Uncertainties in the calculation of NO

and DLOFC temperatures (Inc. summary of IAEA CRP on uncertainties)

Presented: Frederik Reitsma

11/07/2012

TM-62606: 10-12 July 2012

11/07/2012 TM-62606: 10-12 July 2012

Content / Overview

• SUSA Uncertainty Analysis of the PBMR DLOFC Benchmark (Pebbed)

• PBMR-400 TINTE statistical results – ICAPP2004

• IAEA CRP summary

SUSA Uncertainty Analysis of the PBMR DLOFC Benchmark

Work presented by Gerhard Strydom

3rd Consultancy Meeting on Uncertainty Analysis in HTGR Modeling

Vienna, Austria

July 12-14 , 2011

11/07/2012 TM-62606: 10-12 July 2012

11/07/2012 TM-62606: 10-12 July 2012

Content / Overview

• Role of uncertainty analysis in core simulation

• What is SUSA

• Uncertainty and sensitivity results for PBMR400 OECD benchmark

• Some results from the study

• Results from ICAPP conference similar

Role of Uncertainty Analysis in Core Simulation

• 10 CFR 50.46 allows best estimate calculations of safety parameters, rather than conservative code models – uncertainties must be identified and quantified – “BE+Uncertainties” is therefore required for license applications

and safety studies

• Target: – Propagation of uncertainties from XS data to coupled neutronic

and thermal fluid dynamics – approach must be defendable, consistent and preferably within a

finite time

• Work presented here was performed by Gerhard Strydom at INL as a 2010 DOE Level 2 Milestone deliverable – investigate VHTR core simulation uncertainty evaluation options

and produce a typical VHTR sample application (see INL-EXT-10-20531)

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Role of Uncertainty Analysis in Core Simulation – cont.

• Sources of uncertainties – Data

• XS libraries, mathematical models of resonance treatment • Material properties (density, thermal conductivity) • Proposed core/plant layout, geometry, materials to be used,

operational envelope, safety equipment functioning and set points

– Models • Mathematical simplifications, numeric solver schemes • Use of correlations (e.g. decay heat, effective core conductivity) • User approximations: 3-D to 2-D effects, all heat local, no cones in PB • User choices: number of energy groups, diffusion vs. transport vs.

stochastic, boundary conditions, spatial nodalization

– Codes/tools • Propagation of errors between modules/codes, coupling schemes • User errors, source code errors, compilation errors

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Uncertainty Methodology Overview

• Two major approaches are currently used

– Statistical methods (input uncertainty propagation) include

• Use of large number of uncertain input parameters

• Assign subjective probability ranges and distributions to these parameters

• Propagate uncertainty through core models to determine statistical properties of the Figure of Merit (FOM)

• Advantage: No code/model modifications are needed

• BUT: requires fairly large number of model runs (~93 runs for two-sided 95/95 tolerance limits with 95% confidence)

• Examples: GRS code SUSA, SNL code DAKOTA

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Uncertainty Methodology Overview – cont.

– Deterministic methods (output uncertainty propagation) include

• Use of relevant sets of experimental /operational data to establish operational and off-normal databases for a large number of input parameters

• Create time and state hyper-cubes characterizing physical parameters for a wide variety of conditions, transients, etc. (response surface methods)

• Derive error bands enveloping the output FOM, and it requires only a single model run

• BUT:

– is based on adjoint perturbation theory (non-linear thermal fluid correlations are challenging),

– requires extensive reference databases

• University Pisa code CIAU

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SUSA Overview • Software for Uncertainty and Sensitivity Analyses, developed by GRS

(Germany) in the late ‘90s. Now available as a commercial code.

• Based on NRC-accepted Code Scaling, Applicability, and Uncertainty (CSAU) methodology. CSAU uses expert panels to determine PIRTs (Phenomena Ranking Tables) that establish the main contributors to uncertainties in FOMs

• SUSA is a simple Fortran wrapper that supplies statistical capabilities – Generates random input data values (both Latin Hypercube and Simple Random

Sampling is available), based on user-supplied uncertainty distributions and ranges

– Performs model runs (can also be done off-line)

– Analyze output data/FOM for dependencies on input parameters, and quantify the desired statistical parameters (mean, 95/95, etc.)

