EPA 660/2-74-054
August 1974
Environmental Protection Technology 3
Volatilization Losses of
Pesticides From Soils
Office of Research and Oevetopmeot
U.S. Environmental Protection Agency
Washington. D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
<*. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
standards.
EPA REVIEW NOTICE
This report has "been reviewed by the Office of Research and
Development, EPA, and approved for publication. Approval
does not signify that the contents necessarily reflect the
views and policies of the Environmental Protection Agency, nor
does mention of trade names or commercial products constitute
endorsement or recommendation for use.
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EPA-660/2-7U-Q5U
August 1974
VOLATILIZATION BOSSES «P PESTICIDES FROM SOILS
By
Walter J. Farmer
Principal Investigator
and
John Letey
Co-Investigator
Grant No. 801835
Program Element 1BB039
Roap/Task 21 AYP IT
Project Officer
Dr. George W. Bailey
Southeast Environmental Research Laboratory
Environmental Protection Agency
Athens, Georgia 30601
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D. C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $1,45
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ABSTRACT
The volatilization of pesticides following soil application can
be predicted from considerations of the physical and chemical prin-
ciples controlling concentrations at the soil surface. When these
concentrations are maintained at a relatively high level, volatiliza-
tion losses will be determined by the pesticide vapor pressure as
modified by adsorptive interactions with the soil. For pesticides which
have been mixed with the soil or when volatilization has been proceed-
ing for a time so that concentrations at the soil surface are low,
volatilization rates will be determined by the rate at which pesticides
move through the soil to the soil surface. Under conditions when mass
flow in liquid water is negligible, volatilization rates are predict-
able using solutions to the diffusion equations. When mass flow is
operative the prediction of rates of volatilization are more complex.
A computer model has been developed combining both diffusion and mass
flow for predicting the volatilization of soil-incorporated pesticides.
Temperature gradients in soil significantly affect the distribution
of volatile pesticides in soil. Vapor phase diffusion toward areas of
low temperature can occur simultaneously with mass flow in liquid water
toward areas of high temperature.
This report was submitted in fulfillment of Grant No. R-801835,
Program Element 1BB039 by the Department of Soil Science and Agricul-
tural Engineering, University of California, Riverside, under the
sponsorship of the Environmental Protection Agency. Work was completed
as of April 1974.
ii
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TABLE OF CONTENTS
Page
Abstract ii
List of Figures iv
List of Tables v
Acknowledgements vi
Sections
I Conclusions 1
II Recommendations 2
III Introduction 3
IV Factors Controlling Pesticide Volatilization
from the Soil Surface 4
V Theoretical Considerations 7
VI Experimental Design 20
VII Results and Discussion 24
VIII References 52
IX Glossary 55
X Appendices 57
iii
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FIGURES
No. Pag(
1 Comparison between calculated values (solid curve) from 30
Model II and experimental values (horizontal lines) for
dieldrin flux. The experimental values were taken from
Spencer and Cliath (1973). The length of the horizontal
lines indicate the time over which the experimental
values were taken.
2 Comparison between calculated and experimental values 31
for lindane flux from treated Gila silt loam.
Experimental data are from Farmer et al. (1972).
3 Comparison of calculated and experimental values for 33
dieldrin volatilization flux from uniformally treated
Gila silt loam for air moving over the soil surface at
two velocities. Experimental data from Farmer et al.
(1972).
4 Calculated values forthe influence of depth of non- 35
moving air layer on lindane volatility flux from
uniformally treated Gila silt loam.
5 Effect of temperature gradient on the distribution of 48
water and lindane in Gila silt loam.
6 Effect of temperature gradient on the distribution of 49
water, Cl , and diuron in Pachappa sandy loam.
7 Effect of temperature gradient on the distribution of 50
water, Cl , and atrazine in Pachappa sandy loam.
iv
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TABLES
No. Page
1 Chemical designations of pesticides cited in text. 21
2 Pesticide volatilization from treated sand. Sand treated 25
at the rate of 1000 ng/g. Air flow was 480 ml min"1
(2.82 cm sec"-'-) at 30C. Each value is an average of
duplicate determinations.
3 Effect of air flow rate on pesticide volatilization from 26
treated sand. Sand treated at rate of 1000 (j,g/g. Each
value is an average of duplicate determinations.
4 Initial pesticide volatilization rates from treated Gila 28
silt loam at 480 ml min"1 (0.374 cm sec'1), 30C, 10%
gravimetric soil water content and 100% relative humid-
ity.
5 Sample input data. Experimental values of apparent 37
diffusion coefficients (Dvs) with corresponding water
content values (0). Data taken for the pesticide
lindane (Shearer et al., 1973).
6 Sample input data. Soil water content as a function of 38
the hydraulic head and the water conductivity.
7 Sample output data. Water relations and pesticide 39
distribution in soil column 2.4 days after initiation
of pesticide volatilization.
8 Sample output data. Pesticide volatilization flux 40
through the top of the soil column as a function of
time after initiation of volatilization.
9 Initial conditions of soil columns for determining ^
influence of temperature gradients on pesticide movement.
10 Parameters characterizing water flux in soil columns. ^
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ACKNOWLEDGEMENTS
The principal investigators for this study are located at the
University of California Riverside in the Department of Soil Science
and Agricultural Engineering where all the investigations for this
study were carried out.
The development of the diffusion based models for predicting the
volatilization of soil-incorporated pesticides was performed and
written by Dr. Robert Mayer while he was a post-doctoral fellow at the
University of California Riverside.
Dr. Fritz Huggenberger initiated the investigation into the effect
of temperature gradients on pesticide movement in soils while he was a
post-doctoral fellow at the University of California Riverside.
Dr. Robert Mayer completed and wrote up the investigations reported
here.
Dr. Vern Weeks was primarily responsible for development of the
computer program for the combined diffusion and mass flow model for
predicting volatilization of soil-incorporated pesticides.
Other University of California personnel who assisted in carrying
out the investigations reported here are Mrs. Annemarie Westlake and
Mr. Richard Shepherd, both Staff Research Associates in the University.
A number of individuals contributed to this project by their
eagerness to meet together and share ideas. Dr. George Bailey and
his staff at the Southwest Environmental Research Laboratory were
especially instrumental in providing the opportunity for individuals
from various agencies to work together on the Pesticide Runoff Modeling.
These agencies and the personnel involved include Dr. James Davidson
from Oklahoma State University, Dr. Ralph Leonard and his staff at the
USDA Southern Piedmont Conservation Center, Dr. Norman Crawford and
Mr. Anthony Donigian, Jr. of Hydrocomp, Inc. and Mr. Michael Hogan and
Mr. Ron Adams of ESL, Inc.
Dr. William F. Spencer, USDA, ARS, Riverside, California contri-
buted to this project through his ready availability for discussion
and sharing of technical data.
vi
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SECTION I
CONCLUSIONS
1. Pesticide volatilization from soils can be modeled. The
choice of model to use will depend on pesticide characteristics,
application techniques, and climatic factors such as surface wind speed.
2. For soil-incorporated pesticides which have significant
mobility in flowing water, a computer based model is utilized to
predict pesticide volatilization. A numerical solution of the mass
flow and diffusion equations is required for the model.
3. The volatilization of soil-incorporated pesticides which have
limited mobility in flowing water can be predicted using an analytical
solution to the diffusion equations. Five different models have been
developed depending on the initial and boundary conditions which can be
applied to the situation. The solutions to these diffusion-based models
are relatively simple when compared to the mass flow model.
4. When pesticides remain on the soil surface as in the case of
non-incorporated pesticides, vapor density relationships and air flow
rate rather than movement in the soil becomes the factor controlling
the rates of volatilization. Rates of volatilization of surface applied
pesticides can be predicted on the basis of pesticide vapor pressure
following calibration with a known pesticide.
5. The effect of temperature gradients on pesticide movement in
soils can be investigated experimentally. Water flow characteristics
in soils due to temperature gradients must be determined to understand
pesticide movement. Significant pesticide flow toward areas of low
temperature due to vapor diffusion and toward areas of high temperature
due to mass flow with water can occur simultaneously.
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SECTION II
RECOMMENDATIONS
1. Pesticide losses due to volatilization of soil applied
pesticides can be drastically reduced by rapid incorporation into the
soil following application. Most of the loss due to volatilization
takes place within the first few hours following application.
Volatilization is directly related to soil concentration. Rapid reduc-
tion of the concentration of the pesticide at the soil surface by
incorporation will greatly reduce volatilization. An application of
only one kg/ha can result in very high soil concentrations at the soil
surface if not incorporated.
2. Calibration of existing pesticide volatilization models with
field trials should greatly improve their accuracy. Data from field
volatilization trials will also indicate how improvements can be
accomplished in the models.
3. A great deal of study is needed on the effects of temperature
gradients, rainfall events, photodecomposition, and degradation rates
on the concentration of pesticide at the soil surface. The concentra-
tion at the soil surface is probably the greatest factor affecting
rates of volatilization and many factors influence this concentration.
For example, the frequency, intensity, duration and amounts of precipi-
tation determine how much pesticide remains on the soil surface for
volatilization to take place and how much is removed by run-off or
leaching and therefore less subject to subsequent volatilization.
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SECTION III
INTRODUCTION
The quantities of pesticides entering our rivers, lakes, and
streams are of vital concern to those dedicated to preserving environ-
mental quality. Those pesticides which eventually find their way into
our rivers and lakes are rapidly dispersed over wide geographic areas
due to the rapid intermixing of water. This rapid dispersal allows
intimate contact of pesticides with a number of organisms including
man, wildlife, crops and other flora and fauna especially those adapted
to life in an aquatic environment. The present state of our knowledge
indicates the major mechanism by which pesticides enter waterways from
treated land surfaces is by run-off. A second source of less magnitude
is by rain-out of air-born pesticides. Whatever the source of pesti-
cides in water, it will be necessary to adequately describe the fate of
pesticides applied to land surfaces before reliable predictions can be
made of amounts of pesticides entering waterways and to establish
adequate management practices to control these losses.
Pesticide volatilization is one mechanism by which pesticides may
be lost from soils. Other mechanisms include drift, run-off, decompo-
sition (biological, non-biological, photochemical), leaching into
groundwater, and plant uptake. From a quantitative point-of-view, the
predominant mechanism operating at any particular time will depend on
a number of factors including soil characteristics, vegetative cover,
environmental conditions and type of pesticide. Most situations in
which pesticides appear require a knowledge of how each mechanism is
operating to account for the dissipation of all pesticides applied.
The purpose of this project is to define and describe those
factors which are most significant in controlling pesticide volatili-
zation from soil surfaces and to formulate these factors into a mathe-
matical model for predicting pesticide volatilization from treated
soil. A volatilization model is to be developed that can be used to
simulate vapor loss under a variety of soil, watershed, and environ-
mental conditions. It is intended that the models herein developed
will be useful in an overall transport model for predicting quantities
of soil-applied pesticides which are lost due to run-off.
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SECTION IV
FACTORS CONTROLLING PESTICIDE VOLATILIZATION FROM THE SOIL SURFACE
Before describing the factors influencing volatilization it is
necessary to discuss how pesticides get into the atmosphere and to
define volatilization. Pesticides may be present in the atmosphere
due to drift, volatilization, or pesticide-laden soil particles
carried there by wind action. Drift results during spray applications
when wind blown spray particles are carried away from the target area.
The major portion of a pesticide which gets into the atmosphere takes
place at the time of application. This is due both to drift particles
that never reach the ground and to pesticides reentering the atmosphere
by volatilizing after reaching the target area. Thus, by volatiliza-
tion, the inference is that the pesticide is in the atmosphere in the
true vapor phase. Pesticides will also be in the vapor phase by vola-
tilization from the spray droplets before reaching the target. Once
pesticides volatilize either from spray particles or from the target
surface they may recondense as pesticide particles, spray particles,
on air-borne dust, or on adjacent land and plant surfaces. Both pesti-
cide drift and wind blown dusts contribute significant amounts of
pesticides in the atmosphere under certain conditions. However, this
project will deal only with volatilization from land surfaces as this
is the primary pathway of entry into the atmosphere following applica-
tion.
Volatilization as used here will mean the loss of pesticides from
treated soils by evaporation into the true vapor phase followed by
movement into the atmosphere above the soil. Volatilization from
plant surfaces may follow many of the same principles. Since most of
the available information is on volatilization from soils, this project
will deal only with soil-applied pesticides.
The literature relating to pesticide volatilization was recently
reviewed by Spencer, Farmer and Cliath (1973). The reader is referred
to this review for a discussion of the evidence pointing toward pesti-
cide volatilization as a significant factor. In addition the article
presents a detailed discussion of the mechanisms and factors that
influence volatilization rates. Grover et al. (1973) have discussed
the significance of pesticide drift and its relationship to volatiliza-
tion. Finklestein (1969) has presented an extensive review on concen-
trations of pesticides in air.
In order for a pesticide to volatilize from soil, three things
must take place: 1) pesticide molecules within the soil must move to
the soil surface, 2) the pesticide molecule must be present in the
vapor phase at the soil surface and 3) the pesticide molecule must
move away from the soil surface into the atmosphere above the soil.
If the rate at which any of these processes takes place decreases, the
rate of volatilization will also decrease. The rate of volatilization
will then be controlled by the factors influencing these three processes.
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Movement of pesticide molecules to the soil surface may be
either in the vapor or non-vapor phases. The mechanism of movement
to the soil surface may be either by diffusion or by mass flow. The
literature on the movement of pesticides in soil has been recently
reviewed by Letey and Farmer (1974). Movement to the soil surface
will become a limiting factor when pesticide molecules at the soil
surface are depleted and the only way in which additional pesticide
can volatilize is by movement from deeper in the profile.
Once pesticides reach the soil surface their potential for
volatilization will depend on their vapor phase concentration or vapor
density. [Vapor density is related to the vapor pressure by the equation
for perfect gases, p = d (RT/M), where p is vapor pressure, d is vapor
density, R is the molar gas constant, T is the absolute temperature,
and M is the molecular weight of the pesticide. In this report vapor
density will be used interchangeably with the term saturation vapor
concentration (S.V.C.) as used by Hartley (1969)]. Each pesticide
compound has a characteristic vapor pressure. When a pesticide is
applied to a surface its vapor pressure, and therefore its vapor
density, will be reduced depending on the extent of adsorption which
takes place between the pesticide and the surface. The literature on
the factors controlling the vapor density of adsorbed pesticides has
been extensively reviewed by Spencer, Farmer and Cliath (1973).
Briefly, the two most significant factors affecting vapor density, in
addition to the temperature effect, are soil pesticide concentration
and soil water content. Non-polar and weakly polar pesticides are
strongly adsorbed by dry soils. Thus a pesticide may diffuse to the
soil surface in the vapor phase and be adsorbed so that the rate of
volatilization is zero. However, for soil water potentials greater
than approximately -15 bars, pesticide volatilization is independent
of soil water content and is dependent on pesticide concentration in
the soil water. Pesticide vapor density will increase with increas-
ing concentration until the maximum vapor pressure of the pesticide
is reached.
The last hurdle for a pesticide to cross before it can volatilize
is to move away from the soil surface so additional molecules can move
into the vapor phase. The rate of movement away from an evaporating
surface will be dependent to some extent on the rate of diffusion in
air. However, this step in(the volatilization process will normally
be limiting only in cases of high pesticide concentration on the soil
surface or when there is no wind activity and the air above the soil
is stable and quiet.
Any factors, such as surface wind speed, which tends to remove
pesticides from the site of evaporation should cause an increase in
the rate of volatilization. Several investigators have found the
rate of volatilization of pesticides to be directly related to air flow
over the evaporating surface (Harris and Lichtenstein, 1961; Danielson
and Center, 1964, Parochetti and Warren, 1966; Harthy, 1969; Farmer
et al. 1972). On the other hand, factors which may retard pesticide
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dissipation in the atmosphere would be expected to reduce volatiliza-
tion. Most of the studies of pesticide volatilization rates have been
performed with bare soils. The presence of a cover crop, and the type
of cover and its density, would reduce wind speed and turbulence at the
soil surface and therefore should reduce volatilization. Pesticide
movement by diffusion in air would be expected to be slower than move-
ment by air currents.
Sufficient information appears to now be available on factors
affecting pesticide volatilization to attempt formulating predictive
models. Knowledge of the particular conditions existing in the field
hopefully will allow the selection of the proper model to use.
6
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SECTION V
THEORETICAL CONSIDERATIONS
Based on the steps involved in the volatilization processes as
discussed in the previous section, the modeling of pesticide volatil-
ization from soils can be divided into three separate cases. In the
first instance, the volatilization of surface applied pesticides is
considered. In this case, the rate of volatilization will be depend-
ent on the vapor pressure of the pesticide itself, temperature and
wind speed. In the second and third instances soil-incorporated
pesticides are considered and the rate at which pesticides move to
the soil surface is the rate-limiting step in volatilization. In the
second case, only diffusion is considered and in the third situation,
mass flow and diffusion are considered together in moving pesticides
to the soil surface.
SURFACE APPLIED PESTICIDES
Pesticide volatilization will normally be highest during and
immediately following application. This will be especially true when
the application is not incorporated into the soil by disking or other
appropriate means. When the pesticide is exposed on the surface of
the soil it will be subject to rapid volatilization. The following
considerations were designed to model those factors which determine
the rate of volatilization of surface-applied pesticides.
