Health Physics Pergamon Press 1976. Vol. 31 (August), pp. 127-133. Printed in Northern Ireland
PLUME DEPLETION FOLLOWING POSTULATED ATMOSPHERIC PLUTONIUM DIOXIDE RELEASES PAUL H. GUDIKSEN, KENDALL R. PETERSON, ROLF LANGE and JOSEPH B. KNOX
Lawrence Livermore Laboratory, University of California, Livermore, CA 94550 (Received 7 November 1975; accepted 19 January 1976) Abstract-An accidental atmospheric release of plutonium dioxide particles from a nuclear facility may result in deposition of a major fraction of the particles within a few km downwind. Estimates of plume depletion as a function of distance were computed using the atmospheric-diffusion particle-in-cell code. This code is capable of estimating the atmospheric transport, diffusion, gravitational settling, and dry deposition of the PuO, particles within a three-dimensional grid under conditions of boundary layer, stratified shear flow. The calculations show the effect on plume depletion of varying the source height, the particle size, and the type of vegetation. Pasquill F stability was chosen for applicability to nuclear facility safety analyses. The fraction of activity remaining in the plume at a given distance increases with source height and is inversely affected by surface roughness. For submicrometer particles emitted at a height of 1 0 m , the fraction remaining airborne at 30 km downwind is about 0.5 over agricultural land covered with low growing, densely planted leafy vegetables and only 0.2 over brushland. Because of their large gravitational settling velocities, essentially all particles greater than 5 pm emitted at a 10-m height are deposited within 5 km of the facility. As the source height is increased, the effect of varying the type of vegetation becomes minimal. Hence, for a 100-m source height, the fraction of submicrometer-size particles remaining airborne is roughly 0.9 at 30 km over agricultural land as well as brushland and about 0.25 of the 5-pm particles are still airborne at 30 km. INTRODUCTION
To
ASSESS the hazards resulting from an accidental atmospheric release of plutonium dioxide particles as a plume from a nuclear facility, it is necessary to estimate the downwind plume depletion of PuOz particles by gravitational settling and dry deposition processes. The fraction remaining airborne at a given distance depends on the height of release, particle size and density, type of vegetation, windspeed, and atmospheric stability. This report describes the results of a plume depletion study that we performed with our advectiondiffusion particle-in-cell (ADPIC) code (La73). This code is capable of estimating the dispersion of PuOa particles within a threedimensional grid system. The particles are injected continuously as a small volume source at one end of the grid at a specified height and are acted on by gravitational settling, dry deposition, mean horizontal winds, and atmospheric diffusion. Plume depletion is determined by computing the number of particles situated within a particular crosswind volume
127
element of a steady-state plume at selected downwind distances. These values are then compared with those calculated for the corresponding volume elements of a plume with no gravitational settling and no dry deposition. The results described in this report show the effect on plume depletion of varying the source release height, the particle size and deposition velocity, and the type of vegetation. DESCRIPTION OF THE ADPIC CODE
ADPIC is a numerical, three-dimensional, Cartesian, particle-diffusion code capable of computing the time-dependent dispersion of inert or radioactive air pollutants. The code solves the three-dimensional advectiondiffusion equation by the pseudo-velocity technique for a given regional mass-consistent wind field. The governing equations are given in Table 1 (La74). These equations are solved over an Eulerian grid consisting of threedimensional rectangular cells of uniform size. The concentrations of the particles (x) are
128
PLUME DEPLETION FOLLOWING PLLJTONIUM DIOXIDE RELEASES
while the deposition velocity and particle size remain fixed, (2) varying the type of vegetation (agricultural land, semi-arid grassland, and brushland) while the release height and particle size are fixed, and ( 3 ) varying the particle size (0.3, 1, 3, 5 , 8 and 20 pm) while the release height and the type of vegetation are fixed. The calculations were performed using Pasquill F stability for applicability to nuclear facility safety analyses. Several assumptions were required to perform the calculations. These assumptions and their justifications are discussed below. Vertical wind profile Even though winds, like other meteorological parameters, vary with time, altitude and place, it is possible to estimate the average variation of mean wind speed with height within the surface boundary layer by a variety of analytical expressions. In general, either a power or logarithmic law or modification of these have been used in an attempt to describe the profiles below about S00m (Le60; Pa60; Sl68). In this work, we used the following power law:
u = (I"@ defined at the cell centers and the pseudovelocities ( U p )are defined at the cell corners. The locations of the particles are defined by their individual Lagrangian coordinates within the Eulerian grid. Each time cycle consists of an Eulerian and a Lagrangian part. In the Eulerian part, the concentrations are used to calculate the diff usivity velocities, which are then added to the wind advection velocities to yield the pseudo-velocity at each cell corner. In the Lagrangian part, each particle contained in a given cell is transported for one time step with a velocity vector that is computed from the psuedo-velocities at the cell corners and with a volume weighting scheme. This permits a new set of particle coordinates to be computed resulting in a new concentration distribution.
