484+dispersion+lecture

8/4/2019 484+Dispersion+Lecture

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Meteorology / Atmospheric

Dispersion

Figures & Tables from Martin

Chapter 10See also Till & Grogan


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Outline

Definition of Terms

General Dispersion Atmospheric Effects

Stack Effects

Turbulence

Puff Release

Time Average Dispersion

Deposition/Depletion Dry

Resuspension

Wet


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Definition of Terms

Atmospheric Layers:

Troposphere: ground to 10km. Temperature

decreases with height. Weather occurs in this

region

Stratosphere: 10km to 30km. Temperature nearly

constant

Mesosphere: 30km to 90km. Highest temperatureat 50km

Thermosphere: >90km. Ozone layer


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Troposphere4 Layers

Biosphere: below surface to ~50m. Containsall life. Little air motion. Traces of ammonia,methane, radon. Oxygen and CO2 effect by

photosynthesis Boundary Layer: mixing layer where

turbulence and eddies occur 50-100m.Friction effects of surface roughness on windsgenerates low level turbulence. Mostimportant for pollution diffusion


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Troposphere4 Layers

Range Diurnal Influence: surface to 2km.

Temperature changes due to earth surface

temperature fluctuations.

Range of Seasonal Influence: >2km.

Temperature not affected by surface

temperature


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General Dispersion

Source (Ci/s)

(Q)

Dilutant

velocity (u)

Area through

which the

released

material

flows (y, z)


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General Dispersion

DF=dimensionless dispersion factor between 0

and 1.0

uyz= volume dilutents per unit time

Q=amount of pollutant released per unit time


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Atmospheric Dispersion

Atmospheric releases assumed to be a point emittingmaterial at a steady rate of Q (per s)

Material has a turbulence profile that flows past therelease point with a velocity u (m/s) causing it to bemixed there

For uniform turbulence contaminant then release isdiluted in volume of air of width*height*air velocity

Works for plumes trapped in a channeled valley ofwidth y and depth z, which is reasonably accurate forplumes released at a steady rate and confined to flowthrough a specific area such as a plume trapped in achanneled valley of width y and height z.


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Gaussian Distributed Plumes

Point sources where atmosphere isnt confined

Concentration proportional to Q and inversely proportional to thewind speed

Varies downwind thus necessary to introduce a dispersion term toaccount for the non-uniform distribution of concentration.

Measurements have demonstrated concentration varies according toa Gaussian distribution.

For continuously emitting sources, diffusion in the downwinddirection is solely dominated by the wind speed

Vertical and horizontal spread of the plume increase with distance

and are represented by the Gaussian dispersion coefficients y andz, which vary with the downwind distance x.


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General form across the plume (y) and

vertically (z)

Dispersion for the y and z is expressed as the

product of these two Gaussian probabilitydistributions


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Plume Reflection

Accounted for by adding a virtual source also emittingcontaminant at a rate Q an equal distance,H, below the ground toproduce a concentration above the ground

The virtual source emits the contaminant at the same rate Q, thusproducing a general solution for the concentration of the

contaminant throughout the free space above the plane z = 0 (thereflecting barrier or the ground level) due to the virtual source;

= concentration at a distance x downwind, y = horizontal distancefrom the plume centerline and z = height above ground, Q = releaserate of contaminants (per s); u = mean wind speed, typicallymeasured at 10 m above the ground; H = height (+ and) of releasefor the real and the virtual sources; y = horizontal dispersioncoefficient (m), and z = vertical dispersion coefficient (m)


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Plume Reflection

Equation for the concentration in a ground-reflected plume = sum of the concentrationsproduced by real and virtual sources for any valueof y and z.

Ground level concentration (i.e., where z= 0) isusually of interest, so the solution is furthersimplified as which is twice as large due toreflection of the plume

The concentration at the point (x, y, 0) is afunction of the height of release, H.


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Plume Reflection

For main concentration along the centerline

(where y = 0), the equation further simplifies to

For release at ground level (H = 0) the

concentration is very similar to the general flow

equation but with the flow expressed in terms ofthe Gaussian plume dispersion coefficients


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Atmospheric Effects on Dispersion

y and z are governed by atmospheric properties Mainly due to vertical temperature profile on the turbulence field.

