SENSITIVE PARAMETER EVALUATION FOR A VADOSE ZONE FATE
AND TRANSPORT MODEL
Utah State University
Ligan, UT
Jul 89
U.S. DEPARTMENT OF COMMERCE
National Technical Information Service
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EPA/600/2-89/039
July 1989
SENSITIVE PARAMETER EVALUATION
FOR A VADOSE ZONE FATE AND TRANSPORT MODEL
by
David K. Stevens
William J. Grenney
Zhao Yan
Ronald C. Sims
Department of Civil and Environmental Engineering
Utah State University
Logan, Utah 84322
CR 813211
Project Officer
John E. Matthews
Robert S. Kerr Environmental Research Laboratory
P.O. Box 1198
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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TECHNICAL REPORT DATA
(Please read Instructions on ihe reverse before completing)
1. REPORT NO.
EPA/60Q/2-89/Q39
T 1 T~~i r- ... _ . . _ . ""
3.
IEJENT-
4. TITLE AND SUBTITLE
SENSITIVE PARAMETER EVALUATION FOR A VADGSE ZONE FATE
AND TRANSPORT MODEL
5. REPORT DATE
July 1989
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S) ~ '
David K. Stevens, William J. Grenney, Zhao Yan, and
Ronald C. Sims
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Civil and Environmental Engineering
Utah State University
Logan, Utah 84322
10. PROGRAM ELEMENT NO.
CBWD1A
11. CONTRACT/GRANT NO.
CR-813211
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Lab. - Ada, OK
U.S. Environmental Protection Agency
P. O. Box 1198
Ada, OK 74820
13. TYPE OF REPORT AND PERIOD COVERED
Final Report (05/86-Q9/88)
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
Project Officer: John E. Matthews
FTS: 743-2233
16. ABSTRACT ~
This report presents information pertaining to quantitative evaluation of the potential
impact of selected parameters on output of vadose zone transport and fate models used to
describe the behavior of hazardous chemicals in soil. The Vadose Zone Interactive
Processes (VIP) model was selected as the test model for this study. Laboratory and field
experiments were conducted to evaluate the effect of sensitive soil and model parameters
on the degradation and soil partitioning of hazardous chemicals. Laboratory experiments
.were conducted to determine the effect of temperature, soil moisture and soil type on the
degradation rate. Field-scale experiments were conducted to evaluate oxygen dynamics,
through depth and time, for petroleum waste applied to soil. Results of laboratory
experiments demonstrated that the sensitivity of the degradation rate to changes in
temperature and soil moisture was generally greater for low molecular weight compounds and
less for high molecular weight compounds. For the two soil types evaluated, soil type was
more significant with regard to immobilization. Soil type was not found to have an effect
on degradation kinetics for the majority of chemicals evaluated. The effect of oxygen
concentration on chemical degradation as predicted by the test model was found to depend
upon the magnitude of the oxygen half-saturation constant. Oxygen-limited degradation
would be anticipated to occur shortly after the addition of chemicals to soil and during
active microbial metabolism of chemicals.
17.
KEY WORDS AND DOCUMENT ANALYSIS
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18. DISTRIBUTION STATEMENT
RELEASE TO THE PUBLIC.
19. SECURITY CLASS i rins
UNCLASSIFIED
121 NO O F P A (~ F ;
20. SECURITY CLASS (Tins pa
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (R«y. 4-77) PREVIOUS EDI TION i s OBSOLE re
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ii
NOTICE
The information in this document has been funded wholly or in part by the
United State Environmental Protection Agency under Cooperative Agreement CR-
813211 to Utah State University. It has been subjected to the Agency's peer and
administrative review, and it has been approved for publication as an EPA
document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
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iii
FOREWORD
EPA is charged by Congress to protect the Nation's land, air and water
systems. Under a mandate of national environmental laws focused on air and water
quality, solid waste management and the control of toxic substances, pesticides,
noise and radiation, the Agency strives to formulate and implement actions which
lead to a compatible balance between human activities and the ability of natural
systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center
of expertise for investigation of the soil and subsurface environment. Personnel
at the Laboratory are responsible 'for management of research programs to: (a)
determine the fate, transport and transformation rates of pollutants in the soil,
the unsaturated and the saturated zones of the subsurface environment; (b) define
the processes to be used in characterizing the soil and subsurface environment
as a receptor of pollutants; (c) develop techniques for predicting the effect
of pollutants on ground water, soil, and indigenous organisms; and (d) define
and demonstrate the applicability and limitations of using natural processes,
indigenous to the soil and subsurface environment, for the protection of this
resource.
This report presents information pertaining to quantitative evaluation of
the potential impact of selected input parameters on output of vadose zone
transport and fate models that are used to describe the behavior of hazardous
organic chemicals in soil. This evaluation should allow model users to identify
those site and model input parameters that have the greatest potential for
impacting model output.
Clinton W. Hall
Director
Robert S . Kerr Environmental
Research Laboratory
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iv
ABSTRACT
This report presents information pertaining to the development and
quantitative evaluation of the mathematical modeling of hazardous chemicals in
soil. The Vadose Zone Interactive Processes (VIP) model, based upon the
Regulatory and Investigative Treatment Zone (RITZ) model developed at the Robert
S. Kerr Environmental Research Laboratory, was evaluated and modified with regard
to site-specific dynamic processes. The VIP model was modified to simulate the
oxygen transport mechanism in the unsaturated zone, including oxygen transport
in air, water, and free hydrocarbon phases with exchange between each phase and
losses due to biodegradation. Oxygen-limited degradation was added to the model
using a kinetic form that is first order with respect to the organic constituent
concentration and mixed order with respect to oxygen concentration. Model output
was evaluated as a function of soil oxygen tension, and soil temperature.
Laboratory and field experiments were conducted to evaluate the effect of
sensitive soil and model parameters on the degradation and soil partitioning of
hazardous chemicals. Laboratory experiments were conducted to determine the
effect of temperature, soil moisture, and soil type on degradation rate. Field-
scale experiments were conducted to evaluate oxygen dynamics, through depth and
time, for petroleum waste applied to soil.
Results of laboratory experiments demonstrated that the sensitivity of
degradation rate to changes in temperature and soil moisture was generally
greater for low molecular weight compounds and less for high molecular weight
compounds. For the two soil types evaluated, soil type was more significant
with regard to immobilization; soil type was not found to have an effect on
degradation kinetics for the majority of chemicals evaluated.
The effect of oxygen concentration on chemical degradation predicted by the
VIP model was found to depend upon the magnitude of the oxygen half-saturation
constant. Oxygen-limited degradation would be anticipated to occur shortly after
the addition of chemicals to soil and during active microbial metabolism of
chemicals.
Model output results for temperature dependent reactions indicated that
depth-concentration profiles would be sensitive to and directly related to the
temperature correction coefficient (9) for each chemical. Model outputs would
be very sensitive to soil temperature when values for 9 was 1.04 or greater.
For the range of values considered for the mass transfer rate coefficient,
the VIP model was found to accurately represent nonequilibrium
sorption/desorption kinetics enhancement.
Results of laboratory and short-term field studies indicated that site-
specific sensitive parameters need to be addressed in modeling the fate and
behavior of hazardous chemicals in the unsaturated zone of a soil system Site-
specific sensitive parameters, including soil oxygen concentration and
temperature were incorporated into the VIP model in order to evaluate the
influence of these parameters on fate and transport. These parameters are
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important Input for other mathematical models used to describe fate and transport
in the vadose zone.
This report was submitted in fulfillment of Cooperative Agreement number
813211 by Utah State University under the sponsorship of the U.S. Environmental
Protection Agency. This report covers a period from October 1, 1986 to September
30, 1988, and work was completed as of June 1, 1988.
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vi
CONTENTS
Notice ...................
Foreword
Abstract iy
Figures vii
Tables ................... ix
Acknowledgments . % x
1. Introduction .......... 1
Objectives ....... 2
Approach ...... 2
2. Conclusions ......... 4
3. Recommendations 5
4. Soil Treatment Model ............... 6
Sorption/desorption Kinetics . ...... 6
Model Processes ...................... 11
Model Equations ............ 16
Model Boundary Conditions ..... 18
Solution Algorithms ........ 19
5. Sensitive Model and Soil Parameters . 23
Temperature 23
Oxygen ........... . 23
Moisture ............. 24
Soil Type 25
6. Results and Discussion .......... 28
Sensitive Parameters 28
Model Output as a Function of Temperature-
dependent Degradation 36
Model Output as a Function.of Oxygen-
limited Degradation 41
Field Evaluation of Model for Prediction
of Oxygen Dynamics 46
Analytical Solution to Two-Phase Model 49
Effect of Mass Transport Coefficient on
Model Behavior 61
References 66
Appendix A Nonlinear Least Squares Analysis of Temperature Data .... 74
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vii
FIGURES
Number Page
1. Schematic diagram of unsaturated aggregated porous medium 8
2. Apparent loss of acenaphthene 29
3. Apparent loss of fluorene 29
4. Apparent loss of phenanthrene 29
5. Apparent loss of anthracene 29
6. Apparent loss of fluoranthene 30
7. Apparent loss of pyrene 30
8. Apparent loss of benz[a]anthrancene 30
9. Apparent loss of chrysene 30
10. Apparent loss of benzo[a]pyrene 31
11. Apparent loss of benzo[b]fluoranthene 31
12. Apparent loss of benzofk]fluoranthene 31
13. Apparent loss of dibenz[a,h]anthracene 31
14. Benzo[g,h,i]perylene degradation 32
15. Indeno[123-c,d]pyrene degradation 32
16. Concentration histories and the predicted first order models
for chrysene, benzo[b]fluoranthene, and fluorene 39
17. Depth profiles of chrysene at .three different
temperatures after one year 42
18. Depth profiles of benzo[b]fluoranthene at three different
temperatures after one year 42
19. Depth profiles of fluorene at three different
temperatures after one year 42
20. Comparison of the depth profiles with and without oxygen-limits . . 44
21. Constituent and oxygen profiles after 80 days 44
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viii
22. Constituent and oxygen breakthrough curves
predicted by VIP model ...................... 45
23. Depth profiles with five of half oxygen
saturation constant coefficients ................ 45
24. Oxygen simulation at depth 6" .................. 48
25. Oxygen simulation at depth 12" ..... ....... 48
26. Oxygen simulation at depth 24" .................. 48
27. Comparison of the depth profiles calculated by the analytical
solution to the numerical solution (VIP model) with constituent
initially in the water phase 57
28. Comparison of the depth profiles calculated by the analytical
solution to the numerical solution (VIP model) with constituent
initially in the soil phase .................... 58
29. Comparison of the depth profiles calculated by the analytical
solution to the numerical solution (VIP model) with constituent
initially in both phases 59
30. Relative error % vs K in the water phase ............. 60
31. Relative error % vs K in the soil phase 60
32. Breakthrough curve predicted by VIP model with the
initial concentration in the water phase 64
33. Breakthrough curve predicted by VIP model with the
initial concentration in the soil phase .............. 64
34. Breakthrough curve predicted by VIP model with the
initial concentration in both phases 54
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ix
TABLES
Number Page
1. VIP model boundary conditions 19
2.. Percentages of PAH remaining at the end of the 240 day study
period and estimated apparent loss half lives 33
3. Arrhenius parameters for the apparent loss of PAH compounds
in sandy loam soil 34
4. The effect of soil moisture on degradation rate of PAH
compounds in sandy loam soil 34
5. Degradation rates corrected for volatilization for PAH
compounds and pesticides applied to two soils 35
6. Calculated soil/water (Kd), partition coefficients
for chemicals in two soils 37
7. Estimated values of K2g and 6_ , 38
8. Partition coefficients and initial concentrations
used in the study 40
9. Degradation summary from VIP Simulation ,40
10. Estimates of physical and kinetic parameters 43
11. Input data file for simulation of field data
from Nanticoke Refinery 47
12. Model input values for the first two sets of analyses 54
13. Model input values for the last set of analyses 55
14. Descriptions of variables used, units, and data sources 56
15. The definition of the percent relative error and notation 61
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ACKNOWLEDGEMENTS
This study was completed for the U.S. Environmental Protection Agency, R.S.
Kerr Environmental Research Laboratory. Mr. John Matthews was the project
officer.
We wish to acknowledge the support of the U.S. EPA in this endeavor, and,
in particular, the candid discussions with Mr. Joe Williams of the EPA on the
role and the future of Fate and Transport Modeling in environmental protection.
The participation of Dr. Ryan Dupont of the Department of Civil and
Environmental Engineering, Utah State Unversity, in the Nanticoke Refinery field
study to generate data used in this report for model evaluation is greatly
appreciated.
We would also like to thank Dr. Russell Thompson, Department of Mathematics
and Statistics, Utah State University for providing the analytical solutions.
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SECTION 1
INTRODUCTION
A mathematical description of the soil/waste system provides a unifying
framework for the evaluation of laboratory screening and field data that is
useful for the determination of soil treatment potential for a waste.
Mathematical models provide an approach for integration of the simultaneous
processes of degradation and partitioning in soil systems so that an assessment
can be made of the presence of hazardous substances in leachate, soil and air.
Models provide an estimate of the potential for groundwater and air contamination
through a determination of the rate and extent of contaminant transport and
degradation for particular site/soil/compound characteristics. Description of
quantitative fate and transport of chemicals in soil systems also allows the
identification of chemicals that require management through control of mass
transport and/or treatment to reduce or eliminate their hazardous potential (U.S.
EPA 1984, Mahmood and Sims,1986).
Specifically, mathematical models provide a framework for:
(1) evaluation of literature and/or experimental data;
(2) evaluation of the effects of site characteristics on soil treatment
(soil type, soil horizons, soil permeability);
(3) determination of the effects of waste concentration, soil moisture,
and amendments to increase the rate and/or extent of treatment;
(4) evaluation of the effects of environmental parameters (season,
precipitation) on soil treatment; and
(5) comparison of the effectiveness of treatment using different
practices in order to maximize soil treatment.
Thus mathematical models represent powerful tools for ranking design, operation^
and management alternatives as well as for the design of monitoring programs for
soil treatment systems.
Short (1986) developed, the Regulatory and Investigative Treatment Zone
(RITZ) model for evaluating volatilization-corrected degradation and partitioning
of organic constituents in soil systems. The RITZ model is generally based on
the approach used by Jury et al. (1983) for modeling fate and transport of
pesticide in the soil. The RITZ model, developed at the Robert S. Kerr
Environmental Research Laboratory (RSKERL), Ada, Oklahoma (U.S. EPA, 1988b),
incorporates factors involved in soil treatment at a land treatment facility,
including site, soil, and waste characteristics.
The Vadose Zone interactive Processes (VIP) model, was developed at Utah
State University (Grenney et al., 1987), as an enhancement of the RITZ model.
The VIP model allows prediction of the behavior of hazardous substances in
unsaturated soil systems under conditions of variable precipitation, temperature,
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and waste application, and incorporates the effect of oxygen tension on
degradation rate in subsurface vadose zone environments. The model simulates
vadose zone processes including volatilization, degradation, sorption/desorption,
advection, and dispersion (Grenney et al. , 1987). The VIP model has been used
for predicting the persistence and mobility of petroleum-refining wastes applied
to soil treatment systems (Symons et al., 1988), and for the evaluation of the
mobility of pesticides in soil (McLean et al., 1988).
Rational mathematical models of soil treatment are based upon conceptual
models of soil treatment processes. The degradation process represents an
important destructive mechanism for organic substances in soil systems.
Important sensitive variables that affect the degradation of organic chemicals
in soil include temperature, oxygen concentration, moisture, and soil type (U.S.
EPA, 1984 a and b) . Therefore, these variables are anticipated to influence the
degradation rate of a hazardous substance, which is used as an input variable
to these models. These studies incorporated quantitative relationships for
temperature and oxygen concentration into the VIP model for the purpose of
determining the effects of sensitive parameters on model predictions of chemical
fate and transport.