where U is the mean wind speed at height 2 , and U,, is the wind speed measured at a reference height (zo) of 10m. For F stability category, we assumed a surface (10m) wind speed of 1 m/sec. The exponent p is a function of a number of factors including atmospheric stability, terrain features, thermal stratification of the air, and reference height above the surface. Based upon the findings of various authors (DeS9; Le60; Pa60) we assumed the value of p to be 0.3 for stable (F) conditions. Normally, the wind direction shifts with height because of surface frictional effects and vertical variations of horizontal pressure patterns. We assumed the directional shear to be zero up to a height of S0m and So/lOOm above S0m for stable conditions (Le60; Sin62; Th64). Gravitational settling and dry deposition velBASIS OF THE CALCULATIONS oci ties The calculations were performed to show The gravitational settling velocities as a the effect on plume depletion of (1) varying the source release height (10, SO and 100m) function of particle size are given in Table 2.
P. €3. GUDIKSEN, K. R. PETERSON, R. LANGE and J. B. KNOX
129
of the Nuclear Regulatory Commission in accordance with existing regulatory guides. The horizontal diffusion coefficients were derived cra"ifsrlo*al _ _ _ _mmls_ ~ _ from the Pasquill F category standard deviadiameter, sertllng Agricultural Seml-arid tion of plume concentrations versus distance urn caleyory velocity, land grassland Brushlend (S168). The effect of vertical diffusion was 0.03 2 8 0.3 determined by permitting the value of the 0.38 2 8 1 vertical diffusion coefficient to increase 10 LO 3c 3 F 3 25 40 60 5 linearly from 0.1 m2/sec at the surface to 0.5 I 21 35 65 80 8 m2/sec at the top of the boundary layer (as130 130 130 110 sumed to be 100m for stable conditions) and to remain constant at 0.5 m2/sec above this height. This is based on the work oi several They were derived from Stokes' L,aw (Gr57) investigators (Ha66; W066; Mc66; Cr74) who assuming spherical PuOz particles with a den- used meteorological tower data as well as data sity of 11 g/cm3. from diffusion experiments to estimate values The dry deposition velocity is defined of vertical diffusion coefficients. mathematically as the ratio of the deposition The ADPIC code uses a specified volume rate to the surface air concentration. The de- source, which is centered at the given release position velocity depends on a number of fac- height and extends to a radius of 12.5 m. For tors including type of ground cover, the 10-m release height the source extends to windspeed, atmospheric stability, and type the surface. The particles are generated acand size of particles. The dry deposition vel- cording to a Gaussian formulation within this ocities used in this work are also shown in volume, with the maximum number of partiTable 2 as a function of particle size and type cles being generated at the given release of vegetation. These velocities include the height. The source strength remained constant effect of gravitational settling. The values (one unit/sec) throughout the calculations. were based on an extensive literature survey with the greatest emphasis being placed on RESULTS studies of inert particles diffusing under stable conditions (Me59; Co59; C06O; Srn60; Si6l; Because we desired to obtain plume depleBa63; Is63; Ch67; Men61; Wh70; Wa71; tion factors over distances ranging from Sli72; Che73; Ho73; Sc73; Se73). For pur- 0.5 km to as much as 100 km from the source, poses of this study we have assumed that it was necessary to construct several grids to agricultural land consists of low-growing relaresolve the plume over this wide range with a tively densely planted crops such as root crops reasonable number of grid cells. We found or leafy vegetables with reasonably smooth that about 25,000 cells was the maximum grid leaves; semi-arid grassland consists of fairly mesh that could reasonably fit into the large dense dry grass less than 1m in height. Brushcore memory of the CDC 7600 computer land is assumed to be irregularly shaped leafy performing the calculations. Therefore, closebushes up to 2 m in height. in ( 5 km), mid-range (35 km), and long-range
