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All issues Volume 11 (2025) EPJ Nuclear Sci. Technol., 11 (2025) 71 Full HTML
Open Access
Issue
EPJ Nuclear Sci. Technol.
Volume 11, 2025
Article Number 71
Number of page(s) 12
DOI https://doi.org/10.1051/epjn/2025066
Published online 05 November 2025

© X. Doligez et al., Published by EDP Sciences, 2025

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

France’s current nuclear strategy calls for the construction of a new generation of EPR-type reactors that will enable plutonium and uranium to be multi-recycled within the current century. In the longer term, new GEN-4 reactors, such as sodium-cooled fast breeder reactors, are planned to close the fuel cycle. The possible scenarios describing such a strategy are studied using dynamical fuel cycle simulations. These simulations calculate material flows and inventories in each facility, such as reactors, reprocessing units or fuel fabrication plants. The quantified analysis of some foreseen French fleet evolution are regularly published by the industrial stakeholders, as in [1] or in [2].

Those scenarios studies provide information on the evolution of the plutonium inventory in different spent fuel stockpiles and their isotopic compositions. Those quantities are needed to assess the deployment possibilities of future GEN-IV reactors. Previous studies looking at the deployment of ASTRID-type reactors have shown that the quantity of plutonium to be loaded in each reactor is highly dependent on its isotopic composition showing variations up to 40% [3]. Consequently, efforts need to be pursued to increase the representativeness of nuclear scenario calculations and their accuracy.

The aim of plutonium multi-recycling in new pressurized water reactor (such as European Pressurized Reactors or EPR) is to stabilize both plutonium and spent fuel inventory while demonstrating industrial MOX spent fuel reprocessing. As a result, the global plutonium quality, defined as the fraction of fissile nuclei in the isotopic vector, decreases with the number of recyclings, and then with the scenario time. To cope with the low quality of plutonium recovered by spent MOX fuel reprocessing, it could be mixed with plutonium recovered by spent UOX reprocessing such as studied in [2] or in [4]. This new kind of fuel assembly containing plutonium recovered by reprocessing MOX spent fuel is called MOX-MR.

The spent fuel mixing fraction at reprocessing may vary among the scenario time and is then the result of an optimization process that ensures a rather constant plutonium quality. Consequently, MOX-MR fuel-loaded reactors can be modeled with a fixed fraction model in scenario simulations. This kind of model, described in [5], assumes a constant plutonium content in all fresh MOX-MR fuels. The literature mentions a content of 9.54% [6] of plutonium oxide in these assemblies, the other part being depleted uranium oxide.

In fuel cycle simulations, reactors are supposed to be defined by a given irradiation time (or a given average discharged burn-up). By construction, a fixed fraction model does not guarantee a match between the fresh fuel to be loaded and the irradiation time. Consequently, as reactor are supposed to reach the targeted burn-up whatever the fresh fuel composition, some inconsistencies in the scenario simulation may occur if the plutonium isotopic quality is too depreciated.

This paper details the evolution during the scenario of the properties of EPRs loaded with MOX-MR fuels, modeled with a fixed plutonium content. The cycle length, discharged burn-up of fuel assemblies and 2D power factor are considered for this paper. The simulations of the different considered trajectories are performed with CLASS [7], using advanced reactor modeling based on 3D full-core reactor simulations. The historical fleet has been simulated using previously developped models with DRAGON [8] and DONJON [9], detailed in [10] and used in [11].

A new dedicated model has been built for EPR loaded with MOX-MR fuel assemblies. The core configuration studied here considers 50% MOX-MR assemblies such as in [12]. The other half are UOX fuel assemblies. A dedicated loading pattern has been built for this configuration. Depletion simulations are performed by CEA’s softwares APOLLO2 [13] and CRONOS2 [14]. Artificial neural networks (ANN) are then trained on a dedicated database to build reactor metamodels that are then used to quantify the reactor properties as a function of the scenario time. The methodology used for this reactor metamodeling is similar to the one detailed in [15]. The first part of this paper describes this process applied to EPRs loaded with MOX-MR fuels. Our core configuration is detailed, and the ANN are used to compare the reactor properties of [12] showing a good agreement, even if the core configurations are different. In the last subsection, ANNs are used to estimate the possible deviation of reactor irradiation times (of EPRs that multi-recycle the plutonium) given the fluctuation of the plutonium quality expressed in [2].