OBJECTIVES
The primary objective of this research project was to experimentally
determine the effect of sensitive model and soil parameters on soil treatment
and on outputs from vadose zone transport and fate models.
Specific objectives of this research project were to:
(1) Modify the selected test model (VIP) to simulate the oxygen transport
mechanism in the unsaturated zone, including transport in air, water,
and free hydrocarbon phases with exchange between each phase and
losses due to biodegradation.
(2) Evaluate model output as a function of soil oxygen concentration.
(3) Evaluate model output as a function of soil temperature.
(4) Determine the effects of temperature, oxygen, soil moisture, and soil
type on the rate of degradation of organic substances.
(5) Compare model simulations with field subsurface oxygen measurements.
APPROACH
The test model was evaluated with respect to incorporation of oxygen
transport and oxygen-limited biodegradation, and with respect to the effect of
temperature on degradation rate. Oxygen-limited biodegradation was added to the
VIP model using a kinetic form that is first order with respect to the organic
constituent concentration and mixed order (saturation kinetics) with respect to
oxygen concentration. A form of the Arrhenius expression was used in the model
for the purpose of evaluating the effect of temperature. The method of non-
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linear least squares was used to establish the degradation rate at 20°C and the
temperature correction coefficient values (6) for a subset of hazardous
substances. Model outputs were evaluated for sensitivity with respect to oxygen
concentration and soil temperature. A series of simulations was conducted to
evaluate the effects of soil oxygen and temperature on model predictions. The
model also was evaluated with respect to nonequilibrium adsorption/desorption
in order to more accurately simulate the process of immobilization in a soil
system.
A series of laboratory and field experiments were conducted to evaluate the
effect of sensitive soil and model parameters on the degradation of hazardous
substances. Laboratory experiments were conducted to determine the effect of
temperature, soil moisture, and soil type on degradation rate. A field-scale
experiment was conducted to evaluate oxygen dynamics, through depth, for a
petroleum waste applied to the top six inches of soil.
The test model was evaluated in laboratory column studies using a subset
of hazardous substances. Concentration profiles were predicted through depth
and through time under unsaturated conditions.
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SECTION 2
CONCLUSIONS
Specific conclusions based on the objectives of this research project are:
(1) Under field conditions with petroleum waste addition, the test model
successfully predicted the depth location of the decrease in the
oxygen concentration in the air phase, and semi-quantitatively
predicted the oxygen concentration. The model did not predict the
recovery of oxygen with depth.
(2) The effect of oxygen concentration on chemical degradation predicted
by the test model was found to depend upon the magnitude of the
oxygen half-saturation constant and the soil oxygen concentration.
Low oxygen concentrations in the soil would be expected to occur
shortly after waste addition to soil and during active microbial
metabolism of waste.
(3) Model output results for temperature dependent reactions indicated
that depth-concentration profiles were sensitive to and were directly
related to the temperature correction coefficient (9) for each
chemical used in the model. Model outputs were very sensitive to
soil temperature when values for 9 were 1.04 or greater; however,
for chemicals with values for 9=1.02 or less, there was little
sensitivity in the model output with respect to temperature.
(4) Results of laboratory experiments demonstrated that the sensitivity
of degradation rate to changes in temperature, soil moisture, and
soil type was generally greater for low molecular weight compounds
and less for high molecular weight compounds.
(5) The mass transfer rate coefficient, K, was found to control
the extent of dispersion in the absence of an explicit
hydrodynamic dispersion term in the transport model.
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SECTION 3
RECOMMENDATIONS
Based on the results of this research investigation, the following
recommendations are made pertaining to modeling the vadose zone and to
evaluating sensitive soil and model parameters:
(1) An intensive, long-term, field-scale evaluation of fate and transport
model is recommended for hazardous substances present in a complex waste with
respect to air, soil, and leachate phases that builds upon accomplishment of the
objectives of this research project.
(2) Further evaluation of degradation kinetic forms as influenced by oxygen
concentration is recommended. The kinetic form for oxygen-limited
biodegradation provided by Borden and Bedient (1986) increases data requirements
for the model, and the trade-off between increased complexity and model accuracy
requires further analysis.
(3) A larger subset of hazardous substances is recommended for evaluation
of sensitive soil and model parameters that serve as model inputs. While the
incorporation of quantitative relationships for oxygen concentration and
temperature into the test model was possible, further evaluation is required for
development of quantitative relationships for soil moisture and soil type that
can be incorporated into mathematical models of the vadose zone.
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SECTION 4
SOIL TREATMENT MODEL
Models used to simulate solute transport through soil may be classified
into two groups. The first group of models are diffusion-controlled sorption
models or two-region models. The liquid phase of the soil is divided into
mobile and immobile regions. Convective-diffusive transport is confined to a
mobile water phase, while the transfer of solutes into and out of the immobile
soil-water region is assumed to be diffusion controlled. The second group of
models are two-site kinetic (chemical) adsorption models. The governing
nonequilibrium adsorption/desorption system equations use first-order mass
transfer kinetics in considering a two-phase (water and soil environment)
chemical process.
ac as ac a2c
~VW + Da [la]
at at ax ax2
as
*K(KSWC-S)
at
where:
C is the concentration of the chemical in solution (g/m3) ,
S is the amount of chemical adsorbed per gram of soil (g/g),
Vw is the vertical pore-water velocity (m/day),
p is bulk density of the soil (g/m3) ,
6 is the water content (m3/m3),
x is the depth, positive downward (m),
t is time (days),
Da is the dispersion coefficient (m2/day),
Ksw is the partition-coefficient for soil with respect to the water phase
(g/g-soil)/(g/m3-water), and
K (kappa) is the mass transfer rate coefficient (day"1) , a parameter for
describing the exchange rate between the water phase and soil phase.
SORPTION/DESORPTION KINETICS
Lapidus and Amundson (1952) first developed a parabolic partial
differential equation model to describe mass transport of chemicals in porous
media. Hashimoto et al.(1964) discussed these equations and Kay and Elrick
(1967) used these equations to describe the movement of lindane through soils.
Lindstrom and Boersma (1971) obtained the solutions of the resulting initial
value problem with conservation type boundary conditions for the case of water
saturated, sorbing porous medium. In a later paper, Lindstrom et al.(l97l)
suggested a more comprehensive model of sorption, and solved it numerically
involving the relationship between the free and sorbed phases of the medium'
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In addition, Lindstrom and Narasinham (1973) obtained an exact solution to the
problem for the first order kinetics of sorption which requires a large
activation energy.
Two-region Model
More recent attempts to model the solute transport through soil may be
classified into two groups. The first group of models are diffusion-controlled
sorption (physical) models or two region models. The liquid phase of the soil
is divided into mobile and immobile regions. Convective-diffusive transport is
confined to only a fraction of the liquid-filled pores (mobile water phase),
while the remainder of the pores contain stagnant water. This stagnant water
has been visualized as thin liquid films around soil particles, dead-end pores
(Coats and Smith, 1964), non-moving intra-aggregate water (Philip, 1968;
Passioura, 1971) , or as relatively isolated regions associated with unsaturated
flow (Neilsen and Biggar, 1961). The transfer of solutes into and out of the
immobile soil-water region is assumed to be diffusion controlled. Transport
models based on first-order exchange rates of solute between mobile and stagnant
regions were initially discussed in the petroleum and chemical engineering
literature for nonsorbing chemicals (Coats and Smith, 1964). van Genuchten and
Wierenga (1976) presented a schematic diagram to describe the movement of a
chemical through an unsaturated, aggregated sorbing porous medium. Five
different regions can be identified (see Figure 1).
1) Air spaces.
2) Mobile (or dynamic) water, located inside the larger (inter-aggregate)
pores. The flow of fluid in the medium is assumed to occur in this region
only. Solute transfer occurs by both convection and longitudinal
diffusion.
3) Immobile (dead or stagnant) water, located inside aggregates and at the
contact points of aggregates and/or particles. In saturated media this
region is mainly confined to intra-aggregate pores. Note that air-bubbles
and unsaturated conditions may increase the proportion of dead water by
creating more dead-end pores.
4) A dynamic soil region, located sufficiently close to the mobile water
phase for equilibrium (assumed) between the solute in the mobile liquid.
5) A stagnant soil region, that part of the soil matrix where sorption is
diffusion limited. This part of the soil is located mainly around the
micro-pores inside the aggregates, or along dead-end water pockets.
Sorption occurs here only after the chemical has diffused through the
liquid barrier of the immobile liquid phase.
Van Genuchten and Wierenga (1976) extended the above concepts of mobile-
immobile water to include Freundlich-type equilibrium sorption-desorption
processes. Their equations are of the form
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B
DYNAMIC SOfl_ REGION (ip
..MOBILE WATER .
! X A A A X A A X f. -V X >.
STAGNANT S00_ REGION ((l-f)/o
DYNAMIC
REGION
t
Figure 1. Schematic diagram of unsaturated aggregated porous medium
(A) Actual model. (B) Simplified model.
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dcim a2cffi acm
-- ^o,Vm - [2a]
at dt ax2 ax
. - Cim) [2b]
dt
where :
cm and cim are the concentrations (g/m3) in both the mobile and stagnant
regions ,
9m and 0,m are the fractions of the soil filled with mobile and stagnant
water (m /m3), respectively,
vm is the average pore-water velocity in the mobile liquid,
a is a mass transfer coefficient (day"1) ,
R,,, and Rim are retardation factors to account for equilibrium type sorption
processes in the mobile and immobile regions, respectively,
Dm is the dispersion coefficient in the mobile liquid.
The mass transfer coefficient a is interpreted as a diffusion coefficient
divided by some average diffusional path length (Nielsen, 1986). Valocchi
(1985). Nkedi-Kizza et al.(1984), Rao and Jessup (1983), van Genuchten and
Cleary (1979), Rao et al.(1980a,b), van Genuchten and Wierenga (1976), and van
Genuchten et al. (1984) present more discussion on this type of model.
Two-site Model
The second group of conceptual models are two-site kinetic (chemical)
sorption models. Selim et al. (1976), and Cameron and Klute (1977) have
independently proposed this type of model to describe solute sorption on
heterogeneous solid surfaces. Rao et al.(1979) used this type of model for
pesticide sorption, while Hoffman and Rolston (1980) and De Camargo et
al. (1-9-79), used this model for phosphorus sorption. Additional application can
be found in the work of Nielsen et al.(1986) and Nkedi-Kizza et al.(1984). In
this model, two types of sorption sites are hypothesized: type 1 reaches
equilibrium instantaneously and type 2 are time-dependent kinetic sorption
models. The diffusion-controlled process (model 2) is not explicitly analyzed
in this work, however, Nkedi-Kizza et al.(1984) have shown that the diffusion-
controlled model is mathematically equivalent to a first order kinetic model.
The governing solute transport equations for a two-site chemical process
sorptive model are as follows:
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10
ac as ac a2c
(P/O) -VM + Da [3a]
at at ax ax2
as
f(C,S) [3b]
at
where:
C is the concentration of the chemical in solution (g/m3) ,
S is the amount of chemical sorbed per gram of soil (g/g),
Vw is the vertical pore-water velocity (m/day),
p is bulk density of the soil (g/m3) ,
8 is the water content (m3/m3) ,
x is the depth, positive downward (m),
t is time (days),
Da is the dispersion coefficient (m2/day),
Several conceptual models have been proposed and evaluated for describing
the solute sorption-desorption term (as/3t) in Eq. [3b] . Three of the most
common special cases were discussed by van Genuchten (1974):
1) Freundlich equation
S - KCN [4]
Differentiation of Eq [4] with respect to time gives:
as ac
- KNC""1 [5]
a.t at
2) The first order kinetic rate equation
as
- «(KSWC S)
at
3) Exponential equation
as
= k,e
bS
k,e'
-2bS
C - S
[7)
where
ki is the forward kinetic rate coefficient (I/day),
k2 is the backward kinetic rate coefficient (I/day),
b is similar to the surface stress coefficient (g///g), described by Fava
and Eyring (1956). For equilibrium sorption (3S/3t = 0), Eq. [7] reduces
to
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11
S -- e'2*3 [8]
Most previous work considered the equilibrium (type 1) model and to a
lesser extent utilized the nonequilibrium model. Lindstrom et al. (1971) and
Lindstrom and Narasinham (1973) considered nonequilibrium conditions and
discussed the mass transfer coefficient. In this report, we adopt the first
order kinetic model as the topic under discussion.
Mass Transfer Rate Coefficient
Rao et al. (1980a; 1980b) presented a theoretical and experimental analysis
of the mass transfer rate coefficient (a) for a two-region (physical
nonequilibrium) model and indicated that the mass transfer coefficient (a) for
the two-region model is dependent upon the soil particle sphere radius, time of
diffusion, volumetric water contents inside and outside the sphere, and the
molecular diffusion coefficient. However, relatively little is known concerning
the factors that affect the mass transfer rate coefficient (K) in two -site
(chemical nonequilibrium) models.
MODEL PROCESSES
The VIP model as presented in this report extends previous work by Short
(1986) and Grenney, et al . (1987) for use in screening specific hazardous wastes
from land treatment. The model describes a soil column 1.0 meter square with
depth specified by the user. A constituent, which refers to the hazardous
substance being tracked by the model, may be a pure compound or a mixture of
several compounds as long as the behavior of the mixture can be adequately
described by composite constituent parameters.
The model was developed under the following assumptions :
1) One dimensional soil system is assumed.
2) The soil column consists two isothermal layers: a plow zone (Zone of
Incorporation, ZOI) and a lower treatment zone (LTZ) . The plow zone is
a typically defined as the top 15 cm of soil into which the substance is
mixed during application. The LTZ extends below the ZOI to the bottom of
the soil column and contains substances which have been mobilized and
transported downward from the ZOI .
3) Unsaturated flow is assumed. The pore velocity of the water phase is
calculated by dividing the average infiltration rate (Vw') by the water
content of the soil (0W). The water content is estimated from the soil
properties and water net infiltration rate by the procedure of Clapp and
Hornberger (1978):
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12
/Ub+3)
where :
V = recharge rate (cm/ day)
c - saturated hydraulic conductivity (cm/day)
b - coefficient dependent on soil properties.
4) the soil environment within the column is made up of four phases: soil
grains, pore water, pore air, and pore oil.
5) First order non- equilibrium kinetics describes partitioning of the
chemical constituent between the water, soil, oil and air phases, and
partitioning of oxygen between the water, oil and air phases.
6) Degradation of oil and constituents in water, soil, air and soil phases
are expressed as a combination of the first order decay and a modified
Monod function for oxygen limitation.
7) Characteristics of the soil environment (site recharge rate, site
temperature and saturated hydraulic conductivity) can be changed with
depth and/ or time .
8) Waste material is applied to the plow zone at loading rates arid
frequencies specified by the user. It is completely mixed in the plow
zone.
9) The oil in the waste does not migrate. Only the chemical constituents
move with the soil water.
10) Longitudinal dispersion is insignificant in the water phase and neglected,
but included in oxygen and the air phase. Plug flow of water in plow zone
and treatment zone is assumed.
In this model, hydrodynamic dispersion is assumed to be negligible. This
assumption is based on the notion that, under unsaturated flow conditions, flow
velocities and turbulence levels are very small, fractions of those encountered
in saturated porous media. The causes of hydrodynamic dispersion are many but
the effects are primarily influenced by fluid turbulence, large density and
velocity gradients, and anisotropy of the fluid flow regime. Under prevailing
conditions in the vadose zone, these forces do not control the flow regime.
