Impact of the Melt-Refining Process on the Performance of Sodium-Cooled Rotational Fuel-Shuffling Breed-and-Burn Reactors

Abstract

This study assesses a Rotational Fuel-Shuffling Breed-and-Burn (RFBB) fast reactor that operates in breed-and-burn (B&B) mode with a rotational fuel-shuffling scheme and remains within the 200 displacements per atom (DPA) radiation damage constraint of currently verified cladding materials. The design is based on a commercial-scale fast burner reactor called the Super Power Reactor Innovative Small Module (S-PRISM) reactor. To reduce the high DPA values of discharged fuels, the melt-refining process developed in the Experimental Breeder Reactor-II (EBR-II) project is adopted in this study. The effects of the melt-refining process on the performance of the RFBB are investigated via five scenarios and compared with a core to which the melt-refining process is not applied: Scenario I, “Homogenization,” occurs without the removal of fission products (FPs) during the melt-refining process; Scenario II, “Homogenization and FP Removal,” occurs with the removal of FPs to a fraction similar to that in the melt-refining process developed in the EBR-II project; Scenario III, “Homogenization, FP Removal, and Make-Up,” is similar to Scenario II but makes up fuel losses with natural uranium; Scenario IV, “With 1% TRU [transuranics] Losses,” is similar to Scenario III but is evaluated with 1% of actinides not recovered; Scenario V, “With 10% TRU Losses,” is similar to Scenario III but is evaluated with 10% of actinides not recovered. The results show that it is neutronically and thermal hydraulically feasible to establish a B&B mode with the rotational fuel-shuffling scheme and by reconditioning the fuel whenever its cladding reaches its proven 200 DPA radiation damage limit. In Scenario V, the core is subcritical due to a large number of actinides not being recovered during the melt-refining process. The cores of the other scenarios are all critical. The cores of scenarios in which FPs are removed during the melt-refining process have higher excess reactivity than that of the core of Scenario I (“Homogenization”) and that of the core to which the melt-refining process is not applied. The numerical analyses also show that in scenarios that include making up fuel losses during melt refining, the core is fed with more natural uranium make-up fuel during operation and thus has lower burnup. Other characteristics, such as power density distributions, neutron flux profiles, and fertile and fissile nuclide density distributions, are all stable during operation.

Keywords:

• Rotational Fuel-Shuffling Breed-and-Burn fast reactor
• rotational fuel-shuffling scheme
• melt-refining process
• burnup performance

I. INTRODUCTION

Natural uranium contains 0.72 wt% of the fissile isotope ²³⁵U. Present-day light water reactors (LWRs) are usually fed 3 to 5 wt% enriched ²³⁵U. Most current LWRs utilize about 0.6% natural uranium. However, it may be possible to enhance uranium utilization using a special class of fast reactors with the breed-and-burn (B&B) mode of operation, referred to as B&B reactors. As the result of previous study,¹ it is neutronically feasible to establish a B&B mode of operation in a fast reactor that can be safely operated up to an average burnup of at least ~20% fissions per initial metal atom (FIMA), and the uranium utilization of such B&B reactors is ~40 times that of LWRs. The B&B mode of operation, first proposed by Feinberg in 1958 (Ref. 2), is made self-sustainable by producing fissile materials such as ²³⁹Pu (or ²³³Pu) from fertile materials such as ²³⁸U (or ²³²Th) during operation. In a B&B reactor, the fissile elements are first bred into the fuel by neutrons produced in the reactor. The resulting bred fuel is then directly burned in the same reactor to sustain the chain reaction and to supply neutrons for breeding additional fuel. Thereafter, the B&B core is able to continue operating while being fed with depleted or natural uranium only. Therefore, B&B reactors can operate using primarily fertile fuel but also reload fuel, such as natural or depleted uranium, low-enriched uranium, used LWR fuel, or thorium.

Breed-and-burn reactors have been intensively studied as well at the University of California, Berkeley (UCB), in Project No. 09-769 (Ref. 1) and Project No. 12-3486 (Ref. 3); at the Tokyo Institute of Technology with the CANDLE burning fast reactor⁴; and at TerraPower with the TerraPower Traveling Wave reactor.⁵ Unlike the cores in other classes of fast reactors, B&B reactors can operate with loading fuel of fertile materials with natural content. Therefore, B&B reactors require high neutron economy to maintain criticality in operation. The feed fuel must be burned to a sufficient level such that the rate of neutron production increases with burnup and overtakes that of neutron absorption in operation. That is, the generated neutrons are equal (or slightly larger) than the total number of neutrons lost, i.e., lost to absorption and also leakage for sustaining the chain reaction that can contribute to the B&B reactor.