The second part of this paper presents scenario simulations performed with CLASS. As in any event-based software, reactor cycle lengths are input parameters of the simulations that define the loading and unloading of all reactor cores. Consequently, reactors are supposed to be under operation during the whole cycle length. The fuel loading model in CLASS is responsible for identifying the fresh fuel composition that would maintain the chain reaction over the reactor cycle. But with a fixed fraction of plutonium inside MOX-MR fuels, inconsistencies between the reactor irradiation length and the fresh fuel composition may appear. CLASS simulations give access to the isotopic composition of each new fresh fuel among the scenario time, and allow us to verify the coherence of the input parameters (cycle length vs fuel compositions). Different options for spent fuel mixing at reprocessing are considered here, underling the importance of those parameters to guarantee the plutonium quality, the EPRs properties and finally the consistency of the simulation outputs.

2. Modeling EPR loaded with MOX-MR fuel assemblies

2.1. Reactor depletion simulations

2.1.1. Core configuration

The core configuration used for this work was built thanks to information available in [12]. In that paper, the core is loaded with 4 different types of assemblies. 3 kinds of UOX fuel assemblies: 4 without any Gadolinium (UOX-0Gd), 16 containing 4 fuel pins with Gadolinium (UOX-4Gd), 28 with 16 fuel pins containing Gadolinium (UOX-16Gd) and additional 44 MOX-MR fuel assemblies leading to a total of 92 new assemblies at each reloading. Still in that paper, 2 different isotopic vectors and 2 different plutonium contents are considered in order to study the reactor sensitivity to the composition of fresh MOX-MR fuels.

For this work, a new fuel management has been built, presented in Figure 1. To simplify the search for an acceptable loading pattern, only 2 types UOX assemblies had been considered. The total of number of fuel pins containing Gadolinium is kept consistent with the core of [12]. Consequently the 16 UOX-4Gd have been replaced by 4 UOX-16Gd and 12 UOX-0Gd. The pattern has been built to minimize, among the reactor evolution, the maximal 2D power factor defined as the ratio of the power produced by the most powerful assembly over the average power of one assembly. As it has been identified from scratch with a try and test approach, some better loading pattern may be found leading to more robust solutions (i.e. acceptable for a wider variety of plutonium isotopic compositions of with smaller power factors for a given MOX fresh fuel compositions). However, the search of optimized solutions is a time consuming process that was not carried for this work as this loading pattern shows good reactor properties.

thumbnail Fig. 1.

Loading pattern used for modelling EPR loaded with MOX-MR fuel assemblies.

2.1.2. Calculation Scheme

Depletion simulations are performed within a classical two level scheme with APOLLO2 [13] and CRONOS2 [14]. The first one solves the neutron transport equation following the REL2005 recommendations [16]. Diffusion macroscopic data are tabulated as a function of the assembly burn-up, the coolant density and the fuel and coolant temperature. CRONOS2 then solves the diffusion equation on the full geometry, with thermohydraulic coupling, taking into account the temperature and coolant density distributions. The spatial mesh considers a pin-by-pin discretrization.

2.2. Artificial neural networks construction

500 different initial compositions for MOX-MR fuels had been randomly determined using a Latin Hyper-square Sampling (LHS) technique within a phase space that describes the possible fresh fuel composition of MOX-MR assemblies. The same phase space than [15] has been considered as it seems wide enough to cover all possible plutonium isotopic compositions coming from a mix of spent UOX and MOX fuels (and even spent MOX-MR fuels). The sampling space is reminded in Table 1.

Table 1.

Plutonium composition sampling.

For each of those initial compositions, a reactor simulation has been performed recording the irradiation length (expressed in Equivalent Full Power Days or EFPD), the burn-up of each assembly at reactor discharge and their final isotopic composition, and the 2D power factor as a function of the irradiation time. Those data are split in two different databases: one gathering the results of 400 simulations called the training database, and the other gathering the 100 simulations left, chosen randomly, called the testing database. One dedicated artificial neural networks (ANN) have been trained to build different estimators of all these quantities, using the TMVA library [17] version 4.3. Each network configuration (number of hidden layers, number of neurons per layer) has been chosen in order to have a satisfying accuracy. To assess them, a comparison between the ANN estimations and reference simulations has been performed on the testing database. The deviation histograms are then plotted, such as in Figure 2 for irradiation cycle length and 2D power factors, and the standard deviations are then calculated. The neural network configuration is adapted while these standard deviations are greater than 0.5% (1% for the burn-up of each assembly at reactor discharge). The ANN built for the irradiation time estimation is made of 2 hidden layers of 4 neurons and the one for the 2D power factor has 2 hidden layers of 16 neurons. The errors induced by ANN estimations are much smaller than numerical biases induced by the calculation scheme [15] and also smaller to error due to operational uncertainties (such as the cycle length stretch out or the load following, which are not simulated in this work).

thumbnail Fig. 2.

