# PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

## Abstract

This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions.more »

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1361421

- Report Number(s):
- INL/JOU-16-38537

Journal ID: ISSN 0022-3115; PII: S0022311516302793

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Nuclear Materials; Journal Volume: 478; Journal Issue: C

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; Diffusion; Fission gas release; Fuel modeling; Numerical algorithms; PolyPole

### Citation Formats

```
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., and Pastore, G..
```*PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release*. United States: N. p., 2016.
Web. doi:10.1016/j.jnucmat.2016.06.028.

```
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., & Pastore, G..
```*PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release*. United States. doi:10.1016/j.jnucmat.2016.06.028.

```
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., and Pastore, G.. Thu .
"PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release". United States. doi:10.1016/j.jnucmat.2016.06.028. https://www.osti.gov/servlets/purl/1361421.
```

```
@article{osti_1361421,
```

title = {PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release},

author = {Pizzocri, D. and Rabiti, C. and Luzzi, L. and Barani, T. and Van Uffelen, P. and Pastore, G.},

abstractNote = {This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.},

doi = {10.1016/j.jnucmat.2016.06.028},

journal = {Journal of Nuclear Materials},

number = C,

volume = 478,

place = {United States},

year = {Thu Sep 01 00:00:00 EDT 2016},

month = {Thu Sep 01 00:00:00 EDT 2016}

}