementing this cycle and bringing the concentration of MAs up to 4 wt. % makes it possible to reduce the amount of minor actinides produced in the VVER reactor by a factor of 8, and without a loss in the NPP unit power generation. This paper investigates, based on an idea of closing the fuel cycle in terms of minor actinides, the relationship between the MA burnup depth in a VVER-1200 reactor and the enrichment of fresh fuel, the dynamics of unloaded heavy nuclei, and the amount of MAs in additionally loaded fuel. Under investigation are two types of additionally loaded fuel with oxides of minor actinides added to it: based on enriched uranium dioxide or a mixture of (1 – x) ²³²ThO₂+x (96% UO₂) (Kazansky et al. 2023). At the same time, the number of heavy nuclei in fuel does not change when there is a change in the number of loaded MA nuclei, which is measured in the number of the VVER-1200 reactors “served” (the mass of accumulated MA nuclei is about 1% and is removed annually from spent fuel). The number of minor actinides entering fuel is kept at a level that allows having a reactivity margin for the reactor operation at a power of over 2% before the annual refueling. Calculations were undertaken using a fuel assembly model with fuel elements broken down into a number of groups with different fuel burnup depths to simulate the actual loading of the reactor core. This model makes it possible to avoid the power peaking effects and give an answer about the neutronic characteristics of the fuel cycle involving MAs. The calculations made it possible to make a number of important conclusions: more refueling cycles lead to a dynamic equilibrium taking place between the minor actinide amounts loaded and burnt; the number of the reactors served is directly proportional to the enrichment of the make-up fuel and a 20% UO₂ enrichment makes it possible to serve up to 23 VVER-1200 reactors, while using 80% ²³²ThO₂ + 20% (96% UO²) fuel allows 17 VVER-1200 reactors to be served; using MAs extracted from SNF with a burnup of 20 to 50 MW*day/kg leads to the MA composition effect on the reactivity balance being within 4 to 5 β_eff.

minor actinides, nuclear fuel, burnup, thorium fuel cycle, VVER reactor, Monte Carlo method

In the previous part of paper by Kazansky and Karpovich 2021 the possibility was shown for using VVER-type reactors for burning minor actinides without losing power generation. Several important conclusions were made in this respect:

• constant reloading of minor actinides from SNF into fresh fuel in a VVER reactor leads to a dynamic equilibrium occurring between MA accumulation and burnup, and equilibrium occurs in 10 to 30 years depending on the quantity of loaded MAs;
• the rate of MA burning depends on how MAs are disposed in fuel, homogeneous mixing of MAs with all make-up fuel being preferable compared to options for MA disposition in individual fuel elements or with partial mixing with fuel.

The above theses are explained by the effect MAs have on the reactor reactivity. With MAs introduced into the reactor neutron flux, the reactor reactivity changes, this shift growing as the quantity of minor actinides introduced increases (see Fig. 5, paper Kazansky and Karpovich 2021). In addition, the direction of the reactivity shift depends on the MA fission cross-section blocking, i.e. on the density of minor actinides in fuel elements. With the MA density being low, when the cross-section blocking is small, there is an increase in reactivity. A further increase in the quantity of MAs in fuel elements not only leads to a greater fission cross-section blocking effect for heavy nuclei, but also to a smaller vacancy site for makeup fuel, due to which refueling does not lead to a major increase in reactivity.

Another scenario is considered in this paper: one VVER reactor burns MAs produced by many VVER reactors. Such scenario has one undeniable advantage over other minor actinide burning options (Osaka et al. 2008; Gabrieli et al. 2015; Ashraf and Tikhomirov 2020; Liu et al. 2020; Andrianov et al. 2021) – it uses the existing and well-proven reactor technology, which has been implemented in the form of many VVER-1000/1200 units in operation worldwide.

The purpose of this paper is to

• confirm or deny the possibility for extended burning of MAs, when one VVER reactor burns MAs accumulated in the process of operating other reactors, without losing power generation and the reactor life;
• explore the possibility of using uranium-oxide fuel, as well as fuel from a mixture of ²³²ThO ₂ and UO ₂ for burning MAs in a VVER-1200 reactor (hereinafter, the enrichment of uranium-thorium fuel means the mass content of uranium, the enrichment of uranium as such being at all times 96%, that is, nearly pure ²³⁵U).

