RELAP5-3D Uncertainty Analysis

A.J. Pawel and Dr. George L. Mesina

International RELAP Users’ Seminar 2011July 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 31701• 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 => 94 = 6,561 runs @ ~10 sec. per run. 65610s(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

• nth Percentile (Pn) – 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 95-95 Tolerance Interval• For either approach, number of 4-tuples needed to

create a 95-95 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 95th 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) 1159.44 1159.97 1159.96

σ2 (K2) 8.58 8.20 8.13

σ (K) 2.93 2.86 2.85

σ (% of µ) 0.25 0.25 0.25

P95 (K) 1164.40 1164.59 1164.51

Maximum (K) 1168.82 1166.33 1166.51

1-Sided T.I. (K) 1164.26 1164.69 1164.66

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.

  Population Latin Hypercube* Stratified Sample*

µ (kg/s) 15066.59 15092.66 15092.56

σ2 (kg2/s2) 26712.34 24975.40 23610.21

σ (kg/s) 163.44 157.99 153.63

σ (% of µ) 1.08 1.05 1.02

P95 (kg/s) 15357.80 15356.16 15352.49

Maximum (kg/s) 15417.00 15398.80 15405.29

1-Sided T.I. (kg/s) 15335.45 15353.57 15346.06

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.