Isotopic Inventory Calculations in the 21st Century: ALARA and Beyond

1
Isotopic Inventory Calculations in the 21st
CenturyALARA and Beyond

• Paul P.H. Wilson
• January 12, 2002
• Oak Ridge National Lab

2
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Inventory Analysis of Future Systems
• Summary

3
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Inventory Analysis of Future Systems
• Summary

4
What is Isotopic Inventory Analysis?
A detailed accounting of the isotopic composition
of materials used in nuclear systems and fuel
cycles during and after their lifetime in the
system.
Transmutation products
Fission products
Actinides
5
Applications of Isotopic Inventory Analysis

• Facility Analysis
• Fusion reactors
• Accelerator-driven neutron sources
• Fission reactors (power, research, medical)
• Process Simulation
• Neutron activation analysis
• Isotope production
• Nuclear fuel cycles

6
Two Worlds of Inventory Analysis

• Burnup/Depletion Simulations
• Traditional fission systems
• Time scales Slowly varying
• Focus actinides
• Energy range lt few MeV
• Significant coupling between inventory neutron
  flux
• Activation Calculations
• Fusion and accelerator systems
• Time scales Slowly varying or repeating
• Focus transmutation products of low- mid-Z
  elements
• Energy range lt20MeV (fusion) or few GeV (ADS)
• Inventory changes have little effect on neutron
  flux

7
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Physical Modeling
• Mathematical Techniques
• Inventory Analysis of Future Systems
• Summary

8
What Is Activation?
9
Mathematical Representation
10
History of Fusion Activation Codes
11
Desired Activation Code Features

• Basic Features
• 3-D (multi-point)
• User-defined precision
• Exact multi-level pulsing
• Accurate loop handling
• Light ion accumulation
• User-friendly input

• Advanced Features
• Exact modeling of arbitrary operation schedules
• Adaptive selection of mathematical method to
  optimize solution
• Reverse solution for detailed studies

12
Software Design Philosophy

• Accuracy
• Minimize physical approximations
• Optimally accurate mathematical method
• Speed
• Matrix methods for efficient solution of pulsed
  schedules
• Efficient data handling and algorithms
• Simplicity/Versatility
• Modular code with modern practices
• Ability to solve variety of problems with simple
  and versatile input file

13
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Physical Modeling
• Mathematical Techniques
• Inventory Analysis of Future Systems
• Summary

14
Physical Modeling Introduction
A
dA
Activation Trees
B
C
D
E
F
G
H
I
J
K
15
Physical Modeling Tree Straightening

• Each isotope has only one parent
• Permits simplified mathematical methods
• Permits accurate modeling of loops

16
Physical Modeling Linear Chains
A

• depth-first search

C
B
1
1
F
G
H
E
1
1
1
1
K
C
2
2
G
H
2
2
2
2
3
3
3
17
Validity of Loop Straightening
18
Physical Modeling Tree Truncation

• Isotopes have a finite probability of
  transmutation
• infinite activation trees
• need for truncation of trees
• atoms are lost from model

Goal of truncation algorithm reduce atom loss
below user-defined threshold
19
Truncation Issues

• Atom pipelines
• large decay rates Þ conduits out of system
• low inventory ¹ low atom loss

• truncation calculation dN 0

• After-shutdown build-up
• low inventory _at_ shutdown ¹ low inventory after
  shutdown

• test inventory _at_ all cooling times of interest

• Insignificant solutions
• nodes with negligible results

• second tolerance to ignore these nodes

20
Truncation in Multi-Point Problems

• Varying fluxes result in different trees
• Computationally expensive

Zone 5 3 int.
Zone 3 5 int.
Zone 1 45 int.

• group-wise maximum
• reference flux

Zone 4 10 int.
Zone 2 15 int.
Zone 6 1 int.
Mixture 1 (A,B,C) Mixture 2 (C,D)
Mixture 3 (E,F) Mixture 4 (A,F,G)
21
Physical Modeling Pulsing
f
f
22
Physical Modeling Pulsing
f
f
23
Physical Modeling Pulsing
f
f
24
Physical Modeling
Arbitrary Irradiation Schedules
25
Physical Modeling Reverse Problem

• Fewer, shorter chains
• Lower truncation tolerances
• More precise solutions

26
Physical Modeling Summary

• Sufficiently accurate loop handling
• Uniform accuracy across problem
• Accurate and precise solutions
• Both determined by user-defined truncation
  tolerance
• Exact modeling of arbitrary schedules
• Based on matrix methods
• Reverse calculation mode allows detailed study of
  trace products

27
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Physical Modeling
• Mathematical Techniques
• Inventory Analysis of Future Systems
• Summary

28
Mathematical Methods Introduction
29
Laplace Transform
di may be degenerate!!!
30
Inverse Laplace Transform
31
Bateman Solution (Analytical)
Unique poles/eigenvalues no loops
32
Laplace Inversion (Analytical)
For arbitrary multiplicity, require derivatives
of
33
Laplace Expansion (Numerical)
34
Adaptive Selection of Methods