Classes of atmospheric stability defined in terms of the temperatureprofile with height and variations in wind speed/direction

Relative to the dry adiabatic lapse rate, which is9.86 C/km

Vertical temperature profile that is steeper causes a displacedair/contaminant mixture to continue to rise or sink

Temperature profile is the same as the dry adiabatic lapse rate thedisplaced air parcel either up or down will experience an adiabatictemperature change and will thus be dispersed only as far as thedisturbing force moves Results in plumes that spread in the shape of a cone

Temperature profile is less than the dry adiabatic lapse rate, the airparcel will tend to be restored to its original position.


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Coning occurs when temperature profile is

similar to adiabatic lapse rate


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Lapse occurs when the atmospheric temperature profile is steeper than thelapse rate

Air displaced upward, temperature will decrease due to adiabatic coolingbut temperature relative to the surrounding atmosphere will be warmercausing it to continue to rise

Air displaced downward, temperature will increase due to adiabatic heatingbut temperature relative to the surrounding atmosphere will be coolercausing it to continue to sink

Strong lapse produce looping plumes that spread out over a wide area; thus,they are inherently unstable and are highly favorable for the dispersal ofpollutants.


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Temperature inversions yield very thin plumes due to stable conditions.

Air displaced upward cools, more dense than the surrounding so rising stops andreturns to its original level.

Air displaced downward, less dense than the surrounding so sinking stops andreturns to its original level.

Atmosphere said to be stable and pollutant dispersion is minimal

Light winds are generally associated with stable conditions and if the winddirection is steady the plume becomes a long, meandering ribbon that extendsdownwind at the altitude of the stack

Plume spreads out in the horizontal plane like a fanhence the term fanning. Afanning plume is not necessarily an unfavorable condition for the dispersion ofeffluents since the plume is quite wide and does not touch the ground.


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Lofting occurs when a temperature inversion exists below the plumeheight

Typically occurs just after sunset as radiant cooling of the earthbuilds up a nighttime temperature inversion. Stable air exists belowthe plume and unstable or neutral conditions continue to exist above

it. Lofting is a most favorable condition because effluents can disperse

vertically but are kept away from the ground by the stable air below;dispersion thus occurs for great distances throughout large volumesof air.


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Atmospheric Stability Classes

Class A: extremely unstable conditions (bright sun,daytime)

Class B: moderately unstable conditions (sunny, daytime)

Class C: slightly unstable conditions (light cloudiness,

daytime) Class D: neutral conditions (overcast sky, brisk wind, day or

night)

Class E: slightly stable conditions (early evening, lightwinds, relatively clear sky)

Class F: moderately stable conditions (late night, light wind,clear sky)

Class G: very stable (predawn, very light wind, clear sky)


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Quantitative determination of stability class is based on measuredvalues of temperature versus elevation and/or the standard deviationof the mean wind direction


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Calculation Procedure

Determine the stability class that exists during the period ofconsideration Establishes the dispersion coefficients

Class can be chosen by one of three methods: Qualitative determination on the general conditions listed in Table 10-1

Measured values of temperature change with elevation as listed inTable 10-2

Standard deviation of the mean wind vector, also listed in Table 10-2

Dispersion coefficients determined from Figures 10-4 and10-5 for stability classes A to F.

For extremely stable class G conditions, the dispersioncoefficients are computed from class F values since Figures10-4 and 10-5 do not contain curves for stability class G


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Calculation Procedure


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Example 10-2

A stack 60 m high discharges a radionuclide at

a rate of 80 Ci/s into a 6 m/s wind during the

afternoon under overcast skies. Determine the

ground-level concentration (a) 500 mdownwind and 50 m off the plume centerline,

and (b) at the same downwind distance but

along the centerline.


