عدم اطمینان و تجزیه و تحلیل حساسیت از رفتار حرارتی سوخت هسته ای

In the global framework of nuclear fuel behavior simulation, the response of the models describing the physical phenomena occurring during the irradiation in reactor is mainly conditioned by the confidence in the calculated temperature of the fuel. Amongst all parameters influencing the temperature calculation in our fuel rod simulation code (METEOR V2), several sources of uncertainty have been identified as being the most sensitive: thermal conductivity of UO2, radial distribution of power in the fuel pellet, local linear heat rate in the fuel rod, geometry of the pellet and thermal transfer in the gap. Expert judgment and inverse methods have been used to model the uncertainty of these parameters using theoretical distributions and correlation matrices. Propagation of these uncertainties in the METEOR V2 code using the URANIE framework and a Monte-Carlo technique has been performed in different experimental irradiations of UO2 fuel. At every time step of the simulated experiments, we get a temperature statistical distribution which results from the initial distributions of the uncertain parameters. We then can estimate confidence intervals of the calculated temperature. In order to quantify the sensitivity of the calculated temperature to each of the uncertain input parameters and data, we have also performed a sensitivity analysis using the Sobol’ indices at first order.

Most of the physical phenomena occurring in nuclear fuel elements during their irradiation in nuclear power plants are controlled by the temperature. As a matter of interest, we can mention fission product release, fuel densification and swelling, creep of cladding and fuel, etc. In our fuel behavior simulation code, the models corresponding to all these phenomena are very much sensitive to the temperature calculated in the fuel. The confidence we have in the calculated behavior of the code depends mainly on the confidence in the calculated temperature.

From a demonstrative point of view, the uncertainty process has been implemented in its totality: specification of the physical problem, quantification and modeling of the uncertainty sources, uncertainty propagation and quantification of the variance of the calculated temperature, and last sensitivity analysis and importance ranking. This process is validated by the fact that in the case of thermal irradiation experiments, the measurement is contained in the calculated confidence interval in both low and high burn-up tests. In the case of low burn-up irradiation, the width of the 95% confidence interval of the calculated temperature is about ±15 K at 230 W/cm. For high burn-up and transient irradiations, this confidence interval is about ±80 K for a temperature around 1670 K and ±110 K around 1920 K. In all cases, most of this uncertainty is due to the uncertainty on the linear heat rate, and to the lack of knowledge of the thermal conductivity of UO2 either fresh or in irradiation condition. This quantifies the reliability of our fuel performance code METEOR V2 in the area of thermal behavior simulation. Even if the uncertainty on calculated temperature seems limited, its impact on the calculation of other phenomena (fission gas release for example) can be more dramatic. The uncertainty on the linear heat rate being irreducible because of the method used (Muller et al., 2007), the only way to improve the reliability of the calculated temperature is to reduce the uncertainty on the thermal conductivity of fresh UO2 fuel. Improvements in the experimental technique (reduction of the uncertainty on each point) and more numerous data would help in this way.