Table 2. Grnviational settling and deposition velocities as a function of particle seze und type of Vegetation. The deposition uelocitks include the effect of gravitational settling Deposltlo" " r l o c l L a ,
Pd Tr lC le
SLablllry
mals
i.' P
I
20
8.4
F
Miscellaneous assumptions Fumigation conditions were assumed to exist during the first hr after the initial release. This was approximated in the calculation by placing an inversion (reflecting boundary) at a height of 30m for the 10-m release height. For the higher release heights, the inversion was placed at the release height. These conditions were dictated by the needs 3
(100 km) grids were constructed. Little, if any, smoothing was necessary to merge the calculations for each grid size. A calculation was started by injecting the particles (typically about 10,000-20,000) at the source point and allowing them to flow downwind throughout the grid system. The results of the plume depletion calculations as a function of particle size and height of release over agricultural land, semi-arid grassland,
PLUME I>EPLETION FOLLOWING PLUTONIIJM DlOXIDE RELEASES
130
Tyue o f v e g e t a t i o n A g r i c u l t u r a l land
0.1
10
1
Distance
-
km
0 100
0.2 0.4
0.6
0.8 1 . 0
Airborne plume f r a c t i o n
Fro. 1. Plume depletion nomogram for a !O-m release height. To find the airborne plume fraction, enter at the desired distance o n the bottom left scale, move up to the particle diameter. Then move to the right to the selected type of terrain. Finally move down and read the plume fraction airborne on the bottom scale. If particle size or distance estimates are desired for a given airborne plume fraction, the nomogram may be used backwards. The dashed portions of the particle diameter curves represent extrapolations beyond the range of the calculations.
and brushland are shown in a series of nomograms in Figs. 1-3. A review of the figures reveals the following: (1) Particles having diameters greater than 8 pm are deposited on the ground very rapidly (within a few km) because of their larger gravitational settling velocities. (2) For elevated releases, the plume depletion factors remain at unity out to distances of several km from the source. This is caused by the finite transit time required for the particles to be transported from the release height to the surface by vertical diffusion and gravitational settling. (3) The 0.3-pm and 1-pm particles have essentially identical plume depletion factors because their gravitational settling velocities are almost negligible and their deposition velocities are assumed to be the same. (4) For a particular particle size and release height, the plume depletion factors show the
highest values over agricultural land, intermediate values over semi-arid grassland, and the lowest values over brushland. This, of course, is caused by the direct relationship between deposition velocity and surface roughness. ( 5 ) As the source height increases, the effect of varying the vegetation has a minimal effect on the plume depletion. It is realized that these results were derived from calculations with input parameters based on a literature search. Unfortunately, very few field measurements of plume depletion have been carried out because of their extreme difficulty. One set of measurements by Nickola and Clark (Ni74) of particulate zinc sulfide plume depletion relative to a ssKr inert gas plume may be of interest for verification purposes. They released the two tracers simultaneously from a height of 26m over the Hanford field diffusion grid. Their findings
131
P. H. GUDIKSEN, K. R. PETERSON, R. LANGE and J. B. KNOX I
I l l l l l l ~
I
I
l " l 1 1 ~
I
I
IIIII
I
Particle diameter - pm
1
I
1
I
1
l
1
Type o f vegetation Agricul tural 1 and
I
1
0.1
Distance - km
1
1
1
0.2 0.4
0 100
10
1
1
1
1
1
0.6 0.8
1.0
Airborne plume fraction
FIG. 2. Plume depletion nomogram for a 50-m release height. See Fig. 1 for detailed instructions. I
I
I I11111
I
I I I IIII/
I
I
I I I i I
I
Particle diameter - i_lm
/
I
[
I
[
l
I
I
Type of vegetation Agricultural 1 and
0.1
1
10
0
0.2 0.4
0.6 0 . 3
1.0
100
Distance
-
km
Airborne plume fraction
FIG. 3. Plume depletion nomogram for 100-m release height. See Fig. 1 for detailed instructions.