Artificial neural network accuracy for estimation of reactor cycle length on the left and power factor on the right.

To ensure the relevance of our core configuration and our artificial neural networks, these have been used to estimate the irradiation length and the 2D power factor of the 4 initial MOX-MR compositions given in [12]. One of them is considered as a reference composition and the 3 others are obtained by slightly modifying the isotopic vector (called “sensitivity 1”), the plutonium content (“sensitivity 2”) or both (“sensitivity 3”). The results are summarized in Table 2. The agreement is surprisingly good as the calculation scheme is different (and it is known that it can be responsible of biases up to several %) but also the loading pattern that was built specially for this work. The discrepancies observed in Table 2 cannot be attributed to the artificial neural networks. Indeed they are built to reproduce APOLLO2-CRONOS2 calculations with biases smaller than 1% as shown in [15]. Table 2 shows that the fuel management used for this work and the ANN can be used to evaluate reactor properties during a dynamic fuel cycle simulation.

Table 2.

Comparison of ANN estimated reactor properties with the reference [12]. Sensitivity 1, 2 and 3 represents MOX fresh fuel compositions obtain by variation of the isotopic vector, the plutonium content or both of those quantities both from the reference composition.

2.3. Reactor properties evolution during a scenario simulation

The consistency of our estimations with the literature allows us to use our ANN to quantify the performances of EPRs loaded with MOX-MR fuels in different scenario simulations. As an example, the simulation presented in [2] considers MOX-MR fuel assembly with a constant plutonium content, which value is assumed here to be 9.54% such as in [6] and which quality varies from 52% to 56%.

Not knowing the isotopic composition of fresh fuels at each reactor loading, a phase space exploration is used for quantifying roughly the deviation of reactor cycle length. 5000 new isotopic compositions has been randomly chosen (using a LHS sampling within the space validity of our ANN), and reactor properties are estimated for all those compositions.

The Figure 3 shows the cycle length as a function of the plutonium quality (for a given plutonium content of 9.54%) and the maximal 2D power factors as a function of the irradiation cycle length for those 5000 compositions. The blue dots represent the composition leading to an associated irradiation time close to the target value (of 450 EFPD). A ±5% variation has been considered to represent different operational uncertainties. From this figure, it can be deduced that, with the present core configuration, the plutonium quality should be higher than 55% to ensure a cycle length of 450 EFPD. A lower plutonium quality would lead to a smaller cycle length and a higher power factor (that reaches a lower limit with plutonium which quality is close to 62%.

thumbnail Fig. 3.

ANN’s estimation reactor cycle length (in Equivalent Full Power Days) as a function of the plutonium quality on the left and as a function of the reactor power factor on the right. The plutonium content in the MOX-MR fuel assemblies is kept constant for all calculations. Blue dots represent plutonium isotopic compositions that reach the target value (450 EFPD) with a ±5% tolerance.

This lower limit for the plutonium quality depends directly on the targeted reactor irradiation length, the plutonium content and the loading pattern. Indeed, a variation of each of those parameters would induce a systematic bias in the acceptable plutonium quality. Then, it is worth looking at the relative variation of the reactor cycle length induced by a variation of the plutonium isotopic quality. The paper [2] mentions a variation of several %, from 56% to 52%. Cycle length distributions corresponding to plutonium quality in the [51%,52%] interval and in the [55%,56%] are presented in Figure 4 and show respectively average values of 422 and 445 EFPD with a standard deviation of 2%. Hence, it can be deduced that the reactor cycle length varies during the scenario simulation to approximately 5% from the reactor definition. The actual irradiation times of reactors loaded with MOX-MR are consequently not constant, leading to possible inconsistency in the scenario simulation: reactors are discharged latter than they are supposed to. Indeed, the reactor discharged burn-up is expected to be biased up to 5% with the decrease of the plutonium quality among the scenario. However, this deviation seems acceptable as it is limited in front of the multiple other approximations that are made in dynamical fuel cycle simulations.

thumbnail Fig. 4.

ANN’s estimations of reactor cycle length (in Equivalent Full Power Days) distribution for two different plutonium quality: between 52 and 53% on the left and between 55 and 56% on the right. The plutonium content in MOX-MR fuel assemblies is kept constant. The number of occurrence in each histogram is linked the sampling and the blue dots from Figure 3.

Two options for a more precise simulation can be investigated. The first one would be to adapt the plutonium content in regards to the plutonium quality, considering for instance two values, the first one for the interval [52%,54%] and the second one for the interval [54%,56%]. The second option would be to adapt the fuel cycle parameters to constraint more the plutonium quality among the scenario time, by adapting the different mixing proportions of different spent fuel at reprocessing for plutonium recovery.