– Uses MS Excel interface/VB for user interface and data plotting

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PEBBED CRP-5 DLOFC Benchmark Approach

• As an initial HTR test case, SUSA was applied to IAEA CRP-5 PBMR 400 MW benchmark

• A DLOFC transient was performed with the INL code PEBBED, and results compared with an earlier simplified TINTE uncertainty study performed at PBMR

• Although SUSA can be coupled to PEBBED directly and control all aspects of the calculation chain, it was applied as a black-box wrapper around PEBBED for this first test case

• Only minor PEBBED modifications were needed to allow for reading of user-defined multiplication factors, e.g. thermal conductivity, cp, decay heat

• SUSA provided statistical input and output data generation

• FOM: Mean, 5% and 95% tolerance limits of the maximum DLOFC fuel temperature were obtained from SUSA

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SUSA: Input Data Generation – PDF Types and Values

Parameter Mean value

2 Standard deviations (2σ) value PDF type

Reactor power 400 MW ±8 MW (2%) Normal and Uniform

Reactor inlet gas temperature (RIT) 500°C ±10°C (2%) Normal and Uniform

Decay heat multiplication factor 1.0 ±0.057 (5.7%) Normal and Uniform

Fuel specific heat multi factor 1.0 ±0.06 (6%) Normal and Uniform

Reflector specific heat multi factor 1.0 ±0.10 (10%) Normal and Uniform

Fuel conductivity multifactor 1.0 ±0.14 (14%) Normal and Uniform

Pebble bed effective conductivity multi factor

1.0 ±0.08 (8%) Normal and Uniform

Reflector conductivity multi factor 1.0 ±0.10 (10%) Normal and Uniform

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SUSA: Input Data Generation – Power Values

388

390

392

394

396

398

400

402

404

406

408

410

412

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

Case #

To

tal

Po

we

r (M

W)

min allowed variation: 392 MW (2%)

max allowed variation: 408 MW (2%)

Mean value: 400 MW

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SUSA: Model Calculations

• Six SUSA case sets were performed for this study

– Number of model runs: Varied between 100 and 200 to investigate if double the model runs produced a smaller tolerance interval size

– Distribution types: Uniform and normal distribution types were tested

– Dominant contributors: Uncertainty contribution of a few dominant input parameters were compared to the combination of all eight input parameters

– Sampling method: Simple and Latin Hypercube (SRS/LHS)

# Model

Runs Sampling Method

Distribution Type Parameters Varied

100 LHS Uniform Power, RIT, decay heat only

100 LHS Uniform Specific heat and thermal conductivity only

100 LHS Uniform All

100 LHS Normal All

200 LHS Normal All

200 SRS Normal All 11/07/2012 TM-62606: 10-12 July 2012

PEBBED DLOFC Maximum Fuel Temperature vs. Time for the 200 LHS Normal set

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

1700

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (h)

Ma

xim

um

fu

el

tem

pera

ture

(C

)

11/07/2012 TM-62606: 10-12 July 2012

PEBBED DLOFC Maximum Fuel Temperature vs. Time for 200 LHS Normal Set – Peak Values Only

1520

1530

1540

1550

1560

1570

1580

1590

1600

1610

1620

1630

1640

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1680

1690

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

Case #

Max

imu

m F

uel

Tem

per

atu

re (

Cel

ciu

s)

-2σ variation: 1545 (3.7%)

+2σ variation: 1663 (3.7%)

Mean value: 1604

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SUSA Uncertainty Analysis: Summary of Results

Number of Model Runs

Input Data Mean and (95%, 95%) Two-Sided

Tolerance Limits

Input Parameter Sampling Method

Input Parameter Distribution Type

Model Input Parameters Varied

DLOFC Maximum Fuel Temperature

(°C)

Pebble Load Rate (Per

Day)

99 Latin Hypercube Uniform Power, RIT, decay

heat only 1,603 ± 61 2,793 ± 72

100 Latin Hypercube Uniform Specific heat and

thermal conductivity only

1,605 ± 45 2,790

100 Latin Hypercube Uniform All 1,605 ± 76 2,794 ± 72 99 Latin Hypercube Gaussian/Normal All 1,604 ± 59 2,793 ± 55

200 Latin Hypercube Gaussian/Normal All 1,604 ± 59 2,793 ± 55 199 Simple Random Gaussian/Normal All 1,604 ± 58 2,790 ± 57

• Mean distribution values are almost identical for all sets. Power and decay dominates

• Uniform gave slightly larger 95/95 values, due to lower normal “tail” sampling

• No gain above 100 runs (but better sensitivity data with 200 run sets)

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Similar than TINTE studies – ICAPP2004

SUSA Uncertainty Analysis: Summary of Results – cont.