This phenomenon was evaluated by Mears (1971), who suggested a criterion
for trickle-flow reactors at low Reynolds number with first order kinetics,
whereby for dispersion to be safely neglected,
Z 20
- > - ln(C0/Cf)
dp B0
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13
where Z is the depth of the soil, dp is particle diameter, C0 is the influent
concentration, Cf is the effluent concentration, and B0 is Bodenstein number,
which is equal to Vdp/Dj^ (T>± is the hydrodynamic dispersion coefficient and V
is the fluid velocity), Petersen (1963) summarized considerable work that
suggested that B0 = 0.5 for low Reynolds numbers when the hydrodynamic regions
are interlocking. By this criterion using Co/Cf-100 (99% reduction of the
constituent), for hydrodynamic dispersion to be important, Z/dp=>184.2. For
typical soils with 0^=0.02 cm, Z>3.7 cm for axial dispersion to be neglected.
Thus, axial dispersion will only be important for very short columns of little
practical interest. Further, the dispersion process necessarily relies on a
continuum of fluid pathways. In the vadose zone, those pathways are not
continuous - the area of contact through which the flux may occur is a small
fraction of that which exists under saturated flow. Thus, the fluid attributes
necessary for the process to occur are missing. For these reasons, hydrodynamic
dispersion is neglected.
The model simulates the fate of hazardous organic substances in the soil.
The fate of a constituent in the soil column depends on mobilization,
volatilization, and decomposition processes. The model also simulates oxygen
transport in the unsaturated zone which includes transport by air, water, and
free hydrocarbon phases with exchange between each phase and losses due to
biodegradation of the hazardous waste constituents within the soil column.
Equation [9] describes these processes mathematically for one phase in a control
volume slice (thickness - dz) of a one-dimensional (vertical) soil column.
3(C0A) 3(0AD(dC/dz)) d(-V0AC)
dz - dz + dz + VAdz - RC0Adz [10]
at oz oz
where:
A - horizontal area of the control volume, (m2)
C - concentration of the constituent or oxygen in the phase (g/m3)
D - dispersion coefficient for the phase, (m2/day)
dz - depth of control volume, (m)
t - time, (days)
V - vertical pore velocity of the phase, (m/day)
z - depth, positive downwards (m)
6 = volume of the phase within the control volume, (m3 phase/m3 control
volume)
p bulk density of the soil (g-soil/m3 control volume)
R - degradation rate for the constituent or oxygen within the phase,
(I/day)
^ - mass sorption rate into the phase from other phases, (g/day/m3
control volume)
Mobilization (transport)
Once applied to the land and mixed into the plow zone, a constituent may
be mobilized by three mechanisms: advection, dispersion, and migration
between/among phases. Oxygen transport in a soil column may also include these
three mechanisms.
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14
Dispersion. Mobilization by dispersion of the phase within the soil
column is represented by the first term on the right-hand-side of Equation
[9]. Dispersion is simulated for chemical constituents in the air phase.
Dispersion in the water phase has been inactivated in this version of the
model because the nonequilibrium sorption/desorption process (described
later) provided dispersive phenomena sufficient to simulate observed
behavior. However, if and when activated, it will be solved by a scheme
similar to that for air. The oxygen dispersion mechanism is assumed
significant only in the air phase using the air dispersion coefficient
(Da).
Advection. The advection mechanism is represented by the second term on
the right-hand-side of Equation [10]. It may be significant for the water
and air phases. Oxygen transport by advection of the phase within the
soil column is assumed significant for the water and air phases with the
pore velocity of the water (Vw) and air (Va) phases. Although in some
applications advection may also be significant for the oil phase, this
version of the model constrains the oil to the plow zone. Laboratory
experiments on mobility of the oil phase in soil are currently underway
at Utah State University (USU) . The soil grain phase is assumed to be
immobile.
Sorption/desorption. The third term on the right-hand-side of Equation
[10] represents migration of the constituent or oxygen between/among
phases. This mass flux of the constituents or oxygen among phases is
modeled as a sorption mechanism. Grenney et. al (1987), Enfield et. al
(1986) and Lapidus and Amundson (1952) have expressed the sorption
mechanism as a linear gradient process of the following form:
V> - - *(K2 iC2 - Cx) [11]
where:
V> - mass flux of oxygen or constituent (g/m3-day)
Cx = oxygen or constituent concentration in Phase 1 (g/m3)
C2 = oxygen or constituent concentration in Phase 2 (g/m3)
K = mass transfer rate coefficient (day"1)
K2,i ~ linear partition coefficient for Phase 2 with respect to
Phase 1 (g-/m3-Phase 2)/(g-/m3-Phase 1)
In general sorption can occur directly between any two phases that are in
contact, and Equation [11] could be expanded to describe mass flux among more
than two phases at a time. However, estimating meaningful values for the
additional coefficients would be extremely difficult, and so it is assumed that
constituent migration from one phase to another must pass through the water
phase. Consequently, Equation [11] is applied between the water phase and each
of the other phases (Enfield et. al, 1986, Short, 1986). For the case of
oxygen, it is assumed that migration from one phase to another must pass through
the air phase, and there is no oxygen sorbed by the soil grain. Consequently
Equation [11] is applied between the air phase and water or oil phases
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15
Volat11ization
Volatilization is represented in the model by two processes: mass flux into
the air phase and advection/dispersion. The mass flux of the constituent into
the air phase is modeled by a sorption mechanism. The constituent is then
transported with the air phase by advection and/or dispersion, depending on the
conditions at the soil surface.
Degradation
The fourth term of Equation [10] represents the degradation (biochemical,
photochemical or hydrolytic). Field and laboratory studies of other investi-
gators, Sims, et al. (1988) and Sims and Overcash (1983), have indicated that
the use of first order kinetics provides a reasonable approximation for the
degradation of many hazardous substances in soil systems. Baehr and Corapcioglu
(1984) have presented a one-dimensional model for simulating gasoline transport
in the unsaturated zone which includes transport by air, water, and free
hydrocarbon phases with exchange between each phase and losses due to
biodegradation. Borden and Bedient (1986) and Molz et al. (1986) noted that the
microbial metabolism can be limited by a lack of either substrate (carbon and
energy source), oxygen (electron acceptor) or both simultaneously. The removal
of hydrocarbon and oxygen in each phase can be represented by a modified Monod
kinetic relationship where:
dC C 0
[12a]
dt Kc+ C K0+ 0
dO C 0
Mtki/,. [12b]
dt Kc+ C K0+ 0
where:
C is the concentration of the hydrocarbon;
0 is the concentration of oxygen;
M,. is the total microbial concentration;
k is the maximum hydrocarbon utilization rate per unit mass of
microorganisms;
vc is the ratio of oxygen to hydrocarbon consumed;
Kc is the hydrocarbon half saturation constant;
K0 is the oxygen half saturation constant;
t is time.
The degradation expression of the VIP model used in these studies to
evaluate sensitive model parameters combines the first order kinetics described
by Grenney et al., (1987) with a modified Monod function for oxygen limitation:
dC 0
^C [13a]
dt K0+ 0
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16
dO 0
I/c ^c [13b]
dt K0+ 0
where p, is the constituent first order decay rate (day"1) ,
Because the constituent may degrade at different rates in different phases,
separate rate and half-saturation coefficients are provided for each phase in
the model. The apparent degradation rate coefficients are permitted to vary
with depth in the model.
MODEL EQUATIONS
Based on the preceding discussion, the model equations for the four phases
within a soil column of unit cross-sectional area can be expressed as follows:
Ow
at dz K«+ ow
- (*a/0w)/ca(KawCw-Ca)
- (*0/0M)K0(KOWCW-C0)
- (p /0w)«s(KswCw-Cs) [14a]
aca a2ca oa
Va - + Da
at dz dz2 Ka+ oa
+ Ka-av,^-Ca --- [14b]
ea dt
aco 00 GO 300
*0(KOWCW - C0) - -- [14c]
00
acs _ Ow
fir fir r* t~* \
**Q V'^-ew'-'w ~ W«, I
a * on Y» & *
at ^ ow
-------
K00+ 00
17
w " o
[14f]
at
KO+ o0
«oa(KoaOa-00) -
(Po v0 +. 00)
1 d8r
:i4g]
ao
at
ao
/cwa(K,,aOa Ow)
[14h]
ao
ao
- V
at
a2o
Da
az2
K+ o
where :
Cs
Ka
Ko
Ks
p
at
[141]
concentration of the constituent in the oil phase (g/m3)
concentration of the constituent in the air phase (g/m3)
concentration of the constituent in the water phase (g/m3)
concentration of the constituent in the soil phase (g/m3)
constituent partition coefficient between air phase and water
phase (g/m3-air)/(g/m3-water)
constituent partition coefficient between oil phase and water
phase (g/m3-oil)/(g/m3-water)
constituent partition coefficient between soil phase and water
phase (g/g-soil)/(g/m3-water)
soil porosity (m3/m3)
soil bulk density (g/cm3)
constituent degradation rate in the oil phase (day"1)
constituent degradation rate in the oil phase (day"1)
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18
^ - constituent degradation rate in the water phase (day"1)
Hs = constituent degradation rate in the soil phase (day"1)
7 - the degradation rate of the oil phase (day"1)
00 - oxygen concentration in the oil phase (g/m )
Ow - oxygen concentration in the water phase (g/m3)
Oa - oxygen concentration in the air phase (g/m3)
K0 - oxygen half saturation constant with respect to the constituent
decay in the oil phase (g/m3) ,
K,, - oxygen half saturation constant with respect to the constituent
decay in the oil phase (g/m3)
Ka - oxygen half saturation constant with respect to the constituent
decay in the air phase (g/m3)
K00 - oxygen half saturation constant with respect to the oil decay
(g/m3)
Koa = oxygen partition coefficient between the oil and air phases
(g-02/m3-oil phase)/(g-02/m3-air phase)
K^ =- oxygen partition coefficient between the water and air phases
(g-02/m3-water phase)/(g-02/m3-air phase)
/ea constituent transfer rate coefficient between the water and air
phases (day"1)
KO - constituent transfer rate coefficient between the water and oil
phases (day"1)
/es constituent transfer rate coefficient between the water and soil
phases (day"1)
«0a - oxygen transfer rate coefficient between the oil and air phases
(day"1)
/ewa = oxygen transfer rate coefficient between the water and air phases
(day"1)
vc - stoichiometric ratio of the oxygen to the constituent consumed
i/p - stoichiometric ratio of the oxygen to the oil consumed
8a = volume of the air phase within the control volume, (m3-air/m3-
control volume)
0W = volume of the water phase within the control volume, (m3-water/m3-
control volume)
60 = volume of the oil phase within the control volume, (m3-oil/m3-
control volume)
Vw = pore water velocity", (cm/day)
P0 = density of the oil (g/cc)
MODEL BOUNDARY CONDITIONS
The boundary conditions of the VIP model are constituent and oxygen
concentrations at the upper and bottom layers of the soil column, and initial
conditions of concentration and water, air, and oil saturation with depth. The
model boundary conditions are presented in Table 1.
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19
Table 1. VIP Model Boundary Conditions
Boundary
z = 0
z - Z
t - 0
Phase
Air
ca oa 0.
0 P02*
0 P02
Cao oao eao
Water
cw ow 0W
0 K_ P
0 K P02
cwo owo *wo
Soil
°s
--
--
cso
Oil
C0 Oo ^o
--
--
Coo °po ^oo
No. condition required.
+ Partial pressure of oxygen in atmosphere (300 g/m3)
SOLUTION ALGORITHMS
The model Equations [14a] - [14i] are programmed in FORTRAN and solved
numerically. The program will run on IBM-PC, -XT, -AT, and PS/2 compatible
equipment, and has a built-in editor or accepts input files from LOTUS
spreadsheets. An option for graphical output is provided.
The computer code is designed in a modular structure to provide for
convenient enhancement in the future. The modular structure also provides a
convenient means for evaluating the behavior of various processes by isolating
the modules for independent analysis. The main solution algorithm is divided
into functional modules: loading rates, degradation, oil decay, and phase
transport and sorption.
Loading rates
The user specifies the initial oxygen concentration and initial
constituent concentration profile in the soil column and the frequency of waste
application. Each waste application is assumed to be instantaneously and
uniformly incorporated into the zone of incorporation (ZOI). This is
accomplished by establishing a new initial condition to account for the
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20
additional mass in the ZOI each time waste is applied.
Degradation
This module solves the degradation terms of Equations [14a], [14b] , [14d],
[14h] and [14i] for the oxygen and constituents in air, water and soil phases.
The concentration of the oxygen or a constituent remaining in the water, air or
soil phases at the end of a finite time interval (At) is calculated by:
r o i
C,,..,..,.> = C/^BXp -uAt [15]
{. tTat) v«/ r I ~ I
I K0 + 0 J
The solution for the constituent degradation in the oil phase, oil
phase decay, and oxygen consumption is accomplished by expressing the Equation
[14c], [14e] and [14g] as implicit difference equations across the time
increment (At). The resulting equations are then solved simultaneously by the
Newton-Raphson method.
Phase transport
The constituent or oxygen is transported by advection of the water phase
and by advection and dispersion of the air phase. The advective transport of
the water phase is formulated as an explicit, upstream difference (Bella and
Grenney, 1970) as follows:
C(ift+At) - c(i.t) + (C(i-i.t) - C(i|t))VAZ/At [16]
where V is an adjusted velocity and At is calculated such that:
VAt/AZ =1 [17]
This formulation provides an exact solution for the advective water
transport and will preserve a vertical concentration gradient at the leading
edge of the transport wave. The parameter V is obtained by adjusting the pore
velocity of the water, Vw, to account for the retardation caused by sorption as
described later. Experience has been gained over the years concerning the
behavior of numerical solutions for the advection and dispersion of water
quality constituents. The advection and dispersion terms have been solved
successfully for steady and unsteady flow by explicit (Bella, 1970; Holley,
1965; Hann, 1972) and implicit techniques (Hann, 1972; Harleman, 1968- O'Connor
1968; Prych, 1969; Grenney, 1978).
The dispersion terms of the air phase are formulated as an implicit
difference equation:
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21
+ A2 '-'i.t+At + ^3 Ci+ljt+At [18]
A! Da At/Az2
A2 = 1 + 2Da At/Az2
A3 - - Da At/Az2
The system of Equations [18] is expressed in matrix form and solved by
numerical techniques.
Sorpt ion/de sorption
The method involves solving the kinematic terms in each of the Equations
[14a] - [14i]. This is accomplished by expressing them as implicit difference
equations across the time increment (At). For each control volume (i):
At
[19b]
At
The equations for air and soil are identical in form to Equation [19b] for
oil. These equations are rearranged and solved by a one-pass matrix reduction
procedure. The system of equations and the numerical method preserve the mass
balance across the time increment. Oxygen partitioning is calculated using
Equations [19a] and [19b] with the air phase as the common medium.
Modular approach
There are three important benefits to programming numerical techniques in
functional modules. First, the program is easy to modify and upgrade. Second,
more than one solution procedure can be used, thereby allowing the use of a
specific technique (closed-form, explicit, implicit) best suited for the
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22
equations in each module. Third, the behavior of the various physical and
biochemical mechanisms being represented may be evaluated by isolating the
modules for independent analysis. These features also enhance the use of the
model as a research tool because a variety of hypotheses, expressed as
mathematical equations, may be conveniently inserted and tested.
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23
SECTION 5
SENSITIVE MODEL AND SOIL PARAMETERS
Important sensitive variables that may impact soil treatment include
temperature, soil oxygen, soil moisture, and soil type.
TEMPERATURE
Soil temperature is expected to be one of the most sensitive parameters
affecting soil treatment (Smith, 1982) and model output. The effect of
temperature on soil degradation reaction rate may follow the Arrhenius
relationship which has been used to correlate environmental temperature and
reaction rate in soils (Hamaker 1972, Dibble 1979, Lyman et al. 1982, and Parker
1983).
