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Uncertainties on Thermodynamic and Physical Property DataBases for Severe Accidents and their Consequences on Safety Calculations. Christophe JOURNEAU, Claude BRAYER and Pascal PILUSO CEA Cadarache, France DEN/CAD/DTN/STRI/LMA 02/05/2006 1

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02/05/2006 1 DEN/CAD/DTN/STRI/LMA

Uncertainties on Thermodynamic and Physical Property DataBases for Severe Accidents and their Consequences on Safety Calculations.

Christophe JOURNEAU, Claude BRAYER and Pascal PILUSO CEA Cadarache, France

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Outline

  • Introduction
  • Uncertainties on phase diagrams
  • Uncertainties on Physical Properties
  • Application to Severe Accident

Calculations

–Example : Spreading calculations

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

General procedure for calculation

  • Composition and Temperature of corium
  • Thermodynamic Modelling

– Repartition of phases (liquids, solids, vapours) – Composition of Each Phase

  • Physical Properties estimation

– Database – Mixing Law

  • Calculation of corium behaviour using

calculated properties

  • Determination of new temperature/composition
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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Some aspects of thermodynamic modelling

  • Research of the phases composition and

proportions minimizing the system Integral Gibbs Energy G= min or dG=0 and d2G≥0 dG= -SdT+VdP + Σμidni + …

  • Thermodynamic database

+ Minimization software

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Data in Thermodynamic Databases

  • Thermodynamic data for pure elements

(compiled by SGTE)

  • Thermodynamic data for stoichiometric substances
  • H formation at 298.15K (from pure elements)
  • Entropy at 298.15K
  • Cp(T) from 298.15K to gaseous state
  • Thermodynamic data for solutions
  • Mixing laws ( excess Gibbs energy)

G= Greference + Gideal mixing + Gexcess

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

How is the data produced ?

  • Assessment of experimental work.

– Some data (H,Cp) may be directly available – Usually, indirect validation on phase diagrams, partial pressures,…. – Weighing of different works. Expert judgement.

  • Choice of modelling (1 or n sub-lattices, order of excess terms,

nonstoichiometries….)

  • Use of an optimizer to determine the dataset which reproduces

the best the experimental data.

– This operation is done for binary interaction terms first, then on ternaries,…. – The database is incremented gradually, no global reoptimization.

  • NUCLEA, European Database

– 18 elements – >300 binary and ternary diagrams

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Causes of Uncertainties

  • Experimental errors (esp. at high temperatures)
  • Exhaustivity of assessed experiments
  • Modelling errors
  • Optimization errors
  • Errors due to the execution of Gibbs Minimizer

+ Poor convergence/ divergence problems ! (metastability zones or numerical analysis ?)

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

How can we assess the uncertainties? (from an end-user standpoint)

  • The database has been optimized as a whole.

⇒ It is impossible to study independantly the effect of one term in the DB.

  • Expert judgement provided ratings to subsystems (*,**,***,****)

Study of the evolution of database results with successive versions => order of magnitude of uncertainties at version n-1.

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

TMI2 corium liquid fraction

  • Differences < 1.2%w => very consistent output.

TMI2 thermodynamic equilibrium 0,00% 20,00% 40,00% 60,00% 80,00% 100,00% 1 2 1 4 1 6 1 8 2 2 2 2 4 2 6 2 8 3 Temperature (K) Liquid mass fraction (%)

  • 2,00%
  • 1,20%
  • 0,40%

0,40% 1,20% 2,00% Delta liquid fraction (%)

NTDIV012 NTDIV012-TDIV01 NTDIV012-TDIV992

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Typical EPR Concrete

36%w SiO2, 49%w Fe2O3, 5%w CaO, 6%w Al2O3, 4% H2O

  • Large

discrepencies (100-200K) between THMO and TDBCR

  • Consistency of

TDBCR versions.

  • SiO2-Fe2O3

system rated *

typical EPR-concrete composition

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 Temperature K Liquid mass fraction THMO 99 TDBCR971 TDBCR981 TDBCR992 TDBCR001

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Gaseous species over corium-concrete mixture at 2573 K

No large evolutions except appearances of new phases: UO3, Al(OH)2, Disapearance of baryum hydroxides.

