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Title:

Monte Carlo Methods for Isotopic Inventory Analysis

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Tally. 11/20/2003. 2003 ANS Winter Meeting. 10 /19. Status. Early prototyping with Matlab ... Tally. Base. Current Tally. Population Tally. Main Application. SPRNG 2.0 ... – PowerPoint PPT presentation

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Title: Monte Carlo Methods for Isotopic Inventory Analysis


1
Monte Carlo Methods for Isotopic Inventory
Analysis
  • Paul Wilson
  • Phiphat Phruksarojanakun
  • David Paige
  • 2003 ANS Winter Meeting

2
Overview
  • Motivation
  • Basic Algorithm Simple 0-D
  • Details Extensions
  • Status Observations
  • Code Development
  • Early benchmarks
  • Summary Future directions

3
Motivation
  • Some classes of problems are not handled well by
    traditional isotopic inventory analysis codes
  • Material flowing in complex geometries
  • Common fusion blanket designs
  • Constant addition/removal of materials to the
    system
  • Symbiotic fuel cycles with transmuters
  • Liquid fueled fission cycles
  • Chemical reaction steps in material life cycle

f1
f2
4
Simple 0-D Problem Definition
Control Volume
  • Sample Atom
  • Atomic
  • Isotopic
  • Control Volume
  • neutron flux, f
  • residence time, tR

Mean reaction Time tm1/leff
Nuclear Data
5
0-D Analog MC Sampling
  • Convert residence time to number of mean reaction
    times for this isotope
  • Randomly sample number of mean reaction times
    before next reaction
  • If nR gt n, reaction occurs
  • Else, end history and repeat

6
When Reaction Occurs
  • Randomly sample which reaction occurs
  • Determine new isotope
  • Update remaining residence time
  • tR ? tR n ? tm
  • Repeat with new isotope
  • Therefore new tm

7
Comparison to Monte Carlo Transport
Neutral particles Individual atoms
Length of geometric cell
Residence time in control volume
Mean free paths between reactions (macroscopic
cross-section)
Mean times between reactions (effective total
transmutation decay rate)
Energy Isotopic identity
8
Details - Sources
  • Single fixed source
  • Sample discrete PDF of initial atoms
  • Single continuous source
  • Sample time dependent function representing
    in-flow of atoms
  • Multiple sources
  • Sample between magnitude of sources
  • Sample each source appropriately

9
Details - Tallys
  • Atom current Tally
  • Atom population Tally

10
Status
  • Early prototyping with Matlab
  • Current development under C

SPRNG 2.0 Scalable Pseudo-Random Number Generator
Atom
Control Volume
Main Application
MCTools
PRNG Wrapper
Nuclear Data Access
Current Tally
Discrete PDF Template
Tally Base
Population Tally
11
Analytic Benchmark Pure Decay
  • 14O ?14N ? t1/2 70 s ? 1010 particles
    ? error 0.001

12
Computational Benchmark 56Fe Steady-state
Activation vs ALARA
  • 10 yr ? 10-9 ALARA tolerance ? 108 particles
    ? 18 missing products

13
Variance Improvements - Parallelism
14
Variance Reduction Techniques
  • Forced reaction
  • Require a reaction (or many) to take place in
    each control volume
  • Uniform branching
  • Select reaction path uniformly to enhance
    pathways with low probability
  • Uniform source sampling
  • Select initial atoms uniformly to enhance role of
    trace isotopes

15
Analog Extensions
  • 0-D Calculation
  • Simple Flow
  • Complex Flow
  • Loop

16
Flow Benchmarking Equivalents to 0-D Steady State
  • Simple flow tests
  • Create systems with multiple control volumes
    (CVs) but same total residence time and uniform
    neutron flux
  • 2 CVs vs 1 CV
  • 10 CVs vs 1 CV
  • Complex flow tests
  • Create systems with well-defined flow splitting
    uniform neutron flux
  • 5050 flow split
  • 9010 flow split

17
Flow Benchmarking Case Comparison
  • 10 yr ? 10-9 ALARA tolerance ? 108 particles

5050 Complex Flow
1 CV Steady- State
2 CV Simple Flow
9010 Complex Flow
10 CV Simple Flow
18
Summary
  • Concept works well …
  • Analog precision limit worse than
  • 1/ particles for single initial isotope
  • 1/(M particles) for uniform mixture of M
    isotopes
  • Needs parallel performance and
  • Needs variance reduction
  • Variance reduction
  • Early results are promising

to precision limit
19
Future Work
  • Implement test variance reduction
  • Investigate options for pulsed irradiaton systems
  • Probably inefficient to model pulses as separate
    control volumes
  • Pulse frequencies and flow frequencies may not be
    synchronized
  • Opportunities based on delta-tracking transport
    analog
  • Production calculations for fission fusion
    systems
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