NEUTRONIC ANALYSIS ON MOLTEN SALT REACTOR FUJI-12 USING 235 U AS FISSILE MATERIAL IN LiF-BeF 2 -UF 4 FUEL

Neutronic analysis on the Molten Salt Reactor FUJI-12 using the fissile material 235 U in LiF-BeF 2 -UF 4 has been carried out. The problem faced in the use of thorium-based fuel is that the amount of 233 U is small and not available in nature. 233 U was produced through the 232 Th breeding at a cost of $46 million/kg. That is a very high price when compared to 235 U enrichment, which is only $100/kg. The MSR FUJI-12 used in this study is a generation IV reactor with a mixture of liquid salt fuel LiF-BeF 2 -ThF 4 -UF 4 and thorium-based fuel ( 232 Th+ 233 U). In this study, neutronic analysis was carried out by replacing thorium-based fuel with uranium-based fuel ( 235 U+ 238 U). Neutronic analysis was performed using the OpenMC 0.13.0 code, which is a Monte Carlo simulation-based neutron analysis code. The nuclear data library used for neutronic calculations is ENDF B-VII/1. The fuel is used in a LiF-BeF 2 -UF 4 molten salt mixture with three eutectic compositions: fuel 1, fuel 2, and fuel 3. Each fuel composition is optimized by enriching 235 U in UF 4 by 3 % to 8 %. The optimization results show the stability of the reactor criticality value, which is the main parameter so that the reactor can operate for the specified time. The optimization results show that fuel 1 cannot reach its optimal state in each variation of 235 U enrichment. Fuel 2 and fuel 3 can reach optimal conditions at a minimum enrichment of 8 % and 7 % 235 U. The results of the analysis of the distribution of the neutron flux in the reactor core show the distribution of nuclear reactions that occur in the core. The distribution of flux values in fuel 1 shows that the fission chain reaction is not running perfectly. Fuel 2 and fuel 3 are more stable by maintaining maximum flux at the center of the reactor core


Introduction
The demand for electrical energy in 2021 increased by 6 % (over 1,500 TWh) and this was the largest absolute increase ever since the recovery from the financial crisis in 2010. The increase is related to the rapid recovery from the Covid-19 pandemic in 2021. The growth in electricity demand is expected to continue at 3 % to 4 % in 2022 and 2 % in 2024 [1]. The growth in electricity demand in 2021 is followed by a growth in the number of coal power plants by 9 % and fulfills almost half of the growth in electricity demand in 2021 [2]. The use of coal drives global electricity sector emissions to grow by close to 7 %, contributing more than 800 Mt of CO 2 emission growth. By 2024, it is estimated that emissions from coal and gas power plants combined can reach more than 13 Gt CO 2 [1].
Nuclear power plant is one of the renewable energy alternatives that can replace the role of coal in balancing the current world's growing demand for electrical energy. Based on the latest data, there are 440 nuclear reactors in operation and spread in 32 countries with a generated capacity of 39.1119 MWe [3]. MSR FUJI-12 is one type of MSR reactor (Molten Salt Reactor), which is included in one of the generation IV reactor designs. This reactor was developed by Japan with the smallest reactor core size when compared to other similar nuclear reactors [4].
Energy-saving technologies and equipment 7 The availability of 233 U is very low because it is not a natural material and must be produced through 232 Th breeding, so it is very difficult to obtain. Another problem faced in the use of 232 Th+ 233 U fuel is that it is more expensive to produce than natural uranium-based fuels. The production cost for 233 U is $46 million/kg, which is very high when compared to 235 U enrichment, which is only $100/kg [5,6]. The manufacturing process for thorium-based fuels is also more difficult, which can also increase the cost of manufacturing fuel in MSR. Uranium materials that occur in nature are 234 U, 235 U and 238 U. The combination of 235 U and 238 U is a mixture that is commonly used as a fissile and fertile material in nuclear reactor fuels. An investigation to replace the 232 Th+ 233 Ubased MSR FUJI-12 fuel with 238 U+ 235 U needs to be carried out. This is based on the potential for reducing the production cost of the MSR FUJI-12 due to the 233 U production process. Manufacturing thorium-based fuels is also more difficult than uranium, so replacing thorium-based fuels also reduces production costs and simplifies the manufacturing process. In addition, the moderator temperature reactivity coefficient value for the 238 U+ 235 U fuel is considered safer for nuclear reactors. Therefore, it is necessary to conduct a neutronic analysis on the use of 235 U and 238 U in the LiF-BeF 2 -UF 4 fuel mixture as a cheaper and safer MSR FUJI-12 fuel solution.