In this research project the effect of temperature on the rate of
degradation in a Kidman sandy loam soil was experimentally determined for 16
polynuclear aromatic hydrocarbon (PAH) compounds. Soil properties determined
prior to initiation of the study include a soil pH of 7.9, 0.5% by weight
organic carbon, 0.06% by weight total phosphorus, 0.07% by weight total nitrogen
and a water holding capacity of 16% by weight. These compounds were evaluated
because of their presence in petroleum and wood preservative organic wastes and
because of their public health implications (Sims and. Overcash 1983). A
standard solution of 16 PAH compounds in dichloromethane was added to the soil
to achieve an equivalent one percent by weight creosote addition to soil. The
loading used resulted in the following soil concentrations (mg/kg soil dry-
weight) : naphthalene (501), acenaphthylene (30.4), acenaphthene (400), fluorene
(100), phenanthrene (1000), anthracene (600), fluoranthene (400), pyrene (400),
benzo[a]anthracene (30.1), chrysene (200), benzo[b]fluoranthene (9.94),
benzo[k]fluoranthene (9.98), benzofa]pyrene (10.76), dibenz[a,h]anthracene
(10.56), benzo[ghi]perylene (9.96), and indeno[l,2,3-cd]pyrene (5.25).
Temperatures evaluated were 10°, 20°, and 30°C.
Moisture content of the soil-PAH mixtures in glass beaker microcosms was
maintained between 80 and 100% of the soil water holding capacity. Periodically
through time triplicate sets of microcosms at each temperature were removed from
incubation and solvent extracted with dichloromethane. Concentrations of PAHs
in soil were determined by HPLC analysis of the extracts. The study was
terminated after 240 days of incubation.
OXYGEN
Microbial respiration removes oxygen from the soil atmosphere and enriches
it with carbon dioxide. While gases diffuse freely into and out of the soil
environment across the air/soil interface, the oxygen concentration in normal
soil air may be only half that of atmospheric levels, while concentrations of
carbon dioxide may be many times higher than in the surface air (Brady 1974).
A large fraction of the microbial population within the soil environment depends
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24
upon oxygen to serve as its terminal electron acceptor in their metabolism.
Bacteria of the genus Pseudomonas. members of which are often linked to the soil
transformation of xenobiotic compounds, are strict aerobes. Under oxygen-
restricted conditions, facultative organisms, those which use alternative
electron acceptors such as nitrate (denitrifers) or sulfate (sulfate reducers),
and strict anaerobic organisms become the dominant species. Metabolism shifts
from oxidative to fermentative under oxygen limiting soil conditions and becomes
less efficient in terms of energy production and substrate utilization. The
maximum rate of decomposition of degradable hazardous compounds is generally
correlated with aerobic, oxidizing conditions. Excessive levels of degradable
materials may lead to a depletion of oxygen and the formation of anaerobic,
reducing conditions in the soil pores. The rate and extent of decomposition of
many contaminants is limited under these reducing conditions, and anaerobic
metabolism may result in reduced compounds that are odorous and toxic to
microorganisms.
Subsurface oxygen concentration was measured under field conditions where
petroleum waste was applied as part of a soil biodegradation field study at the
Texaco Nanticoke oil refinery at Simcoe, Ontario, Canada. Dissolved oxygen
sensors were placed at 6, 12, and 24 inches below the ground surface prior to
application and incorporation of the refinery waste sludge. Subsurface sampling
wells, -1" in diameter, were hand augured into the soil, and 3/4" PVC Schedule
40 pipes, fitted with air tight o-ring seals, were placed into the wells. The
wells were then backfilled with wet soil to ensure a tight seal around the
outside of the pipe. Soil dissolved oxygen sensors (Jensen Instruments, Tacoma,.
WA) were lowered into the wells and snapped into the air tight seals. The
sensors were connected to a programmable data measurement, collection, and
logging device (Campbell Scientific, Logan, UT) that allowed continuous
measurement of the oxygen content in the soil pores, averaging of the continuous
readings over discrete sampling periods, and storage of the discrete 02 levels
on cassette tape for later processing on a microcomputer. Calibration of the
probes was done in air at least daily, by removing the probes from the sampling
wells, allowing them to equilibrate, and adjusting the amplifier output of the
sensor so that the display reading corresponded to atmospheric levels of oxygen.
Dissolved oxygen sensors were put into service prior to waste application
to collect background measurements of subsurface 02 concentrations. Monitoring
was continued during and after waste application. The full record of raw 02
measurements is provided in Appendix D of this report. A subset of the data
record was selected for study and comparison with VIP model simulation of soil
oxygen dynamics at field scale.
MOISTURE
Soil water serves an important function as a transport medium through which
nutrients diffuse and through which waste products are removed from the
microbial cell surface. Soil water potential is the term used to express the
energy with which water is associated with a soil surface and represents an
energy potential against which organisms must work to extract water from the
soil matrix. Microbial activity generally can be sustained at water potentials
from -5 to lower than 15 bars without significant inhibition, while the lower
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25
limit for bacterial activity is probably about -80 bars (Soil Science Society
of America 1981). Fungi appear to be more tolerant of low soil water potential
than bacteria (Gray 1978, Harris 1981), therefore microbial decomposition of
organic materials in dry soils would be attributed primarily to fungal activity.
Although some information exists regarding soil moisture effects on soil
microbes, extensive information on optimal and marginal water potentials for
growth, reproduction, and survival of individual species of microorganisms in
soil remains limited (Taylor et at. 1980).
At saturation or near saturation conditions as soil pores become filled
with water, the diffusion of gases through the soil is severely restricted,
oxygen is consumed faster than it is replenished in the soil vapor phase, the
soil becomes anaerobic, and major shifts in microbial metabolic activity occur.
Changes in soil microbial metabolic activity can be correlated with oxidation-
reduction potential, or Eh, which is an expression of the electron density of
a system. Effects of high soil moisture content with regard to limiting
diffusion of oxygen in the soil atmosphere have been discussed previously.
Experiments were conducted to determine the effect of soil moisture on the
rate of apparent degradation of a subset of hazardous substances. Soil moisture
levels of -0.33, -1.0, and -5.0 bars matric potential were used. Temperature
was maintained at 20°C, and glass beaker reactors containing 200 g sandy loam
soil were incubated in the dark to prevent photodegradation. Moisture was
maintained at the desired levels by periodic addition of distilled water to each
beaker and mixing with a glass stirring rod. Periodically through time
triplicate sets of reactors at each soil moisture level were removed from
incubation and solvent extracted with dichloromethane according to the method
of Coover et al. (1987). Concentrations of PAHs in soil were determined by
HPLC analysis of the extracts.
SOIL TYPE
Soil texture and clay mineralogy are also important factors affecting soil
microbial processes (Stotzky 1972, 1980). Clays with a 1:1 crystal lattice,
e.g., kaolinite are non-swelling and have low cation exchange capacity, while
1:2 crystal lattice clays, e.g., montmorillonite, swell, trapping water and
dissolved materials between the lattices. The high cation exchange capacities
of clays like montmorillonite greatly increase the buffer capacity at microsite
within the soil, and reduces the impact of protons released into, the soil
environment as product of microbial metabolism. Differential sorption of
organic compounds and inorganic ions by different clays also affects the
availability of substrates and micronutrients to the soil microorganisms.
Soil organic matter is an important soil property that affects sorption as
well as degradation (U.S. EPA, 1984 a and b). Sorbed compounds or ions may be
available for extended periods of time for microbial metabolism and
transformation if retained within the soil matrix by soil organic matter
(Mahmood and Sims, 1986). Detailed discussion of the influence of soil organic
and mineral components are presented elsewhere (U.S. EPA, 1984 a and b) .
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26
Soil pH is also an important soil property. The optimum pH range for rapid
decomposition of most wastes and residues is from 6.5 to 8.5. Bacteria and
actinomycetes have pH optima near neutrality, and do not compete with fungi in
aqueous media, that are more tolerant to acidic conditions i.e., pH levels less
than 5. Competition between fungi and other microorganisms as a function of pH
is less clear in soils, however, where the buffer capacity of clay and humic
materials affects the concentration of protons at the microsite scale (Gray
1978).
Two soil types, a McLaurin sandy loam and a Kidman sandy loam, were
evaluated with regard to degradation and immobilization, or partitioning, of a
subset of hazardous substances. The Kidman sandy loam soil (U.S. EPA 1988) was
described previously in this section under temperature. McLaurin sandy loam
properties include a soil pH of 4.8, 0.94% by weight organic carbon, 0.003% by
weight total phosphorus, 0.02% by weight total nitrogen, and a saturation water
content of 20% by weight. For biodegradation rate determination, selected
substances were mixed with the two soils and incubated in glass beaker reactors
at 20°C in the dark to prevent photodegradation. Moisture content was
maintained at -0.33 bar matrix potential by periodic addition of distilled water
to the soil in the glass reactors and mixing. Periodically through time
triplicate sets of reactors containing each soil type were removed from
incubation and solvent extracted with dichloromethane according to the procedure
of Coover et al. (1987). Concentrations of chemicals were determined by HPLC
analysis of the soil extracts.
Partition coefficients for a subset of "substances were calculated for the
two soil types using quantitative structure -activity relationships (QSARs) .
Partition coefficient for each chemical between soil and water, Kd, is given by:
Cs
Kd -- [20]
Cw
where Kd is the soil/water partition coefficient (dimensionless if Cs and Cw are
in the same units). Cs is the concentration of chemical in the soil phase, and
Cw is the concentration of chemical in the aqueous phase. Kd values for organic
substances can be estimated from Koc (partitioning based upon soil organic
matter) values if the organic fraction of the soil, foc, is known and if it is
assumed that hydrophobic interactions dominate the partitioning processes:
Kd = Koc x foc
where Koc is the organic carbon normalized soil/water partition coefficient.
By assuming that partitioning between water and the organic fraction of
soil is similar to partitioning between octanol and water, a correlation
equation can be used to relate Koc to octanol/water partition coefficient (Kow) .
The correlation equation used to calculate Koc for this project was that of
Karickhoff et al. (1979):
logKoc = 1.0 logKow 0.21 [22]
-------
27
Therefore using K^ values it was possible to calculate Koc for each chemical.
Using the calculated Koc and the measured organic carbon content for each
experimental soil, the partition coefficient, Kj, was calculated.
-------
28
SECTION 6
RESULTS AND DISCUSSION
SENSITIVE PARAMETERS
Temperature
Figures 2 through 15 present the trends observed for decrease in parent
compound concentration with time of incubation for the PAH compounds evaluated
(Coover, 1987). The percentages of each compound remaining in the soil at the
end of the 240 day incubation period are presented in Table 2. Also presented
are the estimated half-lives based on a first-order kinetic model for degradation
and representative half-life values obtained from the literature.
The extent and rate of apparent loss was much greater for PAHs of low
molecular weight and high aqueous solubility. Substantial loss of three-ring
compounds acenapthene, fluorene, and phenanthrene was observed at all
temperatures during the course of the study. Four-ring compounds, including
fluoranthene, pyrene, and benz[a]anthracene demonstrated greatly reduced rate
of degradation under the temperature range from 10° to 30°. Loss of chrysene,
a four-ring compound, and the remaining five and six-ring compounds was minimal
at all three temperatures. Bossert et al. (1984) found similarly that after a
1280 day laboratory simulation of the land treatment process the total remaining
of three-ring, four-ring, five-ring, and six-ring PAHs was 1.4, 47.4, 78.5, and
78.3% respectively. Other investigators have noted this general trend for the
PAH class of compounds (Sims and Overcash 1983, PACCE 1985, Herbes and Schwall
1978).
Baded upon the experimental results obtained for degradation rate as a
function of temperature, the effects of temperature were described by the
Arrhenius equation. The parameters for fluorene, anthracene, fluoranthene,
pyrene and benz[a]anthracene are presented in Table 3. The Arrhenius expression
may be appropriate for quantitatively describing the effect of temperature on
PAH loss rates in soil for those PAH compounds where an effect of temperature
is observed.
The sensitivity of the output of .the mathematical model VIP was evaluated
with respect to the effect of temperature on degradation rate for a subset of
PAH compounds. Presentation and discussion of these results is presented "in a
subsequent subsection Model Output as a Function of Temperature-dependent
Degradation.
-------
1 .U
0.8 §
o °-6ij
D
0.4
0.2
Of)
0
o
. § a. ft * .
0 50 100 150 200
Tim* (d»y)
10»C
30*C
i OB ;
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r\ f\
|8 « 020«C
5 « 30'C
8
§ e
a t A 3
W A £. -
.
250 0 50 100 150 200 250
Tim» (d&y)
Figure 2. Apparent Loss of Acenaphthene Figure 3. Apparent loaa of Fluorene
12*0
''mm
2 i
1 '° $
o 0.8
5 0.6
0.4
0.2
10*C
020*C
30*C
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! £ £ j. C
w
. _
0 50 100 150 200
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n f\
i o A o *
: 2 o o
0
g
c
»io»c o
020*C
306C
250 0 50 100 150 200 250
Tirno (d»y)
Figure 4. Apparent Loss of Phenanthrene Figure 5. Apparent Loss at Anthracene
S3
VO
-------
1.00
0.80
0.60
0.40
0.20
0.00
!-s * . ; 8 :
§ : » s :
5 o
. 0
. : ? .
* 10'C
020"C
30°C *
* .,,,«.
D 50 100 130 200 2
1.00
0.00
$ °'60
0.40
0.20
0.00
50
!^ s s ; ' s s §
' M
s
» 10'C
020°C
30«c m n
3 50 100 150 200 2S
Time (d»y) Time (d»y)
I
1.20 I
1 .00 j
0.00
0.60
0.40
0.20
000
0
'igure 6. Apparent Loss of Fluoranthene.
I
8 8 8 I I
: s § g
s .
10*C
0 20*C
30"C
50 100 ISO 200 25
K2°.
i.ooj
0.80
o
D °'60
0.40
0.20
0.00
0 C
figure?. Apparent Loss of Pyrene.
a
..
! m A *
* M M A
* s A 1 e s
s s
» 10*C
0 20"C
30SC
) 50 100 130 200 23
Time (d»y) Time (d»y)
Figure 8. Apparent Loss of Benz[a]anthracene.
Figure 9. Apparent Loss of Chrysene.
-------
o
u
o
u
1.0
0.8
0.6
0.4
0.2
0.0
i.
* ft *
i * *
j' t : . i
;: «I ' I ;
10'C
o 20*C
30*C
0 50 100 150 200 25
Time (
-------
32
o
O
-x,
u
0.00
1.40 |
1.20
8 .
LOOS ^
0.80
0.60
0.40
0.20
o
A
*10
o20*C
30"C
0 50 100 150
Ttae (day)
Figure 14. Benzo[g.h.ijperylene degradation.
200
250
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
o
8
t *
8 o £ *
i S ' « «
s - g : |
*i
02
3
^_
9
0°C
O'C
oec
0 50 100 150
Tine (clay)
Figure 15. Indeno[123-c.d]pyrene degradation.