To improve neutron economy and achieve both criticality with the B&B mode of operation and a stable power profile in the core, the Rotational Fuel-Shuffling Breed-and-Burn (RFBB) fast reactor has been proposed by a research group at the Tokyo Institute of Technology.^6,7 In this fuel-shuffling concept, fresh fuel is loaded from the periphery of the core and eventually moves toward the center. The fuel moves outward and is then discharged near the periphery of the core. As a result, the B&B region remains stationary, and the power profile and neutron flux distribution are thereby almost unchanged during operation in the equilibrium state. In RFBB operation, the high-reactivity fuels are located at the core center, which is the high-neutron-importance region.

A previous study shows that it is feasible to establish the B&B mode of operation with rotational fuel shuffling in the Super Power Reactor Innovative Small Module (S-PRISM) reactor core based on neutronic and thermal-hydraulic analyses.⁸ The S-PRISM core design is well known as a reference design for a detailed and practical advanced reactor system design. The S-PRISM core design was developed by General Electric⁹ and chosen as a reference core in other projects such as Project No. 09-769 (Ref. 1) and Project No. 12-3486 (Ref. 3) performed at the UCB.

The previous study⁸ demonstrated the feasibility of applying the rotational fuel-shuffling concept to a viable reactor design that is based on the S-PRISM core and/or that could fit within the S-PRISM reactor vessel developed by General Electric. To achieve criticality in the B&B strategy, the core height has been increased from the reference 101.6 to 200 cm, and the pitch-to-diameter (P/D) ratio has been decreased from the reference 1.191 to 1.086. In addition, the core has used the binary metallic fuel U-Zr with 2 wt% zirconium.⁸ As a consequence, the core generates 400 MW(thermal) of power with the rotational fuel-shuffling scheme. The shuffling interval is 1125 to 1250 days, and the possible axial average discharged burnup is from 274.8 to 305.3 GWd/tonne HM. The reference S-PRISM core power level is 1000 MW(thermal) whereas the RFBB core in this study has a power level of 400 MW(thermal). This difference is due to the significantly higher ratio of core average to peak power density of the reference S-PRISM core, and it ensures that the design of the RFBB core would meet the design constraints as in the previous study.⁸

However, because of the long fuel cycle length (FCL) and long resident time of fuel in the core during operation, its fuel cladding would reach radiation damage of nearly 2900 displacements per atom (DPA). So far, the maximum radiation damage that cladding and structural materials have been exposed to is approximately 200 DPA of radiation damage, which occurred in a test at the Fast Flux Test Facility.¹⁰ Therefore, high DPA radiation damage from the discharged fuels must be considered in the development of a more practical and realistic design.

As mentioned in Ref. 8, this issue of high DPA radiation damage could be overcome by either of two promising approaches: One is to shorten the operational time and to reclad the fuel cladding, and the other is to apply a melt-refining process similar to the one experimented with during the Experimental Breeder Reactor-II (EBR-II) project for fuel reconditioning. In comparison with the first approach, the second not only improves burnup with fuel reconditioning but also is attractive in terms of proliferation concerns. The melt-refining process, which is also suitable for metallic fuel, is a proven strategy, having been successfully used at Argonne National Laboratory to recycle EBR-II fuel.^11,12 This melt-refining process has also been selected in other B&B reactor studies to perform fuel reconditioning when cladding reaches the maximum radiation damage.^13,14 The purposes of the present study are to clarify the effects of the melt-refining process on the performance of sodium-cooled B&B reactors with a rotational fuel-shuffling scheme, called rotational fuel-shuffling B&B fast reactors with metal fuel and sodium coolant (RFBB-MS), and to address the fuel cladding integrity issue due to radiation displacement damage and to maintain fuel element integrity under a high-burnup condition.