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Example 10-2 Solution

(a) From Table 10-1, the atmospheric stability is judged tobe class D due to overcast conditions and therelatively brisk wind. From Figure 10-4, it isdetermined that y is 36 m for class D stability at 500

m and z (from Figure 10-5) is18.5 m; therefore, for x= 500 m, y = 50 m, and H = 60 m:

(b) For x = 500 m and y = 0, the second exponential termis equal to 1.0


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Distance of Max Concentration

Interest for design purposes and emergency planning

It occurs along the centerline when the vertical dispersion coefficient hasthe value of 0.707H, which is dependent on the stability class

This specific value is found in Figure 10-5 for the particular stability classand the corresponding value of x (i.e., xmax) at which max occurs isdetermined.

The maximum concentration is calculated using the values ofy and z thatcorrespond to the distance xmax (it is only necessary to determine y sincez has already been calculated based on xmax and the stability class).Themaximum concentration where ry,max and rz,max are determined for the pointdownwind where the maximum concentration occurs.

Applicable to elevated stack releases only; the maximum concentration fora ground-level release is at the point of release and the downwindconcentration gradually decreases with increasing x.


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Example 10-3

Estimate (a) the downwind point of maximumconcentration for effluent released at 10 Ci/s at a heightof 30 m under class F stability into a steady wind of 1m/s; and (b) the maximum concentration at that

location.Solution.

(a) For these conditions, rz = 0.707H = 21.2 m; therefore,as shown in Figure 10-5, rz has the value 21.2 m atabout 1900 m (1.2 miles) which is xmax.

(b) At x = 1900 m, ry = 60 m and rz = 21.2 m (alreadydetermined); thus the maximum concentration is


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Stack Effects

Gaussian plume model can be used for stack releases if the releaseapproximates a point and the wind field has homogeneous turbulence. Can be assumed for tall slender stacks located such that the turbulence induced

by surrounding structures and terrain is minimal

Rule of thumb: top of the stack should be 2.5 times higher than anysurrounding obstructions, may induce turbulence and produce inhomogeneities

at the point of release Gaussian plume conditions may also exist for shorter stacks if releases occur

during moderate to light winds but they may fail to exist even for tall stacks ifwind speeds are very high

Stack exerts effects temperature of the effluent can induce buoyancy (positive or negative)

momentum of the effluent can affect the height at which the plume levels off Effective stack height (plume rise)-elevation above the physical stack

height where the plume levels off (dH) efflux velocity which gives momentum to the effluent as it leaves the stack

horizontal wind speed

differential temperature of the effluent versus that of the receiving air stream.


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Stack Effects

Hot plume will be buoyant and if ejected with a high efflux velocity mayrise quite a bit above the physical stack height before being leveled off by acombination of the wind speed and the cooling effect of the receiving air.

Effective stack height Heffis obtained by adding the calculated plume risedH to the physical stack height:

Model devised for determining dH. Devisedby Davidson using Bryantsdata dH = differential plume rise (m)

d = inside diameter of stack (m)

vs = efflux velocity of stack (m/s)

u = mean wind velocity (m/s) at the top of the stack Ts = temperature in the stack (K)

Ta = temperature of the atmosphere (K).

The first term accounts for momentum effects due to the velocity of thedischarged effluent and the horizontal translation due to the wind field; thesecond term accounts for the temperature differential between the twofluids.


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Summary Gaussian Plume

Only applicable only for the following essential conditions: Release 2.5 times the height of any surrounding structures

Steady-state release rate with homogeneous turbulence

Unobstructed releases over flat, open terrain where completereflection of the plume by the ground (i.e., minimal plumedepletion) can be assumed;

Diffusion times of 10 minutes or more;

Positive values of wind speed (equations fail for zerowindspeed).

Models are often used for other conditions because they arethe only ones available Quality of the results will be influenced by the degree to which

conditions deviate from the model, and the results should beused accordingly.


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Non-uniform Turbulence - Fumigation

During low winds and clear nights, plume concentrations can be quite highduring temperature inversions Radiant cooling of the earths surface, temperature of the air near the ground

becomes cooler than layers above creating a zone of very stable air.

Sun rises, heats the ground, produces a zone of turbulent air, occurs at first nearthe ground but grows in height due to thermal eddies.

