molecule has an effective surface area of about 20 X cm2 (31).Depending on the particular fatty acid, carbon to sulfate mass ratios of 0.01-0.02 are required to form a monolayer for the conditions of this experiment. Investigation of this effect is continuing. An additional consequence of contamination should be noted. The droplet size was calculated on the assumption that the droplet contained only HzS04 and H20. Any contamination would increase the actual particle size. Inspection of Equation 8 indicates that if the actual particle size were larger than the calculated size, even a smaller value of the flux ratio and the reaction coefficient would be required to explain the data. Figure 5 also indicates no strong dependence on relative humidity. This can be compared with the results of Robbins and Cadle (11, 12),who found that a t a relative humidity of essentially zero the reaction coefficient was about 0.1 for particle diameters between 0.2 and 0.9 pm. At a relative humidity greater than 90% they could not measure the rate but speculated that the flux ratio was close to 1.0. For the low relative humidity case, the aerosol of Robbins and Cadle was 98.3% by weight H2S04 with the remainder as H20. This corresponds to a molar ratio of H2S04to H20 of about 10. The lowest relative humidity used in our experiments was 8%,which corresponds to a molar ratio of HzS04 to H20 of 0.4. Despite the substantial difference in the molar H2S04/H20 ratios between the two cases, the chemical steps (i.e,, NH3 HzSO4 NH4+ HS04- or NH3 H30+ NH4+ H 2 0 )are so fast that they play no role in determining the rate in the aerosol system. Thus, other factors such as possible surface effects must be invoked to explain the difference in the two experiments. In summary, the measured rates of neutralization of H2SO4 aerosol by NH3 indicate that sulfate aerosols more acidic than NH4HS04will be found when the rate of production of HzSO4 is fast and the ratio of the precursor molecule SO2 to NH3 is high. A mechanistic understanding of the measured rates is not yet available but will be the subject of future research.
+
+
-
+
+
-
Acknowledgment We are grateful to Dr. Timothy Larson of the University of Washington for his critical reading of the manuscript and helpful suggestions. Literature Cited (1) Junge, C.; Scheich, G. Atmos. Enuiron. 1969,3, 423. (2) Brosset, C.; Andreasson, K.; Ferm, K. Atmos. Enuiron. 1975,9, 631.
(3) Brosset, C. Atmos. Enuiron. 1978,12, 25. (4) Charlson, R. J.; Vanderpol, A. H.; Covert, D. S.; Waggoner, A. P.; Ahlquist, N. C. Science 1974, 184, 156. (5) Charlson, R. 3.;Vanderpol, A. H.; Covert, D. S.; Waggoner, A. P.; Ahlquist, N. C. Atmos. Enuiron. 1974,8, 1257. (6) Vanderpol, A. H.; Carsey, F. D.; Covert, D. S.; Charlson, R. J.; Waggoner, A. P. Science 1975,190, 570. (7) Charlson. R. J.: Covert. D. S.:’ Larson. T. V.:, W a a o n e r . A. P. Atmos. EnLiiron. ‘1978, 12, 39. ( 8 ) Lodge, J. P.: Pate, J. B. Science 1966.153. 408. (9) Cunningham, P. T.; Johnson, S. A. Science 1976,191, 77. (10) Cobourn, W. G.; Djukic-Husar, J.; Husar, R. B., presented a t the Fourth International Conference of the Commission on Atmospheric Chemistry and Global Pollution, University of Colorado, Boulder, Aug 1979. (11) Robbins, R. C.; Cadle, R. D. J . Phys. Chem. 1958,62, 469. (12) Cadle, R. D.; Robbins, R. C. Dicuss. Faraday SOC.1961, 30, 155. (13) Brody, S. S.; Chaney, J . E. J . Gas Chromatogr. 1966,4, 42. (14) Huntzicker, J. J.; Hoffman, R. S.; Ling, C.-S. Atmos. Entiiron. 1978,12, 83. (15) Cobourn, W. G.; Husar, R. B.; Husar, J. D. Atmos. Enuiron. 1978, 12, 89. (16) Kittelson, D. B.; McKenzie, R.; Vermeersch, M.; Dorman, F.; Pui, D.; Linne, M.; Liu, B.; Whitby, K. Atmos. Enuiron. 1978,12, 105. (17) Durham, J. L.; Wilson, W. E.;Bailey, E. B. Atmos. Enuiron. 1978, 12, 883. (18) Tanner, R. L.; D’Ottavio, T.; Garber, R.; Newman, L. Atmos. Enuiron. 1980, 14, 121. 1191 Perhac. R. M. Atmos. Environ. 1978.12. 641. (20) MacCracken, M. C. Atmos. Enuiron.’ 1978,12, 649. (21) Liu. B. Y. H.; Pui, D. 1’. H.: Whitbv, K. T.; Kittelson, D. E.; Kousaka, V.; McKenzie, R. L. Atmos. Enuiron. 1978,12, 99. (22) McMurry, P. H.; Liu, B. Y. H . University of Minnesota, Particle Technology Laboratory Publication No. 380, Dec 1978, NTIS COO-1248-57. (23) Baldwin, A. C.; Golden, D. M. Science 1979,206, 562. (24) Stevens, R. K.; Dzubay, T. G.; Russwurm, G.; Rickel, D. Atmos. Enciron. 1978,12, 5 5 . (25) Berglund, R. N.; Liu, B. Y. H. Enciron. Sci. Technol. 1973, 7, 147. (26) Strom, L. Reu. Sci. Instrum. 1969,40, 778. (27) Maxwell, J. C. Collect. Sci. Pap., Cambridge 1890, 11, 625. (28) Fuchs, N. A,; Sutugin, A. G. In “Topics in Current Aerosol Research”; Hidy, G. M., Brock, J. R., Ed.; Pergamon Press: Oxford, 1971; Vol. 2. (29) Andrew, S. P. S. Chem. Eng. Sci. 1955,4, 269. (30) Lau, N.-C.; Charlson, R. J. Atmos. Environ. 1977,11, 475. (31) Adamson, A. W. “Physical Chemistry of Surfaces”, 3rd ed.; Wiley: New York, 1976. -I-
