Effective Multiplication Factor Analysis of Gas-cooled Reactor using OpenMC code with ENDF/B-VII.1, ENDF/B-VIII.0 and JENDL-5.0 Nuclear Data

As the demand for nuclear energy keeps rising, Generation IV reactor designs continuously improve. One such potential reactor design is the Gas-cooled Reactor. Neutronic analysis is the foundation for ongoing design modifications and alternatives for the Helium Gas-cooled Reactor. An important aspect of neutronic analysis is the nuclear data library. This research compares how different nuclear data libraries impact a Helium Gas-cooled Reactor design by comparing the neutron effective multiplication factor (k-eff) value. This research was conducted by the Monte Carlo method using OpenMC code. ENDF/B-VII.1, ENDF/B-VIII.0 and JENDL-5.0 were used as nuclear data libraries to simulate the reactor design for ten years of depletion time with 1-year timesteps. The reactor is designed in two different spectrums: the fast neutron spectrum design and the thermal neutron spectrum design. The differences between the two designs are in the cladding and reflector materials where the thermal neutron spectrum uses graphite moderator. The results for thermal spectrum design show that while each nuclear data library’s average k-eff values vary, they all produce the same results at timestep zero, with k-eff values around 1.02500. The average k-eff value from simulation using the ENDF/B-VII.1 library is 1.01477, the average k-eff value from simulation using the ENDF/B-VIII.0 library is 1.01122, and the average k-eff value from simulation using the JENDL-5.0 library is 1.01047. Each simulation result has an average uncertainty of 0.00040. The difference is due to the different amounts of data in each library. JENDL-5.0 has the highest amount of data inside its nuclear libraries, followed by ENDF/B-VIII.0 and ENDF/B-VII.1. Meanwhile, the average difference between the different libraries is insignificant for the thermal gas-cooled reactor simulation results. ENDF/B-VIII.0 produces an effective k-average of 1.04437, and JENDL-5.0 produces an effective k-average of 1.04273. Mass change over time results also shows that the transmutation of Uranium-238 into Plutonium-239 occurred. The fast spectrum reactor design shows a greater increase in plutonium-239 than the thermal spectrum design. The three libraries used did not show large differences in results in calculating changes in the mass of Uranium-238 over time due to Uranium-238‘s large mass, but they still showed differences in Plutonium-239‘s mass change over time. The average value difference between libraries in the fast neutron spectrum reactor design is 50 kg, and in the thermal spectrum it is 30 kg.


Introduction
The need for environmentally friendly energy sources is increasing considering the increasing population [1].The condition of air pollution, especially in Indonesia, is increasingly worrying.Nuclear reactors are one of the solutions for future energy sources [2].Nuclear reactor technology continues to develop, currently reaching the fourth generation [3].Two fourth-generation nuclear reactors are the Gas-cooled Fast Reactor (GFR) and the Very High-Temperature Gas Reactor (VHTR).Several studies on developing the neutronic aspect of generation IV reactors, especially GFR and VHTR reactors, have been carried out previously [4][5][6][7].Neutronics analysis is the foundation for creating and designing improvements to the Gas-cooled Reactor, with one important factor in neutronic analysis being the nuclear library.This research aims to compare the effects of different nuclear data libraries on thermal and fast gas-cooled reactor design by considering the effective neutron multiplication factor (keffective) values and several important material nuclear densities using ENDF/B-VII.1,ENDF/B-VIII.0,and JENDL-5.0 nuclear data libraries.

Calculation Methods
Reactor neutronics is one of the important aspects of designing nuclear reactors.Neutronics analysis analyses neutrons' interactions and behaviour, including direction of motion, speed, and interactions with other materials.Neutronic analysis calculations can be carried out deterministic or stochastic.Neutronic analysis can be carried out stochastically using the Monte Carlo method.The Monte Carlo method simulates random neutron movements in a model using a computer [9].A probability distribution of neutrons and particles is required to carry out neutronic analysis.By simulating a large number of neutrons, the average k-effective can be obtained with a small uncertainty, in accordance with the central limit theorem, which states that for a large number, the distribution of mutually independent variables will follow a normal distribution.The uncertainty of the Monte Carlo method simulation can be written with equation 1: Where  2 is the variance of the data, and N is the number of realizations; in the case of this study, it is the number of neutrons.Equation 1shows that the more neutrons simulated, the smaller the variance and uncertainty.
The effective neutron multiplication factor (k-effective) is one of the most important neutronic parameters.K-effective is the ratio of the number of neutrons in the reactor in one generation to the next.A reactor is in a critical state if k-effective is 1, which indicates that the number of neutrons in the reactor is always constant.K-effective is considered subcritical if k-effective is below 1, meaning the number of neutrons always decreases over time.K-effective is considered supercritical if k-effective is above 1, meaning the number of neutrons continues to increase.
The OpenMC code [9] is used to construct the reactor model and simulate neutrons inside the reactor.In this study, five thousand neutrons were simulated in each batch with a batch number of 500 calculations for a total of 2500000 neutrons.The first 50 batches are ignored in the overall average calculation to ensure convergence.The reactor was simulated for 3650 days with timesteps every 365 days.Integration of changes in the amount of material at each timestep is carried out using a predictorcorrector method called CE/CM (constant extrapolation on predictor/constant midpoint on a corrector).The simulation was conducted on a computer with a 10th-generation Intel i5 processor and 8GB RAM.The OpenMC code used was version 1.13.