200
250
-------
33
Table 2
Percentages of PAH Remaining at the End of the 240 Day Study Period and
Estimated Apparent Loss Half Lives
Compound
Acenapthene
Fluorene
Phenanthrene
Anthracene
Fluoranthene
Pyrene
Per cent of PAH
Remaining Estimated Half Life (day)8
10°C 20°C 30°C 10°C 20°C 30°C
5
8
36
83
94
93
0
3
19
51
71
89
0
2
2
58
15
43
<60
60
(50-71)
200
(160-240)
460
(320-770)
f
f
<10
47
(42-53)
<60
260
(190-420)
440
(280-1000)
1900
<10
32
(29-37)
<60
200
(170-290)
140
(120-180)
210
Half lives reported
in the literature (day)
96b,45b,0.3-4°
64b,39b,2-39c
69b,23b,26c,9.7d,14d
28b,17b,108-175c,17d,45d
104b,29b44-182c,39d,34d
73b,27b,3-35c,58d,48d
'(1100-8100) (150-370)
Benz[a]anthracene
Chrysene
Benzo[b]fluoranthene
Benzo[k]fluoranthene
Benzo[a]pyrene
Dibenz[a,h]anthracene
Benzo[g,h,i]perylene
Indeno [ 1 ,2,3-c,d]pyrene
82
85
77
93
73
88
81
80
71
88
75
95
54
87
76
77
50
86
62
89
53
83
75
70
680
(520-980)
980
(710-1500)
580
(400-1100)
910
(640-1600)
530
(300-2230)
820
(520-1920)
650
(420-1300)
600
(450-910)
430
(360-540)
1000
(750-1900)
610
(410-1200)
1400
(840-5700)
290
(170-860)
750
(490-1600)
600
(410-1170)
730
(460-1830)
240
(200-280)
730
(550-1100)
360
(280-510)
910
(500-5310)
220
(160-380)
940
(490-12940)
590
(340-2390)
630
(350-3130)
52b,123b,102-252c,240d,130d
70b,42b,5.5-10.5°,328d,224d
73-130e,85b,65b
143b,74b
91b,69b,30-420c,347d,218d
74b,42b, 100-190°
179b,70b
57b,42b,200-600e
a J1/2 (95 per cent confidence interval)
b Sims (1986), T=20°C
0 Sims and Overcash (1983), T=15-25°C
d PACCE (1985), T=20°C
8 Sims (1982), T=20°C
f Least squares slope (for calculation of t1/2) = zero with 95% confidence
-------
34
Table 3. Arrhenius parameters for the apparent loss of PAH compounds in sandy
loam soil.
Compound
Activation Energy
(Kcal/mol)
Preexponential
Term Ln(A)*
Kinetic Model
Fluorene
Anthracene
Fluoranthene
Pyrene
Benz [ a ] anthracene
5.0
7.5
21.7
40.3
9.4
4.5
12.9
36.3
67.0
12.8
first
zero
zero
zero
zero
* A has units of Mg/g/d f°r zero order model and 1/d for the first order model
Moisture
Results for the effects of soil moisture at 20°C on the rate of degradation
of subset of PAH compounds, incubated in soil as a synthetic mixture of the PAHs
shown, are expressed in terms of half-life values and 95% confidence intervals (CI)
on half-life values in Table 4. Half-life values were calculated based on a first-
order model for PAH disappearance.
Degradation rates were significantly different at different soil moisture
levels for the three-ring PAH anthracene and the four-ring PAH fluoranthene. For
the PAH compounds naphthalene (two-ring), phenanthrene (three-ring), and pyrene
(four-ring), no significant effect of soil moisture was evident. Because of the
Table 4. The effect of soil moisture on degradation rate of PAH compounds in
sandy loam soil
Compound
Naphthalene
Anthracene
Phenanthrene
Fluoranthene
Pyrene
20-40%
tl/2
(days)
30
72
79
530
-
F.C.*
95% CI
15-
50-
53-
462-
-
93 a+
128 a
154 a
578 a
40-60% F.C.
ti/2
(days)
28
46
-
200
7500
95%
14-
CI
93 a
27-173 a
.
165-267 b+
877-
oo a
60-80% F
t
( days )
33
18
58
230
5300
95%
18-
7-
72-
.C.
CI
23
46
147
193-289
2500-
00
a
b
a
b
a
F.C. - field capacity of the soil.
The same letter (a or b) for a compound at two moisture contents indicates
no statistical difference at the 95% level based on a t-test.
-------
35
lack of a rational quantitative relationship between soil moisture content and rate
of degradation, it was not possible to evaluate the mathematical model VIP with
regard to model output as a function of soil moisture.
Soil Type
Results for degradation rates, corrected for volatilization, for a subset of
PAH compounds and eight pesticides incubated individually at -0.33 bar soil moisture
and 20°C, as a function of soil type are presented in Table 5. Half-life values
were calculated based on a first-order kinetic model for degradation; 95% confidence
intervals (CI) are also given.
As indicated in this table, for the PAH compounds investigated, there was no
statistically significant difference in degradation rate as a function of soil type
Table 5. Degradation rates corrected for volatilization for PAH compounds
and pesticides applied to two soils.
Compound
PAHs:
Naphthalene
1 -Methyl - naphthalene
Anthracene
Phenanthrene
Fluoranthene
Pyrene
Chrysene
Benz [ a ] anthracene
7, 12 -Dimethyl
benz [ a ] anthracene
Benzo f b ] f luoranthene
Benz o [ a ] py r ene
Dibenz [ a , h ] anthracene
Dibenzo [ a , i ] pyrene
Pesticides :
Phorate
Aldicarb
Pentachloronitrobenzene
Lindane
Heptachlor
Famphur
Dinoseb
Pronamide
Kidman
tl/2
(days)
2.1
1.7
134
16
377
260
371
261
20
294
309
361
371
32
385
17
61
58
53
103
96
Sandy Loam
95% CI
1.7-2.7 a+
1.4-2.1 a
106-182 a
13-18 a
277-587 a
193-408 a
289-533 a
210-347 a
18-24 a
231-385 a
239-462 a
267-533 a
277-533 a
29-85 a
257-845 a
15-21 a
35-257 a
50-70 a
46-69 a
87-128 a
81-122 a
McLaurin
Cl/2
(days)
2.2
2.2
50
35
268
199
387
162
28
211
229
420
232
24
30
51
65
63
69
92
94
Sandy Loam
95% CI
1.7-3.4 a
1.6-3.2 a
42-61 b+
27-53 b
173-630 a
131-408 a
257-866 a
131-217 a
21-41 a
169-277 a
178-315 a
267-990 a
178-330 a
19-35 a
27-35 b
38-74 b
39-204 a
58-76 a
58-98 a
74-124 a
69-151 a
* The same letter for a compound at two soil types indicates no statistical
difference at the 95% level based on a t-test.
-------
36
for the majority of PAHs. Although a statistically significant difference was
observed for anthracene and phenanthrene, the difference was not consistent for
one soil type.
For the pesticides evaluated, there were statistically significant differences
for degradation rates as a function of soil type for pentachloronitrobenzene and
aldicarb. For the other six pesticides no statistical difference in degradation
rate was observed between the two soil types. Because of the lack of a rational
quantitative relationship between soil type and rate of degradation, it was not
possible to evaluate the test model with regard to model output as a function of
soil type.
Partition coefficients between aqueous and solid phases (Kd) for each soil
type, derived using structure-activity relationships (SAR), are presented in Table
6. Calculated values presented indicate a consistent difference between the soils,
with Kd values higher for chemicals in McLaurin Sandy Loam soil. Since the values
are calculated and not measured, 95% confidence intervals are not relevant. The
difference between the two soils is directly related to the difference in organic
carbon content for the two soils (0.5% for Kidman soil versus 0.94% for McLaurin
soil).
MODEL OUTPUT AS A FUNCTION OF TEMPERATURE-DEPENDENT DEGRADATION
The proper design and management of a hazardous waste land treatment system
requires an understanding of the rates at which hazardous constituents of an applied
waste are degraded. Temperature is the most important climatic factor influencing
rates of decomposition in soils (Smith, 1982). Coover (1987) has conducted
laboratory scale experiments using glass beaker studies for 16 PAH compounds that
are representative of hazardous wastes of concern to the U.S. Environmental
Protection Agency. All experiments were conducted at three temperatures (10°C,
20°C, and 30°C) using a Kidman sandy loam soil. Coover (1987) indicated that the
Arrhenius expression, k - A e(Ea/RT), was useful for describing the effects of
temperature on apparent loss of fluorene, anthracene, and benzfa]anthracene and
other PNAs, but found that its use should be justified on a case-by-case basis.
In the VIP model, a degenerate form of the Arrhenius expression is found by
integrating the differential form between the limits T: and T2:
In
- T2)
K2
[23]
and restricting the temperature range to ±10-15°C, as is the case for most vadose
zone environments. The Eq. [23] , Kx and K2 are the rate constants at Tx and T2, Ea
is the activation energy, and R is the gas constant. Under this restriction, the
term Ea/RT^ remains approximately constant, and Eq. [23] may be written as
(K \
~\~ Q°(Ii ' T*>- [24]
-------
37
Table 6. Calculated soil/water (Kd), partition coefficients for chemicals in
two soils.
Compound
Acenaphthylene
Benz [ a] anthracene
Benzo[a]pyrene
chrysene
Dibenzo [ a ,h] anthracene
Ideno(l,2,3-cd)pyrene
3-Methylcholanthrene
Fluoranthene
1-Methylnapthalene
Naphthalene
Phenanthrene
Pyrene
Benzo [b ] f luoranthene
7 , 12-Dimethylbenz [a]anthracene
Anthracene
Bis- [chloromethyl) ether
Chloromethyl methyl ether
1, 2-Dibromo-3-chloropropane
Dichlorodifluorome thane
1 , 1-Dichloroethylene
1,1, 1-Trichloroethane
1,1,2, 2 -Tetrachloroethane
1,1, 2 -Trichloroethane
1,2, 2 -Trichlorotrif luoroethane
Hexachlorocyclopentadiene
4,4-Methylene-bis(2-chloroaniline)
1,2, 4-Trichlorobenzene
Aldrin
Cacodylic Acid
Chlordane , technical
DDT
Dieldrin
Disulfoton
Endosulfan
Heptachlor
Alpha Lindane
Methyl parathion
Parathion
Phorate
Toxaphene
Warfarin
Aldicarb
log Kd
(McLaurin)
1.72
3.24
3.67
3.24
3.60
5.27
4.73
2.97
1.52
1.01
2.11
2.96
4.19
3.61
2.10
-2.68
-1.41
-0.17
0.13
2.63
-0.16
-0.66
2.68
0.96
1.63
0.65
-2.31
0.44
1.14
0.56
-2.31
1.21
1.55
1.46
0.65
1.06
0.58
0.96
0.19
-1.61
log Kd
(Kidman)
1.38
2.90
3.33
2.90
3.26
4.93
4.38
2.62
1.18
0.67
1.76
2.61
3.86
3.27
1.75
-3.02
-1.75
-0.51
0.47
2.29
-0.50
1.01
2.34
0.62
1.29
0.31
-2.65
0.10
0.79
0.22
-2.65
0.86
1.21
1.12
0.31
0.72
0.24
0.62
-0.15
-1.95
-------
38
Taking antilogs
K,
T2) _ Q(T1 12)
[25]
where 9 - e8'. This form has been used to characterize the effect of temperature
on soil biochemical degradation and mineralization of some compounds in soils
(Hamaker, 1972 and Parker, 1983). Using T2 - 20°C,
KT
j(T-20)
[26]
where KT is the constituent degradation rate at temperature T°C, K20 is the
constituent degradation rate at 20°C, and 9 is the temperature correction
coefficient.
The method of non-linear least squares was used to estimate the degradation
rate at 20°C (K20) and the temperature correction coefficient value (9) of Eq.[26]
for three PNA compounds: chrysene, benzo[b]fluoranthene, and fluorene, using the
data of Coover (1987). Appendix A provides the temperature data and the parameter
estimation for these three compounds. The concentration histories and the predicted
first order models are shown in Figures 16 a, b, and c, for chrysene,
benzo(b)fluoranthene, and fluorene respectively. The estimated K20 and 9 and their
95% confidence intervals are listed in Table 7. Note that for chrysene, the 95%
CI for 9 includes one, so that, for these data, there is no statistically
significant effect of temperature on apparent degradation.
Simulations using these three compounds were run using the VIP model to
evaluate the effects of soil temperature on model predictions. Partition
coefficients and soil initial concentrations of three compounds used in this study
are summarized in Table 8. For this series of runs, a high recharge rate 3.95
(cm3/day/cm2) was used, and the mass transfer rate coefficients for the constituents
and oxygen were 1000 day"1, assuming the constituents and oxygen reached equilibrium
very rapidly.
Table 7. Estimated values of K20 and 9.
Compound
LCLa K20 UCLb
(I/days) (I/days) (I/days)
LCL
9
UCL
Chrysene
Benzo [b ] fluoranthene
Fluorene
0
0
0
.00046
.00144
.0159
0
0
0
.00059
.00168
.0168
0.
0.
0.
00072
00192
0178
0
1
1
.987
.012
.033
1
1
1
.003
.024
.040
1.019
1.036
1.048
Lower 95% confidence limit
Upper 95% confidence limit
-------
39
o
o
o
c"
o
I
c
o
c
o
O
0)
CC
O
O
C
o
c
1)
o
c
o
O
(U
o:
o
o
O
o
c
o
O
T3
0>
O
1U
or
1.2
1.1
1.0
0.9
0.8
0.7
0.6
50
100 150
Time (days)
200
250
Benzo[b]fluoranthene
50
100 150
Time (days)
200
250
50
100 150
Time (days)
200
250
Figure 16. Concentration histories and the predicted first order models
for chrysene, benzo[b]fluoranthene, and fluorene. Model
predictions ( ) decrease with increasing temperature.
-------
40
Table 8. Partition coefficients and initial concentrations used in the study.
Compound
Chrysene
Benzo [b ] f luoranthene
Fluorene
3*°" 3
g/mVg/m3
8.9E+58
1.1E+7"
2 . OE+3b
KSW
g/g/g/m3
1.8E-4b
4.9E-5b
6.2E-5b
K%w
g/m3/g/m3
3.9E-33
1.2E-3a
3.2E-3C
Initial
mg/g-soil
O.la
0.04a
O.ld
a From U.S. EPA (1988).
b From Ryan et al. (1987).
0 Calculated from Henry's Law.
d Coover (1987).
Table 9 lists the summary of degradation data of the three compounds after a
one year simulation in the Kidman sandy loam. The extent and rate of apparent loss
due to the biochemical degradation for the higher temperature is greater than that
for the lower temperature for each of the three compounds studied. However, the
effect of temperature on the apparent loss from decay is different for each
compound, ranging from 20 percent for chrysene to 100 percent loss for fluorene at
30°C.
Table 9. Degradation summary from VIP simulation.
Compound
Chrysene
Benzo [b ] f luoranthene
Fluorene
Temp.
°C
10
20
30
10
20
30
10
20
30
% decayed total mass
g
19
19 26
20
38
45 10
53
98
100 26
100
-------
41
Figure 17 through 19 demonstrate the depth profiles of chrysene,
benzo[b]fluoranthene, and fluorene, respectively, in the water phase after one year
in the Kidman sandy loam. Compared to the profiles for benzo[b] fluoranthene (Figure
18) and fluorene (Figure 19), for chrysene there is little apparent effect of
temperature seen in these profiles with temperature changing from 10 to 30°C. The
plot for fluorene (Figure 19) shows the largest apparent effect of temperature on
the model output profiles. The effect of temperature on the degradation rate
depends on the value of 6. Higher values of 9 (1.040 for fluorene). show more
sensitivity to temperature in the model prediction than that for 6 values close to
1.0 (1.003 for chrysene). This result is in agreement with the mathematical aspect
of Eq. [26].
Fluorene has a low molecular weight of 166 and only three fused rings, while
benzo[b]fluoranthene and chrysene have five and four rings respectively. Figures
17 to 19 and Table 9 demonstrate that the extent and rate of degradation of low
molecular weight PAH compounds increased with increasing soil temperature, but
there was very little apparent degradation and little effect of temperature on
degradation of four and five-ring compounds. Therefore, the high molecular weight
PAHs have the potential to persist for years and have a potential to accumulate
following repeated addition of PAH-containing wastes in land treatment systems.
These results predicted from the test model are in agreement with observations of
Coover (1987) observed in laboratory scale experiments.
MODEL OUTPUT AS A FUNCTION OF OXYGEN-LIMITED DEGRADATION
Simulations were conducted to evaluate the effects of oxygen concentration on the
degradation of the constituent. The physical and kinetic parameters used in this
test are contained in Table 10. For this series of runs, the dispersion coefficient
-for oxygen, Dao, was set to zero to maximize the potential for 02 limitation by
restricting oxygen sources.