3. Scenario analysis

The actual fresh fuel compositions are necessary to go further in the analysis of the MOX-MR loaded EPR properties’ evolution among the scenario. Fuel cycle simulations can provide this information and we present here some results obtained with the CLASS package used for an academic simulation of a possible French fleet evolution. The hypotheses withdrawn to build such a simulation are presented in the first subsection. Results are presented next and show a stabilization of the global in-cycle plutonium inventory as well as a stabilization of the different spent fuel stockpiles for some fuel cycle hypotheses. The different fresh fuel compositions for MOX-MR assemblies among the scenario time are extracted and ANNs, presented in the previous sections, estimate the reactor cycle time, the maximal 2D power factor and the discharged burn-up of each assembly for each irradiation campaign.

3.1. Scenario definition

The scenario starts with a simulation of the historical French fleet such as in [11]. The reactor lifetime of all reactors that are currently operated is supposed to be 60 years. To replace the aging existing reactor fleet, new EPRs are foreseen. For this work, 2 pairs of new reactors are supposed to start in 2037 and 2040 respectively. Then, one EPR a year is deployed to reach 30 new reactors. The reactor deployment is then similar to [2], yet with some differences as the precise starting dates are not mentioned. That paper also mentions 2 EPRs loaded with MOX fuels between 2042 and 2065, which are also considered in our simulations.

In order to maintain the current MOX fabrication capacities until the end date of MOX fuels (that would eventually be replaced by MOX-MR fuels) some of the 1300 MWe historical Pressurized Water Reactors are loaded with MOX fuels (as planned in the reference strategy [18]). The first MOX-MR fuels are supposed to be loaded in the new EPR in 2050. Then, one new reactor a year is loaded with MOX-MR fuels, to reach plutonium stabilization.

The simulation results (presented in the next subsection) show that 15 EPRs should be loaded with MOX-MR in order to stabilize the overall in-cycle plutonium inventory. This number is dependent on the reactor models used in the CLASS simulations as the plutonium production in UOX fuels and its incineration in MOX and MOX-MR fuels depend on the reactor modeling, as it shown in [5]. It may vary up to several units and a precise estimation would require precise model qualifications that are not available. This required number of EPRs for plutonium stabilization impacts greatly the fuel cycle, specifically reprocessing plants and fuel fabrication capacities as one unit represents approximately a variation of 6% in the material flows.

To obtain this number of 15 EPRs, MOX-MR fuels are modeled with a fixed fraction model for fresh fuel fabrication, contrary to MOX fuels where the plutonium content is calculated as a function of its isotopic vector to minimize the 2D power fraction. More details about this models can be found in [10]. UOX fuels consider different 235U enrichments, according to the historical fuel managements. EPRs UOX fuels are supposed to be enriched at 4.2%.

Different mixing fractions at spent fuel reprocessing to recover plutonium have been investigated in this work. 4 different possibilities are considered for this paper and are summarized in Table 3. The two first ones correspond to the proportion given in [2]. They both relies on approximately 40% on spent UOX fuels. A third possibility has been considered where the UOX proportion of spent fuel reprocessing is smaller (20%) leading to a fast resorption of the spent MOX fuel stockpile. Finally, a fourth hypothesis has been studied that consists in taking plutonium from spent UOX fuels if and only if the quantity of plutonium recovered from MOX and MOX-MR spent fuel reprocessing is not sufficient to build fresh MOX-MR fuels.

Table 3.

Blending proportion at spent fuel reprocessing considered for this paper. The figures represent plutonium mass fraction used for MOX-MR fuel fabrication and not spent fuel fraction at reprocessing.

Obviously, as the plutonium content in spent UOX fuel is much smaller than in MOX and MOX-MR spent fuels, reprocessing capacities needed to recover the wanted plutonium are higher in the 2 first hypotheses than in the 2 last ones. It is also expected that the MOX fuel stockpile would be absorbed faster when UOX spent fuels are less reprocessed. It is worth noticing that those blending fractions correspond to plutonium mass fractions used to build new MOX-MR fresh fuel and not fractions of spent fuels that are actually reprocessed. Those fractions differ due to differences of plutonium content in different spent fuels.

During the scenario simulations, if there is not enough plutonium in one of the spent fuel stockpile to ensure the fuel fabrication with the wanted blending proportions, a material substitution is performed. All the plutonium from the default stock is used and, then, a renormalization of the remaining blending fractions is performed. This algorithm avoids plutonium shortage in fresh fuel fabrications due to the eventual impossibilities of one stock to provide plutonium. As a consequence, the blending fractions are not ensured and the plutonium may actually not come from the wanted spent fuel stockpile. The blending proportion hypotheses are then instructions that CLASS tries to follow and not hard constraints.

