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![Page 1: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/1.jpg)
Derivation of Accident Specific Material-at-Risk Equivalency Factors
Jason AndrusChad Pope, PhD PE
Idaho National Laboratory
![Page 2: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/2.jpg)
Overview
• Discussion of problem• Proposed solution• Mathematical derivation• Applied example• Discussion of ideal applications
![Page 3: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/3.jpg)
Problem Statement
• Need for New Method to Establish MAR Equivalency– Spectrum constraints– Material form relationships– Overly restrictive segmented limits
![Page 4: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/4.jpg)
Proposed Solution
• Derive an equivalency method which provides:– Detailed accident comparisons– Process and technical flexibility– Coupling with near-real time tracking system
![Page 5: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/5.jpg)
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
![Page 6: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/6.jpg)
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
i
DCFiDDFiST i BR Q
![Page 7: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/7.jpg)
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
![Page 8: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/8.jpg)
Mathematical Derivation (3/5)
• Equate spectrum CED to reference CED
DCFDDFLPFRFARFDRSAPEGBRQχCED RefRefRefRefRefRefRef
I
iiiiiiiii DCFDDFLPFRFARFDRSAMARBRQ
χ1
![Page 9: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/9.jpg)
Mathematical Derivation (4/5)
• Cancel common terms and simplify
I
ii
ii WF
ASF
ASFMARPEG
1 Ref
DDFLPFRFARFDRSAASF iiiiii i
DCF
DCFWF
ii
Ref
![Page 10: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/10.jpg)
Mathematical Derivation (5/5)
• Equivalency Factor and dose calculation
WFASF
ASFEF i
ii
Ref
I
iii EFMARPEG
1
DCFDDFLPFRFARFDRSAPEGBRQCED RefRefRefRefRefRefRef
![Page 11: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/11.jpg)
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
![Page 12: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/12.jpg)
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.
![Page 15: Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory.](https://reader030.fdocuments.us/reader030/viewer/2022033108/56649d1b5503460f949f0a81/html5/thumbnails/15.jpg)
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)