132
PLUME DEPLETION FOLLOWING PLUTONIUM DIOXIDE RELEASES
indicate that from 3 to 6 % of the particulate zinc sulfide was deposited at a downwind distance of 8 4 2 m in a stable (Pasquill E-F) atmosphere. Assuming Pasquill E stability and a 10mm/sec deposition velocity for zinc sulfide particles having a 5 - p m mass diameter, we calculated the depletion to be less than 5% at 842m, which is in reasonable agreement with the experimental result. Acknowledgments-This work wa5 performed under the auspices of the U.S. Nuclear Regulatory Commission and the U S . Energy Research & Development Administration, under contract No. W7405-Eng-48
REFERENCES Ba63 Barry P. J. and Chamberlain A. C., 1963, Heulth Phys. 9, 1149. Ch67 Chamberlain A. C.. 1967, Proc. R . SOC. Lond. A 296, 45. ('he73 Chemist-Meteorologist Workshop, Jan. 1.519, 1973, sponsored by the Division of Biomedical and Environmental Research, U.S. ABC, Fort Lauderdale, Fla. C059 Convair, 1959, Fission products field release test I, Rept NARF-59-32T (AFSWC-TR59-44) (General Dynamics, Ft. Worth, Texas). Co60 Convair, 1960, Fission products field release test 11, Rept NARF-60-10T (AFSWC-TR60-26) (General Dynamics, Ft. Worth, Texas). Cr74 Crawford T. V., 1974, Progress report, dose-to-man program, Rept DP-1341 (E. I. de Pont de Nemours and Go., Savannah River Laboratory, S.C.). DeS9 DeMarrais G. A., 1959, J . Meteovol. 16, 181. Gr57 Green H. G. and Lane W. R., 1957, Particulate Clouds: Dusts, Smokes, and Mists (Princeton, N.J.: Van Nostrand). Ha66 Hage K. D.. Arneson G., Bowne N. E., Brown P. S . , Entrekin W. D., Levitz M. and Sekorski J. A,, 1966, Particle fallout and dispersion in the atmosphere, final report, Rept SCCR-66-203 1 (Sandia Corporation, Albuquerque, N.M.). Ho73 Hosker R. P. Jr., 1973, Estimates of dry deposition and plume depletion over forests and grasslands, Rept. 85 (Atmospheric Turbulencx and Diffusion Laboratory, Oak Ridge, Tenn.). Is63 Islitzer N. F. and Dumbauld R. K., 1963, Int. J , Air Wat. Pollut. 7,999.
