Neutronic Analysis for The Radial Direction Heterogeneous Core Configuration of GFR with Thorium Fuel

A neutronic analysis has been carried out for the radial direction heterogeneous core configuration in GFR with thorium nitride fuel to obtain the most optimal heterogeneous design has keff > 1 and excess reactivity below one percent. Neutronic analysis was performed using openMC version 0.13.2 based on open-source Monte Carlo simulation with ENDF/B-VII.1 data library. The first calculation is benchmarking openMC and SRAC where the largest error is 2.49% is caused by different data library. SRAC data library is JENDL 4.0. The second calculation is a homogeneous core configuration with 5% to 15% uranium-U233 fuel variation, the stability lies at 8% for the reference of heterogeneous core configuration. The heterogeneous core configuration was performed with three types of fuel percentage and five different geometry variations. Optimum design for geometry F1:F2:F3 = 1 ring:4 rings:1 ring using fuel type F1:F2:F3 = 6.5%:8%:9.5%. Optimum design for geometry F1:F2:F3 = 2 rings:2 rings:2 rings using fuel type F1:F2:F3 = 7.5%:8%:8.5%. Optimum design for geometry F1:F2:F3= 1 ring:2 rings:3 rings using fuel type F1:F2:F3=7%:8%:9%. Optimum design for geometry F1:F2:F3= 1 ring:3 rings:2 rings using fuel type F1:F2:F3 = 7.5%:8%:8.5%. Optimum design for geometry F1:F2:F3 = 1 ring:1 ring: 4 rings using fuel type F1:F2:F3 = 7.5%:8%:8.5%. The most optimum design among the other five designs is the F1:F2:F3 = 2 rings:2 rings:2 rings geometry design because it has a maximum keff of 1.00999 and excess reactivity of 0.99%. This design is carried out for an extended burn-up 15 years and still stable with the characteristics of the neutron flux and fission rate in this design decrease with burn-up time. Fission product in this design also decreased according to the purpose of the generation IV reactor is the prevention of nuclear weapons.


Introduction
According to the National Energy Council in its book entitled "Indonesian Energy Outlook 2019" explained that electricity demand in Indonesia in 2050 increased nine times from 2018 by 2,562 TWh and coal which produces CO2 emissions that cause climate change, still dominates as a fuel for future power plants [2].Indonesia has an ambitious target of Net Zero Emissions (NZE) by 2060.Emissions reductions are used to limit global temperature rise to 1.5°C to avoid the worst impacts of climate change [3].One of the priority actions in support of NZE 2060 is to build Nuclear Power Plants.The generation IV International Forum (GIF) explains there are four objectives of generation IV nuclear reactors such as sustainability, safety and reabillity, economic, and proliferation resistance and physical protection [7].Nuclear Power Plants have reached generation IV reactors, one of which is the Gas-cooled Fast Reactor (GFR).The GFR is a fast reactor with a closed fuel cycle.The GFR has a high level of efficiency and can produce hydrogen that can be used for vehicle or industrial fuel development in the few years [1].
The fuel used in GFR is usually uranium, but the continuous use of uranium causes fuel reserves to deplete, so another alternative is needed to be developed to increase the supply of nuclear fuel using thorium fuel.Based on data published by BRIN, Indonesia has the potential for 89,498 tons of uranium and 143,234 tons thorium [12].The amount of thorium in Indonesia can be used as an alternative fuel to uranium in Nuclear Power Plants.Natural thorium (Th-232) is a fertile fuel that does not fission immediately and tends to produce neutron slowly, so a trigger is needed to start a chain reaction, so the fissile material used is uranium-233 (U-233), which comes from the Th-232 fission chain [6].Previous research has been conducted on neutronic analysis for GFR with thorium nitride fuel using SRAC.Some of the research on GFR using thorium nitride fuel are [14][15][16].
Referring to previous research, the researcher is interested in examining the radial direction of the heterogeneous core configuration for GFR with thorium nitride fuel (ThN-U233N) using the openMC code instead of SRAC.OpenMC was chosen over SRAC because the program is provided free of charge to anyone who obtains a copy of the software [5], while SRAC is a code system developed by the Japan Atomic Energy Agency and its users are still limited because it is paid [8].OpenMC is a new Monte Carlo particle transport code.It focuses on criticality calculations for nuclear reactor simulations [10].The Computational Reactor Physics Group (CRPG) at the Massachusetts Institute of Technology (MIT) has been the leader in the development of openMC [11].The technique used in openMC is known as Constructive Solid Geometry (CSG) modelling to create complex threedimensional shapes [9].In addition to using openMC codes, using thorium nitride as a GFR fuel is very useful in overcoming the problem of nuclear proliferation.Therefore, this heterogeneous core configuration was designed using three types of fuel percentages in five different cases with each case performed ring geometry variations.This study was conducted to compare several ring geometry variations used in the heterogeneous core configuration in order to obtain the most optimal heterogeneous design.The optimal heterogeneous design has an effective multiplication factor around one (  ≥ 1) and excess reactivity below one percent.