It is assumed that the volatilization of a pesticide from a soil
surface is related to the molecular diffusion coefficient of the
compound in air. According to Pick's first law, the rate of molecular
diffusion will be proportional to the diffusion coefficient and to the
saturation vapor concentration (S.V.C.).
q = K..D Ac /L [1]
JL V 3
where q = rate of diffusion, K^ is the constant for the geometry of the
soil, DV = vapor diffusion coefficient, Aca is the vapor concentration
gradient, and L is the length over which diffusion occurs. When the
pesticide is on the soil surface K^ is equal to one. For the case when
KI ^ 0, see section pertaining to soil-incorporated pesticides.
Assuming air flow and turbulence maintain zero concentration at
distance, d, above the pesticide treated area,
&a = c = s.V.G. [2]
a a
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Hartley (1969) has indicated an inverse proportionality of the
diffusion coefficient to the square root of the molecular weight (M)
[3]
where K? is a proportionality factor.
Combining equations [I], [2], and [3]
q = -K S.V.C. M"2 [4]
where
From the perfect gas laws the vapor concentration is proportional
to the vapor pressure (p) times the molecular weight.
c = pM/RT [5]
3
where R is the gas constant and T is the absolute temperature.
Combining equations [1], [2], [3] and [5]
q = K^ PM% [6]
where K1 = -K..K_/RTd. The rate of diffusion or the rate of volatiliza-
tion, f, will be proportional to the vapor pressure times the square
root of the molecular weight. Alternatively, according to Equation [4],
the volatilization rate will be proportional to the saturation vapor
pressure divided by the square root of the molecular weight of the
pesticide.
DIFFUSION BASED MODEL FOR SOIL-INCORPORATED PESTICIDES
When the pesticide concentration at the soil surface is reduced
or depleted, pesticide must move to the surface if volatilization is
to take place. In the absence of appreciable mass transfer due to
water movement, diffusion processes in the soil will account for the
movement of pesticides to the soil surface to replace that lost by
volatilization. The objective of this portion of the project is to
develop mathematical equations for predicting volatilization of soil-
incorporated pesticides as a diffusion controlled process and compare
calculated with measured results. This portion of the study is pub-
lished separately (Mayer, Letey, and Farmer, 1974).
The basic assumption in the mathematical treatment of the move-
ment of pesticides in soils under a concentration gradient is the
applicability of the diffusion laws. The changes in pesticide
8
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concentration within the soil as well as the loss of pesticides at the
soil surface by volatilization can then be predicted by solving the
diffusion equation for different boundary conditions. Recognizing the
analogy between the heat transfer equation (Fourier's law) and the
transfer of matter under a concentration gradient (Pick's law), solu-
tions of the heat transfer equation given by the mathematical theory of
conduction of heat may be used. The mathematical model for predicting
volatilization of pesticides is then given as a set of boundary
conditions sufficient to solve the diffusion equation.
Consider a system where a pesticide is uniformly mixed with a
layer of soil and volatilizing at the soil surface. If diffusion is
the only mechanism supplying pesticide to the surface, and if we
assume isotropic conditions in the soil as well as constancy of the
diffusion coefficient D, then the general diffusion equation is
L_£. _ I 0
= 0 at x = L
Carslaw and Jaeger [1959, p. 97, equation (8)] give a solution
for these boundary conditions that can be used by accepting the follow-
ing analogies:
v (temperature) = c (concentration)
V (initial temperature) = C (initial concentration)
K (thermal diffusivity)
=|-D (apparent diffusion coefficient)
K (thermal conductivity)
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The concentration units for c and C must be expressed on a total
volume basis in order for D to be analogous to K and K.
The solution for equation [7] is then
4Co £ (-I)" r r _,, ...2 2 ,.2,, (2n+l)Tf(L-x) ra,
c = -^- S )2n+l) lexP['D(2n+1) ^ t/^-L ]}cos -1 - 1^ - ^ [8]
n=0
(Carslaw and Jaeger used the boundary condition x = L and we have used
x = 0 at the soil surface. Identical results are achieved by our
using (L - x) in the equations where Carslaw and Jaeger used x) . The
pesticide flux, f (g/cm /sec), through the surface is given as the
concentration gradient at x = 0 times the diffusion coefficient, D:
DC «> _
f = D[0c/Sx] -- ^—j: [1 + 2S (-1) exp(-n L /Dt) ] [9]
X (rrDt) 2 n=l
Model II
The summation term in equation [9] decreases with increasing L and
decreasing D and t. If this term is small enough to be negligible,
equation [9] reduces to
f = DC /(nDt) [10]
This equation is identical with the solution given by Carslaw and
Jaeger [1959, p. 59, equation (3)] for heat flow in an infinite solid.
The concentration for the semi-infinite case is given by
c = CQerf[x/2(Dt)^] [11]
Equations [10] and [11] are applicable also on a finite system (in the
region 0 < x < L) as long as the concentration at the lower boundary of
the soil layer, x = L, is not decreased by pesticide moving in the"
upward or downward direction. To estimate the maximum time at a given
set of parameters for which Model II is adequate, let us assume the
critical value to be a drop of 1% in the initial concentration, CQ, at
the lower boundary of the soil layer. With this assumption the
boundary conditions used in deriving equation [11] are violated if
erf[L/2(Dt)2] < .99
10
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or
t > L2/14.4 D
Model III
Model I assumed that no diffusion occurs across the lower
boundary x = L. This boundary condition is appropriate for laboratory
studies which will be reported later, but not realistic for field
conditions where diffusion can occur downward across the boundary
x = L. The boundary conditions for the latter case are
c=C at t = 0, 0 < x < L
c=0att=0, x>L
c = 0 at t > 0, x=0
Solution of equation [7] with these initial and boundary
conditions is given by Carslaw and Jaeger [1959, p. 62, equation (14)]
as
c = (CQ/2)J2 erf[x/2(Dt)Verf[(x-L)/2(Dt)%]-erf[(x+L)/2(Dt)%]}- [12]
The flux is obtained by differentiating equation [12] with respect to
x, determining dc/dx at x = 0, and multiplying by D. The result is
f = [DC /(TTDt)^][l-exp(-L2/4Dt)] [13]
Note that equation [13] reduces to equation [10] for large values
of L^/4Dt. Less than 1 per cent error will result from using equation
[4] if
exp(-L2/4Dt) < .01
or
t < L2/18.4 D
11
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Model IV
The solutions for the diffusion equation become more difficult
if the concentration at the soil surface is variable instead of being
maintained at zero. The rate of removal of pesticide in the air
layer above the soil may then become a limiting factor in the rate of
volatilization.
A model which accounts for a possible imcomplete depletion at
•the soil surface may be described as follows. A soil layer (0 < x < L)
has a uniform initial distribution of pesticide CQ with no flux allowed
through the lower boundary at x = L. The soil surface, x = 0, is in
contact with a volume, V, of well stirred air (uniform concentration
within the air) from which a volume per unit time and unit area, v, is
withdrawn and replaced by the same volume of air at zero concentration.
The airflow thus removes an amount of pesticide which is equal to the
flow velocity, v, times the concentration within the air, c . The
initial and boundary conditions are
c=C at t = 0, 0 < x < L
dc/dx = 0 at x = L
f=vC at t > 0, x = 0
3
This model is analogous to that of Carslaw and Jaeger [1959, p.
129, equation (11)] in which a slab of uniform initial temperature is
in contact with a mass per unit area of well-stirred fluid which loses
heat by radiation at a rate H times its temperature. The initial
temperature of the fluid is zero C. Their solution is
2 2
oo exp(-Da t)(h-ka ) cos[a(L-x)]
_ _ o n Y* H 5 D r i /. i
c - 2C Li j"? 2 [14]
n=l [L(h-ka ) +a (L-Hc)-rti]cosa L
n n n
where a are the roots of
n
atanfaL) = h - ka2 [15]
Carslaw and Jaeger define h = H/K where K is the thermal
conductivity. For our case K is replaced by the diffusion coefficient,
D, and H by the air flow velocity, v.
The concentration in the air, c , must be expressed in terms of
the concentration at the soil surface, c . This is done by the use of
the absorption isotherm. Adsorption isotherms for lindane and dieldrin
given in literature (Spencer and Cliath, 1970; Spencer, Cliath and
Farmer, 1969) suggests that we may, for a small concentration range
12
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of c consider the isotherm as
s.
ca = R cg [16]
Thus, h in equation [14] appears to be
h = Rv/D- [17]
(Note that both concentrations c and c in [16] must be expressed on
a total volume basis).
The term k, appearing in equation [14] is defined by Carslaw and
Jaeger as the ratio of the heat content of the fluid to the heat
content of the slab. The ratio in the heat flow model is equal to R
in equation [17] so that
k = R [18]
It can be shown that for all cases treated here
k « h or k a2 « h.
Equations [14] and [15] can therefore be simplified to
2
=> exp(-Dot t)h cos[a (L - x)]
c = 2C E - * - % - - [19]
n=l (Lh + a L + h) cos a L
n n
and
a tan(aL) = h [20]
The pesticide flux through the soil surface at x = 0 is then given by
2 2
oo exp(-Da t) h
f = 2DC £ —3 - f - [21]
n=l Lh + a L + h
Carslaw and Jaeger (1959, p. 491) give a table of the first six roots
13
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of the equation
O, tan a = M
[22]
which can be used instead of [20] when L = 1 or by scaling all
variables containing units of length in terms of L.
Model V
Model IV assumes the air above the soil to be sufficiently
stirred that its concentration may be taken to be constant throughout.
This may be due to turbulence as well as to a large diffusion coeffi-
cient within the air. However, Model IV does not take into account
any diffusive transfer of pesticide. When air velocity becomes zero,
the predicted flux through the soil surface becomes zero as well.
This model thus can only be appropriate if the convective flow due to
air movement is considerably greater than the flow due to a diffusion
gradient.
If there is a non-moving air layer in contact with the soil
surface, the following model may be adequate. The diffusion coefficient
of a pesticide in air is D1 and the thickness of the air layer is d.
As a first approximation we may neglect the capacity of the air layer.
For example, Spencer and Cliath (1970) report that at 30 C a soil with
10 ng/cm lindane is in equilibrium with a lindane vapor density in
air of .22 ng/cm . Then, if the concentration in soil at the soil
surface is c and the concentration in air at the soil surface is Re, we
have the flux through the air layer given by
f = D1 Rc/d
when the concentration at the upper edge of the air layer is zero.
The initial and boundary conditions are
c = C at t = 0, 0 < x < L
= 0 at x = L
f = (D'Rcs)/d at t > 0, x = 0
c = c at t > 0, x = 0.
s
These conditions are equivalent to the "radiation" boundary conditions
described by Carslaw and Jaeger (1959). We may than adopt the
solution given by these authors [p. 316, equation (24)] after substi-
tuting h in their equations by
14
-------
h = D'R/Dd [23]
The concentration of pesticide in soil is
o
2D'RC <=° exp(-Da t) cos[a (L-x)]
o v~* n n
c = — - LJ
J 9
n=l [L(D'R/Dd) + La + D'R/Dd]cosa L
n n
with a tan(aL) = D'R/Dd [25]
The flux through the soil surface at x = 0 is
2 2
oo exp(-D(X t) (D'R/Dd)
f = 2DC £ - S-s - y - [26]
°n=l L(D'R/Dd) + La + D'R/Dd
n
Note that equations [24], [25], and [26] are identical with equations
[19], [20], and [21], but instead of
h = Rv/D
we have defined h by equation [23] .
MODEL BASED ON DIFFUSION AND MASS FLOW OF SOIL- INCORPORATED PESTICIDES
As stated for the diffusion based model, movement to the soil
surface becomes the limiting factor in determining pesticide volatili-
zation when the concentration at the soil surface is depleted. The
objective of this portion of the project is to include both diffusion
and mass flow in a mathematical model for predicting volatilization
of soil-incorporated pesticides.
For vertical, isothermal flow in a homogeneous porous material,
the flow equation is
£h = L_ /K(h) 9h\ oK(h)
ah at sz ^ } dz) Oz
h is the pressure head of water in the porous material, measured in cm
of water, z is the depth below the surface and is positive in the up-
ward direction measured in cm, t is the time in days, 99(h)/c)h is the
specific water capacity, where 9(h) is the volumetric water content of
the porous media measured as a function of the pressure head measured
in cm? of water/cm3 of total space, K(h) is the water conductivity as a
15
-------
function of pressure head expressed in cm/day. The boundary and
initial conditions analyzed were as follows:
h = h exp(-0.29fc) at z = 0 and t > 0 [28]
until h = -1.456 x 10 cm = relative humidity = 0.35 at 23 C, then h
remained constant
-K(h) Oh/dz + 1) = 0 at z = -L and t > 0 [29]
h = -300(cm of water)-z or (dh/9z + 1) = 0 for
-L 0 [32]
C = 0,2 cm below z where C 2 0 and t > 0 [33]
C = CQ = Pb(l° V-g/8 soil) at 10 < z < 0 and t = 0 [34]
3
p, = average bulk density of soil (gm soil/cm total space)
Equations [27] and [31] were solved by numerical analysis. The
method of finite differencing the terms in equations [27], [29] and
131] and the method of solving the resulting equations, has been given
16
-------
in a number of papers by Whisler and Klute (1965), Klute, Whisler and
Scott (1965), and Whisler and Klute (1967). The method involves an
interative procedure in which estimates of h (z) were calculated from
previous estimates at each value. The initial conditions of the
problem provided the first estimates for the first time step. Final
estimates for each time step were the first estimates for the next time
step, etc. The final estimates for a particular time step were
determined by comparing each particular estimate with the previous
estimate; if the absolute values of all the differences were less than
some small selected value or if a given number of iterations was
exceeded, the final estimates were accepted and the solution proceeded
to the next part of the problem.
Data relating K, ~,^ ' , and 9 to h were obtained experimentally in
the laboratory by the method described by Weeks and Richards (1967).
Values of h(z,t) were calculated for each time step. From these values,
corresponding values of 9 (z,t) were obtained by linear interpolation
of the 9(h) data, and values of the hydraulic head [H(z,t)], were
H(z,t) = h(z,t) + z, were calculated. Hydraulic gradient values,
VH(z,t), were calculated by numerical differentiation, and the macro-
scopic water velocity (v(z,t)) was calculated from: v(z,t) = -K(h,z)
VH(z,t). Then the water velocity in the pores, V(9), was calculated
from: V(9) = v(z,t)/9(z,t).
Equation 31, with the initial and boundary conditions
['Equations 32, 33 and 34] was solved for C(z,t) by the same method as
in the case of equation 27. Experimental values of D (9) were taken
from the report of Shearer, et al. (1973). Their data were obtained
at 30 C and the individual Dvg(9) values were divided by 2 for use in
the present study since the relations between K, C, 9, and h were
obtained in this case in a room where temperature and relative humidity
were not controlled but remained close to 23 C and 35°/o respectively
during the time of the work. Earlier work of Ehlers et al. (1969)
indicates that D values for 23 C are approximately one-half those for
30 C for lindane and Gila silt loam. In solving equation [31], C1,
the liquid phase concentration was expressed in one of two ways at each
position (z) depending on whether adsorption or desorption occurred at
a particular position since the previous time. Values of the adsorbed
phase concentration [C(z) - C*(z)]m_i were compared with [C(z) - C'(z)]m
values, where m refers to the present time step. When desorption was
indicated,
[35]
Appreciation is expressed to F. D. Whisler, formerly Soil Scientist-
Physicist, U.S. Water Conservation Laboratory, Phoenix, Ariz., now
Professor of Soil Physics, Mississippi State University, Oxford, Miss.,
for the use of his unpublished programs which were modified when
necessary and were used in this study.
17
-------
where K is the constant relating adsorbed and solution phases with
units of cm liquid/g soil, S (z) is the maximum value of the adsorbed
phase concentration (mass of material/gin soil) obtained at a given z.
N is the ratio between the values of exponents of C1 (N desorption/N
adsorption) in the Freundlich equation. The use of Kn and S in
this way was taken from Van Genuchten et al. (1974). N was tatcen to be
0.4 also from Van Genuchten et al. (1974) as near the midrange of their
values for N adsorption/N desorption (2.3 to 3.1 for picloram). N
adsorption was taken to be 1 and K = 2.875 cnr liquid/g soil from
Huggenberger et al. (1972). In the case of adsorption,
C'(z)± = C(z)i/[l + pbK/9(z)] [36]
The subscript, i, in equations [35] and [36] refers to a value of the
variable calculated at the present iteration; i - 1, refers to a value
from the previous iteration.
The final estimates of C(z) were used to calculate C'(z) values
for each time step using equations [35] or [36], and corresponding
adsorbed phase concentration values, S(z), were calculated by differ-
ence. That is,
S(z) = C(z) - C'(z). [37]
Cumulative outflow of water or pesticide was calculated by
integrating numerically:
o o
Outflow = C T f (z,o)dz - f T f(z,t)dz [38]
— Li ~Li
where f(z,o) represents initial values and f(z,t) represents values
of the particular material at time t.
The rate of outflow of pesticide (at chosen times) was determined
by numerical differentiation of the values represented by the integrals
in equation [38] for the chosen times.
