Presented at the COMSOL Conference 2010 Paris
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1 Presented at the CMSL Conference 2010 Paris
2 Solid State Transport of Reactive Charged Particles Application to Metal xidation P. BUTTIN, B. MALKI, P. BARBERIS, B. BARUX
3 Introduction Zirconium corrosion in power plant coolant Fuel assembly life Zr Nuclear Power Plant Picture AREVA NP Fuel assembly Picture AREVA NP Understanding corrosion key factor impact on oxide growth Entreprise - AREVA NP - All rights reserved - p.3
4 bjectives Develop a numerical model for zirconium oxidation Simulation using CMSL Multiphysics Multicomponent transport coupled with internal chemical reaction Zr 2 Zr V Coolant K + = V e V V µ e Anionic conductivity transport V, V, e Electrons trapping V - + e = V - Constraints on system : Electroneutrality + Stoichiometry + Chemical reaction Entreprise - AREVA NP - All rights reserved - p.4
5 Conservative Ensembles Considering ensemble transport (J. Maier, 1994) Conservative ensembles xygen ensemble (Vacancies, oxygen interstitial) Cross effect Electron ensemble (Electrons, hole, ) V V e Thermodynamic of irreversible processes J J e = s = s e η η s s e ee η η e e (Lankhorst, 1996) Ensembles are conservatives for the chemical reaction Chemical reaction : Cross effect between ensembles fluxes Entreprise - AREVA NP - All rights reserved - p.5
6 xygen Flux xygen flux given by: (Wagner, 1977) σ J = µ = D c 4F amb δ 2 Chemical diffusion coefficient σ amb dµ dc δ σ amb dµ D = 2 4F dc : Ambipolar conductivity : Chemical capacity Constraints on system c + 2 c c = 0 Electroneutrality V K e V c + c + c = 0 Stoichiometry V V = c V c V c e Chemical Reaction Transport equation: c t = D δ c All system s information are given by D δ Entreprise - AREVA NP - All rights reserved - p.6
7 xide Growth xide growth given by: de dt ox 1 = J Boundary condition on internal interface co,int Keeping subdomain constant: x = xreal 1 ; e = e reduced real reduced ox ox Simulation in one dimension: xide growth model formulated as boundary weak form Metal xide Coolant e ox de ox /dt, δ int Zr 2-δ δ ext Entreprise - AREVA NP - All rights reserved - p.7
8 xide Growth Model parameters Symbol K D V Description Chemical equilibrium between vacancies Diffusion coefficient of vacancies V D V Diffusion coefficient of vacancies V D e δ int δ ext T Diffusion coefficient of electrons Zirconia non stoichiometry at the M/ interface Zirconia non stoichiometry at the surface Temperature Entreprise - AREVA NP - All rights reserved - p.8
9 Simulations Comparison with experimental data xide thickness (µm) Experimental data* xidation model Time (days) * J. Vermoyal, A. Hammou, L. Dessemond, A. Frichet, Elec. Acta, 2002 Simulation gives good results according to experimental data Entreprise - AREVA NP - All rights reserved - p.9
10 Effect on reaction and transport coefficient Simulations xide thickness (µm) D V D V D V = D V = 0,1D V = 10D V V ionized trapping Time (days) Effect of electron trapping on oxide growth kinetic Entreprise - AREVA NP - All rights reserved - p.10
11 Simulations Effect on zirconia non stoichiometry on inner interface Zr 2-δ xide thickness (µm) 1,8 δ 1 1,2 0,6 δ 2 δ 3 δ 1 > δ 2 > δ 3 0, Time (days) Effect oxygen chemical potential gradient through the oxide Entreprise - AREVA NP - All rights reserved - p.11
12 Conclusions Development of an oxide growth model for anionic transport Model is not specific for zirconium oxidation Assessment of the control parameters on growth kinetics Transport coefficient, stoichiometry, Environmental effect could be add on the model 2D model version when symmetry is broken Entreprise - AREVA NP - All rights reserved - p.12
13 Thank you for your attention! Entreprise - AREVA NP - All rights reserved - p.13
14 Any reproduction, alteration, transmission to any third party or publication in whole or in part of this document and/or its content is prohibited unless AREVA NP has provided its prior and written consent. This document and any information it contains shall not be used for any other purpose than the one for which they were provided. Legal action may be taken against any infringer and/or any person breaching the aforementioned obligations. Entreprise - AREVA NP - All rights reserved - p.14
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