The fuel cycle used in the study is based on multiple recycling: MAs (Np, Am, Cm), which are extracted from SNF in the course of reprocessing, are used then to fabricate new fuel called further fresh fuel. Thus, fresh fuel is enriched uranium dioxide or a mixture of ²³²ThO₂ with 96% UO₂ containing MA nuclei dioxide. The quantity of MAs with the specified fuel enrichment needs be such that the k_∞ value at the end of the reactor cycle (EoC) is not less than 1.02 (taking into account the decrease in the reactor reactivity due neutron escape from the reactor of the simulated core) (Kazansky and Karpovich 2021; Karpovich et al. 2023). For calculations, MAs with the composition shown in Table 1 were added to fuel.

The flow diagram of the closed fuel cycle simulated in this study is presented in Fig. 1.

Figure 1. 

Flow diagram of the simulated fuel cycle.

The VVER-1200 reactor core model used in the fuel cycle calculations is an FA in an infinite multiplying medium. The fuel elements the fuel assembly contains are equally divided into four groups with different burnup depths. Such breakdown allows one to take into account the effect of refueling on the neutron spectrum in the reactor, on the fuel burnup (Kazansky and Karpovich 2021) and on the reactivity balance.

At the very beginning of the fuel cycle calculation, fuel is loaded into each FA zone with an initial enrichment of 4.95% and burnup depths corresponding to one, two and three years of being in the reactor; fresh nuclear fuel with added MAs is placed in zone 4. The calculation is undertaken further as follows:

• calculation is undertaken for the model FA burnup in the course of one calendar year at the average power of one VVER-1200 FA;
• for fuel with four-year burnup, which is withdrawn from the simulated system, the four-year FA pool cooling is additionally calculated to determine the isotopic composition of MAs to be used as part of new fuel for the next refueling; to simplify the calculations, the cooling time is taken into account only for the extracted fuel, as the time was “stopped” for the rest of the model; as it was shown in Kazansky and Karpovich 2021, fuel cooling in the pool needs to be taken into account (²⁴¹Am is accumulated due to the decay of ²⁴¹Pu, and the MA mass increases by about 15%);
• the isotopic composition of the fuel for refueling is calculated: makeup fuel is mixed with MAs from extracted and reprocessed SNF from the simulated FA, to which outside MAs are added with the composition described in Table 1;
• MAs are added by substituting uranium and thorium based on a “nucleus for nucleus” principle, so the total number of heavy nuclei in the fuel rod remains constant, the makeup fuel enrichment remaining also the same;
• the next FA batch is formed: fuel with a four-year burnup is replaced by fresh fuel with an addition of MAs, the remaining three zones continuing to operate with the old composition.

The fuel cycle with MA disposal is calculated for each combination of three parameters: fuel type (uranium or uranium-thorium), makeup fuel enrichment, and mass of loaded MAs. For illustration, the mass of MAs loaded from the outside is expressed not in kilograms, but in the number of VVER-1200 reactors that produce this mass during the year (on the average, one VVER-1200 reactor produces 31.8 kg of MAs per year). The reactor criticality is monitored during the calculations, which shall not fall to below k_∞ = 1.02 in the process of nuclear fuel burnup and MA accumulation as part of the fuel cycle. This limit has been selected based on a preliminary calculation of neutron escape from the VVER-1200 reactor core (Kazansky and Karpovich 2021; Karpovich et al. 2023).

The calculations were undertaken using the Serpent v.2.1.32 Monte Carlo code (VTT, Finland). Fuel burnup is calculated on the predictor-corrector basis (Leppaanen 2015). A database of evaluated nuclear data based on JEFF-3.1.1 was used as part of the library supplied by the code developer (Leppaanen and Viitanen 2013).

Following the fuel cycle calculations (see Fig. 1), the isotope compositions of unloaded SNF were obtained from 37 consecutive refueling cycles, as well as the BoC and EoC dynamics of k_∞. Initially, we shall pay attention to the dynamics of k_∞ when the 20% UO₂ and 80% ²³²ThO₂ + 20% (96% UO₂) fuel is used. The error of the k_∞ calculation for the VVER fuel loads with the use of MAs, generated by evaluated nuclear databases, does not exceed 0.3 β_eff (Karpovich et al. 2023)(for all calculations, the average delayed neutron fraction value is β_eff = 0.56%).

