Automated Variance Reduction for SCALE Shielding Calculations

Automated Variance Reduction for SCALE Shielding

CalculationsDouglas E. Peplow and John C. Wagner

Nuclear Science and Technology DivisionOak Ridge National Laboratory

14th Biennial Topical Meeting of the ANS Radiation Protection and Shielding Division

April 3-6, 2006 Carlsbad, New Mexico, USA

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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY

Motivation

Codes need to solve increasingly difficult problems

Need accurate and fast answers Monte Carlo with importance sampling is

the best variance reduction Codes need to be simple and as automated

as possible

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Background SCALE (Standardized Computer Analyses for

Licensing Evaluation) Collection of codes for performing criticality safety, radiation

shielding, spent fuel characterization and heat transfer analyses

Control modules or sequences automate the execution and data exchange of individual codes to perform various types of analyses

SAS4 – Shielding Analysis Sequence Automated 1-D variance reduction capability for more than a

decade, with limitations Effective for cask midplane and top center dose Not well suited to cask corners and very heterogeneous

geometries Hence, need for Monte Carlo tool with automated 3-D variance

reduction (AVR) for general shielding applications

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CADIS Methodology - Consistent Adjoint Driven Importance Sampling Use Discrete Ordinates to

find approximate adjoint flux From the adjoint flux

Importance map for MC transport (weight windows for splitting and roulette)

Biased source distribution

Biased source and importance map work together

),( Er

E V

dVdEErErqSR ,,

SRErErqErq ),(),(),(ˆ

),(),(

ErSR

Erw

),(),(0 Er

SRErw

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SCALE Implementation of CADIS

Cross sections Multi-group SCALE libraries – many choices Create adjoint and forward cross section sets

Find the approximate adjoint flux GRTUNCL3-D – first collision code TORT – three dimensional DO transport code

Monaco Descendant of MORSE – still in progress Uses SCALE general geometry (KENOVI)

Automate as much as possible

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SCALE Sequence: MAVRICMonaco with Automated Variance Reduction using Importance Calculations

SCALEDriverandMAVRIC

Input

ICE

Monaco

End

Optional: TORT adjoint cross sections

Optional: 3-D discrete ordinates calculation

3-D Monte Carlo

Resonance cross-section processing

BONAMI / NITAWL orBONAMI / CENTRM / PMC

TORT

GRTUNCL-3D Optional: first-collision source calculation

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SCALE Sequence: MAVRIC Monaco with Automated

Variance Reduction using Importance Calculations

Input: Physical Problem

Materials Geometry Source Det. Positions Det. Responses

Monte Carlo info Histories, max time, etc

Adjoint DO info Adjoint source Spacial discretization

1.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-021.E-011.E+001.E+01

0.01 0.1 1 10energy (MeV)

sour

ce e

miss

ion

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

9.0E-06

1.0E-05

0.01 0.1 1 10energy (MeV)

dete

ctor

resp

onse

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Example

Simple cask with ventports

Spent fuel: UO2

(20%), air Uniform

source

Steel, Concrete

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Example Source: photons Response: photon

dose

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

9.0E-06

1.0E-05

0.01 0.1 1 10energy (MeV)

dete

ctor

resp

onse

1.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-021.E-011.E+001.E+01

0.01 0.1 1 10energy (MeV)

sour

ce e

mis

sion

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Analog Monaco

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Example - Discretization

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Example – Adjoint Flux

a. GRTUNCL3D b. TORT c. Sum d. Scale

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Example – Imp. Map/Biased Source

a. Importance map b. Source weights c. Scale

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Example – Biased source distribution

a. Probability per unit volume b. Scale

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Results

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Results

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7

MAVRICMonacoMORSE

Compare MAVRIC and Analog

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Results

Compare MAVRIC and SAS4

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7

MAVRICSAS4 RSAS4 A

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Results

Compare MAVRIC and others: FOM ratios to analog Monaco

3-D BiasingMonaco MORSE SAS4 R SAS4 A MAVRIC

1 1.0 0.1 2079 30402 1.0 4.7 14 3703 1.0 1.1 0.1 0.1 114 1.0 2.9 44511 22065 1.0 1.4 0.3 506 1.0 1.2 0.1 5.5 228

Analog Codes 1-D Biasing

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Results

Compare MAVRIC and ADVANTG: FOM ratios to analog

MAVRIC ADVANTG1 3040 71482 370 4953 11 1254 2206 19255 50 356 228 3443

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Future Work

MAVRIC Sequence Automatic homogenization in importance map Determine standard set of TORT parameters

Monaco Flux tallies for regions Mesh tally

Testing, Testing, then a bit more Testing

Discussion & Questions

Automated Variance Reduction for SCALE Shielding Calculations

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