18
-------
EFFECT OF TEMPERATURE GRADIENT ON PESTICIDE MOVEMENT
Numerous studies have been performed separately on the diffusion
and mass flow of pesticides in soils. (Ehlers, et al.> 1969; Farmer
and Jensen, 1969; Oddson, Letey and Weeks, 1970; Huggenberger, Letey
and Farmer, 1972). However, in actual field situations these two
processes will occur simultaneously; and only by studying these two
processes together will we arrive at a solution which will allow us to
predict the actual movement in the environment. The objective of this
research was to create an experimental system, where both transport
processes occur simultaneously in order to demonstrate the relative
importance of diffusion and mass flow as transport processes for
pesticides under different experimental conditions. By applying a
temperature gradient on a soil column, which has a uniform initial
moisture and pesticide content, such a situation is achieved. The
vapor pressure of any substance increases with increasing temperature.
A vapor pressure gradient is therefore established from the warm to the
cold end of the soil column. Consequently, water and pesticide mole-
cules will move from the warm to the cold end of the column in the
vapor phase. This transfer of water vapor will then create a suction
gradient and cause liquid water and dissolve pesticide molecules to
move in the opposite direction by mass flow. In a closed system, as
studied here, the transfer of water vapor from the warm to the cold
end and the transfer of liquid water from the cold to the warm end are
equally at steady state. Transfer of pesticide molecules as discussed
above will also create a concentration gradient of the pesticides in
the nonvapor phase. Consequently, transfer of pesticide molecules will
also occur by nonvapor diffusion (Ehlers, et al., 1969).
At this point it is not possible to quantitatively predict the
experimental results by theoretical consideration. By considering
pertinent soil and pesticide properties an effort is made however, to
explain the experimental results quantatively.
19
-------
SECTION VI
EXPERIMENTAL DESIGN
The rates of volatilization of dieldrin from treated soil and of
dieldrin, lindane, trifluralin, DDT and DDE from treated quartz sand
were measured in a closed air-flow system by collecting volatilized
pesticide in vapor traps. Chemical designations of pesticides cited in
the text are given in Table 1. Concentrations of dieldrin on Gila silt
loam were 5, 10, 20 and 30 ng g soil (oven dry weight equivalent).
Concentration of pesticide on sand was 1000 p,g g sand. Separate
samples of sand were used for each pesticide. A modification of the
method for measuring volatilization of pesticide given by Farmer,
et al. (1972) was used. A brief outline along with modifications is
given here. The metal soil tray described by Farmer et al. (1972) was
replaced with a plexiglass tray having a soil surface area of 18.49 cm
and a soil depth of one cm. The soil and sand matrix were treated with
pesticides in hexane, the hexane allowed to evaporate and water added
to the matrix to the desired water content. The treated soil or sand
was placed in the plexiglass tray and the tray introduced into the
vapor trapping apparatus. When it was desired to maintain a constant
soil water content during the volatilization experiment, the relative
humidity of the air was kept near 10070 by passing the incoming air
through fritted glass bubblers in water traps. Relative humidities
were checked with a hygrometer built into the air stream. Air flow
rates were controlled with needle valves installed in a manifold and
measured by a soap bubble flow-meter at the end of the trapping system.
The entire vapor trapping apparatus was located inside a constant
temperature incubator and temperature controlled to ±0.5 C. The soil
was Gila silt loam containing 0.58% organic matter and 17.6% clay, pre-
dominantly montmorillonite. The quartz sand was acid-washed with
dilute HC1 and washed with distilled water to pH 7. The pesticide was
extracted from the trapping medium, either ethylene glycol or hexylene
glycol, by watering into hexane. An aliquot was then analyzed by
liquid scintillation analysis or gas-liquid chromatography. For gas-
liquid chromatography a one meter by 3 mm stainless steel column was
used with 2.5% DC-200 plus 2.5% QF-1 on Chrom W80-100 mesh support,
column temperature of 200 C for dieldrin, DDE, and DDT and 183 C for
lindane, and a flow rate of 50 ml Nn per minute.
EFFECT OF TEMPERATURE GRADIENT ON PESTICIDE MOVEMENT
The pesticides used in this study were lindane, diuron, and
atrazine. ^C-labeled diuron and atrazine were used in this study.
The purity of lindane was checked by gas liquid chromatography.
The development of degradation products was insignificant over the
period of time the compound was used. The purity of l^C-labeled and
unlabeled diuron and atrazine was checked by thin layer chromatography
using silica gel GF 254 containing a fluorescent indicator. The sol-
vent systems for diuron were distilled water and a 1:1 (v/v) mixture
20
-------
Table 1. CHEMICAL DESIGNATIONS OF PESTICIDES
CITED IN TEXT.
atrazine
DDE
DDT
dieldrin
diuron
lindane
trifluralin
2-chloro-4-(ethylamino)-6-(isopropylamino)-
s-triazine
1,l-dichloro-2,2,2-bis(£-chlorophenyl)
ethylene
1,1,l-trichloro-2,2-bis(£-chlorophenyl)
ethane
l,2,3,4,10,10-hexachloro-6,7-epoxy-l,4,
4a,5,6,7,8,8a-oxtohydro-1,4-endo-exo-5,8-
dimethanonaphthalene
3-(3,4-dichlorophenyl)-1,1-dimethylurea
y-1,2,3,4,5,6-hexachlorocyclohexane
a >a ,a-trifluoro-2,6-dinitro-N,N-dipropyl-
£-toluidine
21
-------
of distilled water and acetone. The solvent systems for atrazine were
a mixture of petroleum ether, ethylacetate, and acetic acid 30:50:1
(v/v) and a mixture of hexane and acetone 150:45 (v/v). The plates
were examined under UV light. Only one spot could be detected in all
replications. In the trials using ^C-labeled materials the activity
of this spot was determined by liquid scintillation and accounted for
more than 95% of the total activity applied. It was concluded that
all the materials were pure and therefore used without further purifi-
cation.
The soil materials used were the
-------
91.4 cm (3 ft.) stainless steel column was packed with 2.5% DC 200
and 2.570 QF-1 on chromosorb W 80/100 mesh size. Detection was by
electron capture. The column temperature was 192 C, the flow rate
50 ml/min and the resulting retention time for lindane 1.5 rain. The
l^C-vactivity of soil samples containing diuron and atrazine was deter-
mined by liquid scintillation. An aliquot of soil of individual
sections was placed directly into counting vials. Twenty milliliters
of a scintillation solution consisting of 10.4 g of PPO and 166 g
naphthalene dissolved in a solution of 800 ml of xylene, 800 ml of
dioxane, and 473 ml of absolute ethanol were added. To avoid a
special procedure of extraction the C-activity was determined in
the presence of soil. This method has been reported and discussed
in detail by Ehlers et al. (1969). Pesticide and Cl concentrations
are reported as microgram per gram of oven-dry soil.
23
-------
SECTION VII
RESULTS AND DISCUSSION
SURFACE APPLIED PESTICIDES
The volatilization of surface applied pesticides was simulated
using pesticide treated sand. At the high rate of pesticide used,
1000 |j,g per gram of sand, the sand was acting only as a carrier and
exerted essentially no adsorptive forces on the pesticide.
The volatilization of trifluralin, lindane, p,p'-DDE and p,p'-DDT
from treated sand are shown in Table 2. Reasonable agreement was
obtained between the volatilization rate and the saturation vapor con-
centrations of the pesticides as determined by the relationship shown
in equation [4] . In this case, the pesticide flux, f , is used in place
of the rate of diffusion, q.
f = K (S.V.C. )M~ [39]
The value of K ranged from 119 to 133.
The rate of pesticide volatilization is also dependent on the
rate of air movement across the treated surface. In a separate study
the air flow rate was varied between 120 and 960 ml min . In this
experiment the air space above the treated sand in the volatilization
chamber was 214 ml. In the previous study (Table 2) the air space
above the treated surface was 24.4 ml. Increasing the air space
reduces the air flow velocity across the treated surface at any given
air flow rate. The results of this experiment are shown in Table 3 .
As in the previous study there is good agreement between K. and S.V.C.
at any given flow rate. However, Ky and therefore the pesticide flux
increased linearly with increasing flow rate. The slope of the line
was 0.11 with an intercept K = 31.5 and a correlation coefficient of
0.96.
An additional comparison can be made from the data in Tables 2
and 3. There was an average increase of 707» in the K^ values in
Table 3 when the air flow rate was doubled from 480 to 960 ml min .
In order to obtain a similar increase in K in Table 2, the air flow
velocity was increased 7.5 times (2.82 cm sec"-*- vrs. 0.374 cm sec"
at 480 ml min" air flow rate).
In a separate experiment the water flux from the surface of Gila
silt loam was determined in the same manner as the data in Table 3.
Water flux was determined by weight loss of the soil dishes. The S.V.C.
of water at 30 C is 31.3 mg/liter. Water flux was 4.80 x 105 and
7.00 x 10^ ^.g cm" ^ day"-'- at 480 and 960 ml/min, respectively. This
24
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Table 2. PESTICIDE VOLATILIZATION FROM TREATED SAND.
SAND TREATED AT THE RATE OF 1000 u.g/g.
AIR FLOW WAS 480 ml min"1 (2.82 cm sec"1)
AT 30 C. EACH VALUE IS AN AVERAGE OF
DUPLICATE DETERMINATIONS.
Pesticide
Trifluralin
Lindane
Dieldrin
p,p'-DDE
p,p'-DDT
s.v.c.i/
Hg/1
4.29
1.97
0.202
0.109
0.0136
Flux
o
)j,g/cm /day
31.0
14.3
1.23
0.810
0.0924
1*1
V
132
124
119
133
128
— Calculated from vapor pressure with the equation: p = S.V.C.
(RT/M). Values for the saturation vapor pressure were taken
from Spencer and Cliath (1974), Spencer and Cliath (1972),
Spencer and Cliath (1970), Spencer and Cliath (1969).
21
— A proportionality factor calculated from the equation
f =
25
-------
Table 3. EFFECT OF AIR FLOW RATE ON PESTICIDE
VOLATILIZATION FROM TREATED SAND AT
30 C. SAND TREATED AT RATE OF
1000 (ig/g- EACH VALUE IS AN AVERAGE
OF DUPLICATE DETERMINATIONS.
Pesticide
Lindane
Dieldrin
p,p'-DDE
p,p'-DDT
Lindane
Dieldrin
p,p'-DDE
p,p'-DDT
Lindane
Dieldrin
p,p'-DDE
p,p'-DDT
Air*/
flow rate
ml min"
120
120
120
120
480
480
480
480
960
960
960
960
Flux
T -I
g,g cm day x
4.96
0.470
0.303
0.0362
9.19
0.990
0.510
0.0638
14.2
1.50
1.07
0.105
K
V
42.9
45.5
49.7
50.1
79.4
95.7
83.6
88.3
123
145
175
145
— In the volatilization chamber used in this experiment, air flow
rates of 120, 480 and 960 ml min"-'- are equal to air flow veloci-
ties of 0.093, 0.374 and 0.748 cm sec"1, respectively.
26
-------
yielded V^ values of 61.5 and 89.7 for water flux at 480 and 960
ml/min air flow rate, respectively. These K values for water flux
agree reasonably well with those determined for the pesticides. The
agreement is especially good considering the differences in the S.V.C.
and in the molecular weights of water and the pesticides.
These results indicate that pesticide volatilization of surface-
applied pesticides can be adequately described by the relationship
between the saturation vapor concentration of a pesticide and the con-
stant Ky. The saturation vapor concentration or the vapor pressure
of a pesticide is a readily determined laboratory value. The constant,
KV, would be evaluated through field calibration and testing. The
results reported here show that a K calibrated for one compound or
pesticide would be useful in predicting volatilization of other
pesticides.
Pesticide treated sand simulates pesticide applications allowed
to remain on a soil surface. The sand acts as an inert carrier for the
pesticide exerting little adsorptive force on the pesticide. Inter-
action between a pesticide and soil results in adsorptive forces which
may reduce the tendency for a pesticide to vaporize. Table 4 shows the
influence of pesticide concentrations in Gila silt loam on volatiliza-
tion rates. Pesticide volatilization increases with increasing concen-
tration. This is in agreement with the results of Spencer et al. (1969)
They have reported vapor phase sorption isotherms for dieldrin sorption
by Gila silt loam. The equilibrium or saturation vapor concentration
increased with increasing soil pesticide concentration reaching a
maximum vapor density at approximately 30 u-g/g soil pesticide concen-
tration. Values of Kv have been calculated for dieldrin flux from
Gila silt loam using the S.V.C. given by Spencer et al. for the appro-
priate dieldrin soil concentrations. Results are presented in Table 4.
The pesticide flux and the K^. are seen to compare reasonably well with
the values given in Table 3 for dieldrin flux at 480 ml min . However,
Kv increases at lower soil concentrations from 89.8 at 30 u-g/g to 173
at 5 u.g/g. This is apparently due to the decrease in vapor concentra-
tion in the air stream at 5 p,g/g resulting in a greater vapor concen-
tration gradient. This is similar to the effect of increased air flow
rate in Table 3 resulting a greater rate of volatilization. The air
flow rates used in these experiments are extremely low compared to wind
speeds which would normally be(encountered in field situations. Under
field conditions with much greater wind speeds vapor concentration
differences between different soil pesticide concentrations would be
much less and the K^ values thus determined would doubtlessly be in
better agreement.
Assuming the Ky determined for a soil dieldrin concentration of
5 M-g/g is more representative of field conditions with higher wind
velocities, than the fluxes measured from pesticide treated sand at
480 ml/min flow rate should be approximately doubled. Multiplying flux
in u.g/cm2/day by 0.1 gives flux values in kg/ka/day. If a one kg/ha
27
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Table 4. INITIAL DIELDRIN VOLATILIZATION RATES
FROM TREATED GILA SILT LOAM AT 480 ml min"1
(0.374 cm sec'1), 30 C, 10% GRAVIMETRIC
SOIL WATER CONTENT AND 100% RELATIVE
HUMIDITY.
Soil
Concentr a tion
M-g/g
5
10
30
S.V.C.-
M-g/1
0.030
0.073
0.190
Flux
|jLg/cm2/day
0.265
0.545
0.870
K
-V'.
173
146
89.8
— Saturation vapor concentrations obtained from Spencer et al.
(1969)
28
-------
application of dieldrin were surface applied and left unincorporated,
10-20% could be lost in one day due to volatilization alone.
DIFFUSION BASED MODEL FOR SOIL INCORPORATED PESTICIDES
A comparison will be made between calculated results from our
equations and results of published volatilization experiments. All
these experiments, using lindane and dieldrin, were designed to measure
the volatilization of pesticides from the surface of a soil column by
leading an air stream over the surface. To prevent net loss of soil
water and thus prevent transport of pesticide by mass flow to the soil
surface, the air was brought to 100% relative humidity. The amount of
pesticide carried by the air stream was measured for distinct periods
of time.
The rate of volatilization of dieldrin measured by Spencer and
Cliath (1973),is presented in Fig. 1. The soil was Gila silt loam
at a bulk density of 1.4 g/crsr. The initial concentration, CQ, in the
soil was 1.4 x 10^ ng/cm , (10 ppm) . Soil water content was maintained
at 23% (w/w). The temperature was kept at 30 C. Igue (1969) gives an
apparent diffusion coefficient of D = 2.3 mm^/week for dieldrin under
these conditions. Air flow velocity was maintained at 2.15 cm sec~ •
The depth of the column was 11 cm. According to the evaluations given
for Model II, we may assume the column to be infinite in length for at
least 2 x 10^ days after the start of the experiment. The solid curve in
Fig. 1 was calculated according to equation [10]. The good agreement
between measured and calculated values indicate that zero concentration
at the soil surface is, under these conditions, a reasonable assumption.
For very short times after the start of volatilization, the boundary
conditions are violated in that the pesticide concentration at the soil
surface is greater than zero. This may lead to some over estimation of
the initial volatility rates. The low initial measured flux as compared
to the calculated flux may be due to the experimental technique (e.g.
losses by adsorption on walls).
Figure 2 represents data taken from a volatilization experiment
carried out with lindane by Farmer et al. (1972). Parameters for this
experiment were: Gila silt loam, soil water content 107« (w/w), bulk
density 0.75 g/cm^, temperature' 30 C, initial concentration 7.5 x 10^
ng/cm^ (10 ppm), and depth of the column 0.5 cm. With the diffusion
coefficient for lindane under these conditions equal to D = 30 mm2/week
(taken from Ehlers et al., 1969), we calculate that after 22 hours from
the start of the experiment the concentration at the bottom of the
column decreases by more than 17o. This accounts for the considerable
difference between the two solid curves in Fig. 2, calculated from
Model I and Model II.
Figure 2 also shows a curve calculated from Model IV. The air
velocity across the surface of the column was v = 0.433 cm sec" -
R was calculated from the adsorption isotherms given by Spencer and
Cliath (1970), to be R = 3 x 10~5. Therefore h = R v/D becomes equal
29
-------
1,000
10 15
TIME (days)
20
30
35
Fig. 1. Comparison between calculated values (solid curve) from
Model II and experimental values (horizontal lines) for
dieldrin flux. The experimental values were taken from
Spencer and Cliath (1973). The length of the horizontal
lines indicate, the time over which the experimental values
were taken.
30
-------
234
TIME (days)
Fig. 2. Comparison between calculated and experimental values for
lindane flux from treated Gila silt loam. Experimental
data are from Farmer et al. (1972).
31
-------
to 26.1 cm"1 compared to k = R = 3 x 10'5, the equations [19], [20],
and [21] being applicable. The agreement between values calculated from
Model IV and the measured values is quite good at the longer times and
indicates that the flow velocity was not sufficient to create a zero
concentration at the surface.