Fig. 2 shows the dynamics of k_∞ for scenarios when the outside MA flow is received from 23 or 24 reactors. In the event of uranium fuel with 20% enrichment and MAs from 24 reactors loaded into a VVER-1200 reactor, k_∞ falls below the minimum level of 1.02 at the end of the 37^th fuel cycle, and such scenario will lead therefore in practice to the early end of the reactor life. The same can be observed for the 80% ²³²ThO₂ + 20% (96% UO₂) fuel: the annual MA flow from 18 reactors into the simulated VVER-1200 reactor in the course of the 24^th cycle leads to the early shutdown, as the flow from 17 reactors can be disposed of without compromising power generation (Fig. 3).

One can see from Figs 2, 3 that the reactor k_∞ tends to an asymptotic value as the mass of recirculated MAs in the cycle grows, this indicating that a dynamic equilibrium is reached (Kazansky and Karpovich 2021) between the MAs received from the outside and the MAs burnt in the reactor. The dynamic equilibrium is the same for any number of externally received MAs, provided there is still positive reactivity. For the selected makeup fuel enrichment, there is a maximum quantity of MAs that can be disposed of. With only recirculation of MAs, fuel based on 20% UO₂ allows keeping a larger MA mass in the fuel cycle than the 80% ²³²ThO₂ + 20% (96% UO₂) fuel.

The effect of minor actinides on reactor reactivity as fuel burns up is shown in Fig. 4. Transitional and stationary loads were taken, which correspond to life cycles 5 and 35. For illustration, the reactivity dynamics is shown for a 4.95% uranium oxide fuel system with no MAs.

After MAs are added, as can be seen in Fig. 4, there is an immediate abrupt decrease in the reactivity loss rate in the model’s all four zones as fuel burns up in the course of the reactor life. The reason for the decrease in the reactivity loss rate is the ²³⁵U fission cross-sections screening effects, as evidenced by the ²³⁵U macroscopic cross-sections for different reactor fuel cycles (Table 2): a fourfold increase in the uranium enrichment leads to an increase in the fission cross-section, Σ_f, by only 1.55 times. As ²³⁵U burns up, its fission cross-section grows due to a milder self-shielding effect, which makes it possible to make up in part for the reduction in the macroscopic fission cross-section due to the burnup of ²³⁵U.

As MAs are accumulated with each reactor refueling, the fissile curium isotopes contribute to the compensation of the ²³⁵U burnup, allowing a further decrease in the reactivity loss rate.

A further increase in the MA mass in the fuel composition up to the dynamic equilibrium between the MA arrival from the outside and the MA burnup in the reactor leads to a gradual BoC decrease in the reactivity margin. Thus, a combination of the initial reactivity margin and the reactivity loss rate can be achieved by selecting correctly the quantity of MAs loaded annually and enriching make-up fuel so that the reactor does not need to be shut down ahead of schedule and suffer thereby damage in power generation.

When comparing data in Tables 1, 3, one can see that, as MAs recirculate, their isotope composition in fuel shifts gradually towards heavy curium isotopes with a long half-life.

Figure 2. 

Dependence of k_∞ for a 20% UO₂ based reactor on the reactor cycle No. for different quantities of MAs loaded into fresh fuel.

Figure 3. 

Dependence of k_∞ for an 80% ²³²ThO₂ + 20% (96% UO₂) based reactor on the reactor cycle No. for different quantities of MAs loaded into fresh fuel.

Figure 4. 

Reactor reactivity (in absolute values) as a function of time in the course of one reactor fuel cycle for different types of fuel.

The presence of the limiting annual MA flow, which can be disposed of in VVER reactors without compromising power generation, leads to another question: how are the enrichment of makeup fuel and the maximum permissible outside flow of MAs associated with each other? The answer to this question is presented in Fig. 5.

Figure 5. 

Maximum permissible quantity of minor disposed of in one VVER-1200 as a function of makeup fuel enrichment.

It can be seen from Fig. 5 that an increase in the enrichment of make-up fuel increases the maximum allowable quantity of MAs. And fuel based on enriched uranium allows burning much more MAs than thorium fuel with the same content of ²³⁵U.

In the light of the findings, it makes sense to compare the efficiency of disposing of minor actinides with different scenarios considered in the two parts of the paper. The following has been selected as the criteria

• mass of minor actinides burnt up in the process of generating 1 GW∙year of thermal energy; this indicator allows one to abstract from the peculiarities of the scenarios and compare their efficiency in practical terms;
• SWU cost to fabricate fuel for burning 1 kg of MAs.

