X q for releases from area sources
Download
1 / 52

X/Q for Releases From Area Sources - PowerPoint PPT Presentation


  • 111 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' X/Q for Releases From Area Sources' - jontae


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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 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 Sources


Application of gaussian model to release from area sources

Simplify 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 Sources


Examine

Point Source Plume Centerline Pathways

Point Source Sector Average

Area Source Plume Centerline

Area Source Sector Average

Examine



General gaussian x q
General Gaussian X/Q Pathways

Downwind Factor

Vertical Factor

Crosswind Factor



Horizontal and vertical parameters

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

Downwind Distance – x

Atmospheric Stability – Pasquill Category

Horizontal and VerticalParameters


Y lateral diffusion coefficients
PathwaysyLateral Diffusion Coefficients


Z vertical diffusion coefficients
PathwayszVertical Diffusion Coefficients



Simplifications

Ground Level Release Pathways

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 Concentration PathwaysGround Level ReceptorPlume CenterlinePoint Source


Point source geometry
Point Source Geometry Pathways

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



Find average value of q over sector arc length
Find Average Value of Period of Interest/Qover Sector Arc Length


Crosswind integrated concentration
Crosswind Integrated Concentration Period of Interest

This term is cannot be integrated analytically


Easier to use
Easier to Use… Period of Interest

From Standard Math Tables


Crosswind integrated concentration1
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


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

S Stability Class

N Wind Speed Class

Time-Averaged Concentration


Time averaged concentration1

Allowed 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 Concentration


Q variability

Real 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 Variability


Applying jfd data to x q

Use 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/Q


Calculate x q using
Calculate X/Q Using: Period of Interest


Now consider area source

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 Source


Area source for plume centerline assumes

Ground Level Release Period of Interest

Ground Level Receptor

Simple Geometry

Area Source For Plume Centerline Assumes


Simple geometry for near field area source
Simple Geometry for Near Period of InterestField Area Source

Receptor

Area Source

2b

Wind

2a


Calculate average value of function over an area
Calculate Average Value of Function Over An Area Period of Interest

  • Integration Over Area of Source

  • Calculates Plume Centerline Concentration


Ground level 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
Problem to Solve Period of Interest


Problem to solve 2
Problem to Solve - 2 Period of Interest

  • Cannot Be Solved Analytically

  • Use Error Function for Integral Over dy


Error function erf
Error Function Period of InterestErf


Error function identities
Error Function Period of InterestIdentities


Problem to solve 3
Problem to Solve - 3 Period of Interest

Replace With


Problem to solve 4
Problem to Solve - 4 Period of Interest


Problem to solve 5
Problem to Solve - 5 Period of Interest

  • Reduced to Integral of dx

  • Integrate Using Simpson’s Rule


Area source for sector average

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


Simple case

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 Case


Example 1

Ground 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 1


Point source vs area source
Point Source vs Period of InterestArea Source

1600 meters

Receptor

Point Source

Wind

Area Source


Example 1 calculations
Example 1 Calculations Period of Interest

Source = 1 Square Mile

Receptor at Source Boundary


Simple x q for area source

u = 0.022 m/s Period of Interest

x = 20,800 m

zG = 7.5 m

Simple X/Q for Area Source


Geometry for example 2

Wind Period of Interest

Geometry for Example 2

Receptor

Point Source

3200 meters

1600 meters


Example 2 calculations
Example 2 Calculations Period of Interest

Source = 1 Square Mile

Receptor 2 Miles From Boundary


Point source vs area source x q

Larger Sources – Expect Greater Difference Period of Interest

As Distance to Receptor Increases Difference Slowly Decreases

Point Source vs Area SourceX/Q


Aloha
ALOHA Period of Interest


ad