Received for review December 26,1979. Accepted February 12,1980. This material is based upon work supported by the National Science Foundation under Grant No. PFR76-16701 AOl. A preliminary version of this work was presented at the 178th National Meeting of the American Chemical Society, Washington, D.C., Sept 1979, P H YS 146.
A Mathematical Model of Aerial Deposition of Pesticides from Aircraft Conrad 0. M. Miller Process Math Modeling Systems Research Laboratory, Central Research, Dow Chemical U.S.A., Midland, Mich. 48640
In order to maximize the benefits associated with the utilization of chemical pesticides, a mathematical analysis was developed. Twenty-eight sets of deposition observations were analyzed, and a numerical assessment of the spatial distribution of active material, both on-target and downwind of the target area, is described. The “stirred settling from a volume source” model offers the advantage of a systematic approach
824
Environmental Science & Technology
t o data analysis, and has been useful in determining spray droplet particle size distribution parameters used in spray nozzle system comparison studies. For the herbicide treatments studied, the values of the mass median spray droplet diameter and the percent of spray mass under 100 pm were typically 250 pm and 3%,respectively. On-target recovery of herbicide was in the 70-80% range.
0013-936X/80/0914-0824$01 .OO/O
@ 1980 American Chemical Society
The use of aircraft for applying chemicals to control agricultural and forest pests represents an important mode of operation in achieving reduction of physical labor per unit of food production, and in management of forest natural resources. Both fixed-wing and rotary-wing aircraft are used to apply herbicides, insecticides, and fertilizers to cropland, rangeland, and forest. The active material is typically ejected, in a liquid phase, from the aircraft cia spray nozzles located on a header boom which, in the case of a fixed-wing aircraft, is mounted along the trailing edge of the wing. The aircraft is flown repeatedly over the area to be treated until the multiple swath track covers the entire area. The basic application objective is to deposit the active material entirely on the target area. However, due to (a) micrometeorological conditions, (b) the dynamics of spray droplet behavior, (c) the physical properties of the spray formulation, and (d)the height a t which the spray is emitted, the recovery of active material on the target area is less than 100%.T h a t portion of the treatment which is not deposited on the target area is transported downwind, and is subsequently deposited off-target. This is called aerial pesticide drift. In order to maximize the benefits associated with the utilization of chemical pesticides, and minimize the risk associated with chemical pesticide losses to the environment, an experimental study was undertaken. A mathematical model was developed which provides a numerical assessment of (a) the spatial distribution of deposited pesticides and (b) the parameters affectjng recovery. The mathematical model developed in this paper describes deposition of spray droplets or particles from a moving cloud, which is considered to be a volume source. This “stirred settling” model quantifies the effect of (a) spray droplet particle size distribution, (b) spray formulation, (c) amount of active material released, (d) spray emission height, (e) swath width, and (f) swath length. While many excellent experimental studies have been performed in the past, a mathematical description of aerial deposition is lacking. The purpose of this paper is to present a mathematical model that can be used to predict aerial pesticide drift or, given experimental data, estimate spray formulation and nozzle characteristics.
