1. Introduction
In the context of global carbon emissions and the development of carbon-neutral energy, clean energy has become crucial in addressing the challenges posed by energy structure and climate change [
1]. Nuclear energy is a green and clean source with high energy density, efficient power generation, and low carbon emissions [
2]. Compared to other forms of clean energy, such as wind and solar power, nuclear energy is less susceptible to natural environmental factors, and its efficiency and stability more effectively meet the demand for sustainable energy [
3,
4]. Despite its numerous advantages, nuclear energy has many safety concerns [
5]. Therefore, future developments in nuclear technology will prioritize intrinsic safety measures and minimize radioactive material leakage rates [
6,
7].
With advancements in fourth-generation nuclear technology. Tri-structural isotropic coated fuel particles (referred to as TRISO-dispersed fuel particles) are widely used in advanced reactors [
8]. TRISO is an abbreviation of Tri-structural ISOtropic fuel particles, which is a new type of reactor fuel. Tri-structural means that fuel particles are composed of three different structural layers: the fuel core, pyrolytic carbon coating layer and silicon carbide coating layer. The multilayer structure is used to improve the safety and operation performance of nuclear reactors. Isotropic means that the structure of TRISO particles is homogeneous and isotropic in all directions.
The main purpose of TRISO fuel particle design is to improve the intrinsic safety and stability of nuclear reactor fuel. Intrinsic safety means that the reactor has its own safety attributes in design and manufacture. This safety attribute is not disturbed by the outside world and can maintain stable and safe operation even in the case of being out of control or in an accident. For dispersed fuel particles, the coating layer has a certain sealing function, which can effectively prevent the leakage of radioactive fuel and products in the fuel core [
9]; the porous structure of the loose pyrolytic carbon coating layer provides storage space for gaseous fission products, while absorbing the core swelling [
9] caused by fuel core depletion, reducing the risk of fuel element damage. Consequently, TRISO-dispersed fuel particles offer a new direction in enhancing intrinsic safety features and optimizing the use of nuclear energy. Combined with passive heat removal systems, they become essential technologies for small modular reactors (SMR) and micro-reactors.
However, the engineering application of TRISO-dispersed fuel particles also has many shortcomings. For example, the complex engineering structure introduces a significant number of engineering uncertainties. Research on TRISO-dispersed fuel particle intrinsic uncertainty has become a significant issue. The most recent research project addressing this is the International Atomic Energy Agency’s International Coordinated Research Program on Modeling Uncertainty Analysis for High-Temperature Gas-Cooled Reactors (IAEA HTGR UAM CRP) [
10]. The results show that the uncertainty induced by the random distribution of TRISO-dispersed fuel particles is not very large, especially for the reactor’s effective multiplication factor (
Keff), which does not exceed 30 pcm [
11]. However, the fuel manufacturing tolerances and geometrical information induce significant uncertainty in the calculation. Chen Youying, Master of Science from Harbin Engineering University, investigated the influences of the packing fraction of dispersed fuel particles and random dispersion on the uncertainty induced by the transport calculation using different models for a high-temperature gas-cooled reactor with a spherical bed at the fuel sphere scale [
12]. Lou Lei, a researcher of the Nuclear Power Institute of China, investigated the relationship between the deviation of the dispersed fuel uniform mixing model and the diameter of fuel particles and fuel enrichment using the reactor Monte Carlo program (RMC). When the fuel enrichment or particle size is large, the uniform mixing model will bring a large calculation deviation [
13]. Zhang Yongdong, Master of the Shanghai Institute of Applied Physics, Chinese Academy of Sciences, explored the effects of kernel radius and cladding layer thickness distribution on the probability of failure using random sampling [
14] and found that the effective combustion depth of fuel was significantly reduced due to the spatial self-shielding effect and the scattering probability of each layer of material thickness. Dr. Fan Kai, from the Institute of Nuclear Energy and New Energy Technology, Tsinghua University, established a geometric model of the appropriate fuel particle random distribution using the MCNP code and compared it with the regular distribution model to analyze the effect of distribution randomness on the effective multiplication factor [
15]. The results showed that the fuel particles’ random distribution leads to a slightly larger effective multiplication factor than that of the regular model, and the main reason for the deviation between the two models is the difference in the spatial and angular distribution of the two-particle arrangements [
15]. G. Kepisty of AGH University of Science and Technology used 100 independent copies of Monte Carlo burnup simulations to study the statistical error propagation of the full-core HTR model [
16]. The results show that the actual and apparent changes of
Keff are close to each other from the beginning of irradiation to high burnup. It is difficult to use
Keff to observe statistical error propagation in high burnup. The increasing real variation of
Keff has been detected with a delay after entering the regime of unstable simulation at a high burnup.