Literature review and problem statement
The paper [7] presents a comparison of the utilization of 233 U and plutonium in MSR on thorium-based MSR fuel. The results showed that the average number of neutrons produced by the 233 U fuel per neutron absorbed in the thermal energy region was higher than that of plutonium. This shows that it takes less concentration of 233 U to operate the FUJI-12 MSR reactor at a power of 350 MWt compared to the use of plutonium, either in reactor grade or weapon grade enrichment. The problem is that using 233 U in 232 Th-based fuel is still very expensive. This is due to the large production cost of 233 U and the relatively more difficult manufacturing cost of thorium-based fuel.
An approach to replace 233 U with 235 U in 232 Th-based fuels has been implemented in [8]. The results show that the operation of 50 MWt in a mini-FUJI reactor for 5 years can be carried out with a minimum enrichment of 95 % 235 U with a UF 4 composition of 1.96 %. This study shows that it is possible to replace 233 U with 235 U in 232 Th-based fuels. The problem is that the 235 U enrichment required is very large and is in the weapon grade uranium range. This should not be applied to nuclear power plants that are only allowed to enrich the reactor grade uranium range.
The research [9] conducted an approach by comparing fuels based on ( 232 Th+ 233 U)O 2 and ( 235 U+ 238 U)O 2 in the PWR Russian VVER-1200 reactor using the SERPENT code. The results for operating power of 3200 MWt show that fuel based on 232 Th+ 233 U has a lower reproduction factor and number of neutron production than fuel based on 235 U+ 238 U for an operating duration of 1440 days. In addition, it is shown that the fuel based on 235 U+ 235 U has a higher moderator temperature reactivity coefficient value. This research shows that uranium-based fuels have the potential to replace thorium-based fuels. In addition, based on the moderator temperature reactivity coefficient, fuel based on 235 U+ 235 U is safer than that based on 232 Th+ 233 U.
An approach to MSR has been carried out in [10] by comparing LiF-BeF 2 -UF 4 (FLiBe) and NaF-BeF 2 -ThF 4 -UF 4 (FNaBe) fuels in the NERTHUS Thermal Molten Salt Reactor. The total amount of uranium required for FLiBe is greater than for FNaBe. The 235 U enrichment in FLiBe was smaller (2.0935 %) than in FNaBe (19.4512 %). But for continuous power operation, the fuel refueling ratio of FLiBe is much smaller than that of FNaBe. The results of this study [10] are also in line with research [9] with a higher moderator temperature reactivity coefficient value for the beginning of the reactor operation and the end of the reactor operation. Another study [11] compared the corrosiveness of several variations of molten salt fuel in MSR. The level of corrosiveness and LiF-BeF 2 -UF 4 in Hastelloy-N alloy for each variation is 0.5-1.0 m/year, while for LiF-BeF 2 -ThF 4 -UF 4 -0.4-3.5 m/year. This value indicates that the corrosiveness of LiF-BeF 2 -UF 4 is relatively smaller. Based on the research [7][8][9][10][11], identification of the use of fuel based on 235 U+ 238 U in the LiF-BeF 2 -UF 4 fuel mixture in the MSR FUJI-12 reactor needs to be done.

The aim and objectives of the study
The aim of the study is to replace FUJI-12 MSR based on 232 Th+ 233 U with 238 U+ 235 U.
To achieve this aim, the following objectives are accomplished: -to calculate the eutectic composition of LiF-BeF 2 -UF 4 , which has the potential to be used as fuel for MSR FUJI-12; -to calculate the flux distribution in the reactor core of MSR FUJI-12 with a power of 350 MWt and an operating time of 5 years with LiF-BeF 2 -UF 2 fuel.

1. Research procedures
The object of this research is the variation of the eutectic composition of the LiF-BeF 2 -UF 4 fuel and the variation of 235 U enrichment in UF 4 . This research focuses on neutronic analysis using the OpenMC 0.13.0 code and nuclear data library ENDF B-VII/1. The OpenMC code is an open-source neutronic analysis code based on a Monte Carlo calculation simulation. The research proceeded with the flow following Fig. 1.
The optimal operation in Fig. 1 is obtained by looking at the graph of the k-eff value for the reactor operation for 5 years. The optimal composition is a variation of 235 U enrichment that can maintain the k-eff value near the critical state (k-eff = 1) and does not decrease in the subcritical state (k-eff < 1). This situation must last from the start of the reactor operation to the end of the reactor operation.