II. METHODOLOGY

II.A. Reactor Concept

The RFBB studied in this paper is conceptually similar to the core in the previous work⁸ and to the S-PRISM core design by General Electric⁹ and by Argonne National Laboratory in their recent studies of the Advanced Burner Reactor (ABR) (Refs. 15 and 16). It is sodium cooled and uses the binary metallic fuel U-Zr with 2 wt% zirconium. The initially unirradiated fuel nominal density is 17.8 g/cm³ (Ref. 17), and a smear factor of 0.75 is assumed to accommodate the fuel swelling with burnup. To maintain criticality in the B&B mode of operation of a reactor with the same core radius as the S-PRISM core, the original core layout is modified; that is, fuel assemblies replace the 12 control assemblies and 6 gas expansion modules, and the fuel assembly at the core center is filled with coolant. As a result of this modification, the metal-fueled core layout in this study is composed of 252 fuel assemblies, 1 coolant channel, 126 reflector assemblies, and 72 shield assemblies.⁸ The cladding material is the ferritic-martensitic alloy HT-9. The core height is increased from the reference of the S-PRISM core, 101.6 to 200 cm, and the P/D ratio is decreased from the reference, 1.191 to 1.086 (Ref. 8). The core layout is presented in Fig. 1. The active core is surrounded by two layers of radial assembly reflectors and one radial assembly shielding layer, and its composition is as those of the metallic fuel version of the S-PRISM core developed by General Electric.^9,16,18

Fig. 1. Simplified layout of the B&B core and surrounding regions.

II.B. Melt-Refining Process

To keep the fuel cycle as proliferation resistant as possible, and considering that actinide separation is undesirable, the melt-refining process was developed for metallic fuel during the EBR-II project.¹⁹ This fuel-reconditioning process involves several operations, including disassembly of the reactor core subassemblies, decladding, melt-refining proper, refabrication (injection casting), canning and bonding, and reassembly of reactor core subassemblies. During this melt-refining process, the fuels undergo several stages. It is cooled for a sufficient period of time after the reactor is shut down and then transferred to the processing plant, after which the fuel-pin cladding is cut at opposite sides of the pin by roll cutters so that the cladding is left over the fuel pin. The fuel pin is then chopped to the appropriate length before being reconditioned in the melt-refining stage.¹⁹

In the melt-refining stage, the fuels are decladded and melted at about 1300°C for several hours under a high-purity argon atmosphere. The volatile fission elements evaporate, and the reactive fission elements are removed by oxidation with the zirconia of the crucible. According to a previous report,¹⁹ this process can remove nearly 100% of Br, Kr, Rb, Cd, I, Xe, and Cs and at least 95% of Sr, Y, Te, Ba, and rare earths (lanthanides). Thorium and americium are also oxidized with zirconia, and 95% of thorium and americium is removed from the fuel. A small fraction of other actinides would also be left in the crucible. The refined fuel obtained by melt refining is then processed in the first step of new fuel refabrication, referred to as injection casting of new fuel pins. The purpose is to convert the bulk fuel feed material into sound cylindrical castings, called fuel slugs, of proper lengths to produce long fuel pins refabricated with a new clad. The new fuel pins are fabricated into new fuel assemblies that can then be reloaded into the core for a new burnup cycle. It is therefore that the rotational fuel-shuffling scheme associated with the melt-refining process could provide a good measure of alleviating proliferation concerns. In addition, it is feasible to use natural uranium only to operate the B&B reactor and to reduce the waste disposal burden and radiotoxicity in its spent fuels as well.

In the melt-refining process experimented with in the EBR-II program, several percent of the plutonium and other actinides remains in the crud of the zirconia crucible. In order to investigate the effects of the fraction fission products (FPs) that are removed or lost in the fuel recycling process, this study considers the significant loss of TRU due to the melt-refining process; it is assumed that 1% and 10% of all actinides are not recovered, as shown in Table I (Ref. 1).