When the turbulent air zone reaches height of the plume, the trapped plumematerial moves to ground level, producing relatively high concentrations atground level

Effluents emitted during this period are confined by the inversion overhead,and will be dispersed toward the ground by the turbulence in the newlyheated unstable air.


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Non-uniform Turbulence - Fumigation

Ground-level concentration during fumigation is

uh = average wind speed for the layer at He (m/s)

y = lateral plume spread (m), typically for class F stability He = effective stack height (m)

Not applicable when He becomes small (of the order of10 m or less) /Q values will become unrealistically

large For releases


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Example 10-5

If a unit of radioactivity is released from a 100 m stack duringclass F stability during which the wind speed is 2 m/s, whatis the /Q value for a plume centerline location 3000 mdownwind for (a) normal conditions and (b) duringfumigation?

Solution. (a) For non-fumigation (i.e., normal Gaussian plumedispersion), He=100 m, y = 100 m, and z = 280 m.

(b) For fumigation conditions where He = 100 m, and y = 100m (Figure 10-4),which, as expected, is considerably largerthan that calculated for non-fumigation conditions.


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Dispersion - Elevated Receptor

Receptor at elevation higher than base of the stack

uh= wind speed representing conditions at the releaseheight

He = effective stack height above plant grade (m)

ht = maximum terrain height (m) above plant gradebetween the release point and the point for which the

calculation is made (ht cannot exceed He). If (Heht) is less than about 10 m, then the condition

should be modeled as a ground-level release.


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Mechanical Turbulence

Buildings or otherstructures cancompletelydominate the

dispersion pattern Combination of

moderate tostrong winds, alow effluxvelocity, andfairly shortrelease points.


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Building Turbulence

Thoroughly mixes any effluent introduced into abuilding wake and the resulting concentration willbe uniform throughout the wake volume.

Methods can be used to determine theconcentration of a plume confined to flow in thelee of a building

Determining the building wake volume and the

dilution it provides for the emission rate Q Modified ground-release equation

Virtual source method


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Example 10-7

Estimate the street-level concentration at approximately 120mdownwind of the 3 m stack atop the large building in Figure10-7 (h= 15 m; w = 15 m) due to a steady-state release of 5Ci/s of41Ar when the wind speed is 5 m/s.

Solution. The smoke test in Figure 10-7 was conducted during5 m/s winds and clearly shows building wake entrapmentdue to mechanical turbulence induced by the large building;therefore, the plume flows near the ground where its height,as estimated from the figure, is about the same as that of thestack. Its width, which is more uncertain from the figure,

can be assumed to be the width of the building projecteddownwind; i.e., no channeling due to wind streaming. Thecalculated concentration at ~120 m is


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Modified Ground Release

Modified ground-level release equation by Fuquay as:

A, the area of the building on the lee side, adjusted by the factor c toobtain the area through which the plume flows due to the dominant

influence of the mechanical turbulence caused by the building. For downwind distances within about 10 building heights, c ranges

between 0.5 and 2.0.

Use of small values of c (i.e., c = 0.5) yields conservative estimates ofplume concentrations because of the small flow through area of thewake.

cA has the greatest effect on the plume concentration at short distancesdownwind because cA >> yz

larger distances yz will dominate such that the equation accounts forwake effects both close to the building and at locations further downwind

Values ofy and z determined for distances of x measured from the

center of the building.


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Virtual Source

Mechanical turbulence produced by the obstruction causes the releasedcontaminant to flow along the ground

Plume concentration modeled as though it were a ground-level release Ground-level virtual source at a upwind of release so plume produced by the

virtual source would have a height and horizontal spread that just envelops thebuilding as it passes it.

The downwind concentration modeled as a Gaussian-distributed ground levelrelease at the point of interest downwind as though the building were notpresent.

Distances y,x0 and z,x0 are determined for downwind distances measured fromthe location of the ground-level virtual source correspond to a plume that justenvelops a building of height Hb and width W

Used to obtain the upwind virtual source separately into the curves in Figures10-4 and 10-5 for the particular stability class that exists.

