Monte Carlo Methods for Isotopic Inventory Analysis

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Monte Carlo Methods for Isotopic Inventory
Analysis

• Paul Wilson
• Phiphat Phruksarojanakun
• David Paige
• 2003 ANS Winter Meeting

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Overview

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

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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
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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
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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

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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

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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
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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

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Details - Tallys

• Atom current Tally
• Atom populationTally

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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
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Analytic Benchmark Pure Decay

• 14O ?14N ? t1/2 70 s ? 1010 particles
  ? error 0.001

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Computational Benchmark 56Fe Steady-state
Activation vs ALARA

• 10 yr ? 10-9 ALARA tolerance ? 108 particles
  ? 18 missing products

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Variance Improvements - Parallelism
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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

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Analog Extensions

• 0-D Calculation
• Simple Flow
• Complex Flow
• Loop

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Flow BenchmarkingEquivalents 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

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Flow BenchmarkingCase 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
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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
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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