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X/Q for Releases From Area SourcesPowerPoint Presentation

X/Q for Releases From Area Sources

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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

ConcernsHas Been Mostly Ignored Pathways

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 SourcesSimplify Gaussian Model As Follows Pathways

Ground Level Release

Ground Level Receptor

Modify From Point Source Geometry to Square Area Geometry

Application of Gaussian Model to Release from Area SourcesPoint Source Plume Centerline Pathways

Point Source Sector Average

Area Source Plume Centerline

Area Source Sector Average

ExamineStandard Gaussian Model Pathways

General Gaussian X/Q Pathways

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

Downwind Distance – x

Atmospheric Stability – Pasquill Category

Horizontal and VerticalParameters PathwaysyLateral Diffusion Coefficients

PathwayszVertical Diffusion Coefficients

Atmospheric Stability Categories Pathways

Ground Level Release Pathways

Set H = 0

Ground Level Receptor

Set z = 0

Plume Centerline

Set y = 0

SimplificationsGround Level Concentration PathwaysGround Level ReceptorPlume CenterlinePoint Source

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

Calculate Average Value of /Q for Sector Length

Sector Averaged ConcentrationCalculate Average Value of Function Over Sector Length Period of Interest

Find Average Value of Period of Interest/Qover Sector Arc Length

Crosswind Integrated Concentration Period of Interest

This term is cannot be integrated analytically

Easier to Use… Period of Interest

From Standard Math Tables

Crosswind Integrated Concentration Period of Interest

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

Ground Level Concentration Period of InterestGround 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

S Stability Class

N Wind Speed Class

Time-Averaged ConcentrationAllowed By NRC Guidance Period of Interest

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 ConcentrationReal Time/Short Term Period of Interest/Q

Factors of 3 to 10

Long Term /Q

Factors of 2 to 4

From NCRP Report No. 76

/Q VariabilityUse Average Wind Speed (Not Max Wind Speed) Period of Interest

Determine yo for Each Stability Class

Determine Virtual Distance (Xv) for Each Stability Class

Applying JFD Data to X/QCalculate X/Q Using: Period of Interest

Simplifications Period of Interest

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 SourceGround Level Release Period of Interest

Ground Level Receptor

Simple Geometry

Area Source For Plume Centerline AssumesCalculate Average Value of Function Over An Area Period of Interest

- Integration Over Area of Source
- Calculates Plume Centerline Concentration

Ground Level Concentration Period of Interest

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

Problem to Solve Period of Interest

Problem to Solve - 2 Period of Interest

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

Error Function Period of InterestErf

Error Function Period of InterestIdentities

Problem to Solve - 3 Period of Interest

Replace With

Problem to Solve - 4 Period of Interest

Problem to Solve - 5 Period of Interest

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

Similar Development for Point Source Results In - Period of Interest

Area Source For Sector Average- Cannot Be Integrated Analytically
- Integrate Using Simpson’s Rule
- Simpler Function to Integrate Numerically

Calculate X/Q Assuming Period of Interest

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 CaseGround Level Release Period of Interest

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 1Larger Sources – Expect Greater Difference Period of Interest

As Distance to Receptor Increases Difference Slowly Decreases

Point Source vs Area SourceX/QALOHA Period of Interest

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