La73 Lange R., 1973, A three-dimensional computer code for the study of pollutant dispersal and deposition under complex conditions, Rept UCRL-5 1462 (Lawrence Livermore Laboratory, Livermore, CA 94550). L,a74 Lange R. and Knox J . B., 1974, Adaptation of a three-dimensional atmosphe,ric transportdiffusion model to rainout assessments, Rept UCRL-75731 (Lawrence Livermore Laboratory, Livermore, CA 94550). Le60 Lettau H. H. and Haugen D. A., 1960, of Geophysics (New York: Handbook Macmillan). Mc66 McCormick R. A. and Kurfis K. R., 1966, 0. J. R . meteorol. SOC.92, 392. Me66 Megaw W. J. and Chadwick R. C., 19.59, Atomic Energy Research Establishment, Harwell, England, unpublished manuscript. Men67 Menzel R. G., 1967, Airborne radionuclides and plants, in: Agriculture and the Quality of Our Environrnen.t (Edited by Brady N. C.) (AAAS, Washington, D. C., Publ. No. 85). Ni74 Nickola P. W. and Clark G. H., 1974, Measurement of particulate plume depletion by comparison with inert gas plumes, Rept BNWLSA-5135 (Battelle Pacific Northwest Laboratories. Richland, Wash.). Pa60 Panofsky H. A,, Blackadar A. K. and McVehil G. E., 1960, Q. JI. R. meteorol. Soc. 86, 390. Sc73 Schwendiman L. C., Droppo J. G. and Mahalingam R., 1973, Wet and dry deposition of particles and iodine following water-cooled reactor accidents, Rept to W. W. Little, Jr., Hanford Engineering Development Laboratory. Richland, Wash. Sc73 Sehmel G. A,, Sutter S . I,. and Dana M. T., 1973, Dry deposition processes, Rept BNWL1751 Part 1 (Battelle Pacific Northwest Laboratories, Richland, Wash.). Si61 Simpson C. L., 1961, Estimates of deposition of matter from a continuous point source in a stable atmosphere, Rept HW-69292 (Hanford Atomics Product Operation, Richland, Wash.). Sin62 Singer I. A. and Nagle C. M., 1962, A study of the wind profile in the lowest 400 feet of the atmosphere, Rept BNL-718 (T-254) Rrookhaven National Lab., Upton, New York). S168 Slade D. H. (Ed.), 1968, Meteorology and Atomic Energy (Washington, D.C.: U.S. Atomic Energy Commission). Sli72 Slim W. G. N., 1972, On the dry deposition of sea salt nuclei, Rept BNWL-1651, Part 1, UC-53 (Battelle Pacific Northwest Laboratories, Richland, Wash.).
P. H. GUDIKSEN, K. R. PETERSON, R. LANGE and J. B. KNOX Sm60 Small S . H., 1960, Tellus 12, 308. Th64 Thuillier R. H. and Lappe U. O., 1964, J. appl. Meteorol. 3, 299. Wa71 Waldron A. W. Jr., 1971, Expected instantaneous surface line source and point source behavior in a forest environment. Tech. Note
133
DTC-TN-72-601, AD-887-032 (U.S. Army Test and Evaluation Command). Wh70 White E. J. and Turner F., 1970, J. appl. Ecol. 7, 441. W066 Wong E. Y. J. and Brundidge K. C., 1966, J. atmos. Sci. 23, ( 2 ) , 167.
PLUME DEPLETION FOLLOWING POSTULATED ATMOSPHERIC PLUTONIUM DIOXIDE RELEASES PAUL H. GUDIKSEN, KENDALL R. PETERSON, ROLF LANGE and JOSEPH B. KNOX
Lawrence Livermore Laboratory, University of California, Livermore, CA 94550 (Received 7 November 1975; accepted 19 January 1976) Abstract-An accidental atmospheric release of plutonium dioxide particles from a nuclear facility may result in deposition of a major fraction of the particles within a few km downwind. Estimates of plume depletion as a function of distance were computed using the atmospheric-diffusion particle-in-cell code. This code is capable of estimating the atmospheric transport, diffusion, gravitational settling, and dry deposition of the PuO, particles within a three-dimensional grid under conditions of boundary layer, stratified shear flow. The calculations show the effect on plume depletion of varying the source height, the particle size, and the type of vegetation. Pasquill F stability was chosen for applicability to nuclear facility safety analyses. The fraction of activity remaining in the plume at a given distance increases with source height and is inversely affected by surface roughness. For submicrometer particles emitted at a height of 1 0 m , the fraction remaining airborne at 30 km downwind is about 0.5 over agricultural land covered with low growing, densely planted leafy vegetables and only 0.2 over brushland. Because of their large gravitational settling velocities, essentially all particles greater than 5 pm emitted at a 10-m height are deposited within 5 km of the facility. As the source height is increased, the effect of varying the type of vegetation becomes minimal. Hence, for a 100-m source height, the fraction of submicrometer-size particles remaining airborne is roughly 0.9 at 30 km over agricultural land as well as brushland and about 0.25 of the 5-pm particles are still airborne at 30 km. INTRODUCTION
To