Previous Work Akesson and Yates ( 1 ) have provided a comprehensive review of the various aspects of the use of aircraft in agriculture. Brandes ( 2 ) and Grumbles ( 3 )review the aerial application industry, and give recommendations pertaining to operating standards. In an early atternpt to quantify insecticide coverage while spraying for mosquito control, LaMer and Hochberg ( 4 ) observed that the deposition of acute material appeared to be an inverse exponential function of distance from the spray generator for droplet sizes ranging from 2 to 60 pm in diameter. Johnstone et al. ( 5 ) give relationships for vertical and horizontal penetration of an aerosol through a forest canopy. They also consider aerodynamic downwash effects on spray coverage. Sexsmith et al. (6) provide experimental spray deposit distributions for both on-target and off-target areas for a spray formulation having a spray droplet mass median diameter of 210 pm, and range of 20 to 4 5 0 pm. This work supports the computed on-target distribution shown in Figure 4. Coutts and Yates (7) reported drift deposition experiments with the deposited material being collected on Mylar plastic sheets. Their study also included drift data as a function of nozzle orientation in relation to the chord line of the wing. Umback and Lembke (8) present a comprehensive wind tunnel study in an effort to quantify aerial drift. These authors give a dimensional analysis which shows drift as a function of height of release, wind velocity, and spray droplet diameter
for a specific system. Garrett (9) studied single particle dynamics and droplet drag characteristics in order to estimate distance to impact with the ground when droplets are released above ground level in a flowing air stream. Friedlander and Johnston (10) examined deposition of suspended particles in turbulent gas streams within enclosed ducts. Threadgill and Smith ( 1 1 ) give a table showing impact distance of various droplet sizes released from a height of 3.05 m (10 f t ) in an airstream having a horizontal velocity of 4.4 m/s (3 mph). Their trajectory calculations for a nonevaporating drop indicate that 15-pm particles could easily travel 610 m (2000 ft) before impact. Ware et al. (12)studied aerial drift for various types of spray nozzles and concluded that most of the drift was from droplets less than 100 pm in diameter. Glotfelty and Caro (13)present an overview of the general problem of persistent pesticides in the atmosphere. These authors report on-target recovery of active material values from 5 to 50%.While these recovery values may be considered typical for insecticide applications, these numbers are low compared to the on-target recovery values obtained in herbicide applications; that is, recovery is typically in the 70 to 85% range. This review of the literature provides a basis for additional work, and illustrates the need for development of a mathematical model which will provide a numerical assessment of the aerial deposition process.
Mathematical Model Description In developing a model to use in the analysis of deposition data, it is useful to examine a simple, idealized model which describes the equations of motion for a single spherical spray droplet in an air stream having only a horizontal velocity component. Spray Droplet Trajectory Model. Lapple and Shepherd (14) developed the equations of motion, describing single particle trajectories in still air, utilizing experimentally determined drag coefficients. Hughes and Gilliland ( 1 5 )applied this work to their investigation of the motion of small droplets in a gaseous medium. Based on the original work by these investigators, the following two-dimensional model may be written to describe both the velocity of the droplet and its position in a fixed coordinate system (see Figure 1 for coordinate system):
The drag force in the z and x directions is given by:
and:
TD,2 A, = 4 The drag coefficients for the three regions of flow are shown in Equations 6-8. Stoke’s law region (laminar flow):
CD = 24Re,p-’;
< Re,p < 2
(6)
intermediate region:
CD = 1 8 . 5 R e , ~ - ~ / ~ ; 2 < Re,p < 500
(7)
Newton’s law region (turbulent flow): Volume 14, Number 7, July 1980
825
Figure 1. Schematic map of field layout fur spray application with a Cessna Ag Wagon; Waggoner Ranch, Texas drift study, 1977
CD = 0.44;
500 < Re,p
10; therefore acceleration effects may be neglected (pp/pf 800 for this study). Re,p < 100, so that deformation of spray droplets may be neglected. (Dp < 500 pm under application conditions.) Total particle volumelunit volume of gas < 10-3; therefore, each particle can take an independent path, and coagulation may be neglected (on the order of 10-8 for this study). The gas phase in the chamber is in a well-mixed flow state. The rate of deposition, on the bottom of the chamber, due to settlement is decreased below that described by Equation 1 in a tranquil gas medium, because the concentration of particles near the bottom of the chamber is depleted by a turbulent eddy mechanism upward. The deposition rate is a t a minimum when the turbulence is sufficient to eliminate macroscopic concentration gradients (19,20). Stirred settling leads to an exponential decrease in particle concentration and deposition with time. Fuchs (21) and Pasquill (22) also derive expressions equivalent to stirred settling, which show the exponential functionality. For very small particles, such as a very fine aerosol encountered in urban smog studies, Pasquill (22) suggests the use of a deposition velocity as given by Chamberlain (231,rather than the settling velocity given by Equation 13. However, for coarse sprays, such as those used in pesticide applications, Equation 13 may be used to describe the settling velocity. The basic stirred settling equation, which describes the amount of remaining airborne active material having a particle diameter characteristic of the ith particle size fraction in a heterogeneous spray droplet system, is:
= Uf.