A highly paradoxical conclusion follows from Table 4: for uranium-thorium fuel, the SWU cost per 1 kg of MAs burnt up is slightly smaller than in the event of using classic uranium-oxide fuel, although thorium-based fuel uses uranium with a 96% enrichment. At the same time, the fuel cycle considered in the paper with the MA closure is too costly in terms of natural uranium and SWU consumed. This cost can be reduced if the fuel cycle is closed for all heavy nuclei that go back into the reactor not only MAs but uranium as well.

High consumption of SWU for fabricating 5% of fuel for MA burning is explained by the fact that a very small quantity of MAs can be loaded into the reactor in this case without reducing its energy output.

This study used the composition of MAs (see Table 1) extracted from the VVER-1200 fuel with a burnup depth of 56.8 MW∙day/kg and four-year cooling. Fuel from VVER and RBMK reactors with different burnup depths with different compositions of MAs accumulated at SNF warehouses. Therefore, it needs to be found out whether the above findings depend on the composition of the MAs loaded into the reactor.

To begin with, it is necessary to estimate the average ratio of the radiation capture macroscopic cross-sections for all MAs to the macroscopic fission cross-section:

$⟨\alpha ⟩=\frac{{\sum }_{i=1}^n{\Sigma }_c^i}{{\sum }_{i=1}^n{\Sigma }_f^i}$

where ${\Sigma }_{!}^c$ is the macroscopic cross-section of radiation capture for the i^th isotope; and ${\Sigma }_f^i$ is the macroscopic cross-section of the i^th isotope.

The macroscopic cross-sections were calculated for each nuclide with the VVER-1200 reactor neutron spectrum in the infinite dilution approximation.

As one can see in Fig. 6, an increase in the fuel burnup depth leads to an increased ability of MAs to support the fission chain reaction. Therefore, for the problem in question, the composition of MAs is taken, which were extracted from the VVER-1200 fuel with a burnup of 20 MW∙day/kg and four-year cooling (Table 5).

The data in Fig. 7 show that the effect of the MA composition on the reactivity balance in the simulated fuel cycle is 4 to 5 β_eff. Considering that one cluster of absorber elements in the CPS of a VVER reactor has a weight of ~ β_eff, adjustments need to be made to the operation of the reactivity margin compensation system in designing a fuel cycle with MA burning in the VVER reactor. The effect of MA composition on the reactivity balance can be levelled down by mixing minor actinides extracted from SNF with different burnup depths.

Figure 6. 

MA <α> as a function of SNF burnup depth (B) in an infinite dilution approximation.

Figure 7. 

EoC k_∞ and Δρ for the 20% UO₂ fuel as a function of the reactor fuel cycle No. when using MAs extracted from SNF with different burnup depths.

VVER-1200 reactors are fit for MA disposal, and using 20% enriched uranium oxide fuel used in one reactor VVER-1200 allows burning MAs at a rate of about 690 kg/year. The existing discrepancy between the MA compositions being at SNF storage facilities does not change the overall situation and is important only for development of specific fuel cycles (the effect of the MA composition on the reactivity balance in the process of MA recirculation is 4 to 5 β_eff).

Using VVER reactors to address the MA accumulation problem is greatly advantageous to other options for minor actinide handling, since an already proven reactor technology is employed, which has been embodied in many VVER units in Russia and other countries.

Using VVER reactors for MA disposal requires more R&D to be undertaken to develop thorium-based fuel, since the use of traditional enriched uranium fuel leads to a problem in the form of plutonium accumulation, which is not fit for fabricating new nuclear fuel, in terms of its composition, due to being composed of predominantly ²³⁸Pu. Thorium-based fuel has more moderate characteristics in terms of the maximum quantity of MAs disposed of, as compared to enriched uranium, but it can be used to produce pure ²³⁸Pu with the smallest possible amount of impurities in the form of other plutonium isotopes.

Taking into account the results of simulating fuel burnup with minor actinide addition presented in this paper, it makes sense to present in the further part of the study the characteristics of the fuel cycle based on uranium and uranium-thorium fuel, closed in terms of all heavy cores, and its capability to dispose of minor actinides in VVER reactors taking into account technical and economic expenditures.