Validation of OpenMC Code Criticality Value Calculation for GFR Reactor with UN-PuN Fuel

The use of OpenMC code needs to be validated with other code, so that an accurate and valid criticality value is generated. The validation value is affected by the minimum number of particles used. Determination of the minimum number of particles is carried out by varying the number of particles so that they have a convergent value, which is in the range of 100-50000 particles. The results of determining the minimum number of particles are then used to find the minimum number of cycles consisting of active and inactive batches. This study uses the criticality value parameter in the form of an effective multiplication factor (k-eff) as a benchmark for code accuracy. The k-eff values generated by OpenMC and SRAC are then compared and the validation error value is searched. The error value is found by calculating the k-eff (Δk-eff) difference between the two codes. OpenMC code can be said to be validated if it has an error value of less than 1% against the calculation results of the SRAC code. The calculation results of determining the minimum number of particles show k-eff values in the range of 35000 - 50000 minimal changes significantly or not fluctuating. The calculation of k-eff and entropy in cycle 500 shows a convergent value at the active batch value of >30. Based on the data cycle, researchers used 100 active batches and 30 inactive batches to perform validation calculations. The results of the validation calculation using UN-PuN fuel with a plutonium material composition of 10% showed a maximum k-eff error value of 0.819%. The Δk-eff obtained is 0.008.


Introduction
GFR is classified as a nuclear power plant which has the opportunity to replace the role of coal in producing energy in the future [1].GFR or Gas-cooled Fast Reactor is one type of IV generation reactor that prioritizes four main objectives, i.e sustainability, safety and reliability, economics, and proliferation resistance and physical protection [2].The IV generation reactor is a future reactor design with a more advanced system development and has a longer operation of more than 60 years [3].Based on the neutron energy used, GFR reactors are included in the fast reactor class.Fast neutrons carry out fission reactions in the form of capture, scattering, absorption, and collision in the reactor core [4].Neutrons are absorbed by the fuel material, core material, and coolant material.GFR reactors use coolant in the form of helium gas which has inert, single-phase, and stable atomic core characteristics.The GFR cycle system in fuel combustion is closed and operates with outlet temperatures up to 850 O C [5].The use of high temperatures and cooling in the form of helium makes it possible to produce hydrogen gas for alternative energy sources.
GFR reactors have been studied by several researchers in analyzing the level of criticality produced by fuel in fission reactions using the SRAC or Standart Reactor Analysis Code and OpenMC programs [6][7][8][9].The SRAC code is a code that contains a collection of neutron cross section data to analyze the movement of neutron spectra by diffusion at one group to multi group energies [10].The SRAC code is deterministic, meaning that a system of neutron movements within the reactor's active core can be precisely predicted.The SRAC code was first developed by the Japan Atomic Energy Agency or JAEA [11].However, SRAC code cannot be used freely or close source because it has an official license.Therefore, lately many researchers have used OpenMC code because it is open source so it is easy to get and apply.
OpenMC is a neutronic analysis program based on neutron transport code using the monte carlo method [12].The code was developed by the Reactor Computational Physics community at the Massachusetts Institute of Technology since 2011 [13].OpenMC uses stochastic calculations, meaning that the process approaches probabilistically or uncertainty to random variables.Stochastics have a state in which there are several possible events and each event gives a different result.This relates to the neutron transport method used in OpenMC programs.Neutron transport involves fission reactions that cause uncertainty in the number of neutrons born and lost in a generation.The number of particles per generation affects the level of stochastic uncertainty in simulation results [14].Neutron transport is described as a coupled integrative equation with seven variables of energy, space, and time that influence the number of neutron populations as shown in the following equation: OpenMC uses eigenvalue simulations in criticality calculations to determine the distribution of neutron populations in a system [15].The eigenvalue equation comes from the calculation of the neutron transport equation, where if there is a fission source, the neutron source will depend on the neutron flux itself [16].One of the most popular methods for calculating the spatial convergence of fission sources is the entropy of fission sources [17].The entropy of fission sources can be written mathematically using the Shanon entropy equation [18], which is as follows: The parameter  ,, () is the number of fission source particles in the , ,  index cells in generation  divided by the total number of source particles in all cells of generation .The entropy function () is expected to provide a measure of phase space exploration as a function of the number of generations when the neutron distribution reaches a stationary or convergent state [19].The entropy value will determine how many cycles (active batches and inactive batches) are used to calculate the OpenMC and SRAC k-eff value validation.
The use of OpenMC code needs validation to see the level of accuracy of the code that has been created.Validation is carried out by comparing the results of reactor criticality calculations in the OpenMC and SRAC programs.The reactor criticality parameter is in the form of an effective multiplication factor (k-eff) value generated during a predetermined burn-up time.The code is compared to SRAC because it has been validated for a long time and has a license or copyright.The validation result is affected by the minimum number of particles used.The minimum number of particles used should have a convergent k-eff value.Validation calculations have been carried out by previous researchers using UC-PuC fuel in GFR reactors [20].The results of this study show that the OpenMC code made is quite accurate and validated against the results of SRAC calculations.Therefore, in this study, further validation calculations were carried out on different reactor fuels.This study used fuel in