10%H2 - 90%H2O atmosphere 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

O1SI1(G) H1(G) FE1(G) AG1(G) H1O1(G) FE1H2O2(G) O2U1(G) FE1O1(G) O2SI1(G) O2SI2(G) O2ZR1(G) CA1H1O1(G) AL1H1O2(G) H1IN1O1(G) H1SI1(G) O1(G) IN1(G) BA1H1O1(G) H1IN1(G) AG2(G) SI1(G) BA1H2O2(G) H4SI1(G) AL1H1(G) AL1(G) CA1(G) O3U1(G) H3SI1(G) H2SI1(G) CA1H2O2(G) AL1H1O1(G) AL1H2O2(G)

atm TDBCR972 TDBCR981 TDBCR992 TDBCR001

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Gases over In-vessel corium at 3000K

  • Variations can reach factors of 3-10
  • New gaseous species appeared in newer versions (ex. BaH, BaOH, HSr, …)

In-Vessel gases 3000 K [ Test0A1 in 100 m3 ]

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 H2(G) H1(G) IN1(G) FE1(G) SR1(G) O2U1(G) O1U1(G) H1IN1(G) O2ZR1(G) LA1O1(G) H2O1(G) BA1(G) H1O1SR1(G) H1IN1O1(G) ZR1(G) H1ZR1(G) H1O1(G) O1SR1(G) LA1(G) FE1O1(G) U1(G) O3U1(G) BA1O1(G) O1ZR1(G) AG2(G) AG1(G) BA1H1O1(G) BA1H1(G) H1SR1(G) IN2O1(G) atm

TDBCR972 TDBCR981 TDBIV992 TDBCR001 NDTiv012

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Conclusions on Thermodynamic Uncertainties

  • the thermodynamic outputs uncertainties are decreasing with the

latest versions of the databases. All the thermodynamic outputs don’t have the same uncertainties,

  • for the liquidus and solidus temperatures and for the enthalpy, the

uncertainties are getting lower for the successive databases,

  • for the liquid, the uncertainties of the compositions are low,
  • between solidus and liquidus temperatures, the uncertainties are

may be important, especially for less validated systems,

  • for the gaseous substances, the uncertainties are mainly due to the

absence of some vapours from the bases

  • if all the pseudo-binary systems that constitute the corium composition

have been well assessed, it’s possible to have a good confidence that uncertainties on temperature will be less than 50K ;

  • if one or more pseudo-binary systems that constitute the corium

composition have a low assessment quality, at least an uncertainty on the temperature of ± 100 K could be expected.

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Properties of Multiphasic Corium Mixtures

  • Database of Pure-Substance Physical properties
  • Mixture Physical properties depend on the spatial repartition of

phases

– Thermalhydraulic steady state => phase segregation – Rapid cooling => dendrites – Bubbling + shear => emulsions/ suspensions

  • Only one phase
  • 2 liquids (Sedimented)
  • 2 liquids (Emulsioned)
  • Dendritic mushy zone (percolation)
  • Semi-solid suspension
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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Density of Metallic Uranium

  • Solid phase data quite consistent
  • Large dispersion of liquid phase data
  • Critical review by Fischer (FZK) 2000

ρliq = 17270 –1.6010(T-1408) (brown curve)

Uranium

13 000 14 000 15 000 16 000 17 000 18 000 19 000 20 000 300 1300 2300 3300 Temperature K Density kg/m3

Boivineau et al. 93 TAPP McClelland & Sze, 1995 Rohr Wittenberg 70 Grosse et al 61 Fischer 2000 Touloukian 75(alpha phase) MATPRO HEMATIC Touloukian 75 (beta phase) Touloukian (gamma phase) Sheldon & Mulford 1991 Shpil'rain et al. 88 Bridge 56 MATPRO (beta phase) Rohr & Wittenberg 1970(gamma) MATPRO (gamma phase) Lloyd 65 Drottning 82

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Mixing laws for solutions (1)

Hypothesis: Ideal mixing – No excess volume Applicable to solid and liquid solutions

– Molecules of similar molar volumes (at ±30 %) – Excess volumes for metallic alloys (Crawley 74)

  • Maximum : -20 % for Na-In - 15 % for Fe-Si

(at 50-50%at

)

  • Generally < ± 3 %

– For oxides (slags, natural silicates), Excess volume generally < 1% (Nelson & Carmichael 1974)

excess i i i

V V y V + ⋅ =∑

UO2 30.5 cm3/mol U 13.8 ZrO2 22.3 Zr 14.6 SiO2 27 Fe Fe 7.9 7.9 (FeO)2 26 Cr Cr 8.2 8.2

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Which density for liquids below Tfusion ?