Volatilization experiments were conducted with dieldrin by
Farmer et al. (1972), in which different air velocities were used. The
soil was a Gila silt loam, soil water content 107<> (w/w), bulk density
0.75 g/cm , initial dieldrin concentration was 7.5 x 10-^ ng/cm^
(10 ppm), depth of the column was 0.5 cm, and temperature was kept at
20 C. The diffusion coefficient of 1.5 mm^/week was derived from
Igue (1969), assuming a reduction of 50% compared to the value given
by this author to account for the lower temperature (20 C instead of
30 C). A similar reduction with decreasing temperature was found by
Ehlers et al. (1969) for lindane. R was taken from Spencer, Cliath and
Farmer (1969) to be 2.4 x 10~6. With air velocities of 0.433 and 0.108
cm sec , h became 39.46 and 9.86 cm"1, respectively. Again, equations
[19], [20], and [21] apply to this situation to allow calculation of
pesticide flux.
Figure 3 shows the measured rates of dieldrin volatilization at
two different air velocities together with the curves calculated from
Model IV as well as a curve calculated for Model II. It can be seen,
that under the conditions given in the experiment, at the higher air
flow velocity the boundary condition "zero concentration at the soil
surface" is appropriate. This is not true for the lower air flow
velocity, where Model IV better accounts for the lower volatilization
rates.
Note that the calculated curves for Model II and Model IV at the
higher air velocity are very similar. Model IV predicts a lower flux
during the initial time period than Model II» This is reasonable
because initially there is pesticide at the soil surface and a higher
air velocity would be necessary to maintain a concentration equal to
zero at the surface which is required by Model II. As time progresses
and volatilization has occurred, the surface is depleted of pesticide
and the surface concentration can be kept at zero with a lower air
velocity. The low fluxes measured, compared to the calculated, in
the beginning of the experiment are probably due in part to losses by
adsorption on walls.
From the equations presented for Model I and II, it can be seen
that for a given initial concentration and depth of the soil layer,
the flux at any time depends only on the apparent diffusion coefficient.
Since the apparent diffusion coefficient depends on various parameters
including bulk density, water content, concentration, temperature, and
adsorption (Ehlers et al., 1969; Farmer and Jensen, 1970), all equations
presented can only be used if during the time of observation, D remains
constant. Ehlers et al., (1969) showed for lindane that this assump-
tion holds true up to concentrations of about 20 ppm. This agreement
32
-------
300
200
>s
J
I
o>
c
100
Q 50
UJ
0 40
30
-MODEL4,v= 0,433 cm sec"1
•MODEL 2
MODEL 4
v=O.I08 cm sec1
_L
6 8
TIME (days)
10
12
14
Fig. 3. Comparison of calculated and experimental values for
dieldrin volatilization flux from uniformally treated
Gila silt loam for air moving over the soil surface at
two velocities. Experimental data from Farmer et al.
(1972).
33
-------
between measured and calculated pesticide fluxes, if an appropriate
model is chosen, indicates that constancy for the conditions met in
the experiments may also be assumed for the dieldrin diffuse coefficient.
Models I, II, arid IV prove to be valid for describing volatiliza-
tion losses from experiments carried out in the laboratory with appro-
priate boundary conditions. Prediction of volatilization rates of
pesticides under field conditions with these or similar models become
more difficult, mainly because the boundary conditions are not as well
defined as in a laboratory experiment. Yet, the models are valuable at
leasfc in making reasonable estimates of pesticide losses of diffusion.
Let us take, for example, a pesticide incorporated in a soil
surface layer. If the soil surface is in contact with a moving layer
of air, and if diffusion to the surface is the only transport mechanism
for pesticide in the soil, then Model IV should apply. The wind veloc-
ity can be measured as required for the model. One difficulty is that
the model assumes that the air increment passing over each unit area of
surface is initially devoid of pesticide. When a large land area is
treated with pesticide, the wind will become enriched with pesticide as
it passes over the field.
The results presented in Figures 1 and 3 indicate that only very
low wind velocities (less than about 0.04 mi/hr"-*- or 0.016 km/hr) are
required to keep the pesticide concentration at zero at the soil surface.
Thus it would appear that Models I, II, or III could be used with
considerable confidence if there is much air movement.
The situation is different if we have a non-moving air layer above
the surface, for example where the air movement is restricted by a
standing crop. Under these conditions Model V applies.
Figure 4 gives some lindane flux curves calculated for different
values of h. The diffusion coefficient D1 for lindane in air is not
known, but may be derived [Ehlers, et al. (1969), p. 502, equation
(9)] as being 10 cm /day. The initial concentration was assumed to be
10^ ng/cm^, the diffusion coefficient for lindane in the soil 20 mm /
week, R as used above was 3 x 10"^. The depth of the soil layer treated
with pesticide was assumed to be 10 cm. Equation [23] then gives the
values of h which correspond with different values of d, the thickness
of the air layer.
From Figure 4 it can be seen that a non-moving air layer may
restrict the rate of volatilization considerably. Finally it may be
mentioned that since we have under most conditions water movement in
the soil profile, the models presented above predict volatilization
rates from a soil surface better for moderately to strongly adsorbed
pesticides of low mobility with moving water.
34
-------
5,000
2000
ipoo
0?
500
200
100
50
20
10
•MODEL I OR MODELS (h=oo,d = 0)
MODELS (h = IOcm',d = 0.5cm)
-MODEL 5 (h = 5 cm ',d = 1.0 cm)
-MODELS (h=0.5cm!
d=IOcm)
-MODELS (h=0.05cm',d=IOOcm)
12 5 10 20 50 100 200 500 IOOO
TIME (days)
Figure I*. Calculated values for the influence of depth of
non-moving air layer on lindane volatility flux from
uniformally treated Gila silt loam.
35
-------
MODEL BASED ON DIFFUSION AND MASS FLOW OF SOIL-INCORPORATED PESTICIDES
The combined diffusion and mass flow model for predicting volatili-
zation from soil-incorporated pesticides was simulated using lindane in
a column of Gila silt loam. The soil column used for the simulation was
assumed to be 30 cm long with the top 10 cm uniformally treated with
lindane at 10 |J.g/g (13.1 g/cc). This soil and pesticide were chosen for
the simulation because of the information available on the diffusion,
mass flow, adsorption, and volatilization of lindane in Gila silt loam.
The data on column length, soil water content and soil bulk density
assumed for the simulation were chosen to match the experimental condi-
tions used for determining water conductivity in Gila silt loam. Soil
water content was initially nearly uniform ranging from 0.382 g/cc at
the top of the column to 0.392 g/cc at the 30 cm depth. Soil bulk
density was 1.31 g/cc.
Sample input data for lindane diffusion coefficients are presented
in Table 5. The data for lindane diffusion coefficients were taken
from Shearer et al. (1973). The data were corrected to a temperature
of 23 C by dividing the coefficients at 30 C by two. This correction
factor was based on the temperature dependency of lindane diffusion
developed by Ehlers et al. (1969).
The input data for water content, hydraulic head and soil water
conductivity are presented in Table 6. This data was developed for
water evaporation from Gila silt loam as a part of this project.
Adsorption data for lindane on Gila silt loam was taken from
Huggenberger, Letey and Farmer, 1972.
The simulation was run for a one hundred day period assuming no
rainfall events. A sample output data for 2.45 days after the start of
volatilization is shown in Table 7. The pesticide flux through the top
of the soil column as a function of time is shown in Table 8. For the
experimental conditions chosen here the units of pesticide mass will
be ng and the units of lindane flux will be |j,g cnT^ day~^. From the
data in Table 8, volatilization is seen to drop rapidly from an initial
value of 2.7 ^g cm"^ to less than 0.5 ^g cm day"! in the first 3.5
days. The rate of volatilization levels off after the first few days.
Between 31 and 35 days the flux has dropped to 0.012 |o,g cm day" .
Comparison of these rates of volatilization with those of Spencer and
Cliath (1973) shows reasonable agreement between both the magnitudes
of volatilization rates and the changes in rates with time. The
conditions of Spencer and Cliath (1973) are different from the present
in that water was being supplied continuously to the bottom of the soil
column. In the present simulation there was no water movement across
the 30 cm soil depth. However, the data of Spencer and Cliath (1973)
is for lindane volatilization from Gila silt loam with both diffusion
and mass flow operating. Their's is the only such data presently
available under controlled conditions. The data of Spencer and Cliath
(1973) does provide partial confirmation of the predictive model
36
-------
Table 5. SAMPUS INPUT DATA. EXPERIMENTAL VALUES
OF APPARENT DIFFUSION COEFFICIENTS (Dvs)
WITH CORRESPONDING WATER CONTENT VALUES
(9). DATA TAKEN FOR THE PESTICIDE LINDANE
(SHEARER ET AL., 1973).
2 Dvs
cm day"1 x 10^
0.0
0.0
0.0
0.0
1.57
1.36
1.25
1.18
0.857
0.772
0.772
0.772
9
cm3 cm"3 x 102
0.0
1.96
2.62
3.67
5.90
11.8
19.6
26.2
33.4
38.0
44.5
51.0
37
-------
Table 6. SAMPLE INPUT DATA. SOIL WATER CONTENT, WATER CONDUCTIVITY, AND WATER
CAPACITY AS A FUNCTION OF THE PRESSURE HEAD.
ITER. NO. 3 NO. OF POINTS NOT PASSING TEST
30 TIME STEP TIME 2.4700 00 DAY. DELTA TIME 1.1520-01 DAY.
00
TIME IS 5.9290 01 HOURS OR 2.470D 00 DAYS FLUX OUT 3.406D-15 CM/DAY. CUMULATIVE OUTFLOW FROM FLUX 1.990D 00 CM
CUMULATIVE OUTFLOW FROM THETA PROFILE 1.8740 00 CM NO. OF-TIMES OVERITERATEO 0 FLUX BY CUMULATIVE OIFF. 8.2440-01
Q/Q1NF. BY INTEGRAL 1.5960-01 Q/QINF. BY DIFFERENCE 1.694D-01 AVE. K AT SURFACE 2.9360-02 FLUX AT SURFACE 8.431D-01
AMOUNT IN PROFILE AT THIS TIME 9.870U 00 CM FLUID APPLIED AT Z=0 TO THIS TIME 0.0 CM NET GAIN OR LOSS BY FLUX 0.0
CM
I
•2.90D 01
•2.700 01
•2.500 01
2.30D 01
•2.100 01
1.90D 01
•1.700 01
•1.50D 01
Z
CM
1.2000 01
HOOD 01
l.OOOD 01
9.000D 00
8.0000 00
7.000D 00
6.0000 00
5.0000 00
4.0000 00
3.0000 00
•2. GOOD 00
l.OOOD 00
0.0
PRESSURE HEAD HATER CONTENT
-3.7300 02
-3. 7580 02
-3.7940 02
-3.8410 02
-3.8990 02
-3.9700 02
-4.0570 02
-4.1600 02
C
0.0
0.0
5.5960-01
7.3980-01
7.6380-01
7. 5910-01
7.510D-01
7.4170-01
7.329D-01
7.2350-01
6. 8580-01
8. 3910-01
0.0
3.5010-01
3.4900-01
3.4740-01
3.4550-01
3.4300-01
3.4000-01
3.370D-01
3.3400-01
S
MASS/GM SOIL
0.0
0.0
7.9190 00
8.8990 00
9.044D 00
9. 0630 00
9.0650 00
9.0670 00
9.0660 00
9.0890 00
8.931D 00
1.0900 01
0.0
HYO. HEAD
-4.0200 02
-4.0280 02
-4.0440 02
-4.0710 02
-4.1090 02
-4.1600 02
-4.2270 02
-4.3100 02
C + S
0.0
0.0
8.4780 00
9.6330 00
9.8080 00
9.6220 00
9.8160 00
9.8090 00
9.7990 00
9. 8120 00
9.6170 00
1.1740 01
o.a
PORE VEL.
5.794D-02
1. 9740-01
3.4390-01
4.9260-01
6.4470-01
7.9920-01
9.5140-01
1.1120 00
CL
MASS/CCILIO)
0.0
0.0
2.2650 00
3.019D 00
3.1450 00
3.1590 00
3.1620 00
3.1600 00
3.1600 00
3.1610 00
3.0430 00
3.7920 00
0.0
Z
-1.400 01
-1.200 01
-1. 000 01
-8.000 00
-6.000 00
-4.000 00
-2.000 00
0.0
C
0.0
0.0
7.330D-01
9.6920-01
1.0010 00
9.9440-01
9. 8380-01
9.7160-01
9.6010-01
9.4780-01
8.9840-01
1.0990 00
0.0
PRESSURE HEAD
-4.2190 02
-4.3510 02
-4.5070 02
-4.6960 02
-4.9320 02
-5.236D 02
-5.6220 02
-6.1480 02
S
MASS/CC(TOTAL)
0.0
0.0
1.0370 01
1.1660 01
1.1850 01
1.1870 01
1.1880 01
1.1880 01
1.1880 01
1.1910 01
1.170D 01
1.4280 01
0.0
WATER CONTENT HYO. HEAD
3.3220-01
3.2830-01
3. 2370-01
3.1810-01
3. 1110-01
3.0380-01
2.9520-01
2.8420-01
C + S
0.0
0.0
1.1110 01
1.2630 01
1.2850 01
1.287D 01
1.2860 01
1.2850 01
1.2840 01
1.2850 01
1.2600 01
1.538D 01
0.0
-4.359D 02
-4.4710 02
-4.6070 02
-4. 7760 02
-4.9920 02
-5.276D 02
-5.6420 02
-6.148D 02
SM
MASS/GM
0.0
0.0
9.0660 00
9.0690 00
9.0610 00
9.063D 00
9. 0650 00
9.0680 00
9.0690 00
9.089D 00
9.0780 00
1.0900 01
0.0
PORE VEL.
1.1960 00
1.3700 00
1.5530 00
1.7530 00
1.9540 00
2.1940 00
2.4750 00
2.9660 00
DVS
CM2/OAY
8.8240-03
8. 9230-03
9.0310-03
9.1490-03
9.2800-03
9. 4270-03
9.5930-03
9.757D-03
9.9170-03
1.0100-02
1.0300-02
1.0540-C2
1.0790-02
TRANSFER OF MATERIAL-MASS/SO CM/DAY
I
1.200 01
1.100 01
l.OOD 01
9.000 00
•8.000 00
7.001) 00
6.000 00
DIFFUSION
-1.7140-02
-3.2030-02
-3. 4150-02
-2.4790-02
-3. 4250-03
-4.2470-04
3.9720-05
BY WATER
0.0
0.0
1.1380 00
1.6000 00
1.7540 00
1.8460 00
1.922D 00
TOTAL
-1.7140-02
-3.2030-02
1.104D 00
1.5750 00
1.7510 00
1.8460 00
1.9220 00
CONC. GRAO
2.2210 00
3.6360 00
3.8323 00
2. 74 70 00
3.7460-01
4.5760-02
-4.2120-03
Z
-6.000 00
-5.000 00
-4.000 00
-3.000 00
-2.000 00
-1.000 00
0.0
DIFFUSION
3. 9720-05
4.5610-05
5.0570-04
-4.7940-03
-1.2580-02
-2.069D-02
2.5880-01
8Y WATER
1.9220 00
2.0030 00
2.1060 00
2. 2130 00
2.2230 00
2.8050 00
0.0
TOTAL
1.922D 00
2.0030 00
2.1070 00
2.2080 00
2.2110 00
2.7850 00
2. 5880-01
CONC. GRAO
-4.2120-03
-4. 7530-03
-5.1800-02
4.8260-01
1.2420 00
2.0020 OC
-2.4460 01
MASS/CM2 SOIL TRANSFERREO FROM SOLUTION PHASE 2.6950 00
MASS/CM2 SOIL TRANSFERRED FROM ADSORBED PHASE 1.6220 00
TOTAL MASS/CM2 SOIL VOLATILIZED 4.5170 00 ITER. NO. 3 NO. OF POINTS NOT PASSING TEST 0
FRACTION VOLATILIZED 3.4480-02 AMOUNT DOWNWARD PAST Z = -10 CM. 6.3450-03
MASS/CM2 SOIL IN SOLUTION 9.4420 00 MASS/CM2. .SOIL. ^D.SQRBEO 1.1700 02 TOTAL MASS/CM2 SOIL 1.265D 02
-------
Table 7. SAMPLE OUTPUT DATA. WATER RELATIONS AND PESTICIDE DISTRIBUTION
IN SOIL COLUMN 2.1 DAYS AFTER INITIATION OF PESTICIDE VOLATILI-
ZATION.