The above research demonstrates that the current international research situation mainly studies the influence of single-factor uncertainty, especially for the spatially random effect of dispersed fuel particles. However, there are few studies on the comprehensive influence of multiple factors combined with engineering parameters. Therefore, this study focuses on the quantitative analysis of multi-factor comprehensive uncertainty, specifically the following three points: (1) random dispersion uncertainty of the random distribution model and the difference between models under different packing fractions; (2) the effect of material thickness of each layer of TRISO-dispersed fuel particles; and (3) combined with fuel enrichment random sampling, the overall uncertainty of the combination of the random distribution of material thickness in each layer of particles and the spatially random distribution. In the manufacturing process, the errors introduced by materials, processes, equipment and environmental conditions are difficult to completely control and the accuracy can only be controlled within a reasonable range. Therefore, the uncertainty of engineering parameters studied in this paper is accidental uncertainty, which cannot be avoided and has nothing to do with the calculation process itself.
This study concludes that the overall uncertainty of engineering parameters on the transport calculation and the power distribution, which can help to improve nuclear energy safety, can be comprehensively assessed by uncertainty analysis of key parameters and can retain sufficient margins and corresponding measures to ensure the safe operation of the reactor. In addition, it can help to optimize reactor design and operation and enable understanding of potential fluctuations during operation, thus optimizing system performance and efficiency, improving reactor energy efficiency, reducing operating costs, and minimizing environmental impact. In summary, uncertainty analysis is indispensable to TRISO-dispersed fuel particles in nuclear energy engineering.
4. Conclusions
In this study, uncertainty quantification of engineering parameters of TRISO-dispersed fuel particles was conducted, and significant results were obtained. Firstly, the differences between the regular distribution model of the TRISO-dispersed fuel particles and the random distribution model at different packing fractions were analyzed due to the uncertainty introduced by the random distribution and the differences between the two models. Secondly, the effect of the thickness of TRISO-dispersed fuel particles on the transport calculation was investigated. Additionally, quantitative uncertainty analysis was performed by sampling the enrichment sample space, combined with a high-fidelity random model of spatial location random dispersion and multilayer material randomness.
As demonstrated, there is a difference between the regular and random distribution models in transportation calculation, but the difference is not obvious. As the packing fraction increased, the uncertainty induced by the random dispersion of fuel particles increased and then decreased; when the packing fraction was between 25 and 30%, the uncertainty induced by random distribution was maximized (0.029%). The maximum relative difference between the regular distribution model and the random distribution model is 2.066% when the packing fraction is 5%. Under constant UO2 loading, as the radius of the UO2 kernel increases, Keff becomes smaller due to the spatial self-shielding effect and the decrease in fuel utilization. As the thicknesses of Buffer and IPyC cladding layers gradually increase, Keff increases due to the enhancement of moderating ability and increased scattering probability. The quantitative uncertainty induced analysis of uncertainty on engineering parameters such as enrichment, random dispersion, and thickness using the Sampling Statistics Theory showed that the extreme difference is 0.04996, the standard deviation is 0.01003, the relative standard deviation is 0.851%, the 95% confidence interval is (1.15896, 1.19828), and there is a strong positive correlation between the transport calculation results and enrichment samples. In the power distribution, the uncertainty induced by engineering parameters is small in the center region of the reactor core and gradually increases to the periphery of the reactor core, and the maximum is 1.495% in the edge region of the reactor core.
The results of this study show that the transport calculation of TRISO-dispersed fuel particles is affected by several uncertainty factors, the most important of which is fuel enrichment. At the same time, fuel enrichment will be coupled with other engineering parameters to form overall uncertainty. These results provide an important reference for the engineering design and optimization analysis of the TRISO-dispersed fuel particle reactor.