TABLE I Actinides and FP Removal Fractions in the Melt-Refining Process

	TRU Losses
Nuclides	0%	1%	10%
U	–	1%	10%
Th	95%	95%	95%
Am	95%	95%	95%
Other TRU	–	1%	10%
FPs	100% Br, Kr, Rb, Cd, I, Cs
	95% Sr, Y, Te, Ba, La-Lu
Gas FPs	100% H, He, N, O, F, Ne, Cl, Ar, Kr, Xe, Rn

II.C. Calculation Method

The numerical core simulation is done using the Monte Carlo Serpent neutronic code²⁰ with the ENDF-B/VII nuclear data library.²¹ Five thousand neutron histories per cycle and 200 active cycles, while skipping the first 20 cycles for statistical treatment, are used to obtain a target statistical error in k_eff of ~150 pcm. The burnup calculation is carried out for a symmetrical one-sixth core region in the azimuthal direction. The axial direction is symmetrically divided into 11 burnup regions as in the previous study.⁸ In the present study, we focus on the burnup performance of the reactor in the equilibrium state. The period of time in which fuel assemblies are either removed from or added to the core is defined as one FCL. The averaged fuel burnup in the equilibrium state is defined as follows:

$\begin{array}{rl}& AveragefuelburnupinMWd/tonne\\ & =\left[corepowerinMW\left(thermal\right)\right]\times \left(FCLindays\right)\\ & /\left(totalloadeduraniumpercycleintons\right).\end{array}$

The shuffling scheme discussed in this section is the rotational fuel-shuffling scheme as schematized in Fig. 2. In this figure, each fuel assembly position is assigned a position identification number (ID), and the fuel-shuffling flow is from fuel assembly position IDs 1 to 42. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 1. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from 1 to 25), then moved outward, and discharged after 17 fuel-shuffling steps, at position 42.

Fig. 2. Fuel cell model for thermal-hydraulic analyses.

The burnup analysis is performed assuming that recycling takes place when the radiation damage of the clad (that is, the fluence of neutrons with energy exceeding 0.1 MeV) approaches 200 DPA. At that time, natural uranium is added to the fuel to make up for the gaseous and volatile FPs and/or losses of fuel that got out during the melt-refining process. To achieve the equilibrium state of the B&B reactor, a computer interface program was previously developed to automatically conduct core burnup calculations from cycle to cycle. In this study, the first core is loaded with the fuel of natural uranium. The real startup core needs fissile material. To design the startup core is one of the future works, which are in progress. The calculation procedure is performed as follows⁸:

1. Design parameters such as core size, fuel assemblies, fuel-shuffling pattern, operational conditions, and FCL are prepared in the input file.

2. The core burnup calculation is performed to obtain end-of-cycle fuel compositions.

3. The melt-refining operation is performed for the selected fuel assemblies whose maximum value of radiation damage of the fuel clads approaches 200 DPA.

4. The input file is updated with the new fuel compositions obtained in step 3, along with the fuel-shuffling pattern. The core burnup calculation for the next cycle is performed using the new input file.

5. Steps 2 and 4 are repeated until the core reaches an equilibrium condition, as determined based on the convergence of the k_eff, neutron flux distribution, power density distribution, and nuclide number density values of some isotopes such as ²³⁹Pu, ²⁴¹Pu, ²³⁵U, and ²³⁸U.

Thermal-hydraulic analyses are conducted in the steady-state regime to make sure that the core design obeys a number of constraints such as core inlet and outlet temperatures, core pressure drop, maximal core coolant velocity, peak cladding temperature, and peak fuel temperature. In thermal-hydraulic analyses, the hottest subchannel in the core is chosen for thermal-hydraulic analysis to determine whether or not the reactor satisfies the desired design constraints. The thermal-hydraulic analysis is performed using COMSOL 5.4 multiphysics software.²² The geometry model is developed with two-dimensional axisymmetry with R-Z coordinates consisting of the fuel slug, bond layer, cladding, coolant channel, lower end plug, plenum, and upper end plug, as in Refs. 8, 23, 24, and 25. The model geometry of the subchannel analysis for the whole length of the reactor is provided, as can be seen in Fig. 3. The hexagonal cell lattice is simplified so that it is equivalent to a cylinder. This cell lattice model is the hottest channel of a fuel pin in the core. The sodium coolant flows vertically upward through the cooling channel. In the thermal-hydraulic analysis, the power distribution of the fuel rod in the axial direction is obtained from the neutronic analysis.

Fig. 3. The fuel-shuffling pattern and position IDs of fuel assemblies in the core. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 1. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from positions 1 to 25) and then moved outward and discharged after 17 fuel-shuffling steps at position 42.

