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X/Q for Releases From Area Sources

X/Q for Releases From Area Sources. 2009 RETS-REMP Workshop Jim Key Key Solutions, Inc. www.keysolutionsinc.com. Industry Tritium Issues Have Revealed Many Unanalyzed Dose Pathways Storm Drains Ground Water Service Water Discharge Basins or Lakes With Little Water Turnover. Concerns.

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X/Q for Releases From Area Sources

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  1. X/Q for Releases From Area Sources 2009 RETS-REMP Workshop Jim Key Key Solutions, Inc. www.keysolutionsinc.com

  2. Industry Tritium Issues Have Revealed Many Unanalyzed Dose Pathways Storm Drains Ground Water Service Water Discharge Basins or Lakes With Little Water Turnover Concerns

  3. Has Been Mostly Ignored Tritium Concentrations in Bodies of Water Can Continue to Build Up Release from Such Sources are Estimated to be 10 Ci/yr and Higher Evaporation From Area Sources

  4. Simplify Gaussian Model As Follows Ground Level Release Ground Level Receptor Modify From Point Source Geometry to Square Area Geometry Application of Gaussian Model to Release from Area Sources

  5. Point Source Plume Centerline Point Source Sector Average Area Source Plume Centerline Area Source Sector Average Examine

  6. Standard Gaussian Model

  7. General Gaussian X/Q Downwind Factor Vertical Factor Crosswind Factor

  8. General Gaussian X/Q

  9. y(x) and z(x) are functions of Downwind Distance – x Atmospheric Stability – Pasquill Category Horizontal and VerticalParameters

  10. yLateral Diffusion Coefficients

  11. zVertical Diffusion Coefficients

  12. Atmospheric Stability Categories

  13. Ground Level Release Set H = 0 Ground Level Receptor Set z = 0 Plume Centerline Set y = 0 Simplifications

  14. Ground Level ConcentrationGround Level ReceptorPlume CenterlinePoint Source

  15. Point Source Geometry Receptor Point Source Wind x

  16. Wind Directions in Each Sector are Distributed Randomly Over Period of Interest Calculate Average Value of /Q for Sector Length Sector Averaged Concentration

  17. Calculate Average Value of Function Over Sector Length

  18. Find Average Value of /Qover Sector Arc Length

  19. Crosswind Integrated Concentration This term is cannot be integrated analytically

  20. Easier to Use… From Standard Math Tables

  21. Crosswind Integrated Concentration • Function Of Only • Downwind Distance – x • Wind Speed - u

  22. Ground Level ConcentrationGround Level ReceptorSector AveragePoint Source

  23. Wind Directions in Each Sector are Distributed Randomly Over Period of Interest Calculate X/Q Using Joint Frequency Distribution: f(,S,N)  Direction S Stability Class N Wind Speed Class Time-Averaged Concentration

  24. Allowed By NRC Guidance Reg Guides 1.109 NUREGs 0133, 0472, 0473, 1301, 1302 Less Scatter and Variability Than Real Data Dose Models Are Based On 1 Year Annual Exposure Time-Averaged Concentration

  25. Real Time/Short Term /Q Factors of 3 to 10 Long Term /Q Factors of 2 to 4 From NCRP Report No. 76 /Q Variability

  26. Use Average Wind Speed (Not Max Wind Speed) Determine yo for Each Stability Class Determine Virtual Distance (Xv) for Each Stability Class Applying JFD Data to X/Q

  27. Calculate X/Q Using:

  28. Simplifications Ground Level Release Ground Level Receptor Assume Point Source at Center of Release Very Conservative Does not consider that source is initially distributed over large surface area. Plume Centerline Sector Average Now Consider Area Source

  29. Ground Level Release Ground Level Receptor Simple Geometry Area Source For Plume Centerline Assumes

  30. Simple Geometry for NearField Area Source Receptor Area Source 2b Wind 2a

  31. Calculate Average Value of Function Over An Area • Integration Over Area of Source • Calculates Plume Centerline Concentration

  32. Ground Level Concentration Near field conditions or large area sources require that we consider y(x) and z(x) as functions of x

  33. Problem to Solve

  34. Problem to Solve - 2 • Cannot Be Solved Analytically • Use Error Function for Integral Over dy

  35. Error FunctionErf

  36. Error FunctionIdentities

  37. Problem to Solve - 3 Replace With

  38. Problem to Solve - 4

  39. Problem to Solve - 5 • Reduced to Integral of dx • Integrate Using Simpson’s Rule

  40. Similar Development for Point Source Results In - Area Source For Sector Average • Cannot Be Integrated Analytically • Integrate Using Simpson’s Rule • Simpler Function to Integrate Numerically

  41. Calculate X/Q Assuming Ground Level Release Emission Source is One Mile Square Receptor is Due West ½ Mile from Center of Source (i.e. at Boundary) Assume Worst Case Met Conditions Extremely Stabile (Class G) Calm Conditions (0.04 m/s) Least Dispersion Simple Case

  42. Ground Level Release Emission Source is One Mile Square Receptor is Due West ½ Mile from Center of Source (i.e. at Area Boundary) Assume Worst Case Met Conditions Extremely Stabile (Class G) Calm Conditions (0.04 m/s) Least Dispersion Example 1

  43. Point Source vsArea Source 1600 meters Receptor Point Source Wind Area Source

  44. Example 1 Calculations Source = 1 Square Mile Receptor at Source Boundary

  45. u = 0.022 m/s x = 20,800 m zG = 7.5 m Simple X/Q for Area Source

  46. Wind Geometry for Example 2 Receptor Point Source 3200 meters 1600 meters

  47. Example 2 Calculations Source = 1 Square Mile Receptor 2 Miles From Boundary

  48. Larger Sources – Expect Greater Difference As Distance to Receptor Increases Difference Slowly Decreases Point Source vs Area SourceX/Q

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