If the atmosphere near the ground were simply structured, such that convective flows were not present, this model would probably be sufficient to describe the deposition distribution of pesticide. However, in general, the structure of the lower atmosphere is composed of convective flows or turbulent eddies, which must be considered. In the development of the “stirred settling” model, Equation 13 will be used to estimate the effective deposition velocity of the spray droplets. This equation ignores any deposition velocity contribution due to inertial effects and diffusion. S t i r r e d Settling from a Volume Source. The physical system described in this section is schematically represented by Figure 1. A fixed-wing aircraft flies a t a height 2, along a track Y , long, and perpendicular to the windfield traveling a t a velocity of Ef. The aircraft flies a multiple swath track to cover the entire target area, thus ejecting a total of AT(O) amount of active material. Ground-level sampling stations are spaced as shown in Figure 1,with x equal to zero a t the leeward edge of the first swath flown. The primary task of the analysis of this system is to describe the spatial distribution of active material that is (a) deposited on the target area, and (b) deposited downwind due to drift from the target area. The 826
Environmental Science & Technology
which may be integrated between time equal to zero and time equal to t to give: A , ( t ) = A,(O)exp[-u,,t/Z,] (15) In order to conceptually understand how Equation 15 will be applied to a pesticide drift cloud, visualize a quasistationary cloud, as presented in Figure 2. The active material is released into a volume of air that is bounded by two x-y planes a t z equal to zero and t equal to Z,,two y-z planes a t x equal to zero and x equal to the swath width X,,and two x-z planes a t y equal to zero and y equal to the length of the swath,
YS The pesticide cloud is considered to be a settling chamber with its bottom open at ground level, and its motion in the x direction is assumed to correspond to the local wind velocity. With the following assumptions, the “stirred settling from a volume source” model can be shown to be in that class of models which Seinfeld et al. ( 2 4 ) call well-mixed cell models. Assumptions. (a) There is no transport of material across the boundaries of the cloud, except a t the x-y plane where z is equal to zero; that is, diffusive transport is neglected. (b) There is no change in the horizontal wind velocity with height above grade. (c) The motion of the cloud is assumed to correspond to the local wind velocity and direction. (d) The na-
Z
A
Figure 3. Schematic representation of a multiple swath pattern
Figure 2. Schematic representation of stirred settling from a single swath volume source
ture of the particle size spectrum in the cloud changes only because of the deposition mechanism, that is, evaporation, coagulation, and deformation are not considered. In order to account for the spatial dimension of the volume source shown in Figure 2, the cloud is divided into a number of cells whose x dimension is not significant compared to the swath width. Each cell is considered to be a settling chamber with time, t , in Equation 15 being replaced by:
t = Xliif
(16)
The amount of active material, of the ith particle size fraction, remaining airborne is:
A,(x) for x
A, (0) ncelis C exp[-cu,(xk* ncells 1 = 1
=-
+ jAx)]
Figure 4. Target swath distribution representation for treatment 101
(17) which yields the following equation upon differentiation of Equation 25:
> 0, where: = U,,/iifZ,
01,
(18)
Ax = Xslnceiis Xk*
(19)
= (nswath - 1)XS + x
(20)
For a single swath application, xk* equals x . Equation 17 may be reduced to the following closed form: nswath
A1b)=
C
k=l
(21)
A,(O)gl(i,h)gz(i)
(22)
gl(i,h) = exp[-oc,xk*]
(23)
yi = exp[-aiAx]
(24)
The total amount of remaining airborne material for a given spray droplet size distribution and a multiple swath application, depicted by Figure 3, is given by: nSw,th nsize
C C
k=l
i=l
1=1
A similar analysis is made for describing the deposition distribution on the target area. Figure 4 shows the type of spatial distribution that the model predicts for a specific treatment which will be discussed in a later section. (Note that 11208 ng/cm2 is equivalent to 1.0 lblacre.) Spray Droplet Size Distribution Functions
where:
AT^) =
k=l
Ai(O)gl(i,h)gz(i)for x
>0
T h e deposition of active material is defined as:
- 1dAi ( x ) Di(X)= -Y,
dx
(25)
A typical fixed-wing aircraft pesticide ejection system consists of a header boom, whose length is approximately 3/4 of the wingspan, with about 20 spray pressure nozzles mounted on it ( 3 ) .While much is known about spray droplet size distribution prediction for sprays ejected into still air or air in streamline flow, an adequate method has not been developed which takes into account the aerodynamic shear effects imparted to the ejected droplets by the turbulent airstream formed by the airfoil and the propwash. Thus, droplet size information must be obtained from actual tests using specific aircraft, or from wind tunnel airfoil experiments. The “stirred settling” model may also be used to determine droplet size distributions by: (a) choosing a model for the distribution, and (b) determining the values of the parameters in the model by an estimation technique using experimental deposition data. Volume
14, Number 7, July 1980
827
There are several excellent references which discuss particle size distribution models, and the merits of each of these. Bencala and Seinfeld (25) discuss both two- and three-parameter log-normal probability density functions, among others, as applied to analyzing air pollution data. Apt (26) considers the variations of the Weibull function. Mugele and Evans (27) recommend a variation of the log-normal distribution which they call the “upper-limit” equation. Himmelblau (28) treats the properties of many probability density functions, and lists the application of each to physical systems. After consideration of the previously mentioned distribution functions, it was decided to begin with the simplest model; then, after the capabilities of the “stirred settling” model have been tested by additional experimentation, research can proceed to more detailed models. Therefore, the standard normal distribution function was chosen to represent the spray droplet size distribution of pesticide sprays. The following form was incorporated into the mathematical model:
The numerator of Equation 33 is the thermal damping effect, and can be thought of as being proportional to the rate of consumption of turbulent energy by buoyancy forces. The denominator of Equation 33 is proportional to the rate of production of turbulent energy by wind shear. When -dTA/dz is larger than r, atmospheric conditions are unstable, and Ri > 0. The Richardson number is exactly zero when the environmental lapse rate is equal to the adiabatic lapse rate, and is positive for stable conditions; that is, dTA/dz is positive and temperature-inversion conditions prevail. A second criterion has been reported ( 3 3 ) ,which has the advantage of being more easily determined from experimental data than the Richardson number. This criterion is called the stability ratio and is given as: (34) where, in general: S.R. > 0: stable conditions (temperature inversion) (35a) S.R.