In this study, the core investigated in the previous work⁸ is chosen as the reference core, called “Reference.” The core height is 200 cm, and the P/D ratio is 1.086. The core uses the binary metallic fuel U-Zr with 2 wt% zirconium. In previous analyses, the core generated 400 MW(thermal) in a rotational fuel-shuffling scheme with a shuffling interval, i.e., FCL, of 1125 days and a possible average discharged burnup of 274.8 GWd/tonne HM. The effects of the melt-refining process on the performance of the RFBB are investigated under five scenarios and compared with the Reference scenario in which the melt-refining process is not applied to the core. These five scenarios are as follows:

1. Scenario I, “Homogenization,” involves only fuel homogenization and without the removal of FPs during the melt-refining process. This is because the fuels are mixed during the melt-refining stage at about 1300°C for several hours under a high-purity argon atmosphere. As a consequence, the burnup characteristics can be affected by mixed-only fuel during the melt-refining stage of the melt-refining process.

2. Scenario II, “Homogenization and FP Removal,” involves homogenization with the removal of fission products with the similar fraction of the melt-refining process developed in the EBR-II project. In this scenario, the removal of fission products as in the original melt-refining process developed in the EBR-II project is considered to understand its effects on the burnup characteristics of the core.

3. Scenario III, “Homogenization, FP Removal, and Make-Up,” is similar to Scenario II, but natural uranium compensates for the FP losses by burnup and fission product removals during the melt-refining process to conserve the unchanged fuel amount in the fuel pins.

4. Scenario IV, “With 1% TRU Losses,” is similar to Scenario III but is evaluated with 1% of all actinides not recovered.

5. Scenario V, “With 10% TRU Losses,” is similar to Scenario III but is evaluated with 10% of all actinides not recovered.

Scenarios IV and V are investigated because as reported previously,¹⁹ at the melt-refining stage at maximum charge (~11 kg/cycle), ~10% of the melt remains as skull and a larger fraction remains at smaller charges. To investigate the effects of the fraction and type of solid FPs removed in the fuel recycling process, this study considers significant losses (1% and 10%) of actinides as not recovered due to the melt-refining process, as shown in Table I (Ref. 2).

For upper-bound estimation, fuel shuffling is assumed to be instantaneous. Regarding the cooling fuel during the melt-refining process, two cooling intervals are considered. Cooling intervals are taken into account before the melt-refining process (T_c) and after the melt-refining process (T_w). In this study, the cooling time T_c taken before the melt-refining process is conservatively assumed to be 9.125 days (i.e, 2.5 years). The latter cooling time T_w taken after the melt-refining process thereby is equal to (1 FCL – T_c). The changes in nuclide densities during the cooling time periods are calculated considering the radioactive decay of nuclides using an in-house program written in Python script specifically designed to obtain these nuclide densities as in our previous studies.^23,24 It is possible to operate the core continuously by following this procedure. That is, when a fuel assembly is removed for melt refining, a fuel assembly that has already been melt refined is used as the fuel assembly to be loaded into the core instead of that fuel assembly. The melt-refined fuel assembly is then loaded into the core in place of the fuel assembly that was removed from the core for melt refining during the next shuffling. The operating time of the reactor between the fuel shufflings is equal to the melt-refining process time, similar to the case in previous research.²⁴ At a shuffling process, some fuel assemblies are removed from the core for the melt-refining process. At the locations of removed fuel assemblies, the melt-refined fuel assemblies that were removed in the previous shuffling are loaded. The removed fuel assemblies are melt refined during the fuel cycle. At the next shuffling, some fuel assemblies are removed. At the locations of removed fuel assemblies, the melt-refined fuel assemblies are loaded. The procedure is repeated in the equilibrium condition. How to manage the startup core can be a topic of future study.

III. RESULTS AND DISCUSSION

As mentioned in Sec. II, the melt-refining process is applied to recycle the metallic fuel elements and to maintain the cladding material integrity up to the previously demonstrated radiation damage constraint of a 200 DPA cladding level. In this study, 100 DPA corresponds to a fast neutron fluence of 2.2 × 10²³ n/cm² as calibrated in the previous study.^8,23,24,25 The results of the reference core calculations show that the fuel cladding would reach nearly 2900 DPA of radiation damage at the end of equilibrium cycle (EOEC), i.e., at the final burnup step in the equilibrium cycle. In this procedure, the equilibrium condition is determined based on the convergence of the k_eff, neutron flux distribution, power density distribution, and nuclide number density values of some isotopes such as ²³⁹Pu, ²⁴¹Pu, ²³⁵U, and ²³⁸U. This high-radiation damage to the cladding is due to the long FCL and long resident time of fuel in the core during operation.

