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

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

3. Evaporation From Area Sources 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

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

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

6. Standard Gaussian Model

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

8. General Gaussian X/Q

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

10.  y Lateral Diffusion Coefficients

11.  z Vertical Diffusion Coefficients

12. Atmospheric Stability Categories Stability CategoryConditionDescription Lapse Rate AExtremely UnstableSunny Summer Weather-1.9 BModerately StableSunny and Warm-1.9 to –1.7 CSlightly UnstableAverage Day-1.7 to –1.5 DNeutralOvercast Day or Night-1.5 to –0.5 ESlightly StableAverage Night-0.5 to 1.5 FModerately StableClear Night1.5 to 4.0 GHighly StableAdded by NRC> 4.0

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

14. Ground Level Concentration Ground Level Receptor Plume Centerline Point Source

15. Point Source Geometry Receptor Wind Point Source x

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

17. Calculate Average Value of Function Over Sector Length

18. Find Average Value of  /Q over 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 Concentration Ground Level Receptor Sector Average Point Source

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

24. Time-Averaged Concentration 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

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

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

27. Calculate X/Q Using:

28. Now Consider Area Source 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

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

30. Simple Geometry for Near Field Area Source Wind Area Source Receptor 2b 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 Function Erf

36. Error Function Identities

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

41. Simple Case 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

42. Example 1 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

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

44. Example 1 Calculations Geometry  /Q (m/sec2) Point Source Plume Centerline 9.2E-02 Point Source Sector Average 1.5E-02 Area Source Plume Centerline 6.6E-03 Area Source Sector Average 3.2E-03 Source = 1 Square Mile Receptor at Source Boundary

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

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

47. Example 2 Calculations Geometry  /Q (m/sec2) Point Source Plume Centerline 8.1E-03 Point Source Sector Average 1.2E-03 Area Source Plume Centerline 9.2E-06 Area Source Sector Average 5.7E-04 Source = 1 Square Mile Receptor 2 Miles From Boundary

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

52. ALOHA