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
Outline •Introduction •Uncertainties on phase diagrams •Uncertainties on Physical Properties •Application to Severe Accident Calculations –Example : Spreading calculations OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 2 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 OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 3 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 d 2 G ≥ 0 dG= -SdT+VdP + Σμ i dn i + … • Thermodynamic database + Minimization software OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 4 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= G reference + G ideal mixing + G excess OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 5 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 OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 6 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 ?) OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 7 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. OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 8 Aix en Provence, 7-9 October 2005
TMI2 corium liquid fraction TMI2 thermodynamic equilibrium 100,00% 2,00% Liquid mass fraction Delta liquid fraction 80,00% 1,20% 60,00% 0,40% (%) (%) 40,00% -0,40% 20,00% -1,20% 0,00% -2,00% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NTDIV012 2 4 6 8 0 2 4 6 8 0 1 1 1 1 2 2 2 2 2 3 NTDIV012-TDIV01 Temperature (K) NTDIV012-TDIV992 • Differences < 1.2%w => very consistent output. OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 9 Aix en Provence, 7-9 October 2005
Typical EPR Concrete 36% w SiO 2 , 49% w Fe 2 O 3 , 5% w CaO, 6% w Al 2 O 3 , 4% H 2 O • Large typical EPR-concrete composition discrepencies 100% (100-200K) 90% between THMO 80% and TDBCR Liquid mass fraction 70% • Consistency of THMO 99 60% TDBCR versions. TDBCR971 50% • SiO 2 -Fe 2 O 3 TDBCR981 system rated * 40% TDBCR992 30% TDBCR001 20% 10% 0% 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 Temperature K OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 10 Aix en Provence, 7-9 October 2005
Gaseous species over corium-concrete mixture at 2573 K 10%H 2 - 90%H 2 O atmosphere 1.E+00 1.E-01 TDBCR972 TDBCR981 TDBCR992 1.E-02 TDBCR001 1.E-03 atm 1.E-04 1.E-05 1.E-06 1.E-07 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) No large evolutions except appearances of new phases: UO 3 , Al(OH) 2, Disapearance of baryum hydroxides. OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 11 Aix en Provence, 7-9 October 2005
Gases over In-vessel corium at 3000K In-Vessel gases 3000 K [ Test0A1 in 100 m3 ] 1.00E+01 TDBCR972 TDBCR981 1.00E+00 TDBIV992 TDBCR001 1.00E-01 NDTiv012 1.00E-02 atm 1.00E-03 1.00E-04 1.00E-05 1.00E-06 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) • Variations can reach factors of 3-10 • New gaseous species appeared in newer versions (ex. BaH, BaOH, HSr, …) OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 12 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. OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 13 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 OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 14 Aix en Provence, 7-9 October 2005
Density of Metallic Uranium Uranium 20 000 Boivineau et al. 93 TAPP McClelland & Sze, 1995 19 000 Rohr Wittenberg 70 Grosse et al 61 18 000 Fischer 2000 Touloukian 75(alpha phase) Density kg/m3 MATPRO 17 000 HEMATIC Touloukian 75 (beta phase) Touloukian (gamma phase) 16 000 Sheldon & Mulford 1991 Shpil'rain et al. 88 15 000 Bridge 56 MATPRO (beta phase) Rohr & Wittenberg 1970(gamma) 14 000 MATPRO (gamma phase) Lloyd 65 13 000 Drottning 82 300 1300 2300 3300 Temperature K • Solid phase data quite consistent • Large dispersion of liquid phase data • Critical review by Fischer (FZK) 2000 ρ liq = 17270 –1.6010(T-1408) (brown curve) OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 15 Aix en Provence, 7-9 October 2005
Mixing laws for solutions (1) = ∑ ⋅ + V y V V i i excess i Hypothesis: Ideal mixing – No excess volume Applicable to solid and liquid solutions – Molecules of similar molar volumes (at ±30 %) 30.5 cm 3 /mol UO 2 U 13.8 ZrO 2 22.3 Zr 14.6 SiO 2 27 Fe 7.9 Fe 7.9 (FeO) 2 26 Cr 8.2 Cr 8.2 – 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) OECD Workshop on Evaluation of Uncertainties in Relation to Severe Accidents and PSA2 16 Aix en Provence, 7-9 October 2005
Recommend
More recommend