The radiation damage to the cladding in the Reference core and the expected values by the melt-refining process are shown in Fig. 4. It can be seen that with an FCL of 1125 days, the maximum radiation damage to the cladding in some fuel assemblies is much higher than the constraint value. Once the melt-refining process is applied at the EOEC for some proper fuel assemblies, the peak radiation damage to the cladding is conservatively expected to reduce the approximated constraint value of 200 DPA. It is found that the fuel assemblies that should undergo the melt-refining process are those with IDs of 14, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 35, and 40. Most of these 15 fuel assemblies that need to be reprocessed are located near the core center. This is because this core region, which is a high-neutron-flux region that is a high-neutron-flux region and a high-neutron-importance region based on the one-group perturbation theory, is located at the core center in the equilibrium cycle.^7,8

Fig. 4. The maximum radiation damage to the Reference core and its expected DPA value with the melt-refining process. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 1. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from positions 1 to 25) and then moved outward and discharged after 17 fuel-shuffling steps at position 42.

The calculations for the cores undergoing melt refining begin with the fuel compositions at the equilibrium state of the Reference core. The minimum values of k_eff over the cycle in the equilibrium state of the cores are compared in Fig. 5. The core of the “With 10% TRU losses” is subcritical because of the high percentage of actinides not recovered during the melt-refining process. All of the other cores achieve criticality at the equilibrium state. In comparison with that of the Reference core, the k_eff values of the cores increase during the course of the equilibrium cycles. A larger excess reactivity is obtained for the core for which the fuel losses are compensated during the melt-refining process. This high excess reactivity is caused by the addition of natural uranium (mostly ²³⁸U) to compensate for the fuel losses during the melt-refining process, which results in the generation of more fissile material (²³⁹Pu) in the cores, as shown in Figs. 6 and 7. The cores with higher levels of unrecovered actinides during the melt-refining process require larger amounts of compensating natural uranium and have less fissile material content (²³⁹Pu) at both the beginning of equilibrium cycle (BOEC) and EOEC, i.e., at the first and final burnup steps in the equilibrium cycle, as shown in Figs. 6 and 7.

Fig. 5. Changes in k_eff values of the cores in the equilibrium cycle.

Fig. 6. Axial-averaged nuclide number densities of ²³⁸U and ²³⁹Pu at the BOEC in the cores at the equilibrium cycle. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 1. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from positions 1 to 25) and then moved outward and discharged after 17 fuel-shuffling steps at position 42.

Fig. 7. Axial-averaged nuclide number densities of ²³⁸U and ²³⁹Pu at the EOEC in the cores at the equilibrium cycle. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 42. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from positions 1 to 25) and then moved outward and discharged after 17 fuel-shuffling steps at position 42.

To investigate whether or not the core of the “With 10% TRU Losses” can be critical, the FCL, i.e., the shuffling interval time, is adjusted in the range of 1125 to 2600 days. The changes in k_eff values at the equilibrium state are shown in Fig. 8. It is found that these cores can reach an equilibrium state but remain not critical throughout the equilibrium cycle. This suggests that the core design should be modified and/or that the fuel losses unrecovered during the melt-refining process need to be reduced.

Fig. 8. Changes in k_eff values with different FCLs of the core with 10% TRU losses at the equilibrium cycle.

The high-neutron-flux and high-power-density region is retained at the core center region, as shown in Figs. 9 and 10. The power distributions peak at the core center and gradually decrease in the radial direction, as presented in Figs. 11 and 12. The cores that undergo the melt-refining process have slightly lower maximum neutron flux and slightly lower power density because of the effects of both fuel homogenization and removal of FPs. It is clear that the neutron fluxes and the power density distributions are essentially constant shaped from BOEC to EOEC during the equilibrium cycle. This would be a potentially easy and effective way to control the coolant flow rate of each fuel assembly. Because of the gradient of the radial power distribution as shown in Figs. 10, 11, and 12, the B&B reactor would adopt the orifice concept. In the orifice concept, the coolant flow rate of each fuel assembly will be adjusted by a coolant inlet orifice according to the assembly power as a function of the assembly location. In order to reduce the high change in the flow rate in the core, flow zoning devices, such as in research by Prakash et al. in 2011 (Ref. 26), would be applied to the current core design.

