derivation of accident specific material-at-risk equivalency factors
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Derivation of Accident Specific Material-at-Risk Equivalency Factors. Jason Andrus Chad Pope, PhD PE Idaho National Laboratory. Overview. Discussion of problem Proposed solution Mathematical derivation Applied e xample Discussion of ideal applications. Problem Statement. - PowerPoint PPT PresentationTRANSCRIPT
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Derivation of Accident Specific Material-at-Risk Equivalency Factors
Jason AndrusChad Pope, PhD PE
Idaho National Laboratory
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Overview
• Discussion of problem• Proposed solution• Mathematical derivation• Applied example• Discussion of ideal applications
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Problem Statement
• Need for New Method to Establish MAR Equivalency– Spectrum constraints– Material form relationships– Overly restrictive segmented limits
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Proposed Solution
• Derive an equivalency method which provides:– Detailed accident comparisons– Process and technical flexibility– Coupling with near-real time tracking system
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Solution Methodology
• Equate the Committed Effective Dose Equations to a reference material.– Determine a reference nuclide for dose
consequence comparisons– Derive equivalency factors to relate different
nuclides and accidents to the reference.• Benefits
– Establish limits that operators understand– Effectively demonstrates relative hazards
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Mathematical Derivation (1/5)
• CED Equation
/Q = Plume dispersion (s/m3)BR = Breathing rate (m3/s)STi = Source term of nuclide i (Bq)DCFi = Dose conversion factor of nuclide i (Sv/Bq)DDFi = Fraction of nuclide i in plume after dry deposition (no units)N = Number of nuclides contributing to dose (no units)
/ =CED1
N
iDCFiDDFiST i BR Q
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Mathematical Derivation (2/5)
ST Equation
ST = Source term (Bq)MAR = Material-at-risk (g)SA = Specific activity (Bq/g)DR = Damage ratio (no units)ARF = Airborne release fraction (no units)RF = Respirable fraction (no units)LPF = Leak path factor (no units)
LPFRFARFDRSAMARST
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Mathematical Derivation (3/5)
• Equate spectrum CED to reference CED
DCFDDFLPFRFARFDRSAPEGBRQχCED RefRefRefRefRefRefRef
I
iiiiiiiii DCFDDFLPFRFARFDRSAMARBRQ
χ1
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Mathematical Derivation (4/5)
• Cancel common terms and simplify
I
ii
ii WF
ASFASFMARPEG
1 Ref
DDFLPFRFARFDRSAASF iiiiii i
DCFDCFWF i
iRef
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Mathematical Derivation (5/5)
• Equivalency Factor and dose calculation
WFASFASFEF i
ii
Ref
I
iii EFMARPEG
1
DCFDDFLPFRFARFDRSAPEGBRQCED RefRefRefRefRefRefRef
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Applied Example (1/3)
• Consider a simple example “psuedo-fuel”– 2 potential accidents drop or fire– Release values known, ASF calculated
Common to Both
Accidents Drop Accident Fire Accident Calculated ASFs
Nuclide SA DR LPF DDF ARF-Drop RF-Drop ARF-Fire RF-Fire ASF-Drop ASF-Fire
Am-241 3.43E+00 1.0 1.0 1.0 2.30E-05 6.00E-03 1.00E-02 7.89E-05 2.06E-04
Pu-239 6.22E-02 1.0 1.0 1.0 2.30E-05 6.00E-03 1.00E-02 1.43E-06 3.73E-06
Cs-137 8.70E+01 1.0 1.0 1.0 2.30E-05 6.00E-03 1.00E-02 2.00E-03 5.22E-03
Sr-90 1.36E+02 1.0 1.0 1.0 2.30E-05 6.00E-03 1.00E-02 3.13E-03 8.16E-03
I-131 1.24E+05 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.24E+05 1.24E+05
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Applied Example (2/3)
• Calculate Weighting Factors and Equivalency Factors
Nuclide Drop DCF Fire DCF Drop WF Fire WF Drop EF Fire EF
Am-241 2.70E-05 2.70E-05 8.44E-01 8.44E-01 4.65E+01 1.21E+02
Pu-239 3.20E-05 8.30E-06 1.00E+00 2.59E-01 1.00E+00 6.77E-01
Cs-137 6.70E-09 6.70E-09 2.09E-04 2.09E-04 2.93E-01 7.64E-01
Sr-90 3.00E-08 3.00E-08 9.38E-04 9.38E-04 2.05E+00 5.35E+00
I-131 1.10E-08 1.10E-08 3.44E-04 3.44E-04 2.98E+07 2.98E+07
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Applied Example (3/3)
• Risks from individual nuclides as well as accidents can be compared.
• Single metric available for risk comparisons
Nuclide Sample Mass (g) Drop PEG Fire PEG
Am-241 1 4.65E+01 1.21E+02
Pu-239 10 1.00E+01 6.77E+00
Cs-137 1 2.93E-01 7.64E-01
Sr-90 1 2.05E+00 5.35E+00
I-131 1.00E-06 2.98E+01 2.98E+01
Total 13.00 8.87E+01 1.64E+02
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Discussion of Ideal Applications
• Well characterized and consistent processes– Well tracked inventory– Multiple or varied material forms or similar
accidents– Nuclide spectrums where important isotopes can
be readily identified.• Comparison of different scenarios and material
types that all roll up to one limit.
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Conclusion
• New methodology for dose equivalency derived which allows comparison of different accidents.
• Single metric for comparison of hazards of different accident events, nuclide spectra.
• Permits establishment of general limits for events where multiple material forms may roll up into an integral consequence. (i.e. earthquake events)