Material and Reactor Design
The reactor design used in this study was inspired by the European Sodium-cooled Reactor design by Euratom [10] as a reference design.The characteristics of the Gas-cooled Reactor can be seen in table 1.
The Gas-cooled Reactor fuel in this study follows the plutonium-enriched MOX fuel [10] as can be seen in table 2.
The placement of fuel in the reactor core is divided into two areas: inner fuel and outer fuel.The complete reactor core configuration can be seen in figure 1.The reactor is designed in two different spectrums: the fast neutron spectrum and the thermal neutron spectrum.The differences between the two designs are in the cladding and reflector materials, with a comparison shown in table 3:

Results and Discussion
Simulations were carried out for both types of reactors using three different nuclear libraries.The three libraries used are data from ENDF/B-VII.1 [11], ENDF/B-VIII.0[12] and JENDL-5.0 [13].A comparison of the amount of data in each sub-library can be seen in table 4. JENDL-5.0 has the largest amount of data, followed by ENDF/B-VIII.0,then ENDF/B-VII.1.

K-effective values for fast gas-cooled reactor design
Simulation results of a gas-cooled reactor with a fast neutron spectrum using OpenMC for each different library can be seen in table 5.The average k-effective simulation result using ENDF/B-VII.1 is 1.01477, while the average using ENDF/B-VIII.0data is 1.01122, and the average using JENDL.5-0 is 1.01047.The uncertainty of all simulation results is 0.00040.
Table 5 shows that the results using ENDF/B-VII.1 show that the reactor can maintain k-effective values above 1.0 for eight years.Meanwhile, using ENDF/B-VIII.0and JENDL-5.0 as nuclear data libraries shows that the same reactor design could maintain its criticality for seven years.The average k-effectiveness of ENDF/B-VII.1 is greater than the results using other libraries.The data in table IV.2 can also be seen in figure 2 2 shows that the k-effective at the beginning of the reactor operation has almost the same value for all libraries used.Simulations using ENDF/B-VII.1 produce higher effective k-values than ENDF/B.VIII.0 and JENDL.5.0 over time.This difference arises because nuclear data in the library differs, especially in the amount of reaction and neutron interaction data.The difference in the number of neutron interactions can be seen in table 6.
Table 6 shows that the three libraries have different nuclide reaction data, resulting in different depletion results.Different depletion rates make the k-effective values differ over time.

K-effective values for thermal gas-cooled reactor design
Simulation results for reactor design with a thermal neutron spectrum can be seen in table 7.
The average uncertainty of all simulations is 0.00044.The ENDF/B-VII.1 simulation produces an average k-effective of 1.04442, ENDF/B-VIII.0produces an average k-effective of 1.04437, and JENDL-5.0 produces an effective k-of 1.04273.The three simulations have k-effective values higher than 1.0 for nine years.The k-effective results can also be seen in figure 3.
In the thermal spectrum gas-cooled reactor design, the difference in effective k-values is small, even though the libraries used are different.The k-effective value for each library has some disagreements at the beginning of reactor operation, inversely proportional to the results of fast-spectrum reactor design simulations.The initial k-effective value in the simulation using ENDF/B-VII.1 is 1.12858, while

Nuclear fuel material densities for fast gas-cooled reactor design
OpenMC can solve differential equations for changes in the amount of material in a simulated model using various algorithms.In the simulation in this research, the second-order CE/CM algorithm (constant extrapolation on predictor, constant midpoint on corrector) was used.The isotopes whose changes were recorded in this simulation were Uranium-238 and Plutonium-239.
In the fast gas-cooled reactor, the changes in the number of several important isotopes can be seen in table 8.
Changes in Uranium-238 density over time can be seen in figure 4 Meanwhile, changes in Plutonium-239 density in the fast spectrum reactor design can be seen in figure 5. Figures 4 and 5 show that the mass of Plutonium-239 increases with time, while the mass of Uranium-238 decreases with time.This indicates that plutonium-239 transmutation occurred.Adding fissile fuel over time means the reactor design can last for quite a long time, as indicated by the k-effective value, which can be higher than 1.0 for seven years.
The different libraries used also provide differences in the mass change simulation results.The difference in results between libraries for changes in the mass of Uranium-238 is around 50 kg.This difference is quite small compared to the total mass of Uranium-238 at the beginning of reactor operation (6.208 ×10 4 kg).
For the changes in Plutonium-239 density, the different libraries provide more visible differences because the initial amount of Plutonium-239 is 5.55 ×10 3 kg.Of the three libraries used, ENDF/B-VIII.0 and JENDL-5.0 gave close results, while ENDF/B-VII.1 gave quite different results compared to the other two libraries.This difference can be caused because ENDF/B-VII.1 has the smallest amount of data of the three libraries used.