V£>
HEAD
CM
5.400D
2.00CD
•4.000D
•6.000D
•a. oooo
•l.OOOU
•3.000D
•7.5000
•1.500D
•2.500D
•3.500D
•5.0000
•3.1620
01
02
02
02
02
03
03
03
04
04
04
04
05
THETA
CM/CM
4.9000-01
4. 5010-01
3. 38713-01
2.8680-01
2.5490-01
2.3260-01
1.584D-01
1.1790-01
9.4320-02
8.0020-02
7.1800-02
6.400D-02
4. 0400-02
CONDUCTIVITY
CM /DAY
3.7500 00
6. 1210-01
8.6150-02
2.7360-02
1.2120-02
6. 4490-03
2.8820-04
2.1570-05
3.036D-06
7. 1520-07
2.762D-07
1.0620-07
9.1310-08
CAPACITY
2
4
3
1
1
9
1
5
2
1
6
4
2
I/CM
.9000-04
.9000-04
.4720-04
.9600-04
.3060-04
.5390-05
.6700-05
.0620-06
.0250-06
.0310-06
.6060-07
.1220-07
.6240-08
HEAD
CM
-1.0000
-3.0000
-5.0000
-7.0000
-9.0000
-2.000D
-5.0000
-1.0000
-2.0000
-3.0000
-4.0000
-1.0000
-1.4650
02
02
02
02
02
03
03
04
04
04
04
05
06
THETA
CM/CM
4.7500-01
3.8110-01
3.0910-01
2.6930-01
2.4290-01
I. 8050-01
1.3440-01
1.0750-01
8.5980-02
7.5450-02
6.8780-02
5.1210-02
2.9500-02
CONDUCTIVITY
CM/DAY
1.2150 00
1.9440-01
4.5820-02
1.7690-02
8.6900-03
9.0750-04
6.7930-05
9.5600-06
1.3450-06
4.2720-07
1.8930-07
1.0540-07
4.3280-08
CAPACITY
2.
5.
2.
1.
1.
2.
8.
3.
1.
8.
5.
1.
4.
1/CK
9000-04
2090-04
5350-04
5770-04
1070-04
9050-05
6520-06
4610-06
384D-06
3990-07
5370-07
3500-07
1360-09
-------
•p-
o
Table 8. SAMPLE OUTPUT DATA. PESTICIDE VOLATILIZATION FLUX THROUGH THE
TOP OF THE SOIL COLUMN AS A FUNCTION OF TIME AFTER INITIATION
OF VOLATILIZATION.
TIMEIDAYS)
0.0
3.6220 00
9.0370 00
2.5630 01
MASS/SO
1.3100
1.2600
1.2240
1.1810
CM
02
02
02
02
MASS/SO CM/DAY
-2.676D 00 '
-4.6270-01
-3. 8530-01
-2.0510-01
TIME(OAYS)
1.3180 00
4.7740 00
1.3180 01
3.1260 01
HASS/SQ
1.2660
1.2530
1.2240
1.1730
CM
02
02
02
02
MASS/SO CM/DAY
-1.7650 00
-6.1510-01
-2.8890-01
-7.8440-02
TIME(OAYS)
2.4700 00
6.7330 00
2.0100 01
3.5000 01
HASS/SQ
1.2650
1.238D
1.1940
1.171D
CM
02
02
02
02
MASS/SO CM/DAY
-9.6950-01
-6.1490-01
-2.5600-01
5.5530-03
-------
developed in this project.
This model has been run several times varying the values for the
diffusion coefficient and the coefficient for the adsorption of the
pesticide by the soil. This would simulate the volatilization of
pesticides from various pesticide-soil combinations. As expected the
rates of pesticide volatilization decreased when either the diffusion
coefficient decreased or the adsorption coefficient increased.
Field testing of this model is needed to test its validity and to
determine under what conditions it may or may not be applicable.
However, several recommendations can be suggested as to when this model
may be applicable or when other models discussed in this text should be
tried as an alternative.
The combined diffusion and mass flow model would be expected to be
applicable under conditions when wind speed and turbulence are suffi-
cient to maintain nearly zero pesticide vapor concentration in the air
at the soil surface. As discussed with the diffusion based model, the
results presented in Figures 1 and 3 indicate only very low wind
velocities (less than about 0.016 km/hr) are required to keep dieldrin
concentration essentially zero at the soil surface.
The combined diffusion and mass flow model as presented here would
not be expected to apply with a non-moving air layer above the soil as,
for example, when air movement is restricted by a crop cover. Additional
development of the model would require replacing the boundary condition
of zero concentration at the soil surface with one similar to that
developed for Model V of the diffusion based model to be applicable with
a crop cover present. Figure 4 shows that the layer of non-moving air
does not have to be very thick before having a considerable effect on
the volatilization rate.
Another situation not accounted for in the combined model in its
present state is the redistribution of a pesticide in the soil which may
take place after a rainfall-event. The model begins with initially
uniform soil concentration. This is probably reasonable for a compound
that is well incorporated at the time of application. However, if the
pesticide is mobile in moving water, its redistribution in the soil
profile after water is added will depend on both the amount and inten-
sity of the event.
<
It should be noted that from the nature of the input data in
Table 4, volatilization will be nearly always zero from a dry soil
(less than about 100 bars). Most non-polar or weakly polar pesticides
will be strongly adsorbed by dry soils. Any mobile pesticide that is
moved up to the soil surface as water evaporates will be adsorbed at
the surface. This adsorbed pesticide will doubtlessly go off in a
burst of volatilization when the soil is rewetted so that over a long
time average the rate of volatilization may be the same whether the
soil is continuously wet or going through wetting and drying cycles.
41
-------
This assumes, of course, negligible irreversible adsorption during the
drying cycle.
For strongly adsorbed, immobile pesticides, such as trifluralin,
the mass flow component will be essentially zero in the combined diffu-
sion and mass flow model. For these compounds, the diffusion based
models will probably prove very useful. For trifluralin the mass flow
component can be ignored and the diffusion based models utilized.
Bode et al. (1973a, 1973b) have determined the influence of various
soil and environmental factors on the diffusion coefficient of triflura-
lin. These workers used the methods of Ehlers et al. (1969a, 1969b)
for investigations which provides the type of data required by the
diffusion based models.
The most significant input data for all of the models presented
here are soil pesticide concentrations. Actually reasonable estimates
could doubtlessly be made of pesticide volatilization rates using the
model based on surface applied pesticides if frequent data were avail-
able on concentrations at the soil surface. Many situations could be
treated as surface-applied when information is available on the
relationship between vapor density and soil concentrations such as that
Spencer and his coworkers have developed for dieldrin, lindane, DDT and
trifluralin (Spencer, Cliath and Farmer, 1969; Spencer and Cliath, 1970;
Spencer and Cliath, 1972; Spencer and Cliath, 1974). For this model,
the only data necessary are the pesticide vapor densities and the
volatilization rate for a reference compound und,gr similar conditions.
Excellent agreement was obtained in this project' for the K values of
a number of compounds under different conditions. The factor, Ky, takes
into, account many field variables that would be difficult to obtain
independently.
As noted above Spencer and coworkers have developed considerable
data on the vapor sorption isotherms for a number of pesticides on soil.
Furthermore, Spencer et al. have shown a strong negative correlation
between soil organic matter and vapor density for dieldrin (Spencer,
Farmer, and Cliath, 1973) and for trifluralin (Spencer and Cliath, 1974).
The vapor density of soil-applied pesticide decreased with increasing
organic matter of several soils even though the clay content was often
inversely related to the organic matter content. Using information of
this kind it should be possible to make reasonable estimates of pesti-
cide vapor densities on soils without having to determine vapor sorption
isotherms on every soil.
42
-------
EFFECT OF TEMPERATURE GRADIENT ON PESTICIDE MOVEMENT
The initial conditions of the soil columns are given in Table 9.
To be able to understand the distribution of the pesticides as shown
in Figures 5, 6, and 7 the transfer of water in the liquid and vapor
phase in the three experiments is analyzed first. Table 10 shows the
parameters necessary to characterize water transfer in these experiments.
The parameters are the average suction head, h, the suction gradient
along the column at steady state, Vh, the average temperature, T, and
the temperature gradient along the columns, VT. Taking the distance x
increasing from the warm to the cold end results in negative values for
the gradients.
It has to be pointed out here, that due to a leak at the warm end
of the columns 2 and 3 they cannot be considered closed systems. Steady
state water transfer as discussed earlier did therefore not occur in
these two columns. The suction values and suction gradients reported
in Table 9 for these columns are average values taken over the whole
duration of the experiments. The water loss as measured as difference
between the weight at the beginning and end of the experiments was
1.1% and 1.8% for columns 2 and 3 respectively, based on the total
oven-dry weight of the soil in the columns. No weight loss was recorded
for column 1. Since in all experiments the columns were sealed with
equal care, it has to be concluded that while the sealant was adequate
for the lower temperature and vapor pressure of column 1, it was not
sufficient to completely seal off the columns at the higher temperatures
of columns 2 and 3.
L is the transmission coefficient for liquid water as used in
Darcy's law:
J = L Vh [40]
w w
where J is the flux of liquid water. L was calculated from the
following water conductivity functions:
For Gila silt loam:
L = 2.6 x 104 h~2'80 [41]
w
and Pachappa sandy loam:
L = 8.5 x 106 h"4'52 [42]
w
43
-------
•p-
•p-
Table 9. INITIAL CONDITIONS OF SOIL COLUMNS
B P h C
33 w ° °
Experiment Pesticide Soil cm /cm % cm ppm
1 Lindane Gila silt loam 1.26 21.0 388.6 10.0
2 Diuron Pachappa sandy loam 1.61 15.0 70.0 5.0
3 Atrazine Pachappa sandy loam 1.61 15.0 70.0 5.0
-------
Table 10. PARAMETERS CHARACTERIZING WATER FLUX IN SOIL COLUMNS
Experiment
1
2
3
h
cm
395
118
137
Vh
cm/ cm
-2.46
-0.30
-0.57
T
C
21 A
41.4
44.2
VT
C/cm
-0.38
-1.52
-1.81
L
w -
cm/hr x 10
. 1.45
3.74
1.87
L
2 v o
cm /C hr x 10
4.0
8.3
9.5
J
W 5
cm x 10
-357
-112
-105
J
v 5
cm x 10
152
1262
1720
-------
The conductivity functions were determined in separate experiments by
the transient flow method as described by Weeks and Richards (1967).
Equation [42] has been reported previously in a study by Weeks,
Richards, and Letey (1968).
The transmission coefficient for water vapor L was obtained
following the development of Letey (1968), and the flux of water vapor
J calculated from the equation:
J = -L VT [43]
v v
Analyzing the liquid water and water vapor fluxes as given in Table 9,
the following can be observed. The flux of liquid water is highest in
column 1 followed by columns 2 and 3. Considering the longer duration
of experiment 1 as opposed to 2 and 3, the total liquid water transfer
in column 1 was therefore considerably greater than in columns 2 and 3.
On the other hand, the flux of water vapor is greatest in column 3
followed by columns 2 and 1. As mentioned earlier, the fluxes of
water vapor and liquid water should be equal at steady state in a
closed system. The big differences between liquid water and water
vapor fluxes as calculated for columns 2 and 3 can be explained by the
fact that there was a leak at the warm end of these columns as mentioned
earlier. Part of the water vapor generated at the warm end of the
columns escaped out of the system and was not transferred to the cold
end of the columns. Consequently, less water was available for
liquid water transfer from the cold end to the warm end of the soil
columns. The fact that the calculated water vapor flux in column 1
was smaller than the estimated liquid water flux can be explained as
follows. The^values of L were calculated using an average value of
3.0 x 10 cm deg hr corrected for the average temperature of the
experiments as suggested by Letey (1968). Letey (1968) points out
however in his study that L increases with decreasing sand content of
the soil. This average value of L could therefore be a low estimate
for Gila silt loam, a soil with a small proportion of coarse particles.
The distribution of Cl ions at the end of the experiments is
indicative of the transfer of liquid water. The Cl" ion concentration
is higher at the warm end than at the cold end as can be easily seen in
Figures 2 and 3. This indicates a net liquid water transfer from the
cold end to the warm end as expected. The position of the concentra-
tion minimum of the Cl ion can however not be readily explained assum-
ing only unidirectional flow of liquid water. It has to be concluded
that a small amount of liquid water was also transferred from the warm
end to the cold end in experiments 2 and 3. Since the suction head was
low in experiments 2 and 3 especially in the early stages of the experi-
ments this observation is compatible with conclusions reached by Letey
(1968) concerning liquid water transfer due to temperature gradients.
The sharp increase in the Cl" ion concentration at the warm end of the
columns 2 and 3 also reflects the loss of water vapor at the end of the
46
-------
columns and therefore a more rapid liquid water transfer at that end of
the column than on the average over the whole columns. The moisture
distributions leads to the same conclusions. In column 1 the moisture
content is linearly increasing from the warm to the cold end of the
column as expected in a closed system at steady state such as studied
here. In columns 2 and 3 however the moisture content abruptly drops
toward the warm end indicating a net water loss of the system at that
end.
The distribution of lindane in column 1 (Figure 5) appears
plausible from the introductory remarks on the expected pesticide trans-
fer mechanisms involved in the system. Transfer of pesticide molecules
in the solution phase from the cold to the warm end and transfer of
pesticide molecules from the warm to the cold end in the vapor phase
would let us expect a pesticide distribution at the warm end of the
experiment as shown in Figure 5. It is interesting to note that the two
concentration maxima occur at equal distances from the warm and the cold
end respectively. This would seem to be an experimental indication of
equal fluxes of the pesticide in the two directions. Transfer of the
pesticide by diffusion due to a concentration gradient in the nonvapor
phase is obviously smaller than the other two transport processes, since
it would tend to equalize the concentration distribution as shown in
Figure 1. The fact that only approximately 75% of the pesticide added
was recovered in the final analysis is explained by losses during the
sectioning of the column, adsorption of the pesticide on the walls of
the columns and incomplete extraction of the pesticide from the soil
samples. As pointed out earlier, the leak in columns 2 and 3 affected
the water transfer characteristics of these columns to a degree which
makes a direct comparison of the pesticide distributions of colums 2
and 3 with the pesticide distribution of column 1 difficult. Compari-
son of the distributions of the Cl ions and the respective pesticide
distribution in Figures 6 and 7 shows a striking simularity between the
respective curves. The minimal Cl ion concentration in column 3 is lower
than the minimal Cl~ ion concentration in column 2. Accordingly the
maximum concentration of atrazine in column 3 is lower than the minimum
diuron concentration in column 2. The same relationship holds true for
the concentration maxima of Cl~ ions and pesticides at the warm end of
columns 2 and 3. From these results it would seem that the transfer of
diuron and atrazine occurred mostly in the liquid phase as opposed
to the experiment with lindane where equal amounts of pesticide mole-
cules seemed to be transferred in the liquid and vapor phase.
Exact measurements for the different vapor densities in the soils
at the given pesticide concentrations and moisture contents are not
available. The vapor diffusion coefficients are also not known for all
three pesticides in the soil systems under investigation. It is there-
fore not possible to exactly calculate the fluxes of pesticide vapor in
the three experiments at this time. The fact that the vapor pressure
of lindane in air is higher than the vapor pressures of diuron and
atrazine at the temperatures existing in these experiments might however
47
-------
WARM
MOISTURE DISTRIBUTION
vapor
'liquid
COLD
24
23
22
21
_ % (w/w)
I
LINDANE DISTRIBUTION
15
10
DISTANCE (cm)
15
20
Figure 5. Effect of temperature gradient on the distribution of
water and lindane in Gila silt loam.
48
-------
WARM
MOISTURE DISTRIBUTION
15._ % (w/w)
vapor
liquid
COLD
I
Cl~ DISTRIBUTION
lOOOr- ^9/9'
100
10
I
DIURON DISTRIBUTION
5
I
10 15
DISTANCE (cm)
20
Figure 6. Effect of temperature gradient on the distribution of
water, Cl~, and diuron in Fachappa sandy loam.
49
-------
WARM
MOISTURE DISTRIBUTION
14._ % (w/w)
12
vopor
liquid
COLD
Cr DISTRIBUTION
lOOOrt (/xg/g)
100
IO
ATRAZINE DISTRIBUTION
4
2
10 15
DISTANCE (cm)
20
Figure 7. Effect of_temperature gradient on the distribution of
water, Cl , and atrazine in Pachappa sandy loam.
50
-------
be a possible explanation. As discussed earlier in regard to water
vapor loss at the warm end of columns 2 and 3, loss of pesticide vapor
at the warm end of the columns could be another possible explanation
for the concentration minima close to the warm end of the columns and
little transfer of pesticide vapor to the cold end of the columns.
The failure to recover the total amount of diuron and atrazine added
to the columns is explained as above for column 1.
In summary it can be said that the system investigated offers
interesting possibilities to study vapor diffusion and mass transfer
of pesticides simultaneously. In order to calculate the resulting
pesticide fluxes and to compare quantitatively the results of the
experiments using different pesticide compounds, further measurements
of properties of the pesticides in the given soil systems are necessary.
51
-------
SECTION VIII
REFERENCES
1. Bode, L. E., C. L. Day, M. R. Gebhardt, and C. E. Goring. Mechanism
of Trifluralin Diffusion in Silt Loam Soil. Weed Sci. 21:480-484,
1973a.
2. Bode, L. E., C. L. Day, M. R. Gebhardt, and C. E. Goring. Prediction
of Trifluralin Diffusion Coefficients. Weed Sci. 21:485-489, 1974.
3. Carslaw, H. S., and J. C. Jaeger. Conduction of Heat in Solids.
2nd Edition Oxford University Press, Oxford, 1959.
4. Danielson, L. L., and W. A. Centner. Influence of Air Movement on
Persistence of EPTC on Soil. Weeds 12:92-94, 1964.
5. Ehlers, W., W. J. Farmer, W. F. Spencer, and J. Letey. Lindane
Diffusion in Soils. II. Water Content, Bulk Density and Tempera-
ture Effects. Soil Sci. Soc. Amer. Proc. 33:505-508, 1969.
6. Ehlers, W., J. Letey, W. F. Spencer, and W. J. Farmer. Lindane
Diffusion in Soils. I. Theoretical Considerations and Mechansims
of Movement. Soil Sci. Soc. Amer. Proc. 33:501-508, 1969.