ASSESS the hazards resulting from an accidental atmospheric release of plutonium dioxide particles as a plume from a nuclear facility, it is necessary to estimate the downwind plume depletion of PuOz particles by gravitational settling and dry deposition processes. The fraction remaining airborne at a given distance depends on the height of release, particle size and density, type of vegetation, windspeed, and atmospheric stability. This report describes the results of a plume depletion study that we performed with our advectiondiffusion particle-in-cell (ADPIC) code (La73). This code is capable of estimating the dispersion of PuOa particles within a threedimensional grid system. The particles are injected continuously as a small volume source at one end of the grid at a specified height and are acted on by gravitational settling, dry deposition, mean horizontal winds, and atmospheric diffusion. Plume depletion is determined by computing the number of particles situated within a particular crosswind volume
127
element of a steady-state plume at selected downwind distances. These values are then compared with those calculated for the corresponding volume elements of a plume with no gravitational settling and no dry deposition. The results described in this report show the effect on plume depletion of varying the source release height, the particle size and deposition velocity, and the type of vegetation. DESCRIPTION OF THE ADPIC CODE
ADPIC is a numerical, three-dimensional, Cartesian, particle-diffusion code capable of computing the time-dependent dispersion of inert or radioactive air pollutants. The code solves the three-dimensional advectiondiffusion equation by the pseudo-velocity technique for a given regional mass-consistent wind field. The governing equations are given in Table 1 (La74). These equations are solved over an Eulerian grid consisting of threedimensional rectangular cells of uniform size. The concentrations of the particles (x) are
128
PLUME DEPLETION FOLLOWING PLLJTONIUM DIOXIDE RELEASES
while the deposition velocity and particle size remain fixed, (2) varying the type of vegetation (agricultural land, semi-arid grassland, and brushland) while the release height and particle size are fixed, and ( 3 ) varying the particle size (0.3, 1, 3, 5 , 8 and 20 pm) while the release height and the type of vegetation are fixed. The calculations were performed using Pasquill F stability for applicability to nuclear facility safety analyses. Several assumptions were required to perform the calculations. These assumptions and their justifications are discussed below. Vertical wind profile Even though winds, like other meteorological parameters, vary with time, altitude and place, it is possible to estimate the average variation of mean wind speed with height within the surface boundary layer by a variety of analytical expressions. In general, either a power or logarithmic law or modification of these have been used in an attempt to describe the profiles below about S00m (Le60; Pa60; Sl68). In this work, we used the following power law:
u = (I"@ defined at the cell centers and the pseudovelocities ( U p )are defined at the cell corners. The locations of the particles are defined by their individual Lagrangian coordinates within the Eulerian grid. Each time cycle consists of an Eulerian and a Lagrangian part. In the Eulerian part, the concentrations are used to calculate the diff usivity velocities, which are then added to the wind advection velocities to yield the pseudo-velocity at each cell corner. In the Lagrangian part, each particle contained in a given cell is transported for one time step with a velocity vector that is computed from the psuedo-velocities at the cell corners and with a volume weighting scheme. This permits a new set of particle coordinates to be computed resulting in a new concentration distribution.
where U is the mean wind speed at height 2 , and U,, is the wind speed measured at a reference height (zo) of 10m. For F stability category, we assumed a surface (10m) wind speed of 1 m/sec. The exponent p is a function of a number of factors including atmospheric stability, terrain features, thermal stratification of the air, and reference height above the surface. Based upon the findings of various authors (DeS9; Le60; Pa60) we assumed the value of p to be 0.3 for stable (F) conditions. Normally, the wind direction shifts with height because of surface frictional effects and vertical variations of horizontal pressure patterns. We assumed the directional shear to be zero up to a height of S0m and So/lOOm above S0m for stable conditions (Le60; Sin62; Th64). Gravitational settling and dry deposition velBASIS OF THE CALCULATIONS oci ties The calculations were performed to show The gravitational settling velocities as a the effect on plume depletion of (1) varying the source release height (10, SO and 100m) function of particle size are given in Table 2.
