x/q for releases from area sources
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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X/Q for Releases From Area Sources
2009 RETS-REMP 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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Examine
• Point Source Plume Centerline
• Point Source Sector Average
• Area Source Plume Centerline
• Area Source Sector Average
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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
2z
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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Horizontal and VerticalParameters
y(x) and z(x) are functions of
– Downwind Distance – x– Atmospheric Stability – Pasquill Category
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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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Simplifications
• Ground Level Release– Set H = 0
• Ground Level Receptor– Set z = 0
• Plume Centerline– Set y = 0
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Ground Level ConcentrationGround Level Receptor
Plume CenterlinePoint Source
xxu
1Q
zy
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Point Source Geometry
Receptor
Wind
Point Source
x
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Sector Averaged Concentration
• Wind Directions in Each Sector are Distributed Randomly Over Period of Interest
• Calculate Average Value of /Q for Sector Length
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Calculate Average Value of Function Over Sector Length
ab
xF
)x(F
b
ab,aAVE
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Find Average Value of /Qover Sector Arc Length
LengthArc
dyQLengthArc
AveQ
16
x2Length Arc
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Crosswind Integrated Concentration
dy2
yExp
16x2
1
u
1Q
2a
2a2y
2
zyAve
This term is cannot be integrated analytically
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Easier to Use…
2y2
y
2
2dy2
yExp
From Standard Math Tables
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Crosswind Integrated Concentration
2y
zy
2
16x2
1
u
1Q
• Function Of Only– Downwind Distance – x– Wind Speed - u
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xu
03.2Q
z
Ground Level ConcentrationGround Level Receptor
Sector AveragePoint Source
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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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Time-Averaged Concentration
• 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
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/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
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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
Index Class Speed Wind theis N
Index ClassStability theis S
IndexSector theis
Where
N,S,fxu
03.2,xQ
N,S vNzS
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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
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Area Source For Plume Centerline Assumes
• Ground Level Release
• Ground Level Receptor
• Simple Geometry
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Simple Geometry for NearField Area Source
WindArea
Source
Receptor
2b
2a
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Calculate Average Value of Function Over An Area
1212
x
x
y
yy,yx,xAREA yyxx
y,xQ
)y,x(Q
2
1
2
1
2121
• Integration Over Area of Source
• Calculates Plume Centerline Concentration
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Ground Level Concentration
x2
yexp
xxu
1Q
2y
2
zy
Near field conditions or large area sources require that we consider y(x) and z(x) as
functions of x
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Problem to Solve
1212
x
x
y
y2y
2
zy
AREA
yyxx
dydxx2
yexp
xxu1
Q
2
1
2
1
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Problem to Solve - 2
a
a
b
b2y
2
zy
AREA
dydxx2
yexp
xx
1
ub2a2
1
Q
• Cannot Be Solved Analytically• Use Error Function for Integral Over dy
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Error FunctionErf
x
0
t dte2
)x(Erf2
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Error FunctionIdentities
)x(Erf)x(Erf
)x(Erf2
dtex
0
t2
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a
a zy
b
b
2
y
dxxx
1dy
x2
yexp
uba4
1
Problem to Solve - 3
x2
bErf
y
Replace With
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a
a zy
y
a
a zyy
dxxx
x2bErf
uba4
1
or
dxxx
1
x2
bErf
uba4
1
Problem to Solve - 4
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a
a zy
y
Areadx
xx
x2bErf
uba4
1Q
Problem to Solve - 5
• Reduced to Integral of dx• Integrate Using Simpson’s Rule
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Area Source For Sector Average
• Similar Development for Point Source Results In -
a
a zArea
dxux2ba
1Q
• Cannot Be Integrated Analytically• Integrate Using Simpson’s Rule
– Simpler Function to Integrate Numerically
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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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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
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Point Source vsArea Source
Receptor
Wind
Point Source
1600 meters
Area Source
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Example 1 Calculations
Geometry /Q (m/sec2)
Point Source Plume Centerline 9.2E-02
Point Source Sector Average 1.5E-02
Area Source Plume Centerline 6.6E-03
Area Source Sector Average 3.2E-03
Source = 1 Square Mile
Receptor at Source Boundary
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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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Geometry for Example 2
1600 meters
ReceptorPoint Source
Wind
3200 meters
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Example 2 Calculations
Geometry /Q (m/sec2)
Point Source Plume Centerline 8.1E-03
Point Source Sector Average 1.2E-03
Area Source Plume Centerline 9.2E-06
Area Source Sector Average 5.7E-04
Source = 1 Square Mile
Receptor 2 Miles From Boundary
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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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Plume Centerline Comparison
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
800 1800 2800 3800 4800 5800 6800 7800 8800 9800
Distance (meters)
X/Q
(m
/sec
3 )
Area Source Plume Centerline
Point Source Plume Centerline
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Sector Average Comparison
1.E-07
1.E-06
1.E-05
1.E-04
800 1800 2800 3800 4800 5800 6800 7800 8800 9800
x (meters)
X/Q
(m
/se
c3)
Area Source Sector Average
Point Source Sector Average
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Sector Average Comparison
1.E-07
1.E-06
1.E-05
1.E-04
800 1800 2800 3800 4800 5800 6800 7800 8800 9800
x (meters)
X/Q
(m
/se
c3)
Area Source Sector Average
Point Source Sector Average
Point Source Sector Average
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ALOHA