Figure 20 shows a comparison of the concentration distribution with and without
oxygen-limits after 80 days in the water phase. The results demonstrate that there
is no significant difference between the concentration curves with oxygen-limit
degradation. The reason is that the oxygen half saturation constant used was 0.1
g/m3 which is very small compared to the oxygen concentrations 200-298 g/m3 in the
air phase and 4-9.17 g/m3 in the water or oil phase. This small value of the oxygen
half saturation constant caused the term, 0/(K0+0) to approach unity. Therefore
degradation would not be affected by the concentration of oxygen. When the oxygen
half saturation constant value increases to a value near the oxygen concentration,
an increased sensitivity of degradation to the oxygen concentration would be
expected.
-------
42
V
"6
s
i
rO
E
0
cc
I
z
LU
0
O
0
0.600-
0.400-
0.200-
0.000-
0
Chrysene
«
1
10°C
20°C
30°C
0 0.5 1.0 1.
DEPTH (m)
Figure 17. Depth profiles of chrysene at three different temperatures
after one year.
0.600
0.400--
a> 0.200--
O
O
0.000
Benzo[b]fluoranthene
10°C
--- 20°C
30°C
0.0
0.5
1.0
1.5
DEPTH (m)
Figure 18. Depth profiles of benzo[b] fluoranthene at three different
temperatures after one year.
u.u^w
QJ
O
s
I
^E 0.020-
>*x
en
z.
g
cr 0.010-
UJ
O
~Z-
O
0
0.000-
0
, \ Fluorene
\ 1 0°C
1 20°C
30°C
i !
_J
i
i
i
^H
0 0.5 1.0 1
DEPTH (m)
Figure 19. Depth profiles of fluorene at three different temperatures
after one year.
-------
43
Table 10. Physical and kinetic parameters used in model simulation of oxygen
dynamics at field scale.
/iw constituent degradation rate in the water phase, day"1
Ms constituent degradation rate in the soil phase, day"1
Kaw constituent partition coefficient between soil phase
and water phase (g/g-soil)/(g/m3-water)
Ka oxygen half saturation constant in the air phase, g/m3
KQ oxygen half saturation constant in the oil phase, g/m3
K,, oxygen half saturation constant in the water phase, g/m3
K00 oxygen half saturation constant with respect to the
oil decay g/m3
Koa oxygen partition coefficient between the oil and
air phases, (g-02/m3-oil)/(g-02/m3-air)
!( the oxygen partition coefficient between the water and
air phases, (g-02/m3-water)/(g-02/m3-air)
i/c the stoichiometric ratio of the oxygen to the
constituent consumed
v0 the stoichiometric ratio of the oxygen to the
oil consumed
K0a the oxygen transfer rate coefficient between the oil
and air phases, day"1
/cwa the oxygen transfer rate coefficient between the water
and air phases, day"1
Vw' mean daily recharge rate, (cm/day)
c saturated hydraulic conductivity (cm/day)
soil porosity (cm3/cm3)
0.0147d
0.0147d
3.16E-6d
O.la
O.la
O.la
O.la
0.0306be
0.0306b
1000C
1000°
4.30d
100
0.39
a From Borden and Bedient (1986).
b Calculated from Henry's Law.
c Assume oxygen reaches equilibrium very fast.
d From Grenney et al. (1987).
8 Assume oxygen partition coefficient between the oil and air phase is same as
that between the water and air phase.
-------
44
540
450-
360- WITHOUT 02-LIMITS
o
P 270 +
1 80 -
o
z
o 90 +
A A
WITH 02-LIMITS
\
A* A A I A A
0.0
0.5 1.0
DEPTH (m)
1.5
Figure 20. Comparison of the depth profiles with and without
oxygen-limits.
Figure 21 presents the constituent and oxygen concentration curves in the
water phase after 80 days. The soil system is saturated with oxygen from the
top of the soil surface down to a soil depth where the constituent slug is
located. The oxygen concentration decreases over these depths due to the oxygen
demand imposed by microbial degradation of the constituent. No microbial
activity has occurred below the constituent wave front, therefore the oxygen
concentration is maintained at the saturation concentration.
o
o
400-
oOU -
200-
100-
0-
0
0 0.5
t
I
1.0 1
1 O
10
5
5
CD
X
o
DEPTH (m)
Figure 21. Constituent and oxygen profiles after 80 days.
-------
45
Figure 22 shows the breakthrough curves of the constituent and oxygen
concentration in the water phase at a depth of 1.0 meter. The oxygen
concentration decreases when constituent passes this depth due to microbial
degradation of the constituent. After the constituent slug passes a particular
depth, the oxygen concentration is replenished due to the advection transport
mechanism in the air and water phases.
600
400
O
0 200
. }
* *.
*- <
12
8
4
30 60 90
TIME (DAYS)
120
Figure 22. Constituent and oxygen breakthrough curves
predicted by the VIP model.
Figure 23
shows the effect
of the half-
saturation
constant for the
same input data
set, for a range
of K from 0.01 to
10 g/m? in the
air, oil, and
water phases.
These simulations
demonstrate that,
as the value of
this constant
increases, the oxygen-limitation of degradation increases, as would be expected.
ro"
£
CT*
z
0
5
£
i
z
o
z
0
o
1 UW
800-
600
400-
200-
0 -
Ko
* * » A A Ko
* - r» ^1
' T 1
1-^3 i
1 i
D D Ko
T T Ko
* Ko
i_
IL
1 * 0 l~1 !
0.0 0.4 0.8
= 0.0
= 0.01
= 0.1
= 1
= 10
*[! » i
C3 T VI
1.
Figure 23.
DEPTH (m)
Depth profiles with five of half oxygen
saturation constant coefficients.
Under field conditions, where 02 is replenished by dispersion/diffusion
from the atmosphere, this rate limitation will be less severe over the long term
for slowly degradable substrates. However, for short term dynamics, such as
immediately after a waste application, the 02 limits may be very important and,
therefore represent an important module (oxygen dynamics) for inclusion in the
model. Evidence for the field scale depletion of soil oxygen, with depth through
the soil, after waste application was confirmed at Texaco's Nanticoke Oil
Refinery, Ontario, Canada, and is discussed in the next section.
-------
46
FIELD EVALUATION OF MODEL FOR PREDICTION OF OXYGEN DYNAMICS
A field study was conducted as part of a land treatment demonstration for
Texaco's Nanticoke Oil Refinery at Simcoe, Ontario, Canada. USU's involvement
in the project was to characterize the waste being applied under two loading
scenarios (high and low) , and to evaluate the dynamics of the vapor phase
processes for ten days following the application and tilling of the waste sludge,
including volatile organic constituents and oxygen. Details of the study are
provided in a separate report. Our purpose here is to briefly describe the
measurement of subsurface oxygen concentration and to use the VIP model to
simulate the short term dynamics of the oxygen in the subsurface.
The measurements from the high-load plot from the period 6/11/87-6/15/87
were chosen for the simulation. For the purposes of the simulation, the waste
constituents were summed and assumed to be representable by a single constituent
having fate, transport, and degradation properties that were averages of those
for the individual materials. It should be noted that the averaging process was
not rigorous: the values used were simple arithmetic averages of representative
values taken from land treatment studies done at USU. These parameters, soil-
water, octanol-water, and air-water partition coefficients and first order
degradation rate coefficients, were entered into the VIP model with the initial
conditions taken from the background measurements, and waste characteristics and
application rates from field notes. The input file is shown in Table 11.
The model was run for the 5 day period of the data record. The predicted
air phase 02 concentrations at the 6 inch, 12 inch, and 24 inch depths were
extracted from the model output and plotted alongside the raw field data.
Results are presented in Figures 26, 27, and 28, for 6 inch, 12 inch, and 24
inch depths, respectively. The solid lines on the plots represent the model
simulation, and the dashed lines represent the field data.
Results for the 6 inch depth show good agreement between the model
prediction and the field data during the first 80 hours of the simulation. The
model was able to track the descending leg of the record but is unable to
simulate the recovery of the 02 content at this level after 80 hours. For the
12 inch depth, the model was able to predict the general behavior of the data
for 60 hours but was unable to predict the recovery after this time. At a depth
of 24 inches, the model was able to predict the initial drop in the 02 level,
but the predicted trend continued to descend while the field data leveled off.
However, at 60 hours, when the 02 had decreased to about 25 g/m3, the model and
data agreed. However, the test model failed to predict the recovery after about
80 hours.
-------
47
Table 7 Input Data File for Simulation of Field Data from Nanticoke Refinery
Canada Composite
DTZON.DPZON.DZ
DETECT
TOTAL TIME.DZO
TOI
DTOI
SHLB, PHI, ROES
RMUWPZ.RMUWLZ
RKOUPZ.RKOWLZ
RKAWPZ.RKAULZ
RKSWPZ.RKSWLZ
OKOAPZ.OKOALZ
OKWAPZ.OKUALZ
WAR,CONSU,WTFO
WTFU,ROEW,ROEIO
DTAC.DTAF
HO
OHO
RMUOPZ.RMUOLZ
DA.DV
DAO, DVO
RMUAPZ.RMUALZ
RHUSPZ.RMUSLZ
OH
SNUC.SNUO
ZX
CUZ
COZ
CAZ
CSZ
OAZ
OOZ
OWZ
THETOX
TEMP FACTOR
TEMP IN PZ
TEMP IN LZ
VWPRIME
SHC
RK,RWS,RWO,RUA
OR AO, OR AW
1.5096
1.000E-07
5.0000
0.0000
0.1666
4.9000
5.000E-02
1.000E+03
2.000E-01
3.160E-06
3.060E-02
3.060E-02
9.445E+00
0.740E+00
1.800E+02
1.540E-03
1.000E+00
5.000E-02
0.019E+00
0.049E+00
O.OOOE-02
5.000E-02
1. OOOE+00
3. OOOE+00
0.0000
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE-00
3. OOOE+02
9.170E+00
9.170E+00
O.OOOE+00
1.000000
20.0000
20.0000
2.784E-00
1.000E+02
4.600E-02
1.000E+02
0.1500
0.0300
15.0000
0.1666
0.3900
5.000E-02
1.000E+03
2.000E-01
3.160E-06
3.060E-02
3.060E-02
4.000E+03
1.016E+00
1.800E+02
5.000E-02
O.OOOE+00
O.OOOE+00
O.OOOE-02
5.000E-02
1.000E+00
3.000E+00
0.1500
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE-00
3.000E+02
9.170E+00
9.170E+00
O.OOOE+00
20.0000
20.0000
2.784E-00
1.000E+02
1.000E+02
1.000E+02
0.0150
0.0000
0.0000
1.6100
0.160E+00
0.900E+00
1.000E+00
0.3048
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+00
3.000E+02
8.550E+00
8.550E+00
O.OOOE+00
20.0000
20.0000
2.784E-00
1. OOOE+02
1.000E+02
0.0000
0.0000
1.000E+00
0.6096
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+00
3.000E+02
7.940E+00
7.940E+00
O.OOOE+00
20.0000
20.0000
2.784E-00
1.000E+02
1.000E+02
0.0000
0.0000
1.000E+00
0.0000
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+02
O.OOOE+00
O.OOOE+00
O.OOOE+00
20.0000
20.0000
2.784E-00
1.000E+02
0.0000
0.0000
1.000E+00
0.0000
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+00
O.OOOE+02
O.OOOE+00
O.OOOE+00
O.OOOE+00
20.0000
20.0000
2.784E-00
1.000E+02
0.0000
0.0000
0.0000
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+02 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
20.0000
20.0000
2.784E-00 2
1.000E+02 1
0.0000
0.0000
0.0000
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+02
.OOOE+00
.OOOE+00
.OOOE+00
20.0000
20.0000
.784E-00
.OOOE+02
0.0000
0.0000
0.0000
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+02 0
O.OOOE+00 0
O.OOOE+00 0
O.OOOE+00 0
20.0000
20.0000
2.784E-00 2
1. OOOE+02 1
0.0000
0.0000
0.0000
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+02
.OOOE+00
.OOOE+00
.OOOE+00
20.0000
20.0000
.784E-00
.OOOE+02
20.0000 20.0000
20.0000 20.0000
2.784E-00 2.784E-00
1. OOOE+02 1. OOOE+02
-------
Air Phase 02 Simulation Depth = 6"
\ 330
a»
c 300
_o
| 230
"c
to
O 200
§
" 150
CM
O
a 100
en
o
50
VIP Simulation
Reid Data
0 10 20 30 40 50 M 70 SO 90 100 110 120 130
Time (hours)
Figure 24. Oxygen simulation at depth 6"
Air Phase 02 Simulation -- Depth = 12"
350
300
250
200
150
100
VIP Simulation
Field Data
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Time (hours)
Figure 25. Oxygen simulation at depth 12",
Air PHase D£ Simulation Depth = 24"
0 10 20 JO 40 50 60 70 80 90 1OO 110 120 130
Time (hours)
Figure 26. Oxygen simulation at depth 24'
-------
49
The inability of the test model to predict the recovery of the 02 levels
after about 80 hours is felt to be related to the boundary conditions at the
bottom of the treatment zone. For the simulations presented, it was assumed that
the treatment zone extended to the 24 inch level. Below that level the soil was
assumed to be saturated with water, and therefore no oxygen could be transported
from below. A more realistic condition for this physical system, for which the
groundwater was well below the 24 inch level, is a boundary that permits free
transport of vapor. This would provide an oxygen source from below and would
make the 02 concentration decrease more slowly at this level, and also provide
an oxygen source for recovery.
The VIP model therefore was useful for simulating the short term dynamics
of 02 after waste application. The model predicted the location of the decrease
in the air phase 02 concentration, and semi-quantitatively predicted the
concentrations. More precise characterization of model inputs would make
predictions more quantitative. The model failed, however, to predict the
recovery of the 02 concentrations at all levels after about 80 hours.
Reformulation of the boundary conditions at the bottom of the treatment zone may
improve the simulation.
ANALYTICAL SOLUTION TO TWO-PHASE MODEL
Analytical Solution
In this section, we discuss the analytical solution of the equations for
a two-site model with first adsorption kinetics. This model has been studied
extensively in a series of papers by S. Goldstein, which appeared in the 1950's
(Goldstein, 1953a,b and 1959a,b,c). In addition to giving an analytical solution
to the equations, Goldstein investigates the relationship between the equilibrium
model and the kinetic model and gives asymptotic expansions for the solutions.
For the convenience of the reader, we will outline the construction of an
integral representation for the model under consideration in this report. Our
approach is based on an application of the Riemann method to a form of the
telegraph equation which arises in the course of the analysis of the model
equations.
In order to simplify the presentation somewhat, we will first obtain a
dimensionless version of the model equations by introducing dimensionless
variables for the variables and the experimental parameters. In order to
distinguish between the dimensional terms and their dimensionless counterparts,
we will indicate dimensional terms with an * and the dimensionless terms will
be written without the * (note: this does not correspond with the use of
dimensional variables in the remainder of this report). The set of equations
for the model problem can be written in the form of the following one-dimensional
partial differential equation.
-------
50
ac* as* 3c*
at* at* ax*
-oo < X* < «, 0 < t* < oo
as*
/c*(K*8WC* - S*) - Ms'S" [27b]
at*
with initial conditions
C*(x*,0) - f*(x*)
-co < x* < oo
S*(x*,0) = g*(x*)
where
C* is the concentration of the chemical in solution (g/m3) ,
S* is the amount of chemical sorbed per gram of soil (g/g),
Vw* is the vertical pore-water velocity (m/day),
p* is bulk density of the soil (g/m3) ,
0W is the saturated water content (m3/m3) ,
x* is the depth, positive downward (m),
t* is time (days),
In the above equations, S* and 0W are already dimensionless. We will take
the following as dimensionless variables:
C = KSW*C*.
x = x*/L*, and
t = Vw*t*/L*
where L* is an empirical scaling parameter (in our system, L* is the depth of
the initial treatment zone). Combining the above identifications into the system
of equations results in the following Cauchy Problem.
ac
1 P
at
as
as
at
r. en - ..
ac
ax
c
[28a]
-<»
-------
51
. and
Our first step in the analysis of this initial value problem is to
introduce a change of dependent variable to simplify the coupling in the system
of equations. If we assume that
C(x,t) - e(Brt^t> U(x,t) and S(x,t) - e(ax+^t) V(x,t)
are solutions , where
a - (l-p)/c + Ms - MW and
P - -K - Ms.
then the functions U(x,t) and V(x,t) must be solutions to the initial value
problem
Ut - -Ux + (pK + MS)V
-« < x < », 0 < t < «
Vt = «U
with initial conditions
U(x,0) - e'^fCx)
and
V(x,0) = e^gCx).