Design Concept and Calculation Methods
This research begins with benchmarking openMC and SRAC codes.The design parameters used were taken from SRAC data of 10% homogeneous core configuration during five years burn-up.The parameter design used in the research are shown in Table 1 Benchmarking is used to see the amount of error between the result of openMC and SRAC code.The calculation used for benchmarking is according to the reference [4] with the calculation of 1.
This research is focuses on variations in the geometry of the heterogeneous core configuration, which begin with a homogeneous core configuration according to the specifications of Table 1.The data obtained on the homogeneous core configuration is the effective multiplication factor (  ) for five years of burn-up which will be plotted in a graph of effective multiplication factor (  ) with burn-up time to see the flattest graph.
The heterogeneous core configuration is a configuration with several fuel types and the flattest graph of the homogeneous core configuration is used as a reference for the calculation of the heterogeneous core configuration.This heterogeneous core configuration uses three different fuel percentages, which are further varied by five different ring geometries.  1 is a variation of the ring geometry of the heterogeneous core configuration according to Table 2. Fuel 1 is depicted in light blue.Fuel 2 is depicted in brown.Fuel 3 is depicted in green.

Variation 1
Variation 2 Variation 3 Variation 4 Variation 5 Figure 1.Design variations of ring geometry The result of this variation in ring geometry is a most optimum reactor design.This design is said to be critical if it has an effective multiplication factor of around one (  ≥ 1), but it also needs excess reactivity of less than one percent (1%) to be called optimum.Calculation used in excess reactivity according to reference [3] with the calculation of 2.

× 100%
(2) The most optimal design was the extended burn-up for 15 years followed by analysis of neutron flux, fission rate, and fission product.

Result and Discussion
The code used for analysis is openMC code which begins with benchmarking between openMC and SRAC for five years of burn-up.Table 3 is the result of the error value between openMC dan SRAC.The longer burn-up, the greater error value, as shown in Table 3.This is due to the different data libraries used.SRAC uses JENDL 4.0 data library while openMC uses ENDF/B-VII.1 data library.This benchmarking has the largest error value of 2.49% generated by simulating 60,000 particle used for the calculation of homogeneous and heterogeneous core configurations.Figure 2. Homogeneous core configuration Homogeneous core configuration is one that consist of single of fuel percentage.Homogeneous core configuration using a percentage of uranium-233 with a variation from 5% to 15%. Figure 2 shows that the 8% percentage has a constant effective multiplication factor (  ) until the fifth year of burnup because it has the flattest graph like a straight line.Therefore, this 8% percentage is used as the basis for determining the combined percentage with three types of fuel percentage using heterogeneous core configuration calculations.4 shows the variation of three types of uranium-233 fuel in five cases.Each case is varied with all five ring geometry variations to determine the most optimal heterogeneous design.