P. €3. GUDIKSEN, K. R. PETERSON, R. LANGE and J. B. KNOX
129
of the Nuclear Regulatory Commission in accordance with existing regulatory guides. The horizontal diffusion coefficients were derived cra"ifsrlo*al _ _ _ _mmls_ ~ _ from the Pasquill F category standard deviadiameter, sertllng Agricultural Seml-arid tion of plume concentrations versus distance urn caleyory velocity, land grassland Brushlend (S168). The effect of vertical diffusion was 0.03 2 8 0.3 determined by permitting the value of the 0.38 2 8 1 vertical diffusion coefficient to increase 10 LO 3c 3 F 3 25 40 60 5 linearly from 0.1 m2/sec at the surface to 0.5 I 21 35 65 80 8 m2/sec at the top of the boundary layer (as130 130 130 110 sumed to be 100m for stable conditions) and to remain constant at 0.5 m2/sec above this height. This is based on the work oi several They were derived from Stokes' L,aw (Gr57) investigators (Ha66; W066; Mc66; Cr74) who assuming spherical PuOz particles with a den- used meteorological tower data as well as data sity of 11 g/cm3. from diffusion experiments to estimate values The dry deposition velocity is defined of vertical diffusion coefficients. mathematically as the ratio of the deposition The ADPIC code uses a specified volume rate to the surface air concentration. The de- source, which is centered at the given release position velocity depends on a number of fac- height and extends to a radius of 12.5 m. For tors including type of ground cover, the 10-m release height the source extends to windspeed, atmospheric stability, and type the surface. The particles are generated acand size of particles. The dry deposition vel- cording to a Gaussian formulation within this ocities used in this work are also shown in volume, with the maximum number of partiTable 2 as a function of particle size and type cles being generated at the given release of vegetation. These velocities include the height. The source strength remained constant effect of gravitational settling. The values (one unit/sec) throughout the calculations. were based on an extensive literature survey with the greatest emphasis being placed on RESULTS studies of inert particles diffusing under stable conditions (Me59; Co59; C06O; Srn60; Si6l; Because we desired to obtain plume depleBa63; Is63; Ch67; Men61; Wh70; Wa71; tion factors over distances ranging from Sli72; Che73; Ho73; Sc73; Se73). For pur- 0.5 km to as much as 100 km from the source, poses of this study we have assumed that it was necessary to construct several grids to agricultural land consists of low-growing relaresolve the plume over this wide range with a tively densely planted crops such as root crops reasonable number of grid cells. We found or leafy vegetables with reasonably smooth that about 25,000 cells was the maximum grid leaves; semi-arid grassland consists of fairly mesh that could reasonably fit into the large dense dry grass less than 1m in height. Brushcore memory of the CDC 7600 computer land is assumed to be irregularly shaped leafy performing the calculations. Therefore, closebushes up to 2 m in height. in ( 5 km), mid-range (35 km), and long-range
Table 2. Grnviational settling and deposition velocities as a function of particle seze und type of Vegetation. The deposition uelocitks include the effect of gravitational settling Deposltlo" " r l o c l L a ,
Pd Tr lC le
SLablllry
mals
i.' P
I
20
8.4
F
Miscellaneous assumptions Fumigation conditions were assumed to exist during the first hr after the initial release. This was approximated in the calculation by placing an inversion (reflecting boundary) at a height of 30m for the 10-m release height. For the higher release heights, the inversion was placed at the release height. These conditions were dictated by the needs 3
(100 km) grids were constructed. Little, if any, smoothing was necessary to merge the calculations for each grid size. A calculation was started by injecting the particles (typically about 10,000-20,000) at the source point and allowing them to flow downwind throughout the grid system. The results of the plume depletion calculations as a function of particle size and height of release over agricultural land, semi-arid grassland,
PLUME I>EPLETION FOLLOWING PLUTONIIJM DlOXIDE RELEASES
130
Tyue o f v e g e t a t i o n A g r i c u l t u r a l land
0.1
10
1
Distance
-
km
0 100
0.2 0.4
0.6
0.8 1 . 0
Airborne plume f r a c t i o n
Fro. 1. Plume depletion nomogram for a !O-m release height. To find the airborne plume fraction, enter at the desired distance o n the bottom left scale, move up to the particle diameter. Then move to the right to the selected type of terrain. Finally move down and read the plume fraction airborne on the bottom scale. If particle size or distance estimates are desired for a given airborne plume fraction, the nomogram may be used backwards. The dashed portions of the particle diameter curves represent extrapolations beyond the range of the calculations.
