derivation of accident specific material-at-risk equivalency factors

Derivation of Accident Specific Material-at-Risk Equivalency Factors

Jason AndrusChad Pope, PhD PE

Idaho National Laboratory

Overview

• Discussion of problem• Proposed solution• Mathematical derivation• Applied example• Discussion of ideal applications

Problem Statement

• Need for New Method to Establish MAR Equivalency– Spectrum constraints– Material form relationships– Overly restrictive segmented limits

Proposed Solution

• Derive an equivalency method which provides:– Detailed accident comparisons– Process and technical flexibility– Coupling with near-real time tracking system

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

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

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

Mathematical Derivation (3/5)

• Equate spectrum CED to reference CED

DCFDDFLPFRFARFDRSAPEGBRQχCED RefRefRefRefRefRefRef

I

iiiiiiiii DCFDDFLPFRFARFDRSAMARBRQ

χ1

Mathematical Derivation (4/5)

• Cancel common terms and simplify

I

ii

ii WF

ASFASFMARPEG

1 Ref

DDFLPFRFARFDRSAASF iiiiii i

DCFDCFWF i

iRef

Mathematical Derivation (5/5)

• Equivalency Factor and dose calculation

WFASFASFEF i

ii

Ref

I

iii EFMARPEG

1

DCFDDFLPFRFARFDRSAPEGBRQCED RefRefRefRefRefRefRef

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

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

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

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.

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)