spray droplet diameter distribution function S.R. The cumulative distribution function of the mass of spray droplets vs. diameter is thus expressed very simply as: m(Dp) = [I
+ erf(x)]/2
(29)
where:
Sf& S = ( D p - Dp)/up X =
(30) (31)
and the symmetry relationship is erf(-x) = -erf(x)
(32)
A closed form approximation for the error function is given by Abramowitz and Stegun (29). The two parameters to be estimated or input as constants are: (a) the mass median droplet diameter, Dp, and (b) the droplet diameter standard deviation, up [Le., 15.87% of the mass of the spray having diameters smaller than (Dp 0P)l.
Aerial spray treatments using herbicides typically have a mass median diameter of 200-300 pm, while insecticide treatments have a mass median diameter of about 100 pm. Micrometeorological Considerations A detailed discussion of the effects of atmospheric turbulence on dispersion of falling particles is outside the scope of this paper. However, it is appropriate that some specific points be made with regard to aerial application of pesticides. There are many excellent general meteorology references (30, 31); however, the two classic works that treat the dispersion of wind transported material with renowned clarity are provided by Pasquill (22) and Sutton ( 3 2 ) . Concisely, the vertical distribution of wind velocity and temperature in the planetary boundary layer reflects both the turbulence generating and the turbulence damping capability in this mixing layer (also called the Ekman layer). There are a number of criteria which indicate whether or not slightly turbulent motion will remain turbulent or be suppressed. The most fundamental of these criteria is that given by the Richardson number:
1:
0: neutral conditions (mild mixing)
< 0: unstable conditions (turbulent mixing)
(35b) (3512)
Yates et al. (33) give the following numerical classification (Equations 36a-36c). 3.1 2 S.R. 2 1.3: highly stable conditions 1.2 3 S.R. 2 0.1: stable conditions
(36a) (3%)
0 2 S.R. 2 -1.7: unstable conditions
(36~)
The mixing condition of the lower atmosphere (stability), as characterized by the above criteria, is an important determinant of the ultimate fate of spray particles in the midaerosol range, that is, those having diameters between 20 and 50 pm. The effect of stability is more marked for smaller spray droplets, since the larger, heavier droplets tend to experience less vertical dispersion by atmospheric turbulence. Another important determinant is the surface roughness of the crop to which the pesticide is being applied. Thus, both the stability ratio and the type of crop should be reported when describing the deposition experiment. The type of crop used for this study was typical Texas rangeland grasses. The experiment was performed in April. For the herbicide experiments analyzed in this paper, the amount of spray having droplet diameters less than or equal to 50 pm is typically about 2% by mass. While this indicates that a major portion of the spatial distribution of herbicide is not greatly affected by local atmospheric stability conditions, treatments are not applied under temperature-inversion conditions in order to avoid potential long-range transport of that portion of the spray droplets in the mid-aerosol size range. In addition, treatments should not be applied (a) under calm conditions, because erratic air currents might carry fine spray a t high concentration in unexpected directions and to unexpected distances, and (b) when the wind velocity exceeds 4 m/s (10 mph), because horizontal advection becomes significant even for the larger droplets. In summary, the “stirred settling” model should be applicable in convective and, therefore, well-mixed conditions, with very little of the total spray being influenced by atmospheric turbulence. The experiments, to be discussed in the next section, were carried out under conditions corresponding to neutral to unstable atmospheric mixing conditions. Analysis of Experimental Results Twenty-eight experiments were performed by personnel in the Agricultural Products Department of The Dow Chemical Company and the Texas Agricultural Experiment Station. These deposition experiments were designed to
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Environmental Science & Technology
4b 2
S . R . = -0.3
On-Target Recovery = 71.9%
t 100-
0
400
’
800