3.2. CLASS simulation results

The Figure 5 shows the energy production evolution among the scenario simulations. As all the different simulations show no plutonium shortage in the fresh fuel fabrication, and as reactors, in all scenario simulations are defined with the same cycle length, all the scenario simulations show a similar energy distribution.

thumbnail Fig. 5.

Thermal power produced by the whole reactor fleet.

The Figure 6 presents the global plutonium inventory for the different simulations, showing that plutonium equilibrium seems to be reached in all scenarios. It represents the plutonium in all the fuel facilities (reactors, stocks, cooling pools and fuel fabrication units which reaches approximately 560 tons, relatively close to the 600 to 650 tons quoted in [2]. Considering that the software, reactor deployment chronicles, and reactor and processing plant models are different, the comparison is very satisfying (hidden hypotheses are known to be the first source of uncertainty in fuel cycle simulations [19]).

thumbnail Fig. 6.

Global plutonium inventory as a function of the scenario time. The black, red, blue and green curves correspond respectively to the blending proportion 1, 2, 3 and 4 for spent fuel reprocessing.

In our simulations, the global plutonium inventory at equilibrium is very little dependent on the spent fuel blending fraction at reprocessing. This is mainly due to the constant value of plutonium content of MOX-MR fresh fuels and the same production of plutonium in all scenario. Indeed, the plutonium mass needed for each MOX-MR assembly is not dependent on the isotopic vector (and the plutonium quality), then its source. The same amount of plutonium will be loaded in each reactor no matter if it is coming from spent UOX fuels or spent MOX-MR fuels. With a model that would adjust the plutonium content to its isotopy, the conclusions may differ.

The adjustment of the plutonium content according to reactor parameters rises some external question for reactor modeling, such as the criterion chosen for the determination of the fresh fuel composition. Previous work [4] shows that the plutonium content of fresh fuels is strongly dependent on the choice of this criterion that could be irradiation time or power factors for instance.

The Figure 7 shows the evolution of the different spent fuel stockpiles (TOTAL, spent UOX, spent MOX and spent MOX-MR), expressed in tons of heavy metals, for the 4 simulated scenarios. The black and red curves correspond to the first two blending fractions of the Table 3 and the proportion of plutonium coming from spent UOX fuels should be the same. As a consequence, the evolution of the UOX spent fuel stockpile should follow the same trend. However, as explained earlier, the rules of spent fuel reprocessing are applied if and only if the plutonium is available in the different stocks. In the simulation defined by the second blending proportion, there is not enough plutonium in the MOX-MR spent fuels to ensure the fresh fuel fabrication with the correct proportions in 2050, leading to different effective fractions of plutonium coming from UOX spent fuels.

thumbnail Fig. 7.

Heavy nuclei inventory as a function of time in different spent fuel stockpiles, total on the top left, spent UOX on the top right, spent MOX on the bottom left and spent MOX-MR on the bottom right. The black, red, blue and green curves correspond respectively to the mixing proportion 1, 2, 3 and 4 for spent fuel reprocessing.

The blue and green curves correspond respectively to the third and fourth blending fractions. Figures show that the total spent fuel stockpile stabilization is highly dependent on the fuel cycle hypotheses expressed by the different blending fractions.

The presence of a bump in the spent UOX stockpile between 2050 and 2060 is due to the discharge of all the historical reactors that are shut down within a short period of time before the loading of new reactors recycling plutonium. This bump is a direct consequence of the deployment chronicle of new reactors and it can be reduced by matching the different dates of MOX-MR first loading with the shut-down time of old PWR. However, it does not feel natural to consider the dates as an optimization lever regarding the difficulty to start new reactors and regarding the possible political discussions associated to reactors shut down.

The Figure 8 shows the average plutonium quality and the average plutonium content in all spent fuels. The green curve corresponds to the simulation in which UOX spent fuels are used with the lowest priority for the spent MOX-MR fuels and shows the better quality and the higher plutonium dilution. From these plots, it seems that their is a trade off between the spent fuel inventory and the plutonium quality. The higher this latest is, the least concentrated the plutonium is. As a result, their is also a trade-off in case of transition in 2100 from this fleet to a sodium cooled fast reactor fleet, between the number of reactors to be deployed and the reprocessing capacity needed to start those reactors. Indeed, from [20], it appears that 40% more plutonium is needed for one ASTRID like reactor when the plutonium quality is equal to 50% in comparison to a plutonium quality of 75%. As a consequence, choosing to stabilize the spent fuel stockpile to a low level by reprocessing the UOX spent fuels for MOX-MR fuel fabrication leads to a degraded plutonium for future fast reactors but highly concentrated. The number of reactors to be deployed would be reduced, but the fuel cycle capacities would be optimized. On the contrary, choosing to recover firstly the plutonium from MOX spent fuels for MOX-MR fabrication would lead to a higher quality plutonium, diluted in a great amount of UOX spent fuels. In that case, the number of fast reactors that may be deployed would be higher (roughly 40% higher, in the ASTRID case) but the fuel cycle capacities should be increased to recover this diluted plutonium.

thumbnail Fig. 8.