These two values are added to the downwind distance of interest to establishthe value of x at which y,x0 and z,x0 are determined. One can use either or bothdistances for locating the virtual source, but for buildings it is usually based onz,x0


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Example 10-8

Use the virtual source method to estimate the

concentration of radiocesium 200 m downwind of

a source that emits 0.5 Ci/s from a 2 m vent atop a

building that is 30 m tall and 20 m wide duringclass D stability and a wind speed of 6 m/s.

Solution. A ground-level source emitting a plume

that would just engulf a 30 m high building whenit reaches the building corresponds to a z,x0 value

of


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Example 10-8

As shown in Figure 10-4, this value for class Dstability corresponds to a downwind distance of350 m; therefore, the concentration 200 mdownwind of the building is modeled as if it wereemitted from a ground-level virtual sourcelocated 350 m + 200 m upwind.At 550 m y,x0 = 40 m and z,x0 = 20 m and the

concentration at 200 m downwind of the releasepoint is


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Ground-Level Area Sources

Example 10-9. Radon gas is exhaled from a roughly circular area 50 m indiameter at a flux of 10 pCi/m2s. Estimate the concentration of radon in air400 m downwind for an average wind speed of 4 m/s and an assumedcondition of neutral (class D) atmospheric stability.

Solution. The total emission rate for the area is 19,635 pCi/s which can bemodeled as coming from a virtual ground-level point source located

upwind such that the plume width during class D stability conditions justenvelops the area as it passes over it. This value ofy,x0 is

From Figure 10-4 this value ofy,x0 occurs ~100 m downwind of a pointsource during class D stability; therefore, the concentration at all other

distances is modeled as emanating from a virtual point source located 100m upwind of the center of the area. For a location 400 m downwind, or x0 =500 m, y,x0 = 36 m and z,x0 =18.5 m from Figures 10-4 and 10-5,respectively, and radon concentration is


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Puff Releases

Single burst during emergencies when over-pressurization occurs(perhaps even an explosion) or as a result of a sudden spillage Gaussian distribution of the concentration at any point (x, y, z)

measured from the center of the puff is

Qp is the total release of material

* are distinct for expansion of the puff as it moves downwind.

No dilution due to wind speed

Only effect is translocation of the puff downwind determined by theposition of the center of puff downwind.

Dispersion in the x direction is accounted for by the dispersioncoefficient x*, and it and the dispersion coefficients y* and z* areuniquely determined for a contaminant released in a puff based ondata for two downwind distances at 100 and 4000 m, as in Table 10-

3


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Puff Releases


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Puff Releases


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Time-Averaged Dispersion

Most radiological assessments are of long duration Atmospheric conditions vary for extended periods, and it is necessary to

account for such changes by determining a sector averaged /Q value. Typically on an annual or quarterly basis

Based on accumulated meteorological data.

Many nuclear facilities provide one or more meteorological towersequipped to measure wind speed and direction and the vertical temperatureprofile from which stability class is determined. These are accumulated inreal time and a computer program sorts them into the categories needed fordetermining long-term sector-averaged values calculated as

where the quantity x (m) replaces y in the general dispersion equation x is the downwind distance to the midpoint of a subsection of the sector of

interest, multiplied by the sector width = 2/n radians yields the horizontalwidth through which the plume flows


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Usually n = 16 (22.5arcs) each extendingfrom the point of release

All winds blowing into agiven sector are thusrecorded for the sectorand over time will

constitute a fraction ofthe total amount ofmaterial dispersed into agiven sector.