As in the original problem, this is a system of hyperbolic partial
differential equations with constant coefficients. If we choose as a new set
of independent variables £ = x-t and r; = x in the direction of the
characteristics of the system, we obtain a system in canonical form
-°° < T) < oo, -oo < £ < T)
Vf - K
For this system of equations, the initial conditions transform into the Cauchy
conditions
U(i?,i?) - e-^fCfj). and
If we now differentiate the first equation with respect to £ and the second
-------
52
equation with respect to r) , we obtain a single second order hyperbolic equation
in canonical form
U?, + A2U = 0
where A2 - /c(p/e + /is) and the Cauchy conditions can be written
U(i?,ij) - e-^fOj), and
V(fJ.fj) -
This equation is a version of the telegraph equation. With the problem
written in this form, we can apply the theorem on page 124 of Lieberstein (1972)
to obtain the following integral representation of the solution in canonical
coordinates.
+ A*sUo(2Ah(h;£,r7))g(y)+2A2(»? - y)
f (y) I dy [29]
«I0(2Ah(h;C,»?))f(y)+2A2(y
I1(2Ah(y;e,r7))
s(y)
dy [30]
where
7(r;-y) (y-^)\
Upon substituting £=x-t, ry=x and multiplying the result by exp(ax+/9t), we
have established the following integral representation theorem.
Theorem If f,g e C1 (-<*>,<*>) and C and S are the unique functions such that C,
Ct, Cx, S, St, Sx 6 C( (-<*>, <*>)x(0,«>)) defined by
ac as ac
+ P .
at
as
at
at
= «(C S)
-»
-------
53
-<*> < x < <*>
C(x,0) - f(x)
S(x,0) - g(x)
then, for each (x,t) e(-<=o,oo)x(0,«) ,
C(x,t) -
L
Ms)I0(2A7(x-y)(y-x+t)) g(y)
2A2(x-y)
(2Ay(x-y)(y-x+t)')
f(y)
dy
[3la]
S(x,t)
L
kI0(2Ay(x-y)(y-x+ty) f(y)
I1(2A7(x-y)(y-x+t))
2A2(y-x+t) g(y)
(2Ay(x-y)(y-x+ty)
_a(x-y)+/3t
dy
[31b]
We note here, that if f and g are not in Cl, as is the case for the plug
problem, then the above integral representation gives the weak solution to the
problem.
The above analytical solution was. programmed in FORTRAN 77 for
implementation on the VAX 8650 computer at USU. The FORTRAN version was
constructed so as to accept input data files that are identical to those used
in the VIP numerical model described above, to ensure that the comparisons were
made using identical model parameters. The use of the analytical solution for
evaluating the VIP model is now described.
Accuracy of Numerical Model Calculations
For the first set of comparisons, a series of simulations were carried out
using the numerical VIP model and the analytical solution, for the simplified
case described above. Three different sets of initial conditions and five values
of the mass transfer parameter, /e, were used. Model input for the first two sets
of simulations is given in Table 12 and for the last set of simulations is given
in Table 13. Table 14 contains the descriptions of variables used, units and
data sources. Both models were simulated for 12 days, and the accuracy
comparisons were based on 1) visual inspection of the concentration vs. depth
profiles for both the aqueous and soil phases, and 2) comparison of the relative
difference between the solutions at the peak concentrations as a function of the
mass transfer rate parameter, K. Figures 27 to 29 demonstrate the comparisons
of the depth profiles calculated by the analytical solution to numerical solution
-------
54
Table 12. Model input values for the first two sets of analyses.
CO
RHO
XMUC
TIMMAX
2000
1.38E6
0.0
12
2000
1.38E6
0.0
12
2000
1.38E6
0.0
12
2000
1.38E6
0.0
12
2000
1.38E6
0.0
12
SO
PHI
XMUS
TOUT
0.00521
0.40
0.0
6
0.00521
0.40
0.0
6
0.00521
0.40
0.0
6
0.00521
0.40
0.0
6
0.00521
0.40
0.0
6
SHC
KSW
DZ
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
SMLB
VWPRIME
NZOUT
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2 -
RWS
NPLOW
100
12
1.0
12
0.1
12
0.01
12
0.0
12
NTREAT
74
74
74
74
74
(VIP model) with constituent initially in the water, soil and both phases,
-------
55
Table 13. Model input values for the last set of analyses.
CO
RHO
XMUC
TIMMAX
22984
1.38E6
0.0
120
22984
1.38E6
0.0
120
22984
1.38E6
0.0
120
22984
1.38E6
0.0
120
22984
1.38E6
0.0
120
SO
PHI
XMUS
TOUT
0.00521
0.40
0.0
10
0.00521
0.40
0.0
10
0.00521
0.40
0.0
5
0.00521
0.40
0.0
1
0.00521
0.40
0.0
1
SHC
KSW
DZ
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
1.0
2.5E-6
0.015
SMLB
VWPRIME
NZOUT
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2
4.90
0.043
2
RWS
NPLOW
100
15
1.0
15
0.1
15
0.01
15
0.0
15
NTREAT
74
74
74
74
74
-------
56
Table 14. Descriptions of variables used, units, and data sources.
CO. SO = the initial constituent concentration in water (g/m3) and in soil (g/g-
soil) phase. The initial constituent concentration was set to one of the three
initial conditions: initially only in water phase, initially only in soil phase,
and initially in both water and soil phase.
RHO = bulk density (g/m3). This value was chosen from the work of Grenney et
al. (1987).
PHI = soil porosity (m3/m3) , volume of void space/total volume. This value was
chosen from the work of Grenney et al. (1987).
SHC = saturated hydraulic conductivity, m/day, the default value of 1.0 as used
in the EPA Land Treatment Manual was used in this case.
SMLB = soil moisture coefficient. This value was taken from Clapp and Hornberger
(1978).
XMUC. XMUS = first order decay rate for the constituent within the water phase
and soil phase, (day"1). All have been set to zero since no constituent decay
assumed in either water phase or soil phase.
KSW = soil/water partition coefficient, (g/g-soil)/(g/m3-water). The soil/water
partition coefficient was derived from Grenney et al. (1987).
VWPRIME = average recharge rate, (m3/day)/m2. This value was chosen from the
work of Grenney et al. (1987) using naphthalene under high flow rate condition.
RWS - mass transfer rate coefficient, (day"1). This parameter controls the
dispersion on concentration with depth curves and breakthrough curves. A range
of 100, 1, 0.1, 0.01, 0, was used to demonstrate the curve changes with it.
TIMMAX = the length of run, days. 12 days and 120 days were used for
concentration with depth and breakthrough curves analyses, respectively.
TOUT = the time for output, days.
DZ = the depth increment, m. 0.015 was used in this study.
NZOUT - number of depth increment for output file. 2 was used to make 0.03m
depth increment for output file.
NPLOW - number of depth increment for plow zone. 15 was used to make 0.15m depth
of plow zone.
NTREAT = number of depth increment for treatment zone.
-------
2000
1500
O
-------
58
2000
WATER PHASE
Numerical (VIP) Solution
Analytical Solution
1.0
DEPTH (m)
u.uuo
'5
t/i
I
CP
\ 0.004
0^
**~s
~z.
O
\
£ 0.002
~z.
UJ
O
-^
O
CJ
A nnn
SOIL PHASE
" I
/
/
j i
A
Numerical (VIP) Solution
f-=1QQ Analytical Solution
L ,
\
v
>^ , . 1
0.0 0.5 1.0 1.5 2.
DEPTH (m)
0.006
O
CO
I
a>
.004
O
0.002
bJ
O
O
O
0.000
_QQ<
c=0.1
SOIL PHASE
Numerical (VIP) Solution
Analytical Solution
0.0 0.5 1.0 1.5
DEPTH (m)
2.0
Figure 28. Comparison of the depth profiles calculated by the analytical
solution to the numerical solution (VIP model) with
constituent initially in the soil phase.
-------
59
2500
Z 1500
O
1000
z
LJ
O
O
500
/c=100
0.0
WATER PHASE
Numerical i
Analytical Solution
<=!
0.5
1.0
DEPTH (m)
1.5
2.0
0.006
I
0.004
z
g
0.002
0.000
<=100 SOIL PHASE
Numerical (VIP) Solution
Analytical Solution
A
0.0
0.5 1.0 1.5
DEPTH (m)
2.0
0.006
o
tn
I
cn
0.004
O
£
0.002
o
O
o
0.000
SOIL PHASE
Numerical (VIP) Solution
K-Q 01 Analytical Solution
Vc=0.1
0.0 0.5 1.0 1.5
DEPTH (m)
2.0
Figure 29. Comparison of the depth profiles calculated by the analytical
solution to the numerical solution (VIP model) with constituent
initially in both phases.
-------
60
Comparing the depth profiles from the numerical solution and the analytical
solution for five different mass transfer rate coefficients in either the water
phase or the soil phase, there is little visible difference. Figures 30 and 31
present the percent relative error between the results from numerical VIP
solution and analytical solution vs. the mass transfer rate coefficient «K in
the water phase and the soil phase, respectively. Table 15 lists the definition
of the percent relative error and appropriate notation. The relative errors in
both the soil phase and water phase are less than 7 percent over the entire range
of K investigated. Thus, the numerical solution in the VIP model accurately
represented the nonequilibrium sorption/desorption kinetics for the wide range
of mass transfer rate coefficients (0 < K < 1000) considered.
4 days
6 days
10 days
12 days
0.010
0.100 1.000
< (day-1)
10.000
100.000
Figure 30. Relative error % vs K in the water phase.
X
10
8
QL
O K
ct 6
or
LJ
LJ 4
4 days
- 6 days
10 days
12 days
-c/
-2
0.001 0.010 0.100 1.000 10.000 100.000
Figure 31. Relative error % vs K in the soil phase.
-------
61
Table 15. The definition of the percent relative error and
notation.
Definition of Percent Relative Error
Water Phase 100 (ca-Cn) / Ca
Soil Phase 100 (Sa-Sn) / Sa
Definition of the Notation
Water Phase:
Ca: Peak concentration in water phase by analytical solution
Cn: Peak concentration in water phase by numerical (VIP) solution
Soil Phase:
Sa: Concentration in soil phase by analytical solution
Sn: Concentration in soil phase by numerical (VIP) solution
Experimental verification of the VIP model was recently provided by Reinhart
(1988) who studied the transport and fate of eleven organic compounds, including
halogenated aliphatic, chlorinated phenols and benzenes, pesticides, and PNAs,
in laboratory columns packed with municipal refuse. The VIP model was fit to
experimental data for depth profiles and breakthrough .curves by adjusting the
solid-liquid mass transfer rate coefficients and partition coefficients. Based
on this procedure, close agreement between the model and the data were found,
and the best fit values of Ksw agreed well with those found from independent
equilibrium tests. These results will be published in early 1989.
EFFECT OF MASS TRANSFER COEFFICIENT ON MODEL BEHAVIOR
Concentration Distribution Curves
Figure 27 shows the concentration distribution curves in the water and soil
phases after 12 days with the concentration initially in water phase only. For
K equals zero, that is, for no exchange between the water and soil phases, all
of the constituent concentration moves with the water phase at the pore water
velocity, and the constituent concentration in the soil phase is zero because
there is no initial mass in the soil phase. When K increases in value, that is,
when the speed of exchange between water and soil phases increases, the amplitude
of the concentration in water phase decreases, the constituent concentration
releases from the water phase to the soil phase so that there is a long tail
formed for soil phase profile (/e = 0.01 ). When K increases further, the
amplitude of the concentration in the water phase decreases rapidly and the
profile becomes retarded and dispersive, and the amplitude of the concentration
in the soil phase increases but is asymmetric (/e = 0.1 ).
-------
62
As the water phase peak moves sufficiently down in the soil column, the
algebraic sign on dS/dt - «(KSWC - S) changes from + to -, thereby changing this
term in the soil phase transport model from a "sink" to a "source". When K
becomes very large (AC = 100) , the exchange between the water and the soil phases
becomes very fast, the peak concentration in soil and water phases are 0.000415
g-const./g-soil and 166.27 g-const./m3-water respectively, and the instantaneous
partition coefficient is 0.000415/166.27 - 2.496xlO'6 (g/g-soil)/(g/m3-water),
which is very close to the equilibrium partition coefficient 2. 5xlO~6 (g/g-
soil)/(g/m3-water).
The results for the case with the initial mass in the soil phase
demonstrated in Figure 28 is similar to the results with the initial
concentration in the water phase.
The behavior of the water and soil phase profiles shown in Figure 29 shows
the effects of the parameter AC which is the measure of the speed of exchange
between the two phases. For AC equals zero, that is, for no exchange between the
water and soil phase, the curves show that both phases' distribution profiles
tend to be rectangular, the water phase moves due to the pore water velocity and
the soil phase does not move: all of the constituent concentration remains in
the plow zone. As AC increases in value, that is, when the speed of exchange
increases, the amplitude of the concentration decreases, the dispersion of the
distribution increases, and the profile after attaining their peaks begin to
develop long tails (AC = 1) . As AC increases further, the concentration
distribution becomes more dispersed, the original peak of the water phase
decreases, the profile becomes more asymmetric and retarded, the considerable
tails occur, and the resulting concentration at the tailing end in water phase
is higher (AC = 0.1). As AC becomes very large and the exchange becomes very
rapid, the profiles become more nearly symmetrical but move at a retarded
velocity (Grenney et al., 1987). When AC approaches «, the concentration
distributions tend to be rectangular and retarded: the sorption/desorption
processes are fast with respect to the bulk fluid flow rate and "local
equilibrium" can be assumed.
Superpos ition
Figure 27 and Figure 28 show the concentration profiles in the water and
soil phases with constituent concentration initially in the water phase and soil
phase respectively. If the curves for the water phase (or the soil phase) in
Figure 27 and Figure 28 are added together, curves for the water phase (or the
soil phase) in Figure 29 can be obtained. Therefore, the concentration profiles
with initial concentration in two phases can be obtained by adding the
concentration profiles with initial concentration in each phase together either
for the analytical solution or the numerical solution.
-------
63
Breakthrough Curves
Three initial conditions were used: 22984 g/m3 only in the water phase;
0.00521 g/g-soil only in the soil phase; 22984 g/m3 in the water phase with
0.00521 g/g-soil in the soil phase. The numerical solution of the VIP model was
used to investigate the breakthrough curves at a depth of 1.0 meter, for
different mass transfer rate coefficients (/e) in the range from 0 to 100 per day,
with these three initial conditions.
Figure 32 presents the breakthrough curves for the initial concentration
of the water phase only, while Figure 33 shows the breakthrough curves with the
concentration initially only in the soil phase. Figure 34 demonstrates the
breakthrough curves for the initial concentration in both the water and soil
phases. When K equals zero, there is no exchange between the two phases, the
concentration profile in the water phase is a narrow rectangle without
dispersion, and there is no concentration in the soil phase at the point of 1.00
depth. When /c is small, a slow exchange of material between two phases takes
place, causing a significant decrease in the peak concentration and a
considerable tailing in the water phase profile, and a flat low amplitude peak
profile in the soil phase is formed («; = 0.01).
