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Derivation of Accident Specific Material-at-Risk Equivalency Factors

This research paper by Jason Andrus and Chad Pope proposes a new method to establish MAR equivalency, providing detailed accident comparisons and process flexibility. The methodology involves equating the Committed Effective Dose Equations, deriving equivalency factors to relate different nuclides and accidents to a reference, and establishing limits for operator understanding. An applied example showcases the calculation of Weighting Factors and Equivalency Factors. The ideal applications include well-tracked inventory and comparison of different scenarios and material types. The conclusion highlights the benefits of the methodology in enabling hazard comparison and establishing general limits for various events.

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Derivation of Accident Specific Material-at-Risk Equivalency Factors

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  1. Derivation of Accident Specific Material-at-Risk Equivalency Factors Jason Andrus Chad Pope, PhD PE Idaho National Laboratory

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

  3. Problem Statement • Need for New Method to Establish MAR Equivalency • Spectrum constraints • Material form relationships • Overly restrictive segmented limits

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

  5. 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

  6. 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 iinplume after dry deposition (no units) N = Number of nuclides contributing to dose (no units)

  7. 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)

  8. Mathematical Derivation (3/5) • Equate spectrum CED to reference CED

  9. Mathematical Derivation (4/5) • Cancel common terms and simplify

  10. Mathematical Derivation (5/5) • Equivalency Factor and dose calculation

  11. Applied Example (1/3) • Consider a simple example “psuedo-fuel” • 2 potential accidents drop or fire • Release values known, ASF calculated

  12. Applied Example (2/3) • Calculate Weighting Factors and Equivalency Factors

  13. Applied Example (3/3) • Risks from individual nuclides as well as accidents can be compared. • Single metric available for risk comparisons

  14. 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.

  15. 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)

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