7. Farmer, W. J., K. Igue, and W. F. Spencer. Effects of Bulk Density
on the Diffusion and Volatilization of Dieldrin from Soil.
J. Environ. Qual. 2:107-109, 1973.
8. Farmer, W. J., K. Igue, W. F. Spencer, and J. P. Martin. Volatility
of Organochlorine Insecticides from Soil: I. Effect of Concentra-
tion, Temperature, Air Flow Rate and Vapor Pressure. Soil Sci.
Soc. Amer. Proc. 36:443-447, 1972.
9. Farmer, W. J., and C. R. Jensen. 1969. Diffusion and Analysis of
l^C Labeled Dieldrin in Soils. Soil Sci. Soc. Amer. Proc.
34:28-31, 1969.
10. Finkelstein, H. Preliminary Air Pollution Survey of Pesticides. A
Literature Review. U.S. Department of Health, Education and
Welfare, Public Health Service, Raleigh, N.C. (1969).
11. Grover, R., J. Maybank, K. Yoshida, and J. R. Plimmer. Drought and
Volatility Drift Hazards from Pesticide Application. Proc. of the
66th Annual Meeting of the Air Pollution Control Association,
Chicago, Illinois, June 24-28, 1973.
12. Hamaker, J. W. Diffusion and Volatilization. In; Organic Chemicals
in the Soil Environment, Vol. 2. Goring, C.A.I, and J. W. Hamaker
(ed.). New York, Decker, p. 341-391.
52
-------
13. Harris, C. R., and E. P. Liechtenstein. Factors Affecting the
Volatilization of Insecticidal Residues from Soils. J. Econ.
Entomol. 54:1038-1045, 1961.
14. 'Hartly, G. S. Evaporation of Pesticides. In: Pesticidal
Formulations Research, Physical and Colloidal Chemical Aspects.
Gould, R. F. (ed.). Adv. Chem. Series 86:115-134, 1969.
15. Huggengerger, F., J. Letey, and W. J. Farmer. Observed and
Calculated Distribution of Lindane in Soil Columns as Influenced by
Water Movement. Soil Sci. Soc. Amer. Proc. 36:544-548, 1972.
16. Igue, K. Volatility of Organochlorine Insecticides from Soil.
Ph.D. Dissertation, University of California, Riverside, Univ.
Microfilms, Ann Arbor, Mich. (Diss. Abstr. 70-19,242), 1969.
17. Igue, K., W. J. Farmer, W. F. Spencer, and J. P. Martin. Volatility
of Organochlorine Insecticides from Soil. II. Effects of Relative
Humidity and Soil Water Content on Dieldrin Volatility. Soil Sci.
Soc. Amer. Proc. 36:447-450, 1972.
18. Klute, A., F. D. Whisler, and E. J. Scott. Numerical Solution of
the Nonlinear Diffusion Equation for Water Flow in a Horizontal
Soil Column of Finite Length. Soil Sci. Soc. Amer. Proc. 29:353-
358, 1965.
19. Letey, J. Movement of Water Through Soil as Influenced by Osmotic
Pressure and Temperature Gradients. Hilgardia 39:405-418, 1968.
20. Letey, J., and W. J. Farmer. Movement of Pesticides in Soil. In:
Pesticides in Soil and Water. Guenzi, W. D. (ed.). Madison, Wise.,
American Society of Agronomy, 1974. p. 67-98.
21. Mayer, R., J. Letey, and W. J. Farmer. Models for Predicting
Volatilization of Soil-Applied Pesticides. Soil Sci. Soc. Amer.
Proc. 38 (July-Aug. issue) 1974. (In Press).
22. Oddson, J. K., J. Letey, and L. V. Weeks. Predicted Distribution
of Organic Chemicals in Solution and Adsorbed as a Function of
Position and Time for Various Chemical and Soil Properties.
Soil Sci. Soc. Amer. Proc. 34:412-417, 1970.
23. Parochetti, J. V., and G. F. Warren. Vapor Losses of IPC and CIPC.
Weeds 14:281-285, 1966.
24. Shearer, R. C., J. Letey, W. J. Farmer, and A. Klute. Lindane
Diffusion in Soils. Soil Sci. Soc. Amer. Proc. 37:189-193, 1973.
53
-------
25. Spencer, W. F., and M. M. Cliath. Vapor Density of Dieldrin.
Environ. Sci. Technol. 3:670, 1969.
26. Spencer, W. F., and M. M. Cliath. Vapor Density and Apparent
Vapor Pressure of Lindane. J. Agr. Food Chem. 18:529-530, 1970.
27. Spencer, W. F., and M. M. Cliath. Desorption of Lindane from Soil
as Related to Vapor Pressure. Soil Sci. Soc. Amer. Proc.
34:574-578, 1970.
28. Spencer, W. F., and M. M. Cliath. Volatility of DDT and Related
Compounds. J. Agr. Food Chem. 20:645, 1972.
29. Spencer, W. F., and M. M. Cliath. Pesticide Volatilization as
Related to Water Loss from Soil. J. Environ. Qual. 2:284-289, 1973.
30. Spencer, W. F., and M. M. Cliath. Factors Affecting Vapor Loss
of Trifluralin from Soil. J. Agr. Food Chem. (Manuscript accepted),
1974.
31. Spencer, W. F., M. M. Cliath, and W. J. Farmer. Vapor Density of
Soil-Applied Dieldrin as Related to Soil-Water Content, Temperature,
and Dieldrin Concentration. Soil Sci. Soc. Amer. Proc. 33:509-511,
1969.
32. Spencer, W. F., W. J. Farmer, and M. M. Cliath. Pesticide
Volatilization. Chapter in Residue Reviews. Vol. 49:1-47, 1973.
33. Van Genuchten, M. Th., J. M. Davidson, and P. J. Wierenga. An
Evaluation of Kinetic and Equilibrium Equations for the Prediction
of Pesticide Movement Through Porous Media. Soil Sci. Soc. Amer.
Proc. 38:29-35, 1974.
34. Weeks, L. V., and S. J. Richards. Soil-Water Properties Computed
from Transient Flow Data. Soil Sci. Soc. Amer. Proc. 31:721-725,
1967.
35. Weeks, L. V., S. J. Richards, and J. Letey. Water and Salt Transfer
in Soil Resulting from Thermal Gradients. Soil Sci. Soc. Amer.
Proc. 32:194-197, 1968.
36. Whisler, F. D., and A. Klute. The Numerical Analysis of Infiltra-
tion, Considering Hysteresis Into, a Vertical Soil Column at
Equilibrium Under Gravity. Soil Sci. Soc. Amer. Proc. 29:489-494,
1965.
37. Whisler, F. D., and A. Klute. Rainfall Infiltration Into a Vertical
Soil Column. Trans. Am. Soc* Agric. Engr. 391-396, 1967.
54
-------
SECTION IX
GLOSSARY
Definitions of Symbols Used in the Text.
q = rate of diffusion
K, = constant for geometry of the soil
AC = vapor concentration gradient
3
d = depth of air layer
K2 = proportionality factor
K = proportionality factor between volatilization flux and the
saturation vapor concentration
S.V.C. = saturation vapor concentration
R = molar gas constant
T = absolute temperature
K1 = proportionality factor between volatilization flux and the
vapor pressure
-3
c,C = pesticide concentration in soil (g cm total volume)
x,z = distance measured normal to the soil surface
t = time
L = depth of soil layer treated uniformally with pesticide
_3
C = initial soil pesticide concentration (g cm )
f = pesticide flux through the soil surface
V = volume of air
v = air flow velocity
C = pesticide concentration in air
a
C = pesticide concentration at the soil surface
s
R = proportionality factor between C and C
55
-------
D1 = diffusion coefficient of pesticide in air
h = pressure head of water (cm)
9(h) = volumetric water content as a function of the pressure head
(cm^ of water/cm^ of total space)
39(h)/c»h = specific water capacity
K(h) = water conductivity as a function of the pressure head
(cm day )
h = initial pressure head
D (9) = total apparent diffusion coefficient as a function of 9(h)
V(0) = pore water velocity as a function of 9(h)
_3
C' = concentration in solution (mass cm )
_3
p = soil bulk density (g cm )
K = constant relating adsorbed and solution phase pesticide
concentrations
S = maximum adsorbed phase concentration (mass/g soil)
IQ3X
N = ratio of the exponents for desorption to adsorption in the
Freundlich equation for C1.
56
-------
SECTION X
APPENDICES
Page
A. Explanation of Symbols and Variables in Water 58
Evaporation - Pesticide Volatilization Program.
B. Computer Program - Model Based on Diffusion and 65
Mass Flow of Soil-Incorporated Pesticides.
57
-------
Appendix A. Explanation of Symbols and Variables in Water Evaporation-
Pesticide Volatilization Program.
Input Parameters
1. Format Statement 998.
N - The number of intervals between upper and lower boundary.
ITMAX - The maximum number of iterations for any time step.
LPRTC - A print control variable. If LPRTC = 1, results are
printed for every time step. If LPRTC = 5, for example,
results are printed for every 5th time step. Results
are printed for the first and last time step (if the
problem is finished) regardless of the value of LPRTC.
NUMC0L - Can be used to return control at end of one problem to
some point in main program to consider input data for
other problems, etc.
EPSL0N The values of the pressure head for the present iteration
(HEADPI) are compared. If the absolute value of the
difference between any pair of values exceeds EPSL0N,
another iteration is performed, otherwise the solution
of the problem proceeds.
EPSLNC - The values of the pesticide concentration (mass/unit
volume of space (cur) for the present iteration (C0PPBS)
and for the past iteration (CPBSPI) are compared. If the
absolute value of the difference between any pair of
values exceeds EPSLNC, another iteration is performed.
If EPSLNC is not exceeded the solution continues.
2
R = At/(AZ) , where At = interval between time steps (days),
AZ = distance (cm) between space intervals. R initializes
At and is used in solution.
DELTA1\ If the absolute values of the differences between present
DELTA2J time concentration values (C0PPBS) and past time values
(CPSPT) are less than DELTA1 for all points, At and R are
doubled for the next time step. If the differences above
exceed DELTA2, At and R are multiplied by 0.75 and
results are recalculated for a new (smaller) step.
QFRACT - If the amount of water evaporated from the soil column or
profile divided by the initial water content exceeds
QFRACT, the calculations stop and results for the time
step are printed.
58
-------
CM - Length of column or depth of profile in cm.
TIMEMX - The maximum amount of time for evaporation to occur
expressed in days.
2. Format Statement 997.
C0NMAT - Initial concentration of pesticide (mass/gm dry soil).
DEPTH - Depth of initial pesticide distribution in cm.
3
PB - Average bulk density of soil (gm soil/cm space).
K - Adsorption constant (cc liquid/gm dry soil).
EXP0N - Exponent associated with K for desorption (assumed = 1
for adsorption).
NDVSPT - The number of'paired values of the apparent diffusion
coefficient and water content from experimental data.
IN - The number of points at which related experimental
values of hydraulic conductivity, water content, water
capacity, and pressure head are available.
3. Format Statement 995.
AC0NST An empirical constant used in this study and related to
the rate of change of water pressure of the soil surface.
4. Format Statement 978.
2
DVSIN - Apparent diffusion coefficient (cm /day).
3 3
THDSIN - Water content (cm liquid/cm space).
5. Format Statement 996.
HEAD - Pressure head (cm).
3 3
THETA - Water content (cm liquid/cm space).
HC0ND - Water conductivity (cm/day).
CAP - Water capacity (cm ).
59
-------
Other Variables in Dimension Statements of Main Program
HEADC - Pressure head values at the present time step.
HEADPT - Pressure head values at the end of the previous time step.
HEADPI - Initial pressure head values and pressure head values of
each iteration within time steps.
CAPC - Water capacity values at the present time step.
CAPP - Water capacity values at the end of the previous time step.
C0NC - Water conductivity values at the end of the present time
step.
C0NP - Water content values at the end of the previous time step.
THETAC - Water content values at the present time step.
HYHEAD - Hydraulic head (cm) at the present time step.
HYGRAD - Hydraulic gradient values at the present? 'time step.
HYHDPT - Used to store initial pressure head values.
£ - Vertical distance (cm), positive upward.
C - Concentration of pesticide in solution (mass/gm dry soil)
at present time step.
3
CL - Concentration of pesticide in solution (mass/cm space)
at present time step.
Concentration of pest:
at end of previous time step.
3
CTHEPT - Concentration of pesticide in solution (mass/cm space)
3
CTHEPI - Concentration of pesticide in solution (mass/cm space)
at each iteration within time steps.
S - Concentration of adsorbed pesticide (mass/gm dry soil)
at present time step.
SMAX - Maximum value of S obtained at any position (Z)
Concentration of at
present time step.
3
PBSC - Concentration of adsorbed pesticide (mass/cm space) at
60
-------
3
PBSPT - Concentration of adsorbed pesticide (mass/cm space)
at end of previous time step.
C0PPBS - Total concentration of pesticide, adsorbed plus solution
phases, (mass/cm-^ space) at present time step.
2
CPSPT - Total concentration of pesticide (mass/cm space) at
end of previous time step.
3
CPBSPI - Total concentration of pesticide (mass/cm space) at
each iteration.
4
CGRAD - Total concentration gradient (mass/cm space) at present
time step.
CPLUSS - Total concentration of pesticide (mass/gm dry soil; C + S.
THETPT - Initial water content (THETAC) values stored.
l
DV - Initial water conductivity (C0NC) values stored.
DVPT -5rrln.itial water capacity (CAPC) values stored.
DVIN - Apparent diffusion coefficient values from input data
stored.
DVS - Apparent diffusion coefficient values at present time
step.
DVSPT - Apparent diffusion coefficient values at end of previous
time step.
P0REV - Average liquid velocity in pores (cm/day).
ETIME - Elapsed time values (days).
2
T0TMAT - Total amount of pesticide in profile (mass/cm space).
2
FLXMAT - Rate of pesticide movement of surface (mass/cm /day).
ABLCK - Coefficients of equations
BBLCKf- (diagonals) used in
CBLCK tridiagonal matrix.
HBLCK - Right hand side of solution matrix.
YBLCK1 - Dummy variables used
ZBLCJU in solving matrix
61
-------
TEMP2 i - Used for temporary storage
TEMPS I of values needed to calculate
TEMPS 1 values of ABLCK, CBLCK, and
TEMP6 j HBLCK.
TEMP7
TEMP8J
DBLCK\ - Used for temporary storage values,
EBLCKl needed to calculate values of ABLCK, BBLCK and CBLCK.
V - Used for temporary storage.
C0 \ - Used to store CTHETC and PBSC values in
PBSJ reverse order for numerical integration.
Non-dimensioned Variables
0 - N in decimal form
DLZ - AZ
DLE2 - (AZ)2
DLZ02 - AZ/2
TW0DLZ - 2AZ
DLTIME - At (days)
N7 - Number of points to be used for each group of points
in numerical integration subroutine NINT.
N61
N5J
- Used in printing
3
- Initial total pesticide concentration (mass/cm ) space.
RPT - Initial R (input) value retained.
NUMBER - Used with NUMC0L (input) to stop or continue solution
for different columns or chosen situations.
2
AMTPIO - Amount of pesticide (mass/cm ) moving downward past
Z = -10 cm.
SURFIN - Amount of water applied at surface.
TIME - Time in days.
H0URS - Time in hours.
62
-------
DAYS - Time in days.
DLCUM Increment of water outflow (cm) at surface for this time
step calculated from flux times DLTIME.
CUMFL - Sum of DLCUM values.
CUMUL - Cumulative outflow of water calculated by integration
of THETA (9) profile to and including present time.
CUMULP - Cumulative water outflow of previous time step.
CUMULD - Cumulative water outflow of present time step.
FLUXD - Flux at surface (cm/day) from CUMULD/DLTIME.
FLUXS - Flux at surface from water conductivity times hydraulic
gradient.
CUMI \ Initial total water content (cm) of
CUMINTj - column or profile.
AM0UNT - Total water content (cm) at present time.
FLUXO - Water flux across lower boundary.
FRCCUM - Fraction of total possible cumulative outflow-calculations
for problem stop (after values for time step printed)
if absolute value exceeds QFRACT (input).
LAST - Controls printing of values for last time step.
LSTEP - Number of time step.
ITERCI Iteration numbers for water and pesticide calculations
ITERSj - respectively.
ITERX - Number of times ITMAX exceeded.
LSIG "I Numbers of points not passing EPSL0N or
LSIGSf - EPSLNC test.
LSIG1 - Number of points not passing DELTA1 test.
LSIG2 - Number of points not passing DELTA2 test.
ND Determines value of Z 2 cm below the position where
pesticide concentration $0.
NST - Value of Z one cm above that corresponding to value of ND.
63
-------
CSURFI - Initial total pesticide concentration at surface
(mass/cm space).
HSURFI - Initial water pressure at surface.
TEMPI - Temporary value used in BBLCK and HBLCK calculations.
C0NDO - Water conductivity at lower boundary at present time
step.
C0NDS - Water conductivity at surface at present time step.
NITER - One more iteration occurs when value of SMAX determined
for each position.
NVAL - Number of values to be used in numerical integration
program.
Q - Flux of pesticide at Z = -10 cm.
2
SUMCI - Initial amount of pesticide in solution (mass/cm ).