Plutonium quality in all the stocks as a function of the scenario time on the right and plutonium concentration in those stockpile on the left.

3.3. EPR performances’ characterization during the scenario

Scenario simulations give us access to the isotopic composition of each MOX-MR fresh fuel that is loaded. Using our ANNs for reactor irradiation length estimation and 2D power factor, the evolution of reactors properties among the scenario is analyzed here. The Figure 9 shows, on the left, irradiation time for each reactor loaded with MOX-MR fuels for the 4 simulated scenarios. The figure on the right shows the corresponding plutonium quality in the loaded fresh MOX-MR fuels. The black, red, blue and green dots refer respectively to the blending fraction 1, 2, 3 and 4.

thumbnail Fig. 9.

Irradiation cycle time for each EPR loaded with MOX-MR fuels among the scenario time on the right and the corresponding plutonium quality in the right. The black, red, blue and green dots correspond respectively to the blending proportion 1, 2, 3 and 4 for spent fuel reprocessing.

Green dots refer to MOX-MR assemblies that are built with plutonium recovered from UOX spent fuels in last priority. The plutonium quality is depreciated among the scenario time leading to a strong deviation of the reactor irradiation length (almost 30%). Those variations seem too wide to consider this simulation as coherent, as reactors should be refueled almost twice as they are in the simulations. For such degraded plutonium quality, the plutonium content should have been increased in MOX-MR fuels.

Blue dots represent the simulation where 20% of the plutonium from UOX spent fuels is used for fresh MOX-MR fuel fabrication. Once again for this simulation, the plutonium quality is decreasing, yet remaining over 50%. This decrease leads to a deviation of almost 80 EFPD in the reactor irradiation time at the end of the scenario, questioning once again the simulation validity.

Red and black dots, on the other hand, show a relative constant behavior with a limited bias in the reactor irradiation time of approximately 10% deviation. The figure shows some pretty good quality for MOX-MR fresh fuels between 2050 and 2060 (some times higher than 60%). This is because no fuel management is considered for reactor shut down in CLASS simulations. In those particular fleet evolutions, some of the first MOX-MR fuels are built with plutonium recovered from some MOX and UOX spent fuels which has been very little irradiated.

The Figure 10 shows the evolutions of 2D power factors for the simulations corresponding to the blending fractions 1, 2 and 3. The fourth option was discarded due to unreasonable biases in reactor irradiation cycle length. This figure shows that reactor power factors vary among the scenario, from approximately 1.375 to more than 1.45, showing an increase of 3.5%, a small yet noticeable raise. The first loads of MOX-MR fuels lead to high 2D power factor (higher than 1.4), resulting from the good plutonium quality of those assemblies. Those results show that the deployment of MOX-MR fuels should be more investigated to deal with the plutonium quality variation observed in the 15 first years of the MOX-MR deployment. A dedicated loading pattern dedicated to this 2050-2065 period should probably be built on purpose.

thumbnail Fig. 10.

2D Power Factor of EPRs loaded with MOX-MR fuels among the scenario time. The black, red and blue dots correspond respectively to the mixing proportion 1, 2 and 3 for spent fuel reprocessing.

Finally, the evolution of the average discharged burn-up of UOX fuels is investigated for the scenario defined by the first blending fraction hypothesis. UOX fuels that are discharged after 2 or 3 reactor irradiation campaigns are quoted respectively UOX2 and UOX3. Their average burn-ups at discharged are calculated using the corresponding ANN and the results are given in Figure 11 on the left as a function of the scenario time.

thumbnail Fig. 11.

UOX assemblies discharged burn-up as a function of the scenario time on the left and associated plutonium production, as a function of UOX burn-up on the right.

Results show a 12% deviation between the beginning and the end of the scenarios, leading to possible deviations in the plutonium mass balance of UOX fuels for those heterogeneous reactors. To quantify this deviation, the plutonium mass in UOX fuel as a function of the assembly burn-up are extracted from our depletion database. The Figure 11 on the right shows the plutonium concentration in all discharged UOX fuel. The unit is expressed in atoms per barn⋅cm of fuel assembly. For UOX2, a 12.5% variation of the discharged burn-up corresponds to a 14% variation in the plutonium concentration. For UOX3, the sensitivity of the plutonium concentration is lower as a 12% burn-up variation leads to a 9% deviation for plutonium concentration.