2. Monte Carlo method
Neutron analysis is always related to the neutron transport equation. The equation states that the rate of variation of the neutron density (∂n/∂t) is equal to the rate of neutron absorption minus the leakage rate: ψ Ω Ω Ω , The Monte Carlo method approach in OpenMC simulates the reactor criticality at a steady state. The k-eff value is formulated as the eigenvalue (k) obtained by dividing the number of fission v(r, E ′) by the k factor [12 13] so that the equation for calculating reactor criticality can be written as: (2) can be simplified by defining the operators M and S(r): The operator M denotes the total rate of neutron loss and S(r) is the operator for the fission source. If we define Green's function (G) for (5) as: Ω Ω δ δ δ (6) where the notation «0» [12] denotes the starting point in the space phase, (2), can be rewritten only in fission source form; ( ) (8) By assuming the right hand side of (7), with the fission operator F, the eigen equation can be formulated as: The value of k 0 = k-eff, so that the eigen value iteration equation for the Monte Carlo method can be written as: S (i) shows the sample of neutrons for the initial state in the Monte Carlo simulation. Neutrons are then simulated for their transport so that the location of the next generation S (i+1) is determined. Iteration starts from the initial source distribution at S (0) and eigenvalue k (0) [12].

3. Design and parameters
The reactor design used is the MSR FUJI-12 with a cylindrical core, single core arrangement and composed of a core, reflector, and absorber. The configuration of each FUJI-12 MSR core structure is shown in Fig. 2.
The moderator is a component that moderates the neutrons so that the fission chain reaction can be maintained. The moderator is in the form of 271 hexagonal fuel line pins and arranged in a circle. MSR fuel is in the liquid phase, so there is a cylindrical tube through which the fuel flows called the fuel duct in the center of the hexagonal pin. The arrangement of the reactor core components and the arrangement of the fuel pins follow Fig. 3.
There are three compositions of MSR FUJI-12 fuel used in this study. The eutectic material shows the lowest melting point of the composition of a mixture of the same homogeneous compound. The combination of the wrong mole fraction of the fuel mixture can cause clumping and clog the flow rate of fuel in the fuel duct. The eutectic composition variations for the LiF-BeF 2 -UF 4 fuel mixture are shown in Table 1.
The MSR FUJI-12 reactor was operated with an operating power of 350 MWt for 5 years. The reactor operates with the operating parameters in Table 2.     Natural lithium (Li) consists of 7.6 % 6 Li, which has a very high absorption cross section. It is not recommended for nuclear reactor fuel. 7 Li enrichment needs to be carried out in the fuel mixture by 99.95 % to avoid feedback reactivity due to tritium generation by neutron absorption of the Li 6 isotope [16].

Results of the neutronic analysis of molten salt reactor
Fuji-12 using fissile 235U in LiF-BeF2-UF4 fuel