SUMSI - Initial amount of adsorbed pesticide (mass/cm ).
2
T0TI - Initial total amount of pesticide (mass/cm ).
SUMCN - Amount of pesticide in solution at present time
(mass/cm^).
SUMSN - Amount of adsorbed pesticide at present time
(mass/cm^).
2
T0TN Total amount of pesticide at present time (mass/cm ).
T0TV0L - Amount of pesticide volatilized to and including present
time (mass/cm^).
FRACTV - Fraction of pesticide volatilized.
S0LV0L - Amount of solution phase transferred and/or volatilized
0
(mass/cm^).
ADSV0L - Amount of adsorbed phase transferred and/or volatilized
(mass/cm^).
64
-------
Appendix B. Computer Program-Model Based on Diffusion and
Mass Flow of Soil-Incorporated Pesticides.
65
-------
C bVAPORATIQN f-PDM THF SOIL SURFACE WITH TIMP. VARIABLE WATER POTENTIAL
C AT THE SUP PACE.
C VOLiTIL IZATI3N OF 3RGANOCHLJRINF INSFCTICIDFS FU"!M SOIL.
IMPLICIT PEAL*3(A-H, C-Z)
DIMFNSION HEAQ(30),THrT4<30),HCGND(30),CAP(30)
DIMENSIHM HcADC(5l)fHEAOPTI51),CAPP(51),CONP(51),A3LCK(51),3BLCK{5
11) ,C3LCK(51),HBLCK(51),YflLCM5l),ZBLCM51) , CONIC ( 51) , CAPC( 51 ) ,THPTA
2C<5l),HcADPI(5l),Z(e>l) ,HYHFAD(51 )
DIMENSION C(51),S(5i),CL(51),CPSPT(5l),HYGRAD(bl),CTHTTC(51),THETP
ITl51),HYHDPT(51),OV(51),DVPT(51),DVS(51),DVSt>T(51)fCPlUSS(Sl),COPP
?BS(5l),r>Vl,\(?0),CPBSPI(5l) ,DVSIN(20) ,THDSIN(20) ,TtMP2(51) ,TtMP3(51
3),T£MP5(51),TEMP6l5l),V(51),PORtV(5lI,nBLCK(51),FftLCKt51),P3S(51),
ACO(51),P3SC(51),TPMP7(5l),TCMP3J51),cTIME(500),TOTMAT(500),FLXMAT{
5500),SMAX(5l)tCTHFPI(51),PdSPT(5 I) ,CTHFPT(5l),CGPAD(5l)
RrAL*8 K
C FUNCTIONS FOP BOUNDARY CONDITIONS AT SOIL SURFACE FOR HATF.R AND
C PESTICIDE TRANSFER.
SUPFCEIA.B.C) A * DEXP(B*C)
C FUNCTIONS PERTAINING TO ADSORPTION OR OESORPTION OF PESTICIDE.
PBKADS(D) l./(l.+PB*K/0)
PBKDES(A,B,C)=!./(1.+PB*(K/B)**EXPON*(A/C)**(1,-tXPON))
NUMBER = 0
C READ IN INITIAL INFORMATION
RE AD (5, 998) N, ITM AX t LPR TC , NUMCOL , EPSLON, EPSLNICf R t DELTA1, DELTA 2, UFR
lACTtCM.TIMEMX
C READ INITIAL CONCENTRATION OF MATERIAL(CONMAT) IN MASS/UNIT MASS OF
C SOIL, DEPTH OF INITIAL DISTRI3UT10N IN CM, BULK DENS ITY(GK/CC)OF SOIL
C (PB), K(CC(LIQ)/GM SOIL), NO. OF POINTS IN TOTAL APPARENT DIFF. CHEFF
C TAIHLE(NDVSPT), DC NOT EXCFED NO. OF VALUF.S GIVEN IN DIMENSION STAT.
C NO. (IN) OF SETS OF DELATED VALUFS OF PRESSURE HEAO(H^AD), VOLUMETRIC
C HATFR CONTENT(THETA), WATER CONDUCTIVITY(HCOND), AND SPECIFIC WATER
C CAPACITY(CAP).
READ(5,997) CONMAT,DEPTH,PB,K,EXPCN,NDVSPT,IN
P.6AD(5,995) ACONST
C 'READ TOTAL APPARENT DIFF. COEFF. VALUES(DVSTN) ICM2/OAYJ AND CORRES-
C PONDING THFTA VALUFS(THDSIN) (CC LIO/CC SPACF).
RfcAD(5,973)(OVSIN(J),THOSIN(J), J l.NDVSPT)
REAU(5,096)(HEAD(J),THETA( J) ,HCOND( J ) , f AP{ J) ,HEAQ( J+1) , THETA « J<-1) ,
!HCrNO(J+l),CAP(j+l),J I,IN,2)
C INITIAL CALCULATIONS
0 = N
DLZ = CM / 0
DLZ2 = DLZ * DLZ
DLTIME R * DLZ2
DLZ02 = DLZ * 0.5
TWOOLZ = DLZ * DLZ
Nl N •!• 1
NM1 N - 1
N7 N/5
N6 = N / 2
N5 = N6 + 1
Z( 1) -CM
Y = CONMAT * PB
66
-------
RPT = R
00 3 J l,Nl
Z(J+1) Z(J) + DLZ
HEAOPHJ) -300. - Z(J)
3 HYHOPT{J) = HEADPI(J)
CALL INTLY(HCOND,IN,HEAD,IN,CONC,Nl,HfADPI ,M1,1,NI)
CALL INTLY(CAP,IN,HEAD,INfCAPC,Nl,HF.ADPI,Nl,l,Nl)
CALL INTLYUHETA, IN, HEAD, IN, THE T AC ,N1 ,HcADP I ,Nl , 1 ,N1)
C PRINT BEGINNING INFORMATION
WRITE 16,999)
C PRINT INITIAL RUN INFORMATION
MRITE(6,971) N,ITMAX,NUMCOL,EPSLON.QFRACT,CM,DLZ,R,TIMEMX,DLTIME ,
lEPSLNC,DELTAl,r>ELTA2,LPRTC
WRITE(6,994)(HEAO(J),THETA(J),HCOND
-------
o.
CPLUSS(J) 0.
CPSPT(J) - 0.
2 COPP8SU) 0.
00 23 J = 1,N1
HEAD°I(J) HYHDPT(J)
CONC(J) = OV(J)
CAPC(J) = DVPT(J)
THETAC(J) = THETPT(J)
HEADC(J) = HEAnPI(J)
HFADPT(J) HEADPI(J)
HYHTADU) = HEADPFIJ) * Z(J)
CAPP(J) = CAPC(J)
23 CONP(J) = CONC(J)
CALCULATE HYDRAULIC GRADIENT VALUES(HYGRAD)FOR EACH I VALUE.
CALL OUZ2(Z.N1,HYHEADiNl,HYGRADiNl,0,0,l,5iNl,0.,0)
INITIAL PORE VELOCITY.
00 6 J = 1,N
A3LCK(J) (CONC(J) + CONC(J«-1) + CQ-MPJJ) * CONPtJ*!))* .25
6 POREV(J) = <-ABLCK(J))*HYGRAO(J)/THETAC(J)
FLUXS (-ABLCK(N))*<(3.*HEAOC(Nl)-4.*HEAOC(N) *• HEAOC(NMl) )/(TMOO
1LZ) + 1.)
PCRFVINI) = FLUXS / THETAC(N1»
NUMERICAL INTEGRATION FOR INITIAL TOTAL LIQUID CONTENKCUMI).
CALL NINT (THETAC,M,CUMI ,OLZfN7)
CUMUL 0.
CUMINT = CUMI
NO = (CM * OLZ - OEPTH) / DLZ «• .2
CALL INTLC(nvSIN,20fTHOSIN,20,DVS,Nl,TH^TAC,Nl,NDiNl)
CALCULATE INITIAL SOLUTION AMD ADSORBED PHASE CONCENTRATIONS
DO 5 J ND,N1
TEMPSU) OLZ02*PORCV(J)*P3KAOS(THETAC(J»)
DVSPT(J) = DVS(J)
CTHETC(J) = Y*PBKADS(THFTAC(J))
CTHEPHJ) = CTHETC(J)
CTHFPT(J) = CTHETC(J)
PBSC(J) = Y - CTHETC(J)
PBSPT(J) PBSC(J)
CL(J) - CTHFTC(J) / THETAC(J)
C1J) CTHETC(J) / PB
S(J> CONMAT - C(J)
SMAX(J) S(J)
CPLUSS(J) = CONMAT
CPBSPKJ) = Y
COPPBS(J) = Y
5 CPSPT(J) = Y
CSURFI = COPP3S(N1)
NUMERICAL INTEGRATION FOR INITIAL CONDITIONS.
I Nl
NVAL = Nl - ND * 1
DO 7 J = l.NVAL
PBS(J) = PBSC(I)
CPU) = CTHETCU)
68
-------
71=1-1
N? = NVAL / 5
CALL N!NT(CO,Nl,SUMCI,DLZ.N2)
CALL N1NT(PBS,N1,SUMSI,OLZ,N2)
TOTI = SUMCI + SUMSI
IF(NUMBER.GT.l) GO TO 24
C PRINT RESULTS PERTAINING TO INITIAL TIME.
KRI TE(6,990) (Z(J) ,HEAOC(J) ,THETACU) ,HYHEAD(J) ,POREV {J) , Z { J + N6) ,
1HEADCJ J+N6) ,THETACU+N6),HYHEAO(J + N6) ,POREV (J+N6), J 1,N5)
*IR1TE(6,986) CUMI.CUMINT
WRITE(6,973)
WRITE (6,993) 1DVSINIJ),THDSIN(J),J=l,NOVSPT)
WRITE(6,977MZ(J),C(J),S
-------
CALL INTLY(CAP,IN.HEAD,IN.CAPCtNl,HEADPI,Nl,I,N1)
ABLCK(l) = (CO.NCU) * CONC(2» * CONPCl) + CONP{2))* .25
DO 36 J = 2,N
ABLCK(J) = (CONC(J) + CQNCU+1) + CONP(J) + CONP(JM))* .25
C8LCKU-1) = ABLCMJJ
TEMPI = (CAPC(J) + CAPP(J))/R
BBLCK(J-1I = ARLCKU-1) + CBLCK(J-l) + TEMPI
TFMP4 = CBLCK(J-l) - ABLCK(J-l)
36 HBLCK(J-l) = CBLCKU-l)*T£:MP2
-------
00 61 J = ItND
61 POREV(J) = <-ABLCK(J))*HYGRADUI/THETAC(J)
00 611 J NST,N1
POREV(J) = (-A8LCK(J))*HYGRAD(J)/THFTACU)
IF(HEADPIU) * l.D+5) 612,611,611
612 POREVU) = POREV(J>*(HEAD(IN)-HEADPI(J))/HEADUN)
611 CONTINUE
C SURFACE BOUNDARY CONDITIONS
45 FLUXS = l-ABLCMNM * HYGRAOIN1I
47 IF(CSURFI) 64,64,69
69 IFJTIME - .95) 63,64,64
63 COPPBS(Nl) = SURFCE(CSU"FI,{-2.0Di»,TIME)
CTHEPKNl) = COPPBS
-------
68 ABLCK(J) DBLCMJ) + TFMP3U)
DO 32 J = NST.N
CBLCK(J-l) = FBLCK(J-l) - TEMP3CJ+1)
32 HBLCMJ-1) TEMP1*CPSPTU)+EBLCKIJ-1)*TEMP7U)-DBLCK{J-1)*TEMP6(J
108
109
HBLCMNM1) = HSLCK(NHl) * CBLCK(NMl) * CPBSPKNll
SOLVF SYSTEM
CALL TRIDAG(ABLCK,N,BBLCKfN,CaLCK,N,HBLCK,N,YBLCK,N,ZBLCKfN,COP'PBS
l,Nl,NST,N)
COPP3SU) = (4.*COPPBS(2)-COPPBS<3))/3.
EPSILON TEST
LSIGS = 0
DO 109 J = NST.N
IF(C3PPGS(J).LT. 1.0-3) COPPBS(J) = 0.
TEST = COPPBS(J) - CPBSPKJ)
IF-CPSPTU)+CTHEPT(J)
GO TO 111
1106 CTHETC(J) = COPPBS(J)*P3KADS(THETAC(Jil
PBSC(J) = CCPPBS(J) - CTHETC(J)
SMAXU) = PBSC(J) / PB
GO TO 111
IF(CTHFPUJ)) 1100,1100,1108
IF(SMAXU)J 1106,1106,1105
CTHETCU) = COPPBS IJ )*PBKOES( SMAXC J ) .THETAC { J) .CTHEPK J) »
1107
1108
1105
1103,1103,1104
PBSC(J) = COPPBS(J) - CTHETC(J)
111 CTHEPK Jl = CTHETC(J»
IF(LSIGS) 100,*9,100
*9 NITER = NITER * 1
DO 1104 J = ND,N1
IFiPBSPTU) - PBSC(J))
1103 SMAX(J) = P&SCCJI / PB
1104 CONTINUE
IFCNITER - 1) 50,100,50
; DELTA TESTS AND DELTA TIME CHANGES
50 GO TO (54, 112), M
54 LSIGU 0
LSIG2 = 0
DO 51 J - NST.N
TCST = C3PPBSU) - CPSPT(J)
IF(DABS(TEST)-OELTA1) 51,51,52
52 LSIG1 = LSIG1 + 1
IF(DABS{TEST)-DELTA2) 51,51,53
72
-------
53 LSIG2 = LSIG2 + 1
51 CONTINUE
IF(LSIGl) 55,112,55
C DCLTA TIME TOO LARGE
55 IFUSIG2) 56,112,56
56 TIME = TIME - OLTIMF.
DLTIME OLTIME * 0.75
IF(DLTIME-I.D-5I 561,562,562
561 DLTIME = DLTIME / 0.75
TIME = TIME + DLTIME
GO TO 112
562 LSTEP = LSTEP - 1
00 57 J = i.Nl
CTHF.PHJI = CTHEPT(J»
CPBSPIU) = CPSPT(J)
P8SCU) = PBSPT(J)
57 HEAOPI(J) = HEADPTU)
R = R * 0.75
GO TO 25
C NUMERICAL INTEGRATION
112 I = Nl
NVAL = Nl - NO * 1
IF(NVAL-13) 113,113,114
113 N2 = 2
GO TO 121
114 IF(NVAL-18) 115,115,116
115 N2 = 3
GO TO 121
116 IF1NVAL-23) 117,117,118
117 N2 = 4
GO TO 121
118 lF)/TWOOLZ+POR
1EV(21)*CTHETC121)
IF(Q) 12,13,13
12 AMTP10 =DABS(OI * OLTIME * AMTP10
13 TOTN = SUMCN * SUMSN
TOTVOL = TOTI -TOTN
FRACTV = TOTVOL / TOTI
OLCUM = PORfcV(Nl)*THETAC{Nl)*OLTIME
CUMFL - CUMFL * OLCUM
C PRINT RESULTS
C PRINT RESULTS FOR FIRST TIME.
1FILSTEP - 1) 72,72,70
73
-------
70 IF(TIMF - .2) 95,71,71
PRINT RESULTS FDR EACH SELECTED TIME (ACCORDING TO VALUE OF LPRTC).
71 IF((LSTEP/LPRTC)*LPRTC.NE.LSTEP) GO TO 73
72 WRITE (6,973)
FLUXO = (-CONOO) * (U.*HEADC(2> HEAOC(3) - 3.*HEADC{I))/(TWODL
111 * I.)
FPFCUM CUMFL / CUMINT
CHGFLX = SURFIN
CALL DUZ2(Z,Nl,COPPBS,Nl,CGRAO,Nl,0,0,l,5fN,0.,0)
CGRAD(Nl) (CDPPBS(NMl)-4.*COPPBS{N)-t-3.*COPPBS(Nl))/ TWOOLZ
00 76 J ND,N1
V(J) = (-DBLCKU-l))*CG'UD(J)
CO(J) - POREV(J) * CTHETC(J)
P8S(J» = V(J) * CO(J)
CPLUSS(J) COPP6S(J) / PB
C(J) = CTHETC(J) / PB
S(J> = CPLUSS(J) - C(J)
76 CL(J) = CTHETC(J) / THETAC(J)
SOLVOL SUMCI - SUMCN
ADSVOL SUHSI - SUMSN
N3 = (Nl - NO) / 2
N4 = NO + NVAL / 2
WRITE(6,992) ITERC,LSIG,LSTEP,TIHE,DLTIHE
WRITE(6,989) HOURS,DAYS,FLUXO,CUMFL.CUMULtITERXS,FLUXO
WRITE (6, 985) FRCCUM,FRFCUM,CONDS,FLUXS
WRIT£(6,981) AMOUNT,SURFIN,CHGFLX
WRITE(6,990)(Z(J),HEADC(J),THETAC(J),HYHEAD(J),POREV U),Z(J+N6) ,
1HEADCIJ+N6),THETAC(J+N6),HYHEAD(J+N6),POREV (J+N6), J = 2,N5,2)
W3ITE(6,977HZ(J),CU),SU),CPLUSS( J), CL(J),CTH£TC(J),P8SC (J)
l,COPPBS(J),SMAX(J),DVS(J),J=ND,Nl)
WRITE(6,984) ( ZU),V(J),CO(J),PBS(J),CGRAO(J),Z(J+N3),V(J+N3),CO(
U+N3),P3S(J+N3),CGRAD(J+N3),J=NO,N4)
WRITE(6,975) SOLVOL.AOSVOL,TOTVOL
WRITE(6,96S) ITERS.LSIGS
WRITF(6,967) FRACTV
WRITE(6,991) AMTP10
WRITE(6,976) SUMCM,SUMSN,TOTN
WRITE (6,96^) N2
END TfST
IF(LSTEP-l) 73,73,74
74 NPTS NPTS * 1
ETIME (NPTS) TIME
TOTMATdMPTS) - TOTN
73 IFIFRACTV - QFRACT) 90,91,91
90 IF(TIMEMX - TIMF) 91,91,92
92 IF(DABS(FRCCUM)-OFRACT) 95,91,91
91 IF(LAST) 98,94,98
94 LAST = 1
IF((LSTEP/LPRTC)*LPRTC.EQ.LSTEP) GO TO 98
PRINT RESULTS FOR LAST TIME.