1050

1100

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1300

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1400

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1600

1650

1700

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (h)

DLO

FC p

eak

fuel

tem

pera

ture

(C)

Maxima Minima Means 0.050-Qtl 0.950-Qtl

The time-dependent nature of the DLOFC event implies an uncertainty bandwidth that varies with time. It is therefore not straightforward to answer safety related questions on what uncertainty margin should be applied during design and SAR calculations

11/07/2012 TM-62606: 10-12 July 2012

Gerhard Strydom Idaho National Laboratory

Gerhard.Strydom@inl.gov (208) 526-1216

For more info

11/07/2012 TM-62606: 10-12 July 2012

Update on the Status and Scope of the IAEA Uncertainty CRP

Frederik Reitsma

11/07/2012 TM-62606: 10-12 July 2012

11/07/2012 TM-62606: 10-12 July 2012

Overview

• Background

• Purpose and scope of work

• Reference designs – Prismatic

– Pebble bed design

• Status of benchmark tasks – Phases

– Exercises

• Concluding remarks

11/07/2012 TM-62606: 10-12 July 2012

Background

• The continued development of the HTGRs requires verification of HTGR design and safety features with reliable high fidelity physics models and robust, efficient, and accurate codes

• The predictive capability of coupled neutronics/thermal-hydraulics simulations for reactor design and safety analysis can be assessed with sensitivity analysis (SA) and uncertainty analysis (UA) methods

• In order to benefit from recent advances in modeling and simulation and the availability of new covariance data (nuclear data uncertainties) extensive sensitivity and uncertainty studies are needed for quantification of the impact of different sources of uncertainties on the design and safety parameters of HTGRs

• Uncertainty and sensitivity studies are an essential component of any significant effort in data and simulation improvement

• These studies can be used in a convincing and effective manner to perform design optimization and to assess safety features and design margins

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Background

• Cooperative Research Project on Uncertainty treatment in Analysis Proposed – In February 2009 – proposal on behalf of PBMR and Pennsylvania State University – Presentation made at the 21st meeting of the IAEA Technical Working Group on Gas Cooled

reactors (TWG-GCR-21) – Recommended to be implemented

• The project was approved. • Consultancy Meeting to prepare for the CRP on HTGR Reactor Physics, Thermal-

hydraulics and Depletion Uncertainty Analysis – 1st consultancy meeting: 14 – 17 June 2010; IAEA, Vienna – 2nd consultancy meeting: 21 – 22 October 2010, Prague (associated with HTR2010) – 3rd consultancy meeting: 12-14 July 2011, IAEA, Vienna

• CRP launced 2012 – RCM on HTGR Reactor Physics, Thermal-Hydraulics and Depletion Uncertainty , 11-13 April

2012, Oak Ridge National Laboratory, Tennessee, USA

• This CRP is viewed as a natural and logical continuation of the previous IAEA and NEA/OECD international activities on Verification and Validation (V&V) of available analytical capabilities for HTGR simulation for design and safety evaluations.

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Background

• The CRP will also benefit from interactions with the currently ongoing OECD/NEA Light Water Reactor (LWR) UAM benchmark activity by taking into consideration the peculiarities of HTGR designs and simulation requirements.

• In each step identify: – Input uncertainties

– Output parameters to be evaluated

– Data to be propagated

– Cases decoupled (define input uncertainties and not propagate all to next step)

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Reference designs

• Prismatic Design: – The MHTGR (an earlier General Atomics 350MWth design

considered for NGNP) was adopted as the main prismatic reference design.

• Pebble Bed Reactor Design:

– The HTR-Module-based design, upgraded to 250MWth will be the reference design with some simplifications introduced.

• It was further agreed that all designs will start with

detailed Uranium fuel specification and will also have a plutonium (and/or thorium) fuel definition available.

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Prismatic Design Design and Operating Characteristics of the MHTRG-350

MHTGR Characteristic Value

Installed thermal capacity 350 MW(t)

Installed electric capacity 165 MW(e)

Core configuration Annular

Fuel Prismatic Hex-Block fuelled with Uranium Oxycarbide fuel compact of 15.5 wt% enriched U-235 (average)

Primary coolant Helium

Primary coolant pressure 6.39 MPa

Moderator Graphite

Core outlet temperature 687°C.