Fig. 9. The maximum neutron flux distributions in the cores at the equilibrium cycle.

Fig. 10. Axial average power density distributions in the cores at the equilibrium cycle.

Fig. 11. The maximum neutron fluxes and average power density distributions at the BOEC in the cores at the equilibrium cycle.

Fig. 12. The maximum neutron fluxes and average power density distributions at the EOEC in the cores at the equilibrium cycle.

As described in Sec. II, once cladding reaches the radiation damage limit, fuel reconditioning has been performed. As a consequence, the radiation damage to the cladding is reduced as shown in Fig. 13. The analysis results reveal that the maximal cladding radiation damage in the critical cores is reduced from 2900 DPA in the Reference core to about 226 DPA in the melt-refining core. This maximum DPA value is slightly higher than the radiation damage constraint of 200 DPA but is still acceptable.

Fig. 13. Maximum radiation damage to the cladding at the EOEC in the cores at the equilibrium cycle. In this rotational fuel-shuffling scheme, a fresh fuel assembly is loaded at position 1. The fuel assembly is moved inward after the first 25 fuel-shuffling steps (from positions 1 to 25) and then moved outward and discharged after 17 fuel-shuffling steps at position 42.

Table II summarizes the analysis results of the cores. The results show that the coolant inlet/outlet temperature, the maximum coolant velocity, the maximum cladding and fuel temperatures, and the maximum core coolant pressure drop are all lower than the design constraint values. This preliminary analysis indicates the feasibility of establishing the B&B mode of operation with rotational fuel shuffling in the S-PRISM core and of applying the melt-refining process. Compensating for fuel loss and FP removal in the melt-refined process results in more uranium loading per cycle and therefore in reduced burnup relative to scenarios that do not compensate for fuel constituent losses in the melt refining.

TABLE II Summary of Analysis Results of the Cores in the Equilibrium Cycle*

Parameters	With 10% TRU Losses	With 1% TRU Losses	Homogenization, FP Removal, and Make-Up	Homogenization and FP Removal	Homogenization	Reference
Fuel cycle length (day)	1125.0	1125.0	1125.0	1125.0	1125.0	1125.0
Cooling time (day)	912.5	912.5	912.5	912.5	912.5	—
Waiting time (day)	212.5	212.5	212.5	212.5	212.5	—
keff at BOEC	0.9039	1.0200	1.0339	1.0336	1.0053	1.0011
keff at EOEC	0.9478	1.0364	1.0484	1.0445	1.0133	1.0039
Reactivity swing (%∆k/k)	4.86	1.61	1.41	1.06	0.80	0.28
Number of reprocessing fuel assemblies	15	15	15	15	15	0
Total loaded fresh HM per cycle (tonne HM)	1.64	1.64	1.64	1.64	1.64	1.64
Make-up HM per cycle (tonne HM)	0.43	0.09	0.05	0.00	0.00	0.00
Axial-averaged discharged burnup (GWd/tonne Unat)	217.7	261.0	267.0	274.8	274.8	274.8
Average discharged burnup (FIMA)	18.71	21.84	22.33	38.72	38.64	38.37
Peak radiation damage (200 DPA)	268	226	225	226	225	2900
Peak fast neutron fluence (4.0E+23 n/cm^2)	5.36E+23	4.52E+23	4.50E+23	4.53E+23	4.50E+23	5.80E+24
Peak axial power density (450 W/cm^3)	415.3	435.2	425.8	451.3	476.9	403.2
Peak axial linear power density (W/cm)	97.8	102.5	100.2	106.2	112.3	94.9
Peak fast neutron flux (n/cm^Citation2‧s)	4.21E+15	3.92E+15	3.84E+15	4.19E+15	4.43E+15	4.41E+15
Coolant velocity (12 m/s)	6.15	6.15	6.15	6.15	6.15	6.15
Inlet coolant temperature (628 K)	628.2	628.2	628.2	628.2	628.2	628.2
Mixed outlet coolant temperature (783 to 853 K)	791.0	801.0	799.8	812.6	821.8	783.5
Maximum cladding temperature (923 K)	792.5	802.8	801.5	814.8	823.8	784.8
Maximum fuel temperature (1073 K)	802.2	812.6	812.1	825.4	835.8	794.3
Core coolant pressure drop (1.0 MPa)	0.881	0.880	0.880	0.878	0.877	0.883
Average discharged atoms (atom/b‧cm)
^235U	1.0023E-04	4.1928E-05	3.2606E-05	1.1802E-05	1.2483E-05	1.5859E-05
^238U	3.5827E-02	3.4500E-02	3.4295E-02	2.7071E-02	2.7104E-02	2.7221E-02
^238Pu	1.2829E-05	2.2712E-05	2.4130E-05	2.3783E-05	4.7006E-05	4.1848E-05
^239Pu	2.8538E-03	3.6857E-03	3.8169E-03	3.3048E-03	3.3257E-03	3.2205E-03
^240Pu	5.5400E-04	9.8656E-04	1.0558E-03	1.0374E-03	1.0280E-03	9.8640E-04
^241Pu	2.1245E-05	3.5781E-05	3.8015E-05	3.9610E-05	3.7120E-05	4.4835E-05
^242Pu	6.4724E-06	1.2737E-05	1.3544E-05	1.5309E-05	2.4056E-05	2.6813E-05
^244Pu	3.3852E-11	5.5576E-11	5.7350E-11	7.5064E-11	4.7698E-10	7.9883E-10