Variation 1
Variation 2 Variation 3 Variation 4 Variation 5 Figure 3. Result of   on ring geometry variations Based on Figure 3, it shows that the graph of the effective multiplication factor value around one (  ≥ 1) is included in the critical condition, but not all of them are optimal so it is necessary to calculate excess reactivity.5 shows the excess reactivity values of all ring geometry variations.Based on the table, it can be seen that the lowest excess reactivity value below one percent is found in the second variation and in case 5.The second variation uses F1:F2:F3 = 2 rings: 2 rings: 2 rings and case 5 uses heterogeneous fuel percentage F1:F2:F3 = 7.5%:8%:8.5%.This variation is the most optimal heterogeneous design because it has a maximum k eff of 1.00999 and has a maximum excess reactivity of less than one percent (1%) maximum of 0.99%.Table 6.Excess reactivity after extending burn-up 15 years Ring variation Case Burn-up Excess reactivity F1:F2:F3 = 2 rings: 2 rings: 2 rings F1:F2:F3 = 7.5%:8%:8.5%0 15 0.99% 0.38% The results of the burn-up extended burn-up are shown in Figure 4 in the form of a criticality value graph when extending the burn-up 15 years.The graph shows that the effective multiplication factor is still around one (  ≥ 1) until 15 years.Based on Table 6, excess reactivity is also still below one percent (1%) with a nominal at 15 years burn-up of 0.38%.This indicates that the reactor is still optimal and crirical (stable).(b) EOL condition Figure 6.Fission rate BOL and EOL conditions Fission rate is a description of the rate of neutron production per second (neuron/s) produced by the fission reaction in the reactor.The fission rate is influenced by the neutron flux distribution, whose production rate is shown in radial form as in Figure 6, and from the figure it can be seen that the fission rate at the BOL (Beginning of Life) is larger and more evenly distributed.As the burn-up time progresses, the neutron production rate decreases toward the center because the fission reaction decreases, which is indicated by the blueness at the edge of the reactor core corresponding to the EOL (End of Life) condition at the end of the burn-up Figure 7. Fission product ThN-U233N Fission product are related to the mass of fuel which decreases and increases as the burn-up time passes in the nuclear reactor.The decrease in fuel mass in reactor is caused by the burning phase while the increase in fuel mass is caused by the breeding phase.Figure 7 is a graph of changes in fuel mass during 15 years burn-up.Until the final burn-up, thorium (Th-232) experiences a decrease in fuel mass.Uranium (U-233) experienced a decrease in fuel mass until the first year, followed by an increase in fuel mass until the sixth year of burn-up, after which it decreased again.The reduced fuel mass corresponds to the GIF goal to create a Generation IV reactor, i.e., to prevent nuclear fuel from being used to produce nuclear weapons.The change in mass data at the end of the burn-up is shown in Table 7.

Conclusion
The most optimal radial direction heterogeneous core configuration in GFR with thorium fuel is when the geometry F1 (2 rings), F2 (2 rings), F3 (2 rings) and percentage of fuel variation F1 (7.5%), F2 (8%), F3 (8.5%) because it has an effective multiplication factor is around one (  ≥ 1) with a maximum   of 1.00999 and excess reactivity less than one percent (1%) with a maximum value of 0.99%. in this design, the neutron flux and fission rate value decrease as the combustion prosses progresses.The decrease in fuel mass is also in consistent with GIF's goal of producing generation IV reactors, which is to prevent nuclear fuel from being used to make nuclear weapons in the future.

Acknowledgment
The author would like to thank the lecturers who are members of the Applied Materials and Energy Computing Research Group who have provided research ideas.The author also would like to thank LP2M University of Jember for providing assistance in the form of material for the 2023 Research and Community Servise Reasearch Group Grant (KeRis) research grant (DiMas) with aggrement number No. 327/UN25.3.1/LT/2023.

Figure 4 .
Figure 4. Effective multiplication factor after extending the burn-up for 15 yearsThe design of the most optimal heterogeneous core configuration was extended to a burn-up time of 15 years to determine the change in the number of neutrons due to the fission reaction at longer burnups.Table6.Excess reactivity after extending burn-up 15 years Ring variation Case Burn-up Excess reactivity F1:F2:F3 = 2 rings: 2 rings: 2 rings F1:F2:F3 = 7.5%:8%:8.5%0 15 (a) BOL condition 10th Asian Physics Symposium (APS 2023) Journal of Physics: Conference Series 2734 (2024) 012066 IOP Publishing doi:10.1088/1742-6596/2734/1/0120667 (b) EOL condition Figure 5. Neutron flux distribution of BOL and EOL conditions Neutron flux describes the movement of neutron per area per second (neutron/cm 2 s).The neutron flux is characterized by decreasing as it burn-up.The neutron flux distribusikan in Figure 5 shows a very rel BOL (Beginning of Life) condition and becomes smaller as it reaches EOL (End of Life).The red in the neutron flux distribution indicates the amount of neutron scattering occurring in the core area.The orange indicates that the neutron distribution is moving away from the core.The blue indicates that the neutron distribution is becoming smaller.This is cause by neutron leakage from the system and material uptake outside the fuel.(a) BOL condition 10th Asian Physics Symposium (APS 2023) Journal of Physics: Conference Series 2734 (2024) 012066

Table 1 .
. Parameter design used in the research

Table 3 .
Benchmarking results of openMC and SRAC codes

Table 4 .
Variation of fuel percentage in heterogeneous core configuration

Table 5 .
Excess reactivity for all ring geometry variations

Table 7 .
Final mass of fission product 9 9