Download - X/Q for Releases From Area Sources 2008 RETS-REMP and NUMUG Workshop Jim Key Key Solutions, Inc
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X/Q for Releases From Area Sources
2008 RETS-REMP and NUMUG Workshop
Jim Key
Key Solutions, Inc.
www.keysolutionsinc.com
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Concerns
• Industry Tritium Issues Have Revealed Many Unanalyzed Dose Pathways– Storm Drains– Ground Water– Service Water– Discharge Basins or Lakes With Little Water
Turnover
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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
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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
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Standard Gaussian Model
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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
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General Gaussian X/Q
2y
2
2z
2
2z
2
zy
2
yexp
2
zHexp
2
zHexp
u2
1Q
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y Lateral
Diffusion Coefficients
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z
Vertical Diffusion
Coefficients
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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
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Ground Level Concentration
2y
2
2z
2
zy 2
yexp
2
Hexp
u
1Q
Set z = 0
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Crosswind Integrated Concentration
dy2
yexp
2
Hexp
u
1Q
2y
2
2z
2
zy
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Integral Reduces To:
2y2
y
2
2dy2
yexp
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Crosswind Integrated Concentration
2z
2
z
2y2
z
2
zy
2
Hexp
u
2
22
Hexp
u
1Q
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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
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Ground Level Sector Averaged Concentration
2z
2
z 2
Hexp
16x2u2
2Q
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Ground Level Sector Averaged Concentration – Ground Release
xu
03.2Q
z
Set H = 0
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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
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Ground Level Sector and Time Averaged Concentration –
Ground Release
N,S NzS
N,S,fxu
03.2,xQ
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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.
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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).
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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.
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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
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Geometry for Point Source
1600 meters
Receptor
Point Source
Distance – 800 m
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Simple X/Q for Point Source
• u = 0.022 m/s
• x = 800 m zG = 7.5 m
02E50.1800022.07.7
03.2QX
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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.
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Geometry for Area Source
1600 meters
Receptor
Point Source
Virtual Distance – 20,800 m
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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
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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
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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
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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
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X/Q for Stability Class A
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Annual Average X/Q for Receptor
• Point Source X/Q = 6.4E-06
• Area Source X/Q = 5.7E-07
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Point Source vs Area SourceX/Q
• Larger Sources – Expect Greater Difference
• As Distance to Receptor Increases Difference Slowly Decreases
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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
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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