I I ‘I 0 400 1200 1600 2000 2400 2 I Distance Downwind. Feet
Figure 5. Treatment 101 (Triclopyr).Experimental deposition data and corresponding “best fit” model determination
provide information regarding the effects of different spray nozzle types, spra:y formulations and carriers, and total volumes per acre on target swath recovery, and aerial pesticide drift. While a comprehensive discussion of the results of all these experiments is outside the scope of this paper, three of the experiments, which illustrate the use of the “stirred settling” model, will be discussed. Primary Elements of the Experimental Program. The fixed-wing aircraft used to deposit the herbicide formulations was a 300-hp Cessna Ag Wagon, fitted with an airfoil boom with 20 nozzles mounted on it. In order to improve the spray pattern of this particular aircraft, the boom was mounted below the trailing edge of the wing and was essentially level from end to end rather than following the contour of the wing. Active material was released from a height of approximately 3 m (10 f t ) in each experiment. The target area was oriented such that the positive x axis was pointed north (magnetic).Four swaths were flown for each experiment. The swath length was 1609 m (5280 ft), and the swath width for all flight conditions was 13 m (42 ft). The nozzles used in treatment 101 were Spray Systems No. 4664 bodies without core plates, equipped with D-5 orifices. Nozzle orientation was to the rear and 30’ downward from the chord line of the wing. Operating pressure was 120 psig, giving a total spray volume of 1 gal/acre. The nozzles used in treatments 110 and 114 were Delavan Raindrop@RD 7-45 types. The respective orientation and operating pressure were 15’ and 23 psig for treatment 110, and 30’ and 23 psig for treatment 114. Deposit sampling stations were located a t 50 in (165 ft), 100 m (330 ft), 201 m (660 ft), 402 m (1320 ft), and 805 m (2640 ft) downwind of the leeward edge of the target area. Samples were collected on Mylar plastic cards attached to metal plates 0.46 m (1.5 ft) above ground level. Each sample was a composite of 10 square cards, having a characteristic dimension of 0.1 m (4 in.). Two sample lines were located within the target area.
I
800
1200
1600
2000
I 2400
2E )O
Distance Downwind, Feet
Figure 6. Treatment 110 (2,4-0 and picloram).Experimental deposition data and corresponding “best fit” model determination
Sample lines A and B were located 30.5 m (100 ft) from the center line (see Figure 1).Each line consisted of 10 sample locations spaced approximately 3 m (10 ft) apart, with the 1st and 10th samples located a t x equal to -12 m (-39 ft) and -39.3 m (-129 ft),respectively. The 10 samples for each line were analyzed as a composite, thus giving two data points on the target area. The intent here was not to describe a detailed swath coverage pattern, but to provide a mass balance check on the deposition data. A portable micrometeorological station was set up to measure (a) wind velocity and direction, (b) environmental lapse rate, (c) dry bulb temperature, and (d) wet bulb temperature. Stirred Settling Model “Best Fit” of Data. In order t o estimate the values of the spray droplet size distribution parameters which best fit the data, a digital computer algorithm was implemented on an IBM 370/158 MVS computer system. The primary elements of the algorithm included Equations 13,25,27, and 29 with a two-level direct search technique used to determine optimal values of Dp and up. The objective function, which was minimized, is the sum of the squared values of the relative errors, and is given by Equation 37:
. .
Convergence iseasily obtained, because incremental changes in the value of D, affect the fit of the data a t short downwind distances more than changes in up,while incremental changes in the value of up dramatically affect the fit of the data a t long downwind distances. Treatments 101,110, and 114 represent three types of data sets which were examined. Treatment 101 represents the single active component series of experiments. The data and the curve represented by the model are depicted in Figure 5. Treatment 110 represents a two-active-component series, where one component was present in such small amounts that only two data points were obtained. For these experiments, Volume
14,
Number 7, July 1980 829
I 04 8 6
104
8
I
4
2
2
I 03 8 6
. $ E
4
E
2
E
2
-'i
IO' 8
.
