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. Concerns.

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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


Concerns

Industry Tritium Issues Have Revealed Many Unanalyzed Dose Pathways

Storm Drains

Ground Water

Service Water

Discharge Basins or Lakes With Little Water Turnover

Concerns


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

Evaporation From Area Sources


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

Application of Gaussian Model to Release from Area Sources


Examine

Point Source Plume Centerline

Point Source Sector Average

Area Source Plume Centerline

Area Source Sector Average

Examine


Standard gaussian model

Standard Gaussian Model


General gaussian x q

General Gaussian X/Q

Downwind Factor

Vertical Factor

Crosswind Factor


General gaussian x q1

General Gaussian X/Q


Horizontal and vertical parameters

y(x) and z(x) are functions of

Downwind Distance – x

Atmospheric Stability – Pasquill Category

Horizontal and VerticalParameters


Y lateral diffusion coefficients

yLateral Diffusion Coefficients


Z vertical diffusion coefficients

zVertical Diffusion Coefficients


Atmospheric stability categories

Atmospheric Stability Categories


Simplifications

Ground Level Release

Set H = 0

Ground Level Receptor

Set z = 0

Plume Centerline

Set y = 0

Simplifications


Ground level concentration ground level receptor plume centerline point source

Ground Level ConcentrationGround Level ReceptorPlume CenterlinePoint Source


Point source geometry

Point Source Geometry

Receptor

Point Source

Wind

x


Sector averaged concentration

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

Calculate Average Value of /Q for Sector Length

Sector Averaged Concentration


Calculate average value of function over sector length

Calculate Average Value of Function Over Sector Length


Find average value of q over sector arc length

Find Average Value of /Qover Sector Arc Length


Crosswind integrated concentration

Crosswind Integrated Concentration

This term is cannot be integrated analytically


Easier to use

Easier to Use…

From Standard Math Tables


Crosswind integrated concentration1

Crosswind Integrated Concentration

  • Function Of Only

    • Downwind Distance – x

    • Wind Speed - u


X q for releases from area sources

Ground Level ConcentrationGround Level ReceptorSector AveragePoint Source


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

Time-Averaged Concentration


Time averaged concentration1

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


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

/Q Variability


Applying jfd data to x q

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


Calculate x q using

Calculate X/Q Using:


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

Now Consider Area Source


Area source for plume centerline assumes

Ground Level Release

Ground Level Receptor

Simple Geometry

Area Source For Plume Centerline Assumes


Simple geometry for near field area source

Simple Geometry for NearField Area Source

Receptor

Area Source

2b

Wind

2a


Calculate average value of function over an area

Calculate Average Value of Function Over An Area

  • Integration Over Area of Source

  • Calculates Plume Centerline Concentration


Ground level concentration

Ground Level Concentration

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


Problem to solve

Problem to Solve


Problem to solve 2

Problem to Solve - 2

  • Cannot Be Solved Analytically

  • Use Error Function for Integral Over dy


Error function erf

Error FunctionErf


Error function identities

Error FunctionIdentities


Problem to solve 3

Problem to Solve - 3

Replace With


Problem to solve 4

Problem to Solve - 4


Problem to solve 5

Problem to Solve - 5

  • Reduced to Integral of dx

  • Integrate Using Simpson’s Rule


Area source for sector average

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


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

Simple Case


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

Example 1


Point source vs area source

Point Source vsArea Source

1600 meters

Receptor

Point Source

Wind

Area Source


Example 1 calculations

Example 1 Calculations

Source = 1 Square Mile

Receptor at Source Boundary


Simple x q for area source

u = 0.022 m/s

x = 20,800 m

zG = 7.5 m

Simple X/Q for Area Source


Geometry for example 2

Wind

Geometry for Example 2

Receptor

Point Source

3200 meters

1600 meters


Example 2 calculations

Example 2 Calculations

Source = 1 Square Mile

Receptor 2 Miles From Boundary


Point source vs area source x q

Larger Sources – Expect Greater Difference

As Distance to Receptor Increases Difference Slowly Decreases

Point Source vs Area SourceX/Q


Aloha

ALOHA


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