Fission gas release

Fuel performance codes [1] like TRANSURANUS [2, 3] predict the behavior of nuclear fuel rods, such as the temperature, internal pressure, and fission gas release. This use case presents several simplified Gaussian process surrogate models for fission gas release fitted to training data generated with TRANSURANUS. Fission gas release is expressed as a fraction of what is created by the fission reaction. They are derived from the work by [robertson2024].

Each of the models has two inputs:

  • Single atom diffusion multiplier denoted by x_{\mathrm{diff}}.

  • Fraction released due to micro-cracking, denoted by x_{\mathrm{crack}}.

Each model corresponds to different sets of experimental conditions. The number of different sets of environmental conditions is denoted by \sampleSize_{\mathrm{exp}}, and in the following we use the index i (1 \leq i \leq \sampleSize_{\mathrm{exp}}) to identify a given set of environmental conditions.

For each set of environmental conditions i, fission gas release was measured, and the measured value is denoted by y_i. The measured values are extracted from the International Fuel Performance Experiments (IFPE) database. Measurement uncertainty is represented by a normal distribution with mean y_i, and its standard deviation \sigma_{y_i} is a known function of y_i:

\sigma_{y_i} = \sqrt{\left( \frac{y_i}{20} \right)^2 + 10^{-4}}

The model corresponding to the environmental conditions i is denoted by \model_i. The values of the single atom diffusion multiplier x_{\mathrm{diff}, i} and of the fraction of gas released due to micro-cracking x_{\mathrm{crack}, i} corresponding to the measured y_i are unobserved.

The relationships between these quantities are represented in the following network. Full arrows represent deterministic relationships, while dashed arrows represent probabilistic relationships (e.g. a truncated normal distribution, with truncation bounds determined by the range of the model).

Relationships between the variables

References

  • [1] Van Uffelen, P., Hales J., Li, W., Rossiter, G. and Williamson, R. A review of fuel performance modelling, J. Nucl. Mater., vol. 516, pp. 373–412, 2019.

  • [2] Lassmann K., TRANSURANUS: a fuel rod analysis code ready for use, J. Nucl. Mater., vol. 188, pp. 295–302, 1992. pdf

  • [3] Magni, A., Del Nevo, A., Luzzi, L., Rozzia, D., Adorni, M., Schubert, A., and Van Uffelen, P., The TRANSURANUS fuel performance code, in Nuclear Power Plant Design and Analysis Codes, Elsevier, 2021, pp. 161–205. doi: 10.1016/B978-0-12-818190-4.00008-5.

  • [robertson2024]

Acknowledgement

The project this use case is derived of was developed as part of WP6 - “Advance fuel performance modeling” in the EU-supported APIS project, with the aim to deliver a new calibration methodology to the stakeholders. Funded by the European Union. Views and opinions expressed on the present page, and in the examples built upon this use case are however those of the authors only and do not necessarily reflect those of the European Union or Euratom. Neither the European Union nor the granting authority can be held responsible for them. Further, the project was developed with funding from the Swedish Nuclear Centre.

API documentation

class FissionGasRelease

Data class for the fission gas release example.

Attributes:
measurement_valuesPoint

Observed values y_i (1 \leq i \leq \sampleSize_{\mathrm{exp}}) taken from the International Fuel Performance Experiments (IFPE) database

measurement_uncertaintyFunction

Function y_i \mapsto \sigma_{y_i}

modelslist of Function

List of the \model_i models (1 \leq i \leq \sampleSize_{\mathrm{exp}})

Methods

getInputDescription

Examples

>>> from openturns.usecases import fission_gas
>>> # Load the fission gas release models
>>> fgr = fission_gas.FissionGasRelease()

Examples based on this use case

Bayesian calibration of hierarchical fission gas release models

Bayesian calibration of hierarchical fission gas release models