RELAP5-3D Uncertainty Analysis A.J. Pawel and Dr. George L. Mesina International RELAP Users’ Seminar 2011 July 25-28, 2011

Overview Methodology Test Cases Required programs and scripts Results Conclusions

Methodology Identify qualified test cases For each case, identify: –Figure of Merit (FOM) –Parameters that have heavy influence on the Figure of Merit (expert judgment required) –Realistic ranges for the values of these parameters Run each test case with input decks modified for every feasible combination of input parameters Collect the FOMs and perform relevant statistical calculations, such as the production of means, variances, order statistics, and 95/95 tolerance intervals.

FLECHT-SEASET Test Flecht-Seaset Model Diagram Forced Reflood Exp’t FOM: Peak Clad Temp (PCT) PCT depends on: System Pressure 40 ± 10 psi Temperature of the Inlet Water 127 ± 4 ºF Reflood Flow Rate 6.1 in/s ± 10% Peak Power 2.3 kW/m ± 10%

Scripting Selecting which values of the parameters to be varied on each run should be automated. Matrix of values given to C-script with instructions to run RELAP5-3D in nested loops. –# parameters varied = # nested loops –Execute RELAP5-3D With the same input deck? Sift through the output by hand?

Input Modification FORTRAN 90/95 program to modify an existing input deck. Place comment cards in the input deck before lines that are to be modified with instructions on how the modification should occur. Input modification program recognizes the strings and calls the relevant modification subroutine. Writes the modified input deck to a new file with a new (distinct) name –Name based on command line arguments. –This is very useful, as will be shown later.

Output Collection FORTRAN 95 program to collect input parameters and FOM from RELAP5-3D input and output files. Input modification program takes input parameters from file of pre-selected values. Figure of merit in a special control variable added to the input deck prior to processing. Writes the five values to a new file with a unique name based on the indices of the parameter values used. –Again, this is useful.

Supercomputing Even small jobs (e.g. 9 values/parameter) are time- consuming. –4 input parameters => 9 4 = 6,561 ~10 sec. per run s(hour/3600s) ~ 18.2 hours. Apply INL Massively Parallel Computer: Fission –Appro distributed memory cluster –12,512 cores on 391 nodes Runs are independent; “embarrassingly parallel” –Run time reduced to ~20 minutes

Statistics Mean – expected value of the FOM Variance – roughly, how much the FOM varies Standard Deviation – square root of the variance n th Percentile (P n ) – value above n% of the FOM values Tolerance Interval – expected range of values –One-sided: gives only an upper/lower bound –Two-sided: gives both upper and lower bounds –A γ/β Tolerance Interval is such that a fraction of the population, γ, is in the tolerance interval with probability β

Sample Reduction Techniques Latin Hypercube –Each value of each parameter used exactly once (E.G. in 2D, diagonal of times table) –Same number of values per axis. –Values generally randomized, not on diagonal Stratified Sampling –Break input parameter domain into small groups (strata) of values for each parameter –Select value from each stratum, form 4-tuples Create at least two 4-tuples per stratum

Use 59 samples for Tolerance Interval For either approach, number of 4-tuples needed to create a one-sided tolerance interval is 59. User preselects (randomly generates) 59 4-tuples and runs RELAP5-3D 59 times Statistical results are reasonably close to 6561 runs –59 runs can be repeated with different random sample. –Statistical results reasonably close each time Maximum of a sample of 59 is an estimator of the 95 th percentile of the population

A Different Hypercube

FLECHT-SEASET Results *LHC and SS numbers are averages over ten trials. Population Latin Hypercube* Stratified Sample* µ (K) σ 2 (K 2 ) σ (K) σ (% of µ)0.25 P 95 (K) Maximum (K) Sided T.I. (K)

Marviken Critical Flow Test 22 Facility Description Critical Flow Test Figure of Merit: mass flow rate Flow rate depends on: Temperature in Pressure Vessel 484 ± 0.6 K Temperature in Outlet Nozzle 441 ± 0.6 K Steam Pressure 4,930 ± 9 kPa Nozzle Diameter 0.5 m ± 1% Marviken Model Diagram

Marviken Results *LHC and SS numbers are averages over ten trials. PopulationLatin Hypercube*Stratified Sample* µ (kg/s) σ 2 (kg 2 /s 2 ) σ (kg/s) σ (% of µ) P 95 (kg/s) Maximum (kg/s) Sided T.I. (kg/s)

Conclusions The Developmental Assessment manual of RELAP5- 3D has demonstrated that the program models these facilities acceptably well. The small standard deviations in all cases suggest that for reasonable variations in key parameters, the code is sure of its answer. One-sided tolerance limits testify that the facilities would remain within regulatory specifications with better than 95/95 confidence. In the applications investigated here, RELAP5-3D is a reliable reactor systems modeling software.