and brushland are shown in a series of nomograms in Figs. 1-3. A review of the figures reveals the following: (1) Particles having diameters greater than 8 pm are deposited on the ground very rapidly (within a few km) because of their larger gravitational settling velocities. (2) For elevated releases, the plume depletion factors remain at unity out to distances of several km from the source. This is caused by the finite transit time required for the particles to be transported from the release height to the surface by vertical diffusion and gravitational settling. (3) The 0.3-pm and 1-pm particles have essentially identical plume depletion factors because their gravitational settling velocities are almost negligible and their deposition velocities are assumed to be the same. (4) For a particular particle size and release height, the plume depletion factors show the
highest values over agricultural land, intermediate values over semi-arid grassland, and the lowest values over brushland. This, of course, is caused by the direct relationship between deposition velocity and surface roughness. ( 5 ) As the source height increases, the effect of varying the vegetation has a minimal effect on the plume depletion. It is realized that these results were derived from calculations with input parameters based on a literature search. Unfortunately, very few field measurements of plume depletion have been carried out because of their extreme difficulty. One set of measurements by Nickola and Clark (Ni74) of particulate zinc sulfide plume depletion relative to a ssKr inert gas plume may be of interest for verification purposes. They released the two tracers simultaneously from a height of 26m over the Hanford field diffusion grid. Their findings
131
P. H. GUDIKSEN, K. R. PETERSON, R. LANGE and J. B. KNOX I
I l l l l l l ~
I
I
l " l 1 1 ~
I
I
IIIII
I
Particle diameter - pm
1
I
1
I
1
l
1
Type o f vegetation Agricul tural 1 and
I
1
0.1
Distance - km
1
1
1
0.2 0.4
0 100
10
1
1
1
1
1
0.6 0.8
1.0
Airborne plume fraction
FIG. 2. Plume depletion nomogram for a 50-m release height. See Fig. 1 for detailed instructions. I
I
I I11111
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Type of vegetation Agricultural 1 and
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1
10
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0.2 0.4
0.6 0 . 3
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100
Distance
-
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Airborne plume fraction
FIG. 3. Plume depletion nomogram for 100-m release height. See Fig. 1 for detailed instructions.
132
PLUME DEPLETION FOLLOWING PLUTONIUM DIOXIDE RELEASES
indicate that from 3 to 6 % of the particulate zinc sulfide was deposited at a downwind distance of 8 4 2 m in a stable (Pasquill E-F) atmosphere. Assuming Pasquill E stability and a 10mm/sec deposition velocity for zinc sulfide particles having a 5 - p m mass diameter, we calculated the depletion to be less than 5% at 842m, which is in reasonable agreement with the experimental result. Acknowledgments-This work wa5 performed under the auspices of the U.S. Nuclear Regulatory Commission and the U S . Energy Research & Development Administration, under contract No. W7405-Eng-48
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133
DTC-TN-72-601, AD-887-032 (U.S. Army Test and Evaluation Command). Wh70 White E. J. and Turner F., 1970, J. appl. Ecol. 7, 441. W066 Wong E. Y. J. and Brundidge K. C., 1966, J. atmos. Sci. 23, ( 2 ) , 167.