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The fraction of wind blowing into a given subsection of a sector is furthersubdivided into wind speed groupings which are further subdivided intoeach of the stability classes If the released material is distributed into n= 16sectors = 2p/16 and each sector-averaged is:

fi = the fraction of the time (e.g., month, year) the wind blows towardsector I

Fjk= the fraction of fi during which each stability class j exists for windclass k (direction and speed) in sector I

x = the median downwind distance for a subsection of sector I uk= the median wind speed for a chosen group

zj = the vertical diffusion coefficient (m) for each stability class j

H = the effective stack height (m)


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Example 10-11

Meteorological data were accumulated for one month (720 h)at a facility that releases a radionuclide at an average rate Q(Ci/s) from a 50 m stack. During the one-month periodwinds were from due west11.25 for 240 h which blewreleased material into sector 4. Wind speeds occurred

between 0 and 2 m/s for 60 h, 24 m/s for 80 h, and 48 m/sfor 100 h. Stability classes existed for each wind speedgroup as follows: For 02 m/s winds: class F for 60 h.

For 24 m/s winds: class B for 40 h; and class C for 40 h.

For 48 m/s winds: class C for 20 h; and class D for 80 h.Determine the monthly sector-averaged /Q for a downwind

subsection of sector 4 between 1.0 and 3.0 km.


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Example 10-11

Solution. The median downwind distance for thesubsection is 2 km, for which the verticaldiffusion coefficients zj for each stability classfrom Figure 10-5 are: 22 m for class F; 230 m for

class B; 120 m for class C; and 50 m for class D.When these zj values are combined with theeffective stack height of 50 m, the exponentialdispersion term, , for each (F, B, C, and

D) is 0.0756, 0.977, 0.917, and 0.607,respectively. The median speed ukand the Fjkfractions for each wind speed group and stabilityclass are:


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Example 10-11

F or class F stability and wind class 02 m/s, Fjk=60/240 = 0.25 and the median wind speed uk= 1 m/s.

F or class B stability and wind class 24 m/s, Fjk=40/240 = 0.167 and the median wind speed uk= 3 m/s.

F or class C stability and wind class 24 m/s, Fjk=40/240 = 0.167 and the median wind speed uk= 3 m/s.

F or class C stability and wind class 48 m/s, Fjk=20/240 = 0.0833 and the median wind speed uk= 6 m/s.

F or class D stability and wind class 48 m/s, Fjk=80/240 = 0.333 and the median wind speed uk= 6 m/s.


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Example 10-11

Since the sector-averaged is to be determined for

the midpoint of one subsection of sector 4

which is at a median distance x = 2000 m and

fi = 240/720, the sector-averaged value forsector 4 is


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Deposition/Depletion

Large particles may settle out and plume contaminantsmay be deposited on vegetation, ground surfaces, orother objects due to physical and chemical processes.

Effects of such processes on plume concentrations are

overall quite small compared to inputs from the sourceof release, and they are generally ignored incomputations of downwind concentrations.

More important effect is an accumulation of

contaminants on vegetation and the ground where theymay become entrained in food pathways and/or becomea source of direct exposure from the ground surface.


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Dry Deposition

Represented as an areal contamination CA related to the air concentration by a constant of

proportionality vd called the deposition velocity

where QTOT is the total amount of material releasedover the period

vd is termed the deposition velocity because it has units

of m/s Values of vd have been determined experimentally by

measuring the areal contamination (e.g., Ci/m2) duringperiods of known air concentration over an area


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Example 10-12

Estimate the areal contamination due to dry deposition ofiodine-131 (a) on the ground downwind of a 100 m stackthat releases 109 Bq (2.7x102 Ci) of iodine-131 if theaverage value over the period of release is1.55 x107 s/m3 and (b) on grass for the same conditions.

Solution. (a) From Table 10-4, the deposition velocity forelemental iodine on soil is 3.3x103 m/s. Thus the arealcontamination is

(b) For long-term deposition on grass, it is appropriate toassume an average atmospheric stability condition of classD (neutral) such that vd = 8x10

3.Thus


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Dry Deposition

Material deposited onto a surface (e.g., grass or soil) isalso subject to removal by weathering and biologicalprocesses denoted as a biological half-life Tb.

If the material is radioactive the combined effect of

these processes is described by an effective half-lifeTeff, values of which are listed in Table 10-5 for selectedradionuclides on selected surfaces often considered inradiological assessments.

The effective half-life can be used in the usual way todetermine an effective removal constant keff, which iscalculated as keff= ln 2/Teff.


