X/Q for Releases From Area Sources

2008 RETS-REMP and NUMUG 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

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

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

Standard Gaussian Model

General Gaussian X/Q

2y

2

y 2

yexp

2

1

u

1Downwind Factor

Crosswind Factor

Vertical Factor

2

z

2

2z

2

z 2

zHexp

2

zHexp

2

1

General Gaussian X/Q

2y

2

2z

2

2z

2

zy

2

yexp

2

zHexp

2

zHexp

u2

1Q

y Lateral

Diffusion Coefficients

z

Vertical Diffusion

Coefficients

Atmospheric Stability CategoriesStability

Category Condition Description

Lapse

RateA Extremely Unstable Sunny Summer Weather -1.9

B Moderately Stable Sunny and Warm -1.9 to –1.7

C Slightly Unstable Average Day -1.7 to –1.5

D Neutral Overcast Day or Night -1.5 to –0.5

E Slightly Stable Average Night -0.5 to 1.5

F Moderately Stable Clear Night 1.5 to 4.0

G Highly Stable Added by NRC > 4.0

Ground Level Concentration

2y

2

2z

2

zy 2

yexp

2

Hexp

u

1Q

Set z = 0

Crosswind Integrated Concentration

dy2

yexp

2

Hexp

u

1Q

2y

2

2z

2

zy

Integral Reduces To:

2y2

y

2

2dy2

yexp

Crosswind Integrated Concentration

2z

2

z

2y2

z

2

zy

2

Hexp

u

2

22

Hexp

u

1Q

Sector Averaged Concentration

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

• Divide Crosswind-Integrated Concentration by Sector Arc Length

16

x2

Ground Level Sector Averaged Concentration

2z

2

z 2

Hexp

16x2u2

2Q

Ground Level Sector Averaged Concentration – Ground Release

xu

03.2Q

z

Set H = 0

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

Ground Level Sector and Time Averaged Concentration –

Ground Release

N,S NzS

N,S,fxu

03.2,xQ

Estimation of Release from Area Source

• Assume Point Source at Center of Release– Very Conservative– Does not consider that source is initially

distributed over large surface area.

Estimation of Release from Area Source

• Turner (Workbook of Atmospheric Dispersion Estimates, 1994)– Treat area source as having initial horizontal

standard deviation - yo - related to area width.

– Horizontal standard deviation for square source is approximated by L/4.3 (L= Length of a side of the area).

Estimation of Release from Area Source

• Turner (Workbook of Atmospheric Dispersion Estimates, 1994)

– Select “Virtual Distance” - xy - based on yo.

– Calculate X/Q using distance of x + xy.

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

Geometry for Point Source

1600 meters

Receptor

Point Source

Distance – 800 m

Simple X/Q for Point Source

• u = 0.022 m/s

• x = 800 m zG = 7.5 m

02E50.1800022.07.7

03.2QX

Simple X/Q for Area Source

• Calculate yo based on 1 mile side– 1600 meters/4.3 = 372 m

• From y table/plot look up distance corresponding to yo for stability class of interest.– 20000 m

• Calculate X/Q for virtual distance:20,000 + 800 = 20,800 m.

Geometry for Area Source

1600 meters

Receptor

Point Source

Virtual Distance – 20,800 m

Simple X/Q for Area Source

• u = 0.022 m/s

• x = 20,800 m zG = 7.5 m

04E76.5800,20022.07.7

03.2QX

Applying JFD Data to X/Q

• XOQDOQ Provides Summary of JFD Data by Stability Class, Sector and Wind Speed

JOINT FREQUENCY DISTRIBUTION OF WIND SPEED AND DIRECTION ATMOSPHERIC STABILITY CLASS A

UMAX (M/S) N NNE NE ENE E ESE SE SSE S SSW SW WSW W WNW NW NNW

0.04 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.34 0.01 0.03 0.02 0.01 0 0.01 0.01 0.01 0.02 0.01 0.02 0.01 0.01 0.016 0.013 0.006 3.13 0.09 0.2 0.25 0.15 0.07 0.07 0.11 0.26 0.31 0.16 0.15 0.14 0.12 0.074 0.057 0.06

5.36 0.18 0.23 0.2 0.17 0.14 0.15 0.23 0.55 0.91 0.51 0.26 0.14 0.29 0.109 0.092 0.175

8.05 0.27 0.13 0.01 0.03 0.05 0.08 0.12 0.27 1.15 0.85 0.13 0.06 0.09 0.123 0.137 0.334

10.7 0.08 0.02 0 0 0 0 0.02 0.06 0.33 0.2 0.02 0 0.01 0.082 0.084 0.095 13.00 0.01 0 0 0 0 0 0 0.01 0.03 0.03 0 0 0.01 0.007 0.022 0.012

JFD for Receptor in West Sector

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

Calculate X/Q Using:

Frequency theis N,S,f

Class Speed Wind theis N

ClassStability theis S

Sector theis

Where

N,S,fxu

03.2,xQ

N,S vNzS

X/Q for Stability Class A

Annual Average X/Q for Receptor

• Point Source X/Q = 6.4E-06

• Area Source X/Q = 5.7E-07

Point Source vs Area SourceX/Q

• Larger Sources – Expect Greater Difference

• As Distance to Receptor Increases Difference Slowly Decreases

Point Source vs Area Source

1.0E-08

1.0E-07

1.0E-06

1.0E-05

0 2000 4000 6000 8000 10000

Distance

X/Q

Point Source Area Source

Point Source vs Area SourceX/Q

• For Nearby Receptors Rule of Thumb Appears to be X/QArea ~ 1/10 X/Qpoint

• For Distances Out to 10,000 meters

X/QArea ~ 1/2 X/Qpoint