Design and Calculation Method
The study determined the minimum particle count and validated the OpenMC code using UN PuN fuel with a plutonium composition of 10% during 5 years of burn-up.The 10% plutonium composition is used because it has a more stable k-eff value or flat chart trend and is critical until the end of combustion (k-eff ≥ 1).The volume fraction of UN-PuN fuel used is 60% because it gets a more optimal criticality value.Cladding uses Silicon Carbide (SiC) material because it has a high melting point and low chemical influence [21].This research requires parameter data and GFR reactor design specifications as a reference in conducting simulation calculations.The data refers to the parameters and specifications of the previously optimized SRAC code, which are listed in Table 1.SRAC reference data uses JENDL 3.2 version of cross section library data [22].Data analysis in this study consisted of 3 stages, i.e determining the minimum number of particles, determining the minimum number of cycles through entropy data, and code validation.Determination of the minimum number of particles is done by varying the number of particles smallest to largest to show a pattern of k-eff values that do not fluctuate or convergent.The minimum number of particles also adjusts to the specifications of the device used.The more particles, the running simulation process runs quite long and heavy.The simulation of determining the minimum number of particles in this study has a range of 100-50000 particles tested at each point.The range of values has shown a fairly high level of accuracy.After the data for the minimum number of particles is determined, entropy calculations are performed to determine the minimum number of cycles (active batch and inactive batch) in the OpenMC and SRAC k-eff value validation calculations.Code validation is done by comparing the k-eff value between the two codes (OpenMC and SRAC) against the burn-up time for 5 years.The code can be said to be validated if it has a maximum error value (%error k-eff) less than 1% [23].The error value is obtained from the calculation of the difference between the k-eff value (∆k-eff) of the OpenMC and SRAC code calculations.If the error value is still more than 1%, then a reset of the parameters and specifications of the GFR reactor design is carried out.The validated OpenMC code can be used by researchers in further research related to neutronic analysis in UN-PuN-fueled GFR reactors.The following formulas and research flows used in this study are as follows: production of neutrons from fission in one generation k = neutron absorption and leakage in the previous generation

Results and Discussion
The calculation results of determining the minimum number of particles are shown in Figure 2 which presents a graph of the relationship between the k-eff value and the number of particles at each point.The calculation starts from particles with a number of 100 to 50000 particles.Based on Figure 2 shows the results of chart trends in the range of 100 to 35000 charts k-eff still fluctuating.While in the range of 35000 to 50000 the value of k-eff minimal significant change or not fluctuating.Therefore, researchers use a minimum particle count of 50000 particles because these values have already converged.In addition, it also considers the ability of computer specifications used when conducting simulations.The more particles used, the longer the simulation process will be.A total of 50000 particles were simulated with iterations of 100 batches and 30 inactives.Batch relates to the number of repetitions for a random sample, while inactive relates to the number of batches that are inactive.SRAC and OpenMC graphs have similar graphic trends.SRAC and OpenMC graphics have the characteristic of sloping from the beginning to the end of burn-up.This shows the characteristics of GFR reactors that have good breeding because they use fast neutrons in a fission chain reaction.The accuracy of the calculation of the k-eff between the two codes for each burn-up point can be said to be validated because it has a maximum error value of < 1%, which is 0.819%.The maximum difference k-eff (∆keff) is 0.008.Data on the difference and error values for each year of burn-up are shown in Table 2.The OpenMC code created is valid and precise, so it can be used for further calculations related to neutronic analysis of UN-PuN-fueled GFR reactors.

Conclusion
Research that has been done can be concluded that the minimum number of particles that can be used in OpenMC simulations is 50000 particles because it has shown convergent values or not fluctuating.The use of cycle of 100 active batches, 30 inactive batches, and 50000 particles resulted in accurate validation values of k-eff difference (∆k-eff) of 0.008 and maximum error (% error k-eff) of 0.819%.

Acknowledment
The

10th
Asian Physics Symposium (APS 2023) Journal of Physics: Conference Series 2734 (2024) 012065 IOP Publishing doi:10.1088/1742-6596/2734/1/0120653 the form of UN-PuN or Uranium Plutonium Nitride to analyze the minimum number of particles and validation error values.The reactor used is a GFR with a power of 300 MWth with the type of SMR or Small Modular Reactor and burn-up time for 5 years.

Figure 1 .
Figure 1.Flowchart of OpenMC code validation research

Figure 2 .
Figure 2. Determination of minimum number of particles

Figure 3 .
Figure 3. Determination of minimum number of cycles

Table 1 .
GFR reactor design parameters and specifications

Table 2 .
OpenMC and SRAC code validation error and difference value data author would like to thank the lecturers who are members of the Nuclear Science And Technology Applications 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 Service Re-search Group Grant (KeRis) research grant (DiMas) with agreement number No. 3274/UN25.3.1/LT/2023.