*Values in the brackets are the constraint values.

IV. CONCLUSIONS

This study investigates the effects of the melt-refining process on the performance of sodium-cooled B&B reactors, called RFBB-MS reactors, with a rotational fuel-shuffling scheme that addresses fuel cladding integrity due to radiation displacement damage and maintains fuel element integrity under a high-burnup condition. The design is based on a commercial-scale fast burner reactor (the S-PRISM reactor). Five scenarios of a core undergoing the melt-refining process are investigated and compared to a core without the melt-refining process: Scenario I, “Homogenization,” is without the removal of FPs during the melt-refining process; Scenario II, “Homogenization and FP Removal,” includes the removal of FPs to a fraction similar to that in the melt-refining process developed in the EBR-II project; Scenario III, “Homogenization, FP Removal, and Make-Up,” is similar to Scenario II but makes up for fuel losses with natural uranium; Scenario IV, “With 1% TRU Losses,” is similar to Scenario III but is evaluated with 1% of actinides not recovered; and Scenario V, “With 10% TRU Losses,” is similar to Scenario III but with 10% of actinides not recovered. It is found that it is neutronically and thermal hydraulically feasible to establish a B&B mode with the rotational fuel-shuffling scheme by reconditioning the fuel whenever its cladding reaches the proven 200 DPA radiation damage limit. In Scenario V, the core is subcritical due to the high percentage of actinides not recovered during the melt-refining process. In all of the other scenarios, the cores are critical. Scenario IV shows some excess reactivity, so the reactor can be critical even if the losses are between 1% and 10%. The numerical analyses also show that the cores in scenarios that include making up fuel losses during the melt-refining process have lower burnup than the other cores due to a larger amount of natural uranium fed each cycle accounting for FP and actinide losses during the melt-refining process. Other characteristics, such as power density distributions, neutron flux profiles, and fertile and fissile nuclide density distributions, are all stable during operation. The analysis results show that a sodium-cooled metal fuel RFBB would be feasible because its melt-refining process limits the DPA of fuel cladding to only slightly higher than 200 DPA. In this study, to simplify the core design and obtain upper-bound estimates, there are no reactivity control assemblies in the core. In future work, further analyses will simulate and investigate a practical reactor design with this concept such as design of the reactivity control systems and the initial core configuration, which are also needed. Analyses of reactivity feedback of the coolant temperature reactivity coefficient, coolant voiding reactivity, fuel temperature reactivity coefficient, and power coefficient are also going to be carried out.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National University of Mongolia under grant number P2022-4374; and by the Vietnam National Foundation for Science and Technology Development under grant number 103.04-2020.06.