Further Development for Further Development for Criticality Safety AnalysisCriticality Safety Analysis

Tatiana Tatiana IvanovaIvanova and and YannYann RichetRichet

UACSA Expert Group Kick-off Meeting

IRSN Fontenay-aux-Roses

December 5, 2007

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 2

General PurposeGeneral Purpose

Creation and validation of a technique to designate the calculational biases and uncertainties for code used for the criticality safety assessment

222tndmndmeff akkk σσσ +++∆+∆=∆

∆keff - computational bias,∆km - bias due to computational method,∆knd - bias due to nuclear data,σm - uncertainty of the bias due to computational method,σnd - uncertainty of the bias due to nuclear data,σt - technological uncertainty,

- a multiplier.a

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 3

The Tools Function and StatusThe Tools Function and Status

The MACSENS tool is developed and under the validation and modification (Presented by Y. RICHET)

222tndmndmeff akkk σσσ +++∆+∆=∆

The Software tool is to be developed to implement the Generalized Linear Least Square Method (GLLSM) based methodology (Presented by T. IVANOVA)

222tndmndmeff akkk σσσ +++∆+∆=∆

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 4

Initial Data for the GGLM Based ToolInitial Data for the GGLM Based ToolCrossCross--section Covariance Datasection Covariance Data

S=PtW-1P+(∆k-HP)tU-1(∆k-HP)Wn,m= (δσn/σn)(δσm/σm) ρn,m

δσ - cross-section uncertainties σn,σm

ρn,m- correlation coefficient (n=1,…N, m=1,…M)

Covariance data produced by NJOY/ERROR from ENDF/B-V, -VII, JEF2.2, JEFF3.1 etc files.

Low-fidelity covariance data

“Home made” covariance matrices

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 5

Initial Data for the GGLM Based ToolInitial Data for the GGLM Based ToolSensitivity CoefficientsSensitivity Coefficients

S=PtW-1P+(∆k-HP)tU-1(∆k-HP)

nn

icicni

kkH

σσ∂∂

= ,,,

APOLLO2 Results (2D Deterministic Method)

TSUNAMI-3D Results (3D Monte Carlo - Joint Based Perturbation Method)

MORET 4 (3D Monte Carlo - Correlated Sampling Method)

Further development of MORET 4 code (3D Monte Carlo)

σn– cross sections

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 6

Initial Data Set for the GGLM Based ToolInitial Data Set for the GGLM Based ToolUncertainties of ExperimentsUncertainties of Experiments

S=PtW-1P+(∆k-HP)tU-1(∆k-HP)

Benchmark uncertainties from ICSBEP Handbook

Creation of uncertainties covariance matrices for experiments of interest

Use of uncertainty covariance matrices produced within the framework of ISTC 815 (IPPE) for experiments from ICSBEP Handbook

Evaluation of French experiments

Ui,j= δki δkj ρi,jδki , δkj – experimental uncertainties kc,i, ke,iρi,j – correlation coefficients (i=1,…I, j=1,…J)

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 7

Initial Data Set for the GGLM Based ToolInitial Data Set for the GGLM Based ToolCalculationCalculation--toto--Experiment DifferenceExperiment Difference

S=PtW-1P+(∆k-HP)tU-1(∆k-HP)

∆ki=(kc,i-ke,i)/ ke,i

APOLLO2-MORET 4 Validation Database (1800 experiments): Results obtained with JEF2.2, JEFF3.1, ENDF/B-VI.4 based 172-gr. cross sections

Comparison with MCNP and/or TRIPOLI-4 reference results for validation of calculational scheme

EG UACSA Kick-off Meeting IRSN Fontenay-aux-Roses December 5, 2007 Page 8

The GLLSM Based Tool Validation The GLLSM Based Tool Validation

Use of ISTC 815 results – biases and uncertainties produced by INDECS code (IPPE) for some MOX powder fabrication applications

Benchmarking within the framework of the EG on Uncertainty Analysis for Criticality Safety Validation

Comparison with TSURFER code (ORNL) results