GO TO 72
SFT UP BLOCKS FOR NEXT TIME
95 CALL INTLY(HCOND,IN,HEAO,IN,CONC,N1,HEADPI,Ni,l,Nl)
74
-------
CALL INTLY(CAP,IN,HEAD,IN,CAPC,Nl,HEADPI,Nl,l,Nl)
00 96 J l,Nl
CO(J) = 0.
PBS(J) = 0.
TEMP8U) TEMP3(J)
OVSPT(J) = DVS(J)
PBSPTU) PBSC(J)
CTHEPIU) = CTHETC(J)
CTHEPT(J) = CTHETC(J)
CPSPT(J) = COPPBSU)
CPBSPKJ) = COPPBS(J)
CAPP(J) CAPCU)
CONP(J) CONC(J)
96 HEAOPT(J) HEAOC(J)
DELTA TIME TOO SMALL
IF(LSIGl.EQ.O.ANO.LSIGS.EQ.O) GO TO 254
GO TO 25
254 R = R + R
DLTIME DLTIME + OLTIME
GO TO 25
98 LSIG1 = I
CALCULATE FLUX RATES(FLXHAT-MASS/SQ CM/OAY)
81 CALL DUZ2(ETIME,NPTS,TOTMAT,NPTS,FLXMAT,NPTS,0,0,1,5,NPTS,0.,0)
WRITE (6,973)
WRITEt6,965)(ETIME(J),TOTM4T(J),FLXMAT(J), J - 1,NPTS)
WRITE(6,974) CONMAT,PB,K,DbPTH
101 IFINUMBEH - NUMCOL) 1,99,99
99 CALL EXIT
964 FORMAT ( • «•• , 126X, 15)
965 FORMAT ('0',2X,3(' TIME(OAYS) MASS/SQ CM MASS/SQ CM/DAY')/{«
1',1P9E14.3»
967 FORMAT(• ','FRACTION VOLATILI ZED•,25X,1PE13.3)
968 FnP.MAT( •«•• ,65X, • ITER. NO.',I3,' NO. OF POINTS NOT PASSING TEST',I
14) . i
971 FORMAT('0«,'NO. OF INTERVALS',14,• MAX. NO. QF ITERATIONS•, 13,•
1NO. OF COLUMNS',13,' EPSILON =',1PE10.2,» FRACTION OF OUTFLOW FO
2R STOPSE10.2/' ','LENGTH OF COLUMN',1PE10.2,' CM DELTA!' ,E 10.2, •
3 CM INITIAL R',F.10.2,' MAX. TIME • ,F10.2, ' OAYS INITIAL DELTA TI
4ME',E10.2/' '.'EPSILON TEST VALUE FOR ITERATION DIFHERFNCES =',l
5PE9.2,1 MIN. DIFFERENCE =',E9.2,' MAX.1 DIFFERENCE =',C9.2,« PRIN
6T INTERVALS SI2)
973 FORMAT(' I1)
974 FORMATCO1,' INITIAL MASS/GM SOIL ', 1PE11 .3, ' BULK DENSITY ' ,F9. 2, '
1GM/CC',' K',E11.3,' CC(LIQ)/GM SOIL'/' '.'DEPTH OF INITIAL DISTRI
2BUTION',OPF5.0, • CM')
975 FDRMAT{'0','MASS/CM2 SOIL TRANSFERRED FROM SOLUTION PHASE',1PE13.3
I/' '.'MASS/CM2 SOIL TRANSFERRED FROM ADSOPBED PHASE',1PC13.3/• ','
2TOTAL MASS/CM2 SOIL VOLATILIZED',14X,1PP13.3)
976 FORMATC ' ,12X,'MASS/CM2 SOIL IN SOLUTION' , 1PE13.3, • MASS/CM2 SOIL
1 ADSORBED',E13.3,' TOTAL M*SS/CM2 SniL',E13.3)
977 FORMAT('0',7X,'Z',12X,'C',12X,'S',10X,»C + S',8X,« CL ',11X,'C',12
1X,'S',10X,'C + S',10X,'SM',11X,'OVS'/' «,7X,'CM',18X,'MASS/GM SOIL
2S14X, ' MASS/CCILIQ I ' , 13X,'MASS/CC < TOTAL )',17X,' MASS/GM ',6X,'CM2/DA
75
-------
3Y'/C *»IP10E13.3I)
978 FORMAT (8E10.3)
980 FORMAT12FIO.O,3F10.3,F10.0)
981 FORMAT {• AMOUNT IN PROFILE AT THIS TIME1,1PE11.3,• CM «,'FLUID
IAPPLIED AT Z=0 TO THIS TIME•,Ell.3,• CM '.'NET GAIN OR LOSS BY FL
2UX',E11.3,« CM')
982 FOPMAT (4E10.3)
983 FORMAT (2F10.3)
984 FORMAT!1 •,48X,'TRANSFER OF MATERIAL-MASS/SQ CM/DAY•/•••,2(8X,'Z',
17X,'OIFFUSION',4X,'BY WATER't7X,'TOTAL•,6X,'CONC. GRAD')/(2(1PE13.
22,4E13.3»)
985 FORMATC ','Q/QINF. BY INTEGRAL',IPEll.3,• Q/QINF. BY DIFFERENCE*
1.E11.3,' AVE. K AT SURFACE',El 1.3,• FLUX AT SURF ACE',Ell.3)
986 FORMATCO','INITIAL CUMULATIVE WATER',1PF11.3,• INFINITE OUTFLOW
1.E11.3)
989 FORMATC'0','TIME IS'rIPEll.3,• HOURS OR',F11.3,' DAYS FLUX OUT',
1E11.3.' CM/DAY. CUMULATIVE OUTFLOW "FROM FLUX•,E11.3,• CM'/' CUMUL
2ATIVE OUTFLOW FROM THFTA PROFILE',IPEll.3,• CM NO. OF TIMES OVERI
3TERATED',I4,' FLUX BY CUMULATIVE 01FF.',Ell.3)
990 FORMAT('0',2(8X,'Z',5X,'PRESSURE HEAD',' WATER CONTENT',' HYD. HE
IAD ',' PORE VEL.')/C2(1PE13.2,4E13.3)))
991 FORMAT C+',65X,'AMOUNT DOWNWARD PAST Z= -10 CM.',IPE16.3)
992 FOMATCO'.'ITER. NO. ',13,' NO. OF POINTS NOT PASSING TEST',IS,15
I,' TIME STEP TIME',IPEll.3,' DAY. DELTA TIME',Ell.3,' DAY.')
993 FORMATC'0',13X,'EXPERIMENTAL VALUES OF APPARENT DIFFUSION COEFFIC
IIENTS(DVS) WITH CORRESPONDING WATER CONTENT VALUES(THETA).•/• ',52
2X,'OVS(CM2/DAY',4X,'THETACCM/CM)•/(• ',46X,1P2E16.3))
994 FORMATC ',2(10X,'HEAD',12X,'THETA',7X,'CONDUCTIVITY•,6X,'CAPACITY
I')/' ',2(11X,'CM',13X,'CM/CM',IOX,'CM/DAY',11X,'I/CM •)/(• ',1PE1
27.3.7F16.3))
995 FORMATCE10.5)
996 FORMAT(8E10.3)
997 FORMAT<2F10.0,F10.2,2F10.3,2I5)
998 FORMAT(I4,M2,6E10.3,2F5.0)
999 FORMATI'I'.'EVAPORATION OF WATER FROM THE SOIL SURFACE WITH NO FLO
1W OF FLUID ACROSS THE LrtWER BOUNDARY. EVAPORATION RATE IS VARIABL
2F WITH TIME.'/' •,'VOLATILUATION OF ORGANIC MATERIAL FROM THE SOI
3L SURFACE OCCURS AFTER TIME = 0 WITH CONCENTRATION(MASS/GM SUIL) =•
4 0 AT THE SURFACE.')
END
76
-------
C SUBROUTINE OUZ2 WILD POINT, SMODTH, AND/01? PI FFFRENTIATE.
C SUBROUTINE TO PREFORM WILD POINT REPLACEMENT,. SMOOTHING AND/OR
C DIFFERENTIATION IN A RANDOMLY SPACED VARIABLE. X(I) IS THE INDEPEN-
C DCNT VARIABLE, Yll) THE DEPENDENT VARIABLE TO BE MODIFIED AND YOU)
C THE RESULT OF THE MODIFICATION. Y AND YO MAY BE THE SAME OR OIFFER-
C ENT TABLES EXCEPT THAT IF MORT THAN ONE OPTION IS SPECIFIED OR IF
C ONE OPTION IS SPECIFIED FOR MULTIPLE USEAGE Y 4ND YO MUST BE THE
C SAME TABLE. THE OPTIONS ARE IWP=WILD POINT PASSES, ISM=SMOOTHING
C PASSES AND IOF=DIFFERENTIATE PASSES WITH THE OPTIONS EXECUTED IN THE
C ORDER GIVEN. IPAR=NUMBER OF POINTS TO BE USED IN FORMING PARABOLA,
C N=NUMBER OF X VALUES IN TABLE, WP=NUMBER OF STANDARD DEVIATIONS FOR
C WILD POINT CRITERIA. NANC=0 FOR NO ANCHORING, 1 TO ANCHOR FIRST
C POINT ONLY, 2 TO ANCHOR LAST POINT ONLY, OR 3 TO ANCHOR BOTH FIRST
C AND LAST POINTS. NANC IS APPLICABLE ONLY FOR WILO POINTING AND/OR
C SMOOTHING OPERATIONS. IPAR HAS AN UPPER LIMIT OF 25, MUST BE
C ODD AND MUST NOT BE GREATER THAN N, NOR LESS THAN 5.
C SUBROUTINE- SUPPLIED BY UCR COMPUTER CENTER- JOHN JAMES, PRINCIPAL
C PROGRAMMER.
SUBROUTINE DUZ2 (X,N1,Y,N2,YO,N3,IWP,ISM,IDF,IPARI,NI,WP,NANC1
IMPLICIT REAL*8(A-H, 0-Z)
REAL*8 X,Y,YO,XS,YS,A,B,C,0
DIMENSION XS(25),YS(25),A(25,3>,B(25),C(3,3),Om
DIMENSION X(N1),YCN2),YO(N3)
N = NI
IF (N - 5) 130,130,200
200 IPAR = IPARI
PNT1 - Y(l)
PNTN - Y(N)
IPARI - (IPAR - l)/2
FIPAR IPAR - ^
IF (IWP) 1,2,1
C IWP NON-ZERO WHEN WILO POINTING REQUIRED
1 IMT = IWP
M = 1
GO TO 6
2 IF (ISM) 3,4,3
C ISM NON ZERO WHEN SMOOTHING REQUIRED (WILD POINTING COMPLETED)
3 IMT = ISM
M = 2
GO TO 6
ft IF (IDF) 5,130,5
C IDF NON-ZERO WHEN DIFFERENTIATION REQUIRED (SMOOTHING COMPLETED)
5 IMT = IOF
M = 3
6 DO 129 INP = 1,IMT
DO 128 I = l.N
IF (I-l) 101,101,103
101 DO 102 J = 1,IPAR
XS(J) X(J)
102 YS(J) = Y(J)
103 IF (I-IPAR1-1) 104,104,105
104 IP = I
GO TO 109
77
-------
105 IF (I + IPAR1 - N) 106,106,108
106 DO 10T J = 2.IPAR
XS(J-l) XSU)
107 YS(J-l) = YSU)
J = I * IPAR1
XS(I°AR) = XUI
YS(IPAR) = Y(J)
IP = IPAR1 * I
GO TO 109
108 IP = I * IPAR - N
10? 00 110 J = IfIPAR
A(J,3) 1.0
A(J,2) = XSU) - XS(IP)
A(J,1> = A(J,2)*AU,2)
110 B(J) = YS(J)
00 111 J = It3
D(J) = 0.0
DO 1101 K = 1,3
1101 C(J,K) = 0.0
111 CONTINUE
GO TO (112,114,114),M
112 DO 113 J = 1,3
113 A(IP,J) = 0.0
B(IP)- = 0.0
114 DO 121 J = 1,3
00 118 K = J,3
00 115 L - 1,1 PAR
115 C(J,K) = C(J,K) * A(L,J) * A(L,K)
IF (K-J) 118,118,116
116 CU,IO = C(J,K) / C(J,J)
DO 117 L = 1, IPAR
117 A(L,K) = A(L.K) -CU,K) * A(L,JI
118 CONTINUE
DO 119 L - I, IPAR
119 0(J> DU) * A(L,J) * B(L)
D(J) = 0(J)/C(J,J)
DO 120 L = 1, IPAR
120 B(L) = BID - DU) * A(L,J)
121 CONTINUE
GD TO (122,126,127),M
122 SIGMA = 0.0
DO 123 J = 1, IPAR
123 SIGMA = SIG*A + 3(J)*B(J)
SIGMA =DSORT (SIGMA/FIPAR)
IF(WP*SIGMA-DABS (YS(IP)-DI3))) 126,126,125
125 YOU) = Yd)
GO TO 128
126 YQ(I) = 0(3)
GO TO 128
127 YOU) = 0(2) - 0(3) * C12,3)
128 CONTINUE
GO 70(1281,1281,129),M
1281 IF (NANC) 1282,129,1282
78
-------
1282 IF (NANC-2) 1283,1285,1284
1283 YOU) = PNT1
GO TO 129
1264 YOU) PNTl
1285 YO(N) = PNTN
129 CONTINUE
GO TO (2,4,130),M
130 RETURN
END
C LINEAR INTERPOLATION
SUBROUTINE INTLYJY,N,X,Nl,YP,N2,XP,N3,L,Ll)
IMPLICIT REAL*8(A-H, 0-Z)
REAL*8 Y,X,YP,XP
DIMENSION Y
-------
SOLVFS TRIOIAGONAL MATRIX
SUBROUTINF TRIDAGU,Nl,B,N2,C,N3tH,N4,Y,N5,Z,N6,V,N7,IVAL,ILAST)
IMPLICIT REAL*8(A-H, 0-Z)
RFAL*8 A,8,C,H,Y,Z,V
DIMENSION A(Nl),B(N2),C(N3»,H(N4),Y(N5)tZ(N6),V(N7)
DO 1 J IVAL,ILAST
OENOM = 6(J-1) A(J-l) * Y(J-U
IF(DENCM) 11,10,11
10 OENOM = 1.0-17
11 YIJJ C(J-l) / DENOM
I 2(J) = * 50
1. * (XU+3) <- XU+4)))/ 288.
SUM = SUM + A
1 CONTINUE
RETURN
END
80
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
I. Ke: rt
w
•J Tide
VOLATILIZATION LOSSES OF PESTICIDES FROM SOILS
P.
Farmer, Walter J., and Letey, John
University of California
Riverside, California
-12. Sponsoring Organization Environmental Protection Agency
R 801835
13. "ypf Keif.
EnvironmentaJL Protection Agency report number, EPA-660/2-7U-05U, August 197^
The volatilization of pesticides following soil application can be predicted from
considerations of the physical and chemical principles controlling concentrations
at the soil surface. When these concentrations are maintained at a relatively high
level, volatilization losses will be determined by the pesticide vapor pressure as
modified by adsorptive interactions with the soil. For pesticides which have been
mixed with the soil or when volatilization has been proceeding for a time so that
concentrations at the soil surface are low, volatilization rates will b'e determined
by the rate at which pesticides move through the soil to the soil surface. Under
conditions when mass flow in liquid water is negligible, volatilization rates are
predictable using solutions to the diffusion equations. When mass flow is operative
the prediction of rates of volatilization are more complex. A computer model has
been developed combining both diffusion and mass flow for predicting the volatili-
zation of soil-incorporated pesticides.
Temperature gradients in soil significantly affected the distribution of volatile
pesticides in soil. Vapor phase diffusion toward areas of low temperature can
occur simultaneously with mass flow in liquid water toward areas of high temperature.
J7a. Descriptors
Organochlorine insecticides, herbicides, volatilization, predictive models, vapor
density, lindane, dieldrin, trifluralin, DDT, DDE, transport processes, diffusion,
mass flow, adsorption, water pollution.
17b. Identifiers
Pesticide Runoff Model
ITc. COWKR Field &-Gr<-.i>p
19. Security C.'ass.
(Report)
20. Security Class.
21. liu. of
Pages
22. Price
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. O. C. 2O24O
W. J. Farmer
r.,V:,-L.,,ti,; University of California. Riverside 92502
U.S. GOVERNMENT PRINTING OFFICE: 1974—582-415:158
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