1. Optimization of LiF-BeF 2 -UF 4 fuel
Optimization of LiF-BeF2-UF4 fuel for all variations is shown in Fig. 4. The optimization was carried out by simulating 15,000 neutron particles in 50 batches, consisting of 40 active batches and 10 inactive batches. This limitation results in a standard deviation error value in the range of 110 pcm to 115 pcm. Fig. 4 shows the value of k-eff, which is a reactor criticality parameter for the three compositions of fuel 1, fuel 2 and fuel 3 with 3-8 % 235 U enrichment. Based on Fig. 4, the optimal k-eff value for power operation of 350 MWt for 5 years can only be achieved by fuel 2 and fuel 3. The optimal state can be achieved when the k-eff value approaches the critical state (k-eff = 1) from the beginning of the operating period to the end of the operating period. The minimum enrichment of 235 U required for fuel 2 and fuel 3 to reach a critical state is 8 % and 7 %, respectively. Fuel 1 cannot reach the optimal operating state for each variation of 235 U enrichment. The highest 235 U enrichment of 8 % can only help fuel 1 reach a critical point at the beginning of life (BOL) and then drop to a sub-critical state (k-eff < 1). Fig. 5 shows a neutron spectrum analysis of the three variations of the fuel mixture. The peak flux values of all variations of the fuel mixture are in the thermal energy range. Fuel 1 has the highest flux value and indicates that the burn-up of fissile fuel ( 235 U) in fuel 1 occurs more quickly. This could lead to a shortage of fissile fuel ( 235 U) to sustain reactor operation for 5 years. The peak flux of fuel 1 has a large difference from fuel 2 and fuel 3. The characteristics of fuel 2 and fuel 3 are almost similar. The peak flux difference between the two is not too far, so it has almost similar k-eff characteristics for 350 MWt power operation for 5 years.
The amount of 3 H (tritium) greatly affects the corrosiveness of the fuel to the fuel pipe in MSR. Fig. 6 shows that the amount of 3 H in fuel 1 is the largest and continues to increase a b Fig. 2. Reactor design: a -the shape of the reactor core; b -the configuration of the core constituent material until the end of operation. A drastic increase in the amount of 3 Fig. 7 shows the value of macroscopic cross section fission and absorption as a function of energy (eV). The difference can be seen by reviewing the thermal, epithermal, and fast energy ranges. Fuel 3 has the highest macroscopic cross section fission and absorption values in the thermal energy range. In the epithermal energy range, the macroscopic cross section absorption of fuel 3 is lower than that of the other two fuels. Meanwhile, in the fast energy range, the macroscopic cross section fission of fuel 3 is higher than that of the other two fuels. Based on Fig. 5, the FUJI-12 MSR reactor is a type of reactor with a spectrum of thermal energy. Referring to this, in Fig. 7, fuel 1 and fuel 2 have similar fission and absorption probabilities for the thermal energy range. Fig. 8, 9 show the value of the flux distribution in the core reactor on the XY and XZ sections. Fig. 8 shows the flux distribution for the initial state of the reactor mass (BOL). Fig. 9 shows the flux distribution for the end state of the reactor life. Fig. 8, 9 show the distribution of neutron flux at the beginning of operation (BOL) and the end of operation (EOL). Based on Fig. 8, 9, fuel 1 has the widest maximum flux distribution at EOL and BOL. The distribution of neutron flux in fuel 2 and fuel 3 is almost the same and has a much different total area from fuel 1 in the BOL and EOL conditions.

Discussion on the composition of uranium-based fuels that have the potential to replace thorium-based fuels
Based on the research results, fuel 2 and fuel 3 have almost the same characteristics and have the greatest potential to become MSR FUJI-12 fuel for 350 MWt power operation for 5 years. Fuel 1 has a flux value that is too high, so that fissile fuel ( 235 U) is not enough for reactor operation for 5 years (Fig. 5). The composition of the eutectic mixture of LiF-BeF 2 -UF 4 for fuel 1 also produces a larger amount of 3 H (Fig. 6). LiF turns into hydrogen fluoride ( 3 HF) during the reactor operation. The material is very corrosive and dangerous for the reactor fuel pipe [17]. The optimization results also show that only fuel 2 and fuel 3 were able to reach the optimal state for 350 MWt power operation for 5 years (Fig. 4). Fuel 2 requires a minimum of 8 % 235 U enrichment and fuel 3 -a minimum of 7 % 235 U enrichment. Fuel 1 cannot reach the optimal state for each variation of 235 U enrichment. This is because the total amount of uranium in fuel 1 is very small. Uranium is the main material in fission reactions. Fuel 1 requires more 235 U enrichment to last 5 years. However, 235 U enrichment that is too large can increase excess reactivity and potentially cause the reactor to explode due to an uncontrolled fission chain reaction.
Based on Fig. 8, 9, the distribution of the maximum neutron flux is spread over the center of the reactor either on the XY or XZ axes. The distribution characteristics for fuel 2 and fuel 3 are almost the same, in contrast to fuel 1, which has a maximum neutron flux distribution with a larger area. The difference is very visible in the state of BOL and EOL. Larger maximum neutron flux distribution in fuel 1 indicates greater fission production or burning of almost all fissile materials. In contrast to fuel 2 and fuel 3, which are better at maintaining the fissile material so that the maximum neutron flux can be maintained at the center of the reactor core.
Neutronic analysis in molten salt reactor FUJI-12 using OpenMC 0.13.0 shows that fuel 2 and fuel 3 have potential neutronic parameters to replace thorium-based fuel. These results need to be developed further because the simulation method with OpenMC 0.13.0 uses a static system. MSR is a reactor with fuel that is constantly moving, so it needs further analysis with a dynamic system. Combination with thermal-hydraulic analysis needs to be done as a comprehensive step in the nuclear reactor safety analysis.

Conclusions
1. The eutectic composition of LiF-BeF 2 -UF 4 in fuel 2 and fuel 3 has the potential to be used as a liquid salt fuel mixture in MSR FUJI-12 with an operating power of 350 MWt for 5 years.
2. The distribution of maximum neutron flux in fuel 2 and fuel 3 is more stable than in fuel 1 for both BOL and EOL conditions.