4
$
S.R. = 0.0
8 6
4
gl 5
if= 2 . 4 1 m / s
103
5
rci
A(0) = 5.40 kg
z" 102 $ 0
6
8
6
! 4
-m
-
I
L
1 2
1 2
IO'
10'
6
6
4
4
2
2
a
8
1 00 1
Distance Downwind, Feet
100 Distance Downwind, Feet
Flgure 7. (a)Treatment 114 (2,4,5-T and picloram). 2,4,5-T experimental deposition data and corresponding "best fit" model determination. (b) Treatment 114 (2,4,5-Tand picloram). Picloram experimental deposition data and corresponding "best fit" model determination
Dpand upwere determined from the major component data, and used to predict the deposit of the minor component. Figure 6 shows that the fit of the picloram data, from parameters estimated from the 2,4-D data, is quite good. Treatment 114 represents a two-active-component series where both components were present in sufficient amounts, such that both sets of data could be used independently for parameter estimation. This was done, with the results depicted in Figures 7a and 7b. The values of the estimated parameters, for the two components, should agree. Thus, an additional check was provided on the experimental technique and the model. The values of spray droplet size distribution parameters are given on the respective figures. While detailed experimental swath pattern data generally follows the smooth trend depicted in Figure 4 (see Akesson and Yates ( I ) , Figure 61, and Sexsmith e t al. ( 6 ) ) ,there is variability around this trend as a result of the aerodynamic effects caused by the aircraft. For this reason, prediction of overall on-target recovery from deposition data (where the influence of the aircraft is considerably less) and the use of the "stirred settling" model is a better approach to follow. The model forces a mass balance, and thus must account for 100% of the active material released. Computed values of the recovery of active material, based on the estimated parameter values, are given in Figures 5 through 7b in parentheses. After spray droplet size distribution parameters have been estimated for a specific nozzle configuration, spray formulation, wind speed, aircraft type, and swath track, various alternate application strategies may be examined. For example, (a) nozzle type comparison studies can be performed, (b) application recommendations can be made regarding flight height to achieve a given recovery for a given wind speed, and (c) multiple swath recovery computations can be made based on data from a single swath experiment. 830
Environmental Science & Technology
Concluding Remarks A mathematical model has been presented that has assisted in the numerical assessment of aerial pesticide deposition data. This fundamental model, while notably simple, offers the advantage of a systematic approach to data analysis. While the model includes the concept of a well-mixed air layer near the ground, no allowance has been made for including quantitative turbulence parameters based on meteorological observations. This may seem like a significant shortcoming of the model. However, in actual application practice, treatments are applied only under a narrow range of meteorological conditions to ensure maximum recovery on-target. Thus, this limitation is not considered to be significant compared to the demonstrated usefulness of the model. Further investigation into the capabilities of the stirred settling model should provide a research data base for development of more detailed models. Acknowledgments The experimental program was designed and implemented by J. B. Grumbles and W. G. Wright, Herbicide Research Development Specialists, Agricultural Department, Dow Chemical U.S.A., and personnel of the Texas Agricultural Experiment Station, Vernon, Tex. The quantitative analytical work was performed by B. L. Johnson. Valuable insight to the aerial application industry was provided by C. A. Reimer, Agricultural Department, Dow Chemical U.S.A. This work was performed for and is published by permission of the Agricultural Departm-eni of The Dow Chemical Company, in consultation with the Texas Agricultural Experiment Station. Nomenclature A, ( t ) = amount of remaining airborne active material having a particle diameter characteristic of the i t h particle size fraction
(8)Umback, C. R.. Lembke, W. E.. 1965 Winter Meeting of the
A , = projected area of a spherical droplet normal t o path, m2 CD = empirical drag coefficient, dimensionless D, = spray droplet diameter, m Dp = mass average droplet diameter, m erfo() = value of the error function with argument, x FD,,, = drag force in the x or z direction, N g = gravitational acceleration, m/s2 g, = dimensional constant, 1 (kg.m)/(Nd) rn(D,) = mass fraction of spray droplets having diameters less than or equal t o D,, dimensionless Re,p = particle Reynolds number, dimensionless Ri = Richardson number, dimensionless T A = ambient air temperature, K uX,* = component droplet velocity in the x or z direction, m/s Uf = average wind velocity, m/s u s = terminal settling velocity of droplet, m/s n = downwind distance measured from leeward edge of first swath, m X , = swathwidth,m y = crosswind distance, m Y , = swath length, m z = vertical distance above grade level, m 2, = height a t which active material is released, m r = adiabatic lapse rate, 0.0098 K/m v f = kinematic viscosity of air, m2/s x = pi, 3.141592.. . p f = air density, kg/m3 p, = spray droplet density, kg/m3 0, = standard deviation of spray droplet diameters, pm 4 = objective function