The modeling of the EPRs in our scenario simulations leads to a variation of the discharged burn-up of UOX assemblies, and consequently to a variation of the plutonium mass balance in the UOX fuels. Consequently, taking into account the real discharged burn-up of UOX fuel assemblies would lead to a smaller production of plutonium in the UOX fuel. Finally, the constant plutonium content in MOX-MR fresh fuels leads to two main errors: reactors should be refueled more often, and plutonium production is smaller than expected. The global plutonium inventory, and spent fuel stockpile stabilization might be affected by those errors and our future work will be dedicated to error propagation.

From all those results, it is possible to conclude that scenario simulations with a fixed fraction model for MOX-MR fresh fuel fabrication may be considered as coherent as long as the blending of different plutonium sources ensure a rather constant plutonium quality for fresh fuels. Yet, a 10% variation of each reactor irradiation length may be considered as a source of errors in the scenarios definition. This 10% variation is in coherence with the dispersion of the plutonium quality observed in the scenario simulation results. It may lead to deviations in the plutonium mass balance of UOX fuel assemblies that should be further investigated.

In order to upgrade the confidence in nuclear scenario simulations, a new model will be investigated in the future, adjusting the plutonium content in the MOX-MR fresh fuels regarding the plutonium isotopic composition. Other possible models should adjust the mixing proportion during the spent fuel reprocessing to ensure a constant plutonium quality.

4. Conclusion

This paper aims to evaluate the actual reactor properties among a nuclear scenario involving plutonium multi-recycling in PWRs simulated with CLASS. This strategy is known to depreciate the plutonium quality, defined as the proportion of fissile nucleus in its isotopic vector. To cope this issue, the stream of plutonium recovered by MOX spent fuel reprocessing is mixed with a stream of plutonium coming from UOX spent fuels. Fuel assemblies that are loaded with multi-recycled plutonium are called MOX-MR fuels. They differ from classical MOX fuels by the plutonium content that should be higher as the plutonium is degraded.

In this paper, different possible trajectories are studied with CLASS in order to quantify the potentialities of such strategies. The simulations calculate the isotopic inventory, as a function of time, in all the fuel cycle units (reactor, reprocessing plants, fuel fabrication plants,...). The modeling of the fuel fabrication is specifically challenging, as it should adapt the different fresh fuel compositions to the reactor characteristics and to the plutonium isotopic vector. Another way to deal with this difficulty is to adapt plutonium streams during the scenario in order to keep constant the plutonium isotopic vector and then, the plutonium content. The impact of the choice of the so-called fuel loading model has been previously studied [5], but it may be negligible if the plutonium isotopic vector is kept constant in the scenario, as proposed in the work published in [2]. However, a slight deviation may lead to strong errors in the simulations. Indeed, the loaded fuel may no longer withstand the reactor irradiation length, leading to non physical reactor campaign.

This paper quantifies the deviations, among scenario simulations, of the properties of reactors loaded with MOX-MR fuels modeled with a fixed plutonium content. To do so, a specific fuel management has been developed for new EPRs that would multi-recycle the plutonium. The loading pattern has been built from scratch thanks to information available in [12]. Then, a dedicated database of reactor depletion simulations has been built, in order to train artificial neural networks that are used as estimators of different reactor characteristics such as the burn-up of each discharged assembly, the reactor cycle length, or the 2D power factors. A phase space exploration of the possible plutonium isotopic composition shows that a variation of 4% in the plutonium quality leads to a variation of approximately 5% in the reactor cycle length.

CLASS simulations give access to the precise isotopic composition of all fresh MOX-MR fuels loaded during the scenario. Several blending proportions of plutonium from spent fuels have been studied to quantify the impact of these parameters. A fixed fraction model has been used for fresh MOX-MR fabrication, knowing that some blending proportion would lead to non physical simulations as the loaded fuels may not allow reactors to operate for the desired cycle time.

Results show that in all the scenario, the plutonium reach a similar inventory (close to 560 tons in our simulations) by the end of the century. The analysis of reactor properties with the built neural networks show strong deviations in the reactor cycle times, varying to almost 80 EFPD even with a plutonium quality always higher than 50%. The evolution of the plutonium quality will consequently lead to an increase in the 2D power factor, yet limited if the variation of the plutonium quality is limited.