  • Between Tfusion andTsol, the

refractory component is still present in the liquid phase

  • Which density to be used

below Tfusion ?

  • UO2 present in corium-concrete
  • xidic phase for 1000 K below

Tfusion !! Hypothesis #1

Constant volume

Vmolar (T<Tfusion) = Vmolar (Tfusion) Hypothesis #2

Constant expansion coefficient Vmolar(T) = Vmolar (Tfusion) [1 + α (Tfusion) (T-Tfusion)]

SiO2 %mol UO2 Tfusion T sol

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

The 2 hypotheses below Tfusion

UO2

7500 8000 8500 9000 9500 10000 10500 11000 11500 500 1000 1500 2000 2500 3000 3500 4000 Temperature K density kg/m3

JK Fink & Petri 97 JK Fink & Petri 97 (liquid) liquid hypoth 1 Fink et al. 81 Fink et al 81 Strizhov et al. 95 Chu et al. 95 Espinosa et al 2000 MAAP Christensen 1962

Hypohtesis #2 Hypothesis #1

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Influence of these uncertainties to global calculation

Different types of uncertainties are present when calculating a SA experiment or a reactor case.

  • 1. Uncertainties on initial/boundary conditions

2.Uncertainties on physical properties 3.Uncertainties due to modelling approximations

  • Development of a methodology

– n-Parameter analysis – 2 values for each parameter => 2n calculations – Reduced map

  • Example of Application

– VE-U1 Spreading test – Post test calculations with THEMA (CEA Spreading code) – 11 parameters 2048 calculations !! – 128 calculation performed. Wilk’s quality level > 96%

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Parameters used in the exercises

values of the studied parameters parameter used if not studied parameter low value high value V2.2mod 1c V2.3mod6 η0 Shaw correlation coefficient 0.021 0.034 studied studied A Shaw correlation coefficient 0.01 0.024 studied studied melt liquidus temperature, (K) 2175 2325 studied 2250 initial melt temperature (K) 2015 2185 studied studied assumption for the inlet flow rate high flow rate low flow rate studied studied surrounding temperature (K) 300 700 studied 300 melt emissivity 0.6 1 0.8 studied solidification model bulk freezing crust and bulk studied crust and bulk solidification temperature (K) 1300 2000 1300 studied transport of the upper crust no yes no studied melt density (kg/m3)

  • std. values ±250 or ±500

(depend. on T) studied

  • std. values

melt therm. conduct. (W/m/K) 1 5 studied studied melt heat capacity

  • std. values ±10 %

studied studied

  • therm. resist. with substratum

(K.m2/W) 0.006 studied studied substratum thermal conduct. (W/m/K) 0.8 1.4 1.1 studied

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Correlations between parameters and Spreading length

Most correlated parameters 1.Flow rate. Especially at initial instants of spreading

  • 2. Viscosity Law exponent µ=µ° eA(T-Tliq)

3.Liquidus Temperature 4.Inlet Temperature

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Correlations between parameters and substrate temperature

  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 8 s 16 s 24 s 32 s 40 s 8 s 16 s 24 s 32 s 40 s substratum tem p., cell 6, brick surface substratum tem p., 1 cm below the brick surface correlation coefficien therm . resist. eta0 A Tinlet flow rate Tsolidif m elt em issivity upper crust tr. m elt cond.

  • substr. cond.

m elt C p

Most correlated parameters 1.Substrate conductivity 2.Thermal contact resistance 3.Melt conductivity 4.Flow rate and Inlet Temperature

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Conclusions

  • Uncertainties due to uncertainties on Physical

Properties and through those to thermodynamic modeling remain important.

  • Sensitivity analyses are useful to determine which

properties should be prioritized.

  • R&D on corium viscosity has been performed for the

validation of the EPR spreading concept, reducing these uncertainties.

  • Several physical properties are still poorly known,
  • esp. mixing laws
  • Phase diagrams (thermodynamic database) must be

improved e.g. in the corium-concrete diagram to reduce remaining uncertainties.

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OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 Aix en Provence, 7-9 October 2005

Acknowledgement

The works reported in this presentation were supported by the European Commission 4th and 5th Framework programme through the CSC, ECOSTAR and ENTHALPY projects. Some work on the European Thermodynamic Database are continuing within SARNET