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Example 10-13

If a plume that contains a concentration of 106Ci/m3 of I-131 (T1/2 =8.02 d) exists during the fall season over dry pasture grass for 2 hfollowing an incident, estimate (a) the areal contamination on thepasture for the 2 h period, and (b) the equilibrium value of the arealcontamination if the airborne concentration persists over the area.

Solution. (a) From Table 10-4, vd

is 102 m/s, and from Table 10-5, theradiological and biophysical effective half-lives are 8.02 and 13.9 d,respectively. The effective half-life is thus 5.08 d and the effectiveremoval constant is 0.1364 d1.The areal deposition for the 2 hperiod is

(b) The equilibrium value which occurs after about 35 d is


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Resuspension

Long-lived (or stable) contaminants that build up over time may also becomeresuspended to produce elevated concentrations of the material above theimmediate area or perhaps translocated to other areas.

Resuspension near the surface is largely governed by wind speed and surfaceroughness and surface creep processes which widen the area of contamination.

The air concentration of resuspended long-lived materials is directly related to theareal contamination of the soil and its depth of distribution.

Surface level contamination is of most significance if the soils are loose and dryand the area is open and subject to high winds.

Material will weather due to various environmental effects and that theresuspension factor will thus change with time following deposition of the material.

One of the most widely used calculation models for determining a weathered valuefor ks is where t is the amount of time in years after deposition. This empiricalrelationship is based on desert-type soil and should be used with caution.


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Example 10-14

For plutonium in air above a desert-like plot uniformly contaminated atan initial level of 0.2 Ci/m2, calculate the air concentration ofplutonium (a) initially, (b) at 1 y after the initial deposition, and (c)at 10 y after the initial deposition.

Solution. (a) At t= 0, ks = 105 and the airborne concentration is

(b) At 1 y, ks = 5.08x106, and the airborne concentration is 1.02x106

Ci/m3.

(c) At 10 y, ks = 1.25x108, and the resulting airborne concentration is2.5x109Ci/m3.

For locations with moist soils and vegetation a smaller resuspensionfactor would need to be chosen and the relationship used in Example10-14 would not be applicable.


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Wet Deposition

Contaminants can also be removed from a plume by precipitation, wet deposition of the plume material on vegetation, the ground, and

other exposed surfaces.

Both wet deposition and dry deposition contribute to arealcontamination; however, each is considered separately even thoughboth may occur during a precipitation period.

The amount of wet deposition is similar to that used for drydeposition, but in this case the constant of proportionality is acombination of the rainfall rate R and the washout ratio Wv.

The amount of washout is a function of the size and distribution ofraindrops and the physiochemical features of the plume.

These parameters, themselves functions of the space coordinates (x,y, z), cause the amount of washout to be a space-dependentparameter; however, as a practical matter it is assumed to beconstant with respect to space because of scant empirical data.


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Wet Deposition

The areal contamination CA,wet (per m2) due to wet deposition is

v = the contaminant concentration (Ci/m3) in the air above the area

R =rainfall rate (mm/h) Wv = volumetric washout rate (volume of air/volume of rain)

m= the plume depletion constant (h/mm) which is related to rainfall rate;

k = vegetation washoff coefficient (mm1)

ke = effective removal constant that accounts for radioactive removal andbiological processes other than washoff;

t = duration of precipitation (h) The areal contamination CA,wet(t) will thus build up to an equilibrium

condition as a function of the rainfall rate R, the removal coefficient k, andthe effective removal constant ke. The areal ground concentration is also afunction dry deposition, which is often ignored for precipitation events.


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Example 10-15

Calculate the equilibrium deposition of radioiodine by rainout for anaverage atmospheric concentration of 105 Ci/m3 when the rainfallrate R =2.5 mm/h, the washoff constant k = 0.025 mm1, m = 0.025h/mm, the washout coefficient Wv = 8.3x10

4 m3 air per m3 of rain,and the effective removal constant = 0.1364 d1.

Solution. Since the equilibrium value is sought, the exponential buildupterm = 1; thus

484+dispersion+lecture

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