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X/Q for Releases From Area Sources

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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

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

Simplify Gaussian Model As Follows

Ground Level Release

Ground Level Receptor

Modify From Point Source Geometry to Square Area Geometry

Point Source Plume Centerline

Point Source Sector Average

Area Source Plume Centerline

Area Source Sector Average

Downwind Factor

Vertical Factor

Crosswind Factor

y(x) and z(x) are functions of

Downwind Distance – x

Atmospheric Stability – Pasquill Category

Ground Level Release

Set H = 0

Ground Level Receptor

Set z = 0

Plume Centerline

Set y = 0

Receptor

Point Source

Wind

x

Wind Directions in Each Sector are Distributed Randomly Over Period of Interest

Calculate Average Value of /Q for Sector Length

This term is cannot be integrated analytically

From Standard Math Tables

- Function Of Only
- Downwind Distance – x
- Wind Speed - u

Ground Level ConcentrationGround Level ReceptorSector AveragePoint Source

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

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

Real Time/Short Term /Q

Factors of 3 to 10

Long Term /Q

Factors of 2 to 4

From NCRP Report No. 76

Use Average Wind Speed (Not Max Wind Speed)

Determine yo for Each Stability Class

Determine Virtual Distance (Xv) for Each Stability Class

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

Ground Level Release

Ground Level Receptor

Simple Geometry

Receptor

Area Source

2b

Wind

2a

- Integration Over Area of Source
- Calculates Plume Centerline Concentration

Near field conditions or large area sources require that we consider y(x) and z(x) as functions of x

- Cannot Be Solved Analytically
- Use Error Function for Integral Over dy

Replace With

- Reduced to Integral of dx
- Integrate Using Simpson’s Rule

Similar Development for Point Source Results In -

- Cannot Be Integrated Analytically
- Integrate Using Simpson’s Rule
- Simpler Function to Integrate Numerically

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

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

1600 meters

Receptor

Point Source

Wind

Area Source

Source = 1 Square Mile

Receptor at Source Boundary

u = 0.022 m/s

x = 20,800 m

zG = 7.5 m

Wind

Receptor

Point Source

3200 meters

1600 meters

Source = 1 Square Mile

Receptor 2 Miles From Boundary

Larger Sources – Expect Greater Difference

As Distance to Receptor Increases Difference Slowly Decreases