• Adaptively chosen for each matrix element
• Tij represents transfer on sub-chain between
  isotopes j and i inclusive
• If NO loop on sub-chain
• Use Bateman solution
• Otherwise use Laplace Expansion
• If Laplace Expansion does not converge
• Use Laplace Inversion

35
ALARA Status/Summary

• ALARA is in use for a number of projects
• US Fusion Neutronics ARIES, HAPL, ZP3
• International Fusion Materials Irradiation
  Facility IFMIF (FZK)
• ALARA is nearly available at RSICC (v. 2.7.x)
• ALARA is under continuing development

36
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• Inventory Analysis of Future Systems
• Summary

37
Goals for Future Nuclear Systems

• 7 (of 11) Generation IV Requirements (May 2000)
• Waste Disposition
• Minimal waste
• Solutions for all waste streams
• Public acceptance of waste solutions
• Proliferation Resistance
• Minimal attractiveness to potential proliferation
• Evaluation of Proliferation Resistance
• Safety
• No need for offsite response
• As Low As Reasonably Achievable radiation
  exposure
• 9 (of 21) Generation IV Roadmap Criteria (Jan
  2002)

38
Future Systems New Challenges

• ATW/AAA/ADS
• Liquid accelerator targets spallation and
  activation products
• Process streams with fissile material and fission
  products
• Symbiotic fuel cycles
• PWR CANDU DUPIC (Korea)
• LWR FBR ADS
• Various chemical processes in between

39
Future Systems New Challenges

• Generation IV (V? VI?)
• Online chemical processing of flowing fuels
• Thorium fuel cycles
• Fusion Power Plants
• Inertial fusion target material recycle
• Liquid walls
• Liquid breeders
• Online chemical processing

40
Future Complications

• Flows and cycles of material with various time
  scales and processes
• e.g. fusion blanket

41
Future Complications

• Flows and cycles of material with various time
  scales and processes
• e.g. fusion blanket

42
Future Complications

• Flows and cycles of material with various time
  scales and processes
• e.g. fusion blanket

43
Complicated Coolant Flows
f (n/cm2.s)
t(s)
1
2
3
Blanket
f (n/cm2.s)
t(s)
Neutrons
f (n/cm2.s)
t(s)
44
Complicated Coolant Flows
f (n/cm2.s)
t(s)
1
2
3
Blanket
f (n/cm2.s)
t(s)
Neutrons
f (n/cm2.s)
t(s)
45
Complicated Coolant Flows
f (n/cm2.s)
t(s)
1
2
3
Blanket
f (n/cm2.s)
t(s)
Neutrons
f (n/cm2.s)
t(s)
46
Complicated Coolant Flows
f (n/cm2.s)
t(s)
1
2
3
Blanket
f (n/cm2.s)
t(s)
Neutrons
f (n/cm2.s)
t(s)
47
Reaction Rates Flow Paths
sf1
sf2
A
Blanket
1
2
3
10-10
10-6
B
Neutrons
10-10
10-6
E
g
48
Approximations
1
2
3
Blanket
H/X
f (n/cm2.s)
Neutrons
t(s)
49
Approximations
1
2
3
Blanket
H/X
f (n/cm2.s)
Neutrons
t(s)
50
Approximations
1
2
3
Blanket
H/X
f (n/cm2.s)
Neutrons
t(s)
51
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
52
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

53
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

54
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
55
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

56
Analog Extensions

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

57
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

58
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
59
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 promising
• Figure of merit under development

to precision limit
60
Future Work

• Investigate options for pulsed irradiation
  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

61
Future Developments

• ALARA
• Support for fission data
• Depletion feedback with new deterministic methods
• New projects
• Fuel cycle analysis
• Interface with probabilistic analyses of
  proliferation risk

62
Summary

• Isotopic inventory analysis brings together
  traditional burnup/depletion analysis and
  activation analysis
• Inventory analysis methods can benefit from
  constant improvement
• Renewed interest in advanced nuclear systems
  gives new and interesting research opportunities

63
EXTRAS !!!!
64
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• About Fusion Activation Calculations
• Physical Modeling
• Mathematical Techniques
• ALARAs Features
• Applications
• Inventory Analysis of Future Systems
• Summary

65
Summary Current Features

• Straightforward input file creation
• Multi-point solutions in a variety of geometries
• Accurate loop solutions in the activation trees
• User-defined calculation precision/accuracy
• Exact modeling of arbitrary hierarchical
  irradiation schedules
• Full easy-to-read activation tree output
• Flexible output options
• Unlimited number of reaction channels
• Reverse calculation mode