American Society of Agricultural Engineers, Chicago; 1965; A.S.A.E. Paper No. 65-702. (9) Garrett, A: J., 1968 Annual Meeting of the American Society of Agricultural Engineers, Utah; 1968; A.S.A.E. Paper No. 68-138. (10) Friedlander, S. K., Johnston, H. F., Ind. Eng. Chem. 1957,49, 1151-1156. (11) Threadgill, E. D., Smith, D. B., 1971 Winter Meeting of the American Societv of Amicultural Eneineers. Chicaeo: - , 1971: A.S.A.E. Paper N;. 71-66?. (12) Ware, G. W., Cahill. W. P.. Estesen. B. J.. J . Econ. Entomol. 1975,68, 329-330. (13) Glotfelty, D. E., Caro, J . H., ACS Symp. Ser. 1975,17, 42-62. (14) Lapple, C. E., Shepherd, C. B., Ind. Eng. Chem. 1940, 32, 605-61 7. (15) Hughes, R. R., Gilliland, E. R., Chem. Eng. Prog. 1952,48(10), 497-504. (16) Yen, C. Y., Yu, T. H., Chem. Eng. Prog. S y z p . Ser. 1966,62(62), 100-1 11. ( 1 7 ) Sinclair, D., “Handbook of Aerosols”; U.S.A.E.C.: Washington, D.C., 1950; p p 64-76. (18) Ranz, W.E., U.S. Public Health Service Research Grant S-19, 1956, Bulletin No. 66, Technical Report No. 1. 119) Davies. C. N.. “Surface Contamination”: Academic Press: New York, 1966; pp 393-445. (20) Davies. C. N., “Surface Contamination”: Peraamon Press: New York, 1967; pp 115-121. (21) Fuchs, N. A., “The Mechanics of Aerosols”; Pergamon Press: Yew York, 1964; pp 250-287. (22) Pasquill, F., “Atmospheric Diffusion”, 2nd ed.; Wiley: New York, 1974; pp 252-269,327. (23) Chamberlain, A. C., Int. J . Air Pollut. 1960, 3, 63-88. (24) Seinfeld, J. H., Roth, P. M., Reynolds, S. D., Chem. Eng. Comp u t . 1972,1, 17-31. (25) Bencala, K. E., Seinfeld, J. H., Atmos. Enuiron. 1976, 10, 941-950. (26) Apt, K. D., Atmos. Enuiron. 1976,10, 941-950. (27) Mugele, R. A., Evans, H. D., Ind. Eng. Chem., 1951,43, 13171324. (28) Himmelblau, D. M., “Process Analysis by Statistical Methods”; Wiley: New York, 1970; pp 10-42. (29) Abramowitz, M., Stegun, I. A,, Eds., “Handbook of Mathematical Functions”; Dover: New York, 1965; p 299. (30) Berry, F. A., Bollay, E., Beers, N. R., “Handbook of Meteorology”, McGraw-Hill: New York, 1973. (31) Byers, H. R., “General Meteorology”, 4th ed.; McGraw-Hill: New York, 1974. 132) Sutton. 0. G.. “Micrometeoroloev”: McGraw-Hill: New York. -” 1953; pp 56-104. (33) Yates. W. E.. Akesson. N. B.. Coutts. H. H.. 1964 Winter Meeting of the American Society of Agricultural Engineers, New Orlean; 1964; A.S.A.E. Paper No. 64-609-A.
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I
Literature Cited (1) Akesson, N. B., Yates, W.E., “The Use of Aircraft in Agriculture”; F.A.O. Agricultural Development Paper No. 94; Food and Agriculture Organization of the United Nations: Rome, 1974. ( 2 ) Brandes, G. A,, Agric. Chem. 1967,22(1),43-47. (3) Grumbles, J. B.. Rangeman’s J . 1975,2(2), 50-56. (4) LaMer, V. K., Hochberg, S., Chem. Rev. 1949,44, 341-352. (5) Johnstone, H. F., Winsche, W. E., Smith, L. W., Chem. Reu 1949, 44, 353-371. (6) Sexsmith, J. J., Hopwell, W. W., Anderson, D. T., Russel, G. C., Hurtig, H., Can. J. Plant Sci. 1957,37, 85-96. ( 7 ) Coutts, H.‘H., Yates, W. E., 1965 Annual Meeting of the American Society of Agricultural Engineers, University of Georgia; 1965; A.S.A.E. Paper No. 65-157.
Received for recieu: J u n e 8 , 1979. Accepted March 4,1980
Groundwater Leaching of Organic Pollutants from in Situ Retorted Oil Shale. A Mass Transfer Analysis Gary L. Amy’”, Anthony L. Hines2, Jerome F. Thomas, and Robert E. Selleck Department of Civil Engineering, University of California, Berkeley, Calif. 94720
Oil shale is a mineral material from which oil can be produced by pyrolysis of organic matter that occurs within the oil shale matrix. Most of the organic matter found in oil shale consists of Kerogen, a high molecular weight, three-dimensional polymer. The oil produced is in the form of condensible hydrocarbon vapors, which are subsequently condensed and cooled to produce a semiviscous liquid. Present address, Department of Civil Engineering, University of Arizona, Tucson, Ariz. 85721. Present address. Department of Chemical and Petroleum-Refining Engineering, Colorado School of Mines, Golden, Colo. 80303. 0013-936X/80/0914-0831$01.OO/O
Not all of the organic matter originally present in oil shale is converted to oil. During pyrolysis, various carbonaceous byproducts are formed. One of the most important byproducts of pyrolysis, from an environmental viewpoint, is retorted oil shale or spent shale (i.e., the residual solid material remaining after pyrolysis). After pyrolysis, some residual organic matter remains associated with the spent shale. A portion of this residual organic matter resides within the pores of the spent shale matrix, partly as a cokelike substance, partly as oil that was not extracted, partly as miscellaneous organic compounds produced as byproducts of pyrolysis. In addition, some residual organic
@ 1980 American Chemical Society
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