Core inlet temperature 259°C.

Mass Flow Rate 157.1 kg/s

Reactor Vessel Height 22 m

Reactor Vessel Outside Diameter 6.8 m

Permanent

Reflector (2020

Graphite)

Replaceable

Reflector Block

(H-451 Graphite)

Replaceable Reflector

Block with CR Hole

(H-451 Graphite)

Fuel Block with

RSC Hole (H-451

Graphite)

Fuel Block (H-451

Graphite)

Core Barrel

(Alloy 800H) Coolant Channel RPV (SA-533B)

Neutronic

Boundary

Outside Air

120o Symmetry Line

TM-62606: 10-12 July 2012

The 250MWth Pebble Bed Design

– Based on HTR-Modul design

– increase of the power and the axial height

– Number of control rods / shutdown system

• to be defined as for Modul (6 / 18)

• Length of RCS increased arbitrarily

– Coolant flow to bottom of core (between RPV and barrel) adopted

– Carbon bricks in side, top and bottom reflector

– Control rods in vessel – no CR ejection – only single CR withdrawal case looked at in later phases

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Methodology - I

• PHASE I: LOCAL STAND-ALONE MODELLING – EXERCISE 1 (I-1): “LOCAL NEUTRONICS” – EXERCISE 2 (I-2) MESO-SCALE THERAL-HYDRAULIC COUPLING – EXERCISE 3 (I-3) STAND-ALONE POWER EXCURSION TRANSIENT

CASE (FUEL THERMAL RESPONSE)

• PHASE II: GLOBAL STAND-ALONE MODELLING – EXERCISE II-1A – CORE PHYSICS: CRITICALITY (STEADY STATE)

STAND-ALONE NEUTRONICS CALCULATIONS – EXERCISE II-1B – CORE PHYSICS: STAND-ALONE KINETICS WITHOUT

FEEDBACK – EXERCISE II-2A: “STAND-ALONE THERMAL-HYDRAULICS” FOCUSED

ON CORE AND SYSTEM THERMAL-HYDRAULIC MODELING (NORMAL OPERATION)

– EXERCISE II-2B: “STAND-ALONE THERMAL-HYDRAULICS” FOCUSED ON CORE AND SYSTEM THERMAL-HYDRAULIC MODELING (DLOFC TRANSIENT)

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Methodology - II

• PHASE III: DESIGN CALCULATIONS

– EXERCISE III-1: “COUPLED STEADY-STATE”

– EXERCISE III-2: “COUPLED DEPLETION”

• PHASE IV – SAFETY CALCULATIONS

– EXERCISE IV-1: “COUPLED CORE TRANSIENT”

– EXERCISE IV-2: “COUPLED SYSTEM TRANSIENT”

– EXERCISE IV-3: “COUPLED NEUTRONICS THERMAL HYDRAULICS CALCULATION – STARTING CONDITION FOR THE TRANSIENTS”

11/07/2012

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Concluding remarks

• Good progress made in Uncertainty CRP work scope

• CRP started in 2012

• Working groups already established

• The OECD/NEA LWR Uncertainty Methods effort strongly supports the CRP

• Will make an important contribution to understand and develop uncertainty treatment for GCR / HTGR

• Important input to temperature uncertainties and the topic of this meeting

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References 1. Presentation: SUSA Uncertainty Analysis of the PBMR DLOFC Benchmark,

3rd Consultancy Meeting on Uncertainty Analysis in HTGR Modeling, Vienna, Austria, July 12-14 , 2011; Gerhard Strydom, Scientist, Reactor Physics Analysis and Design, Idaho National Laboratory

2. TINTE Uncertainty Analysis of the Maximum Fuel Temperature During a DLOFC Event for the 400 MW Pebble Bed Modular Reactor, Gerhard Strydom, Paper 4165, Proceedings of ICAPP ’04, Pittsburgh, PA USA, June 13-17, 2004

3. The IAEA Coordinated Research Program on HTGR Reactor Physics, Thermal-hydraulics and Depletion Uncertainty Analysis: Description of the Benchmark Test Cases and Phases, Frederik Reitsma, Gerhard Strydom, Bismark Tyobeka, Kostadin Ivanov, To be presented at HTR2012, Tokyo, Japan, October 28 – November 1, 2012