66
ALARA Status

• ALARA is a fully developed and validated
  alternative to other activation codes.
• (standard for ARIES, IFMIF)
• Development of ALARA is continuing to include
  more features, increasing its flexibility and
  versatility.
• (v. 2.5.0 Jan 2002)

67
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• About Fusion Activation Calculations
• Physical Modeling
• Mathematical Techniques
• ALARAs Features
• Applications
• Inventory Analysis of Future Systems
• Summary

68
ALARA in ARIES

• User UW Fusion Technology Institute
• Used exclusively since 1999 (replaced DKR)
• Routine reactor component analysis
• Typical problems perform calculation at over 450
  points in 40 regions filled with 10 materials
  (80 isotopes) in lt1 hour
• Recently modeling advanced schedules for
  specialized components

69
ALARA in ARIESRecycling of IFE Hohlraum Material

• Following single pulse, material cools, is
  recycled and re-fabricated into new capsule
• Recycling equipment has dose limit
• ALARA used to determine minimum cooling time
  before reprocessing/refabrication

L. El-Guebaly, et al, Feasibility of Recycling
Hohlraum Wall Material, ARIES Project Meeting,
Madison, WI, April 2002s
70
ALARA in IFMIF

• User Forschungszentrum Karlsruhe (FZK)
• FZK/Russian collaboration for lt150 MeV activation
  data
• Large number of activation channels
• FISPACT (FZK workhorse activation code) has
  hard-coded reaction table
• ALARA has library-driven reaction information
• Newest version IEAF-2001 (NEA Databank) has 679
  nuclides
• Various investigations of data importance and
  data benchmarking

71
ALARA in IFMIFData Benchmarking

• Experimental Parameters(U. von Möllendorff,
  Fus. Eng. Des. 51(2000)919 )
• Neutron Source 40 MeV d on thick Li-target (En
  lt 55 MeV)
• Neutron Flux 4.3 x 1011 n/cm2/s
• Irradiation Time 2.1 h
• Sample Vanadium foil( m V-99.87, Al-0.025,
  O-0.041, Si-0.017, Fe-0.016, N-0.013 )

Simakov, et al, Activation Analyses of
Vanadium irradiated by d-Li neutrons using
IEAF-2001 cross sections, Workshop on Activation
Data EAF 2003, Prague, 24-26 June 2002
72
ALARA in IFMIFData Benchmarking
Simakov, et al, Activation Analyses of
Vanadium irradiated by d-Li neutrons using
IEAF-2001 cross sections, Workshop on Activation
Data EAF 2003, Prague, 24-26 June 2002
73
Overview

• Background on Isotopic Inventory
• Fusion Activation ALARA
• About Fusion Activation Calculations
• Physical Modeling
• Mathematical Techniques
• Code Validation
• ALARAs Features
• Inventory Analysis of Future Systems
• Summary

74
Validation Benchmark Specification

• IAEA FENDL Calculational Activation Benchmark
• 1-D radial model (44 zones, 318 intervals)
• Wide variety of materials TF Coils, Pb/B4C
  shield, Inconel VV, SS316/H2O blanket, Be coated
  Cu FW
• 175 Group neutron fluxes
• FENDL 2.0 Activation and Decay libraries
• Steady-state problem
• 3 Years continuous operation
• Pulsing problem
• 94500 Pulses of 1000 s with 1200 s dwell
• Compare to FISPACT-97 and DKR-Pulsar 2.0

75
Steady-State Problem 1 Hour

• DKR does not track light ion accumulation
• FISPACT calculation performed with higher
  precision

76
Steady-State Problem 1 Century
77
Pulsing Problem
vs DKR
78
Advanced Feature Validation

• Arbitrary Irradiation Schedules
• 94500 Pulses
• 2 X 47250 pulses
• 4 X 23625 pulses
• 100 X (250 250) 100 x (225220)
• 10 X 2500 10 x (125125) 100 x 445

79
Advanced Feature Validation

• Reverse Calculation mode
• Targets isotopes in forward calculation
• 51Cr, 54Mn, 55Fe, 57Co

80
Inventory Analysis Waste

• Inventory calculations needed to characterize
  waste
• activity decay heat
• waste disposal ratings contact dose
• Some proposed waste solutions are themselves
  nuclear systems
• Accelerator Transmutation of Waste ATW
• Waste or Product?
• Possibility for recycling of materials with low
  levels of radioactivity

81
Inventory Analysis Proliferation

• No comprehensive methodology or metric for
  quantitative assessment of proliferation
  resistance
• Accurate inventory calculations are input for
  other considerations
• chemical form of fissile inventory
• accessibility of fissile inventory
• ability to monitor changes in fissile inventory
• Inventory calculations as part of monitoring
  procedure?

82
Inventory Analysis Safety

• Based on release of radioactive isotopes
• To eliminate need for off-site response, need to
  demonstrate negligible release levels
• Radiation protection policy changes
• Importance of radioactivity calculations if the
  Linear Non-Threshold theory is abolished