Finally, this work shows the importance to adjust the blending fraction at reprocessing to ensure a constant plutonium isotopic composition with fixed fraction model. As a consequence, two types of fuel loading model can be imagined. The first one would adapt the plutonium content in MOX-MR fuel as a function of the plutonium isotopic composition to ensure an average burn-up close enough to the wanted value. The second one would adapt plutonium streams’ blending fraction in the reprocessing unit to ensure a rather constant plutonium quality in the fabrication process leading to a constant plutonium content in fresh fuels. Our next work will investigate the potentialities of a dual approach, in which the plutonium content is set for an interval of plutonium quality.

Inconsistencies between the fresh fuel composition and the irradiation cycle length will also lead to errors in the plutonium production in the UOX fuel assemblies discharged from the heterogeneous EPRs. Indeed, the deviation of the discharged burn-up of UOX fuels quantified in this work is higher than 10%. The mass balance of plutonium is then impacted leading to errors that should be propagated in our future work.

Funding

This research did not receive any specific funding.

Conflicts of interest

The authors have nothing to disclose.

Data availability statement

This article has no associated data generated or analyzed.

Author contribution statement

Conceptualization, all authors; Methodology, all authors; Formal Analysis, all authors; Investigation, all authors; Writing Original Draft Preparation, X. Doligez; Writing – Review & Editing, all authors; Formal analysis and Visualization, X. Doligez. All authors have read and agreed to the published version of the manuscript.

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Cite this article as: X. Doligez et al., Properties’ evolution of reactors loaded with MOX-MR fuels in plutonium multi-recycling scenarios in PWR, EPJ Nuclear Sci. Technol. 11, 71 (2025), https://doi.org/10.1051/epjn/2025066

All Tables

Table 1.

Plutonium composition sampling.

In the text
Table 2.

Comparison of ANN estimated reactor properties with the reference [12]. Sensitivity 1, 2 and 3 represents MOX fresh fuel compositions obtain by variation of the isotopic vector, the plutonium content or both of those quantities both from the reference composition.

In the text
Table 3.

Blending proportion at spent fuel reprocessing considered for this paper. The figures represent plutonium mass fraction used for MOX-MR fuel fabrication and not spent fuel fraction at reprocessing.

In the text

All Figures

thumbnail Fig. 1.

Loading pattern used for modelling EPR loaded with MOX-MR fuel assemblies.
In the text
thumbnail Fig. 2.

Artificial neural network accuracy for estimation of reactor cycle length on the left and power factor on the right.
In the text
thumbnail Fig. 3.

ANN’s estimation reactor cycle length (in Equivalent Full Power Days) as a function of the plutonium quality on the left and as a function of the reactor power factor on the right. The plutonium content in the MOX-MR fuel assemblies is kept constant for all calculations. Blue dots represent plutonium isotopic compositions that reach the target value (450 EFPD) with a ±5% tolerance.
In the text
thumbnail Fig. 4.

ANN’s estimations of reactor cycle length (in Equivalent Full Power Days) distribution for two different plutonium quality: between 52 and 53% on the left and between 55 and 56% on the right. The plutonium content in MOX-MR fuel assemblies is kept constant. The number of occurrence in each histogram is linked the sampling and the blue dots from Figure 3.
In the text
thumbnail Fig. 5.

Thermal power produced by the whole reactor fleet.
In the text
thumbnail Fig. 6.

Global plutonium inventory as a function of the scenario time. The black, red, blue and green curves correspond respectively to the blending proportion 1, 2, 3 and 4 for spent fuel reprocessing.
In the text
thumbnail Fig. 7.

Heavy nuclei inventory as a function of time in different spent fuel stockpiles, total on the top left, spent UOX on the top right, spent MOX on the bottom left and spent MOX-MR on the bottom right. The black, red, blue and green curves correspond respectively to the mixing proportion 1, 2, 3 and 4 for spent fuel reprocessing.
In the text
thumbnail Fig. 8.

Plutonium quality in all the stocks as a function of the scenario time on the right and plutonium concentration in those stockpile on the left.
In the text
thumbnail Fig. 9.

Irradiation cycle time for each EPR loaded with MOX-MR fuels among the scenario time on the right and the corresponding plutonium quality in the right. The black, red, blue and green dots correspond respectively to the blending proportion 1, 2, 3 and 4 for spent fuel reprocessing.
In the text
thumbnail Fig. 10.

2D Power Factor of EPRs loaded with MOX-MR fuels among the scenario time. The black, red and blue dots correspond respectively to the mixing proportion 1, 2 and 3 for spent fuel reprocessing.
In the text
thumbnail Fig. 11.

UOX assemblies discharged burn-up as a function of the scenario time on the left and associated plutonium production, as a function of UOX burn-up on the right.
In the text

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