Oxygen Diffusion Model in LWR Fuel using Thermochimica in

MOOSE/BISON

Theodore M. Besmann

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Outline

Modeling of oxygen diffusion in LWR nuclear fuelImplementation of thermodynamics model for nuclear

fuel and for oxygen diffusion in nuclear fuelExamples

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Motivation

Thermochemical equilibrium calculations are only one of the tools for estimation of the nuclear fuel’s chemical state and behavior.

During irradiation, the FP are continuously generated and change due to transmutation and decay, the oxygen chemical potential changes with the burnup and production of fission products, and temperature and chemical potential gradients affect the formation of various phases and species transport and spatial distribution.

A thermochemistry equilibrium solver needs to be a part of a larger multi-physics simulation system in order to achieve its full potential.

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Thermochemical Model of LWR Nuclear Fuel

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Modeling of Oxygen Transport in LWR Fuel

Modeling of species diffusion in multicomponent systems is a challenging problem

For simple systems, Fick’s law approximation is commonly usedThe concentration gradients are the driving forces of diffusion.

Recent work on multi-physics modeling of oxygen transport in hyper-stoichiometric LWR fuel assume that they are pseudo-binary systems that can be described as dilute solutions of oxygen interstitials in the oxygen sublattice.

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Modeling of Oxygen Transport in LWR Fuel

For hyper-stoichiometric oxides, the atomic fractions of oxygen interstitials, c, are then related to the deviation from stoichiometry, x, in the fluorite phase.X = O/M – 2 ; C = X

The problem is cast in the form of standard Fickian diffusion with x as the primary transporting variable.

The assumption of a binary system is adequate for fresh fuel.

For complex multicomponent systems, a more fitting form of the driving force for species transport is the gradient of their chemical potential.

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Modeling of Oxygen Transport in LWR Fuel

The current implementation of O2 transport model follows LeClaire’s approach of using Fick’s law with the diffusion coefficient D fitted as an empirical function of temperature and concentration.

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Implementation of O2 Transport Model in BISON

Based on the deviation of stoichiometry of the UO2 solid solution phase.

The calculation of the deviation is based on the O/M ratio of the UO2 solid solution phase.

The assumption is that a three sub-lattice CEF model is used to represent this phase. The first sub-lattice represents the cations on their normal sites, the second sub-lattice represents oxygen anions on their normal sites (or vacancies) and the third sublattice represents interstitial oxygen anions or vacancies.

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Thermal and O2 Transport Models Implementation

Material model properties for thermal diffusion and O2 diffusion were taken from papers by Mihaila et al. 2009, 2012, 2013.

Thermal diffusion

O2 diffusion

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Implementation of O2 Transport Model in BISON

Thermodynamic calculations are performed as initial conditions for O2 transportFor given burnup, fission product inventory is calculated and used

as initial condition to calculate O/M and deviation from stoichiometry x=O/M-2

Oxygen diffusion is coupled with thermal diffusion and initial conditions for x

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Example Model Input for Initial Conditions

 [ICs] [./mat_1]

block = 1

type = UO2PXOxygenIc

variable = oxygen

temp = temp

pressure = 1.0

U = 3.6971E+03

O = 8.4030E+03

Pu = 5.7050E+01

Ba = 3.5550E+01

Ce = 5.4720E+01

Cs = 5.7380E+01

I = 5.3120E+00

La = 2.5200E+01

  Mo = 1.0080E+02 Nd = 7.8800E+01

Pd = 6.7630E+01

Pr = 2.1840E+01

Rb = 9.3000E+00

Rh = 7.5310E+00

Ru = 8.9420E+01

Sr = 2.1870E+01

Tc = 1.8530E+01

Te = 1.2290E+01

Xe = 1.3150E+02

Y = 1.1550E+01

Zr = 9.8930E+01

[../]

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Example Problem

Temperature (left) and oxygen (right) distribution for a test problem with a temperature gradient in a cubic domain.

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Conclusions

A computational model for O2 diffusion in LWR fuel was developed

The model is based on the deviation of stoichiometry of the UO2 solid solution phase.

The model is used for the demonstration of the capabilities of the thermodynamics solver for simulation of the state of nuclear fuel.

A more rigorous model based on the chemical potential as the driving force for the diffusion is under development.