Nuclear fuel material densities for thermal gas-cooled reactor design
The changes in the mass of Uranium-238 and Plutonium-239 isotopes over time for thermal neutron spectrum reactor design can be seen in table 9. Changes in Uranium-238 density over time can be seen in figure 6.
Meanwhile, the changes in Plutonium-239 mass in the thermal spectrum reactor design can be seen in figure 7.
Just as in the fast spectrum, the decrease in Uranium-238 is followed by an increase in Plutonium-239, indicating the presence of plutonium transmutation.The difference between the simulation results of the thermal spectrum design and the fast spectrum is that the rise in Plutonium-239 is not as large as in the fast spectrum design.In the fast spectrum simulation, the peak mass amount of Plutonium-239 was obtained in the 7th year, while in the thermal spectrum, the peak amount of Plutonium-239 was in the 6th year.The three libraries provide results for changes in uranium-238 that are small, as seen in figures 4 and 6, with a difference at around 30 kg.Uranium-238's large initial mass makes the difference less noticeable.The differences in results between libraries can be seen in the changes in Plutonium-239 mass over time.The calculation using three libraries has initial values that are not too different in year 1, but the differences increase over time.JENDL-5.0 gives the greatest results while ENDF/B-VIII.0shows the smallest results.

Conclusion
Simulation of the fast neutron spectrum gas-cooled reactor design using OpenMC gave the same results for ENDF/B-VII.1,ENDF/B-VIII.0,and JENDL-5.0 at the beginning of reactor operation.With an initial effective k-value of around 1.02500.Differences appear at timesteps other than t=0, with the average k-effective of ENDF/B-VII.1 being 1.01477, ENDF/B-VIII.0being 1.01122, and JENDL-5.0 being 1.01047.All simulations have an uncertainty of 0.00040.The differences in simulation results with different libraries are due to differences in the amount of data for each library.Meanwhile, the average difference between the different libraries is insignificant for the thermal gas-cooled reactor simulation results.ENDF/B-VIII.0produces an effective k-average of 1.04437, and JENDL-5.0 produces an effective k-average of 1.04273.The changes in the mass of Uranium-238 and Plutonium-239 over time show that a decrease in the mass of Uranium-238 will increase the mass of Plutonium-239.This indicates that the transmutation of Uranium-238 into Plutonium-239 occurred.The fast spectrum reactor design shows a greater increase in plutonium-239 than the thermal spectrum design.The three libraries used did not show large differences in results in calculating changes in the mass of Uranium-238 over time.The average value difference between libraries in the fast neutron spectrum reactor design is 50 kg, and in the thermal spectrum is 30 kg.The difference in results from the three libraries can be seen in the data on changes in Plutonium-239 over time.In the fast gas-cooled reactor design, the ENDF/B-VIII.0and JENDL-5.0 give close results, while ENDF/B-VII.1 gives greater results than the other two libraries.This difference can be caused by ENDF/B-VII.1 having the smallest amount of data of the three libraries used.Meanwhile, in the thermal gas-cooled reactor design, the three libraries have initial values with small differences in the first year, but the changes become greater over time.JENDL-5.0 gives the higher values while ENDF/B-VIII.0gives the smallest values.

Figure 2 .
Figure 2. Comparison of k-effective for fast gas-cooled reactor using different nuclear libraries

Figure 4 .Figure 5 .
Figure 4. Uranium-238 over time from three different nuclear data libraries on the fast spectrum reactor design

Figure 6 .Figure 7 .
Figure 6.Uranium-238 over time from three different nuclear data libraries on the thermal spectrum reactor design 2. Each simulation took 11 hours.

Table 1 .
General Reactor Parameters

Table 3 .
Reactor core material

.
Tabel 4. Comparison of the number of nuclide data in different nuclear libraries

Table 5 .
Comparison of k-effective for fast gas-cooled reactor using different nuclear libraries 6 Figure

Table 6 .
Number of nuclide reaction data for different nuclear libraries.

Table 7 .
Comparison of k-effective for fast gas-cooled reactor using different nuclear libraries

Table 8 .
, Comparison of mass changes with time in the fast neutron spectrum reactor using different nuclear libraries

Table 9 .
Comparison of mass changes with time in the thermal neutron spectrum reactor design using different nuclear libraries