With increasing values of the mass transfer coefficient, a broad low
amplitude peak of the water profile is formed and the concentration at the
tailing end of the water profile is higher, the concentration amplitude of the
soil profile is getting higher, and both of the profiles become symmetrical in
shape and exhibit dispersion (K = 0.1). As K approaches «, the profile of the
water phase tends to be rectangular again, but maintain a wider and lower
amplitude peak than when K equals zero. The profile of the soil phase also tends
to be rectangular, but shows a significant increase in the peak concentration.
Dispersion Due to K
The curves in Figure 32 and Figure 33 demonstrate that for intermediate
values of K (0.1
-------
64
ZE.4
2E4
2E4
1E4
8000
4000
0
C
WATER PHASE
K = 0 *= 100
ic = 0.01 K = 1
ic - 0.1
a"
- _
30 60 90 12
6000
4000
2000
0
0
TIME (days)
Figure 32. Breakthrough curve predicted by the VIP model with the
initial concentration in the water phase.
O
i= 1000
§
~z.
u
0 500
O
O
Q
WATER PHASE j \
j ^
< = 100 I
<= 1 /
-c = 0.1
-c = 0.01
' = o
-
1 H
/ I K
/ K
/ \
^ ! -UN
r ^-7-1 ^r~^r
0 30 60 90
TIME (days)
~~
12
Figure 33. Breakthrough curve predicted by the VIP model with the
initial concentration in the soil phase.
2E4
2E4
1E4
8000
4000
0
WATER PHASE
. « = 0 ic = 1 00
" K = 0.01 <: = 1
ic = 0.1
n
//H,
^ ^^' / i '~^r '
3 30 60 90 1;
6000
4000
2000
0
0
TIME (days)
Figure 34. Breakthrough curve predicted by the VIP model with the
initial concentration in both phases.
-------
65
Estimation of K from VIP Model
Figures 32 through 34 demonstrate that the calculated breakthrough curves
trom the VIP model vary with K values. Once a breakthrough curve from field
data is obtained and compared on the same graph with a group of different values
or K, there should be one curve for a specific value of /e which is in close
agreement to the field data within a certain level of confidence. This can be
estimated by "curve-fitting" the model to the measured data (van Genuchten and
Wierenga, 1977; van Genuchten et al., 1977; Gaudet et al., 1977; Rao et al.,
1979; Rao et al., 1980a; Rao et al., 1980b). These techniques were discussed
by Rao et al. (1979). The VIP model provides a methodology by which estimates
of K may be obtained, similar to that described by Liu and Weber (1981) for
estimating film diffusion coefficients in activated carbon adsorption columns.
Since relatively little is known about the factor K or the functional form which
K follows, this technique can provide a means to estimate K under different
experimental conditions for analysis of the effects of those conditions on *.
This will lead to improved understanding of hazardous waste constituent
interactions in the vadose zone.
-------
66
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Rao, P. S. C., D. E. Rolston, R. E. Jessup, and J. M. Davidson. 1980b. Solute
transport in aggregated porous media: Theoretical and experimental evaluation.
Soil Sci. Soc. Am. J. 44:1139-1146.
Reinhart, R.D. 1988. Personnel communication.
Ryan, J., Loehr, R. and Sims, R. 1987- The land treatability of appendix VIII
constituents present in petroleum refinery wastes: Laboratory and modeling
studies. Prepared for the American Petroleum Institute.
*
Ryan, J. 1986. Land treatment: A waste management alternative, p.347. In Loehr,
R.C. and Malina, J.F. (Eds.). University of Texas Center for Research in Water
Resources, Austin, Texas.
Schwarzenbach, R.P., and J. Westall. 1981. Transport of nonpolar organic
compounds from surface water to groundwater. Environmental Science and
Technology. 15(11):1360-1367.
Selim, H. M., J. M. Davidson, and R. S. Mansell. 1976. Evaluation of a two-site
adsorption-desorption model for describing solute transport in soils, -paper
presented at Proceedings, Summer Computer Simulation Conference, Nat. Sci. Found.
Washington, D. C. July 12-14.
Short, T.E. 1986. Modeling of processes in the unsaturated zone. In Land
Treatment: A hazardous waste management alternative, p. 211-240. In R.C. Loehr
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Research in Water Resources. University of Texas .at Austin, Austin, Texas.
Sims, R.C. and M.R. Overcash. 1983. Fate of polynuclear aromatic compounds (PNAs)
in soil-plant systems. Residue Reviews. 88:1-68.
Sims, R.C. 1982. Land treatment of polynuclear aromatic compounds. Ph.D.
Dissertation. North Carolina State University. Raleigh, North Carolina.
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R.C. and Malina, J.F. (Eds.). University of Texas Center for Research in Water
Resources, Austin, Texas.
Smith, O.L. 1982. Soil microbiology: A model of decomposition and nutrient
cycling, p. 161. In M. J. Bazin (Ed.). CRC Press, Inc., Boca Raton.
Soil Science Society of America. 1981. Water potential relations in soil
microbiology, p.151. SSSA special publication No.9. Soil Science Society of
America, Madison, WI.
Stevens, D. K., P. M. Berthouex and T. W. Chapman. 1986. The effect of tracer
diffusion in biofilm on residence time distributions. Wat. Res. 20(3):369-375.
-------
72
Stotzky, G. 1972. Activity ecology and population dynamics of microorganisms in
soil. CRC Critical Reviews in Microbiology 2:59-137.
Stotzky, G. 1980. Surface interactions between clay minerals and microbes,
viruses and soluble organics, and the probable importance of these interactions
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J. Melling, P.R. Rotter, and B. Vincent (Eds.). Microbial adhesion to surfaces.
John Wiley and Sons, New York, NY.
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in soil: Model predictions and experimental results. J. Wat. Poll. Cont. Fed.,
(in press).
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U.S. EPA. 1986. Permit guidance manual on hazardous waste land treatment
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-------
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Utah.
-------
74
Appendix A
Nonlinear Least Squares Analysis of Temperature Data
Non-Linear Least Squares Parameter Estimation
Benzo[b]fluoranthene Temperature Data
After 5 iteration(s), converged parameter estimates are
^20
.167757E-02
day'1
X(l)
Time
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
60.00
60.00
60,00
60.00
60.00
60.00
60.00
60.00
60.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
120.0
120.0
120.0
120.0
120.0
120.0
120.0
X(2)
Temp.
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
Co
103676E+01
OBS
c/c0
1.150
1.130
1.070
1.180
1.120
1.190
1.260
1.160
1.020
1.080
.9700
1.030
.9600
.8900
1.050
.9200
1.050
1.020
.9100
.9600
.9700
.8800
.8900
.8800
.8100
.8300
.8400
.8000
.8100
.8300
.8200
.8100
.8200
.7800
.7600
.7600
.8800
.8900
.8500
.8700
.8900
.7600
.7400
e
.102365E+01
ETA
Predicted
1.037
1.037
1.037
1.037
1.037
1.037
1.037
1.037
1.037
1.023
1.023
1.023
1.020
1.020
1.020
1.015
1.015
1.015
.9574
.9574
.9574
.9375
.9375
.9375
.9130
.9130
.9130
.9151
.9151
.9151
.8855
.8855
.8855
.8495
.8495
.8495
.8840
.8840
.8477
.8477
.8477
.8040
.8040
Resid
.1132
.9324E-01
.3324E-01
.1432
.8324E-01
.1532
.2232
.1232
-.1676E-01
.5691E-01
-.5309E-01
.6912E-02
-.5952E-01
-.1295
.3048E-01
-.9502E-01
.3498E-01
.4976E-02
-.4736E-01
.2636E-02
.1264E-01
-.5749E-01
-.4749E-01
-.5749E-.01
-.1030
-.8297E-01
-.7297E-01
.1151
-.1051
-.8510E-01
.6551E-01
-.7551E-01
-.6551E-01
-.6950E-01
-.8950E-01
.8950E-01
.4044E-02
.5956E-02
.2278E-02
.2228E-01
.4228E-01
-.4396E--01
-.6396E-01
-------
75
120.0
150.0
150.0
150.0
150.0
150.0
150.0
150.0
150.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
.8000
.8500
.8700
.8700
.7700
.7400
.7500
.7100
.7300
.8300
.7800
.8000
.8000
.8400
.6400
.6400
.7400
.8000
.8400
.7200
.7700
.7200
.7400
.6700
.7100
.6400
.7600
.7800
.7800
.7400
.7300
.8300
.7900
.7000
.7400
The objective function value is
The number of function calls is :
The number of eigenvalue calculations is
The linear theory covariance matrix is :
.143E-07
.138E-05 .228E-03
-.229E-06 -.178E-04 .350E-04
The linear theory correlation matrix is :
8040
8495
8495
8495
8061
8061
8061
7544
7544
8163
8163
7665
7665
7665
7080
7080
7080
7845
7845
7845
7289
7289
7289
6644
6644
6644
7538
7538
7538
6931
6931
6931
6234
6234
6234
400225E+00
62
.3961E-02
.4821E-03
.2048E-01
.2048E-01
.3611E-01
.6611E-01
.5611E-01
.4444E-01
.2444E-01
.1366E-01
.3634E-01
.3345E-01
.3345E-01
.7345E-01
.6797E-01
.6797E-01
.3203E-01
.1554E-01
.5554E-01
.6446E-01
.4107E-01
.8925E-02
.1107E-01
.5643E-02
.4564E-01
.2436E-01
.6179E-02
.2618E-01
.2618E-01
.4685E-01
.3685E-01
.1369
.1666
.7657E-01
.1166
1.000
.7647
-.3229
1.000
.1988
1.000
95% Confidence Intervals for the Parameters are :
No. Lower Theta Upper
k,0 1 .14385E-02 <
C 2 1.0066 <
« 3 1.0118 <
.16776E-02 <
1.0368 <
1.0236 <
.19166E-02 day"1
1.0669
1.0355
-------
76
.2 f
o
O
O
c"
_o
"o
1^
c
0)
u
c
O
o
0)
O
D
a
0)
ft:
1.0
0.9
0.8
0.7
0.6
0
Benzo[b]fluoranthene
io°c
Model A 20°c Data
T 30°C
50
00 150
Time' (days)
200
0.5 0.6 0.7 0.8 0.9 1.0
Predicted Reduced Concentration,
250
o
o
"x^^
-0
15
^
TJ
'cn
-------
77
Non-Linear Least Squares Parameter Estimation
Chrysene Temperature Data
After 2 iteration(s), converged parameter estimates are
kzo C0 6
.100580E+01 .100295E+01
.589910E-03
day'1
X(l)
Time
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
60.00
60.00
60.00
60.00
60.00
60.00
60.00
60.00
60.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
120.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
150.0
150.0
150.0
X(2)
Temp.
10.00
10 . 00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20 . 00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
OBS
C/C0
.9900
.9700
.9600
.9700
.9700
1.010
1.070
1.040
.9600
.9700
.9700
.9500
1.010
.9600
1.010
1.030
1.080
1.000
.9900
1.000
.9900
.9700
1.000
1.020
.9800
.9800
.9800
.9000
.9200
.9300
.9300
. 9-300
.9600
.9400
.9200
.9300
.9700
.9900
.9900
1.000
1.010
.9400
.9500
.9800
.9300
.9400
.9400
ETA
Predicted
1.
1.
1.
1,
1.
1.
1.
1.
1.
1.
1.
1.
.006
.006
.006
.006
.006
.006
.006
.006
.006
.000
.000
.000
.9999
.9999
.9999
.9997
.9997
.9997
.9718
.9718
.9718
.9708
.9708
.9708
.9698
.9698
.9698
.9531
.9531
.9531
.9515
.9515
.9515
.9500
.9500
.9500
.9390
.9390
.9371
.9371
.9371
.9351
.9351
.9351
.9230
.9230
.9230
Resid
.1580E-01
.3580E-01
.4580E-01
.3580E-01
.3580E-01
.4202E-02
.6420E-01
.3420E-01
.4580E-01
.3005E-01
.3005E-01
.5005E-01
.1012E-01
.3988E-01
.1012E-01
.3029E-01
.8029E-01
.2939E-03
.1818E-01
.2818E-01
.1818E-01
.8209E-03
.2918E-01
.4918E-01
.1021E-01
.1021E-01
.1021E-01
.5307E-01
.3307E-01
.2307E-01
.2154E-01
.2154E-01
.8457E-02
.9968E-02
.2997E-01
.1997E-01
.3101E-01
.5101E-01
.5294E-01
.6294E-01
.7294E-01
.4919E-02
.1492E-01
.4492E-01
.7012E-02
.1701E-01
.1701E-01
-------
78
150.0
150.0
150.0
150.0
150.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
20.00
20.00
20.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
.8900
.8700
.8900
.8300
.9200
.9300
.9000
.9700
.9800
.9500
.8500
.8200
.9600
.9100
.9500
.8200
.9300
.8700
.9000
.8500
.8500
.8400
.8200
.8300
.8300
.8300
.8400
,9300
,9900
.8600
.8600
.9206
.9206
.9206
.9182
.9182
.9073
.9073
.9045
.9045
.9045
.9016
.9016
.9016
.8918
.8918
.8918
.8886
.8886
.8886
.8853
.8853
.8853
.8766
.8766
.8766
.8730
.8730
.8730
.8693
.8693
.8693
.139167E+00
34
ns is 4
.3062E-01
.5062E-01
.3062E-01
.8819E-01
.1808E-02
.2274E-01
.7263E-02
.6553E-01
.7553E-01
.4553E-01
.5161E-01
.8161E-01
.5839E-01
.1819E-01
.5819E-01
.7181E-01
.4139E-01
.1861E-01
.1139E-01
.3533E-01
.3533E-01
.4533E-01
.5661E-01
.4661E-01
.4661E-01
.4302E-01
.3302E-01
.5698E-01
.1207
.9335E-02
.9335E-02
The objective function value is
The number of function calls is
The number of eigenvalue calculations is
The linear theory covariance matrix is :
.393E-08
.432E-06 .736E-04
-.299E-07 .201E-05 .621E-04
The linear theory correlation matrix is :
1.000
.8027 1.000
-.6049E-01-.2971E-01 1.000
95% Confidence Intervals for the Parameters are :
No. Lower Theta Upper
k20 1 .46471E-03 < .58991E-03 < .71511E-03 day'1
C0 2 .98868 < 1.0058 < 1 0229
e 3 .98722 < 1.0029 < 1.0187
-------
79
o
O
0
D
O
C
O
o
"D
OJ>
U
D
T)
CD
0.8
0.7
Chrysene
io°c
Model A 20°c Data
0
50
00 150
Time (days]
200
250
0.2
0
CJ
o
15
Z5
T5
' (f)
CD
0.
0.0
-0.1 -
-o.:
0.9
Chrysene
io°c
« 20°c
* 30°C
0.9 1.0 1.0
Predicted Reduced Concentration,
o
1 1
-------
80
Non-Linear Least Squares Parameter Estimation
Fluorene Temperature Data
After 4 iteration(s), converged parameter estimates are
^20
.155144E-01
day"1
X(l)
Time
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
60.00
60.00
60.00
60.00
60.00
60.00
60.00
60.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
94.00
120.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
150.0
150.0
150.0
150.0
X(2)
Temp.
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
Co
982529E+00
OBS
C/C0
.9400
.9300
.9300
.9400
.9500
.9700
1.000
.9500
.8700
.8700
.8900
.8600
.8600
.8300
.8700
.7400
.7700
.7000
.8200
.8200
.8200
.2300
.2500
.2800
.1700
.1700
.7400
.7600
.7600
.1700
.2000
.2300
.1200
.1300
.9000E-01
.7100
.3400
.1900
.1800
.2400
.1200
.1100
.9000E-01
.1600
.1700
.1200
.5000E-01
e
.107437E+01
ETA
Predicted
.9825
.9825
.9825
.9825
.9825
.9825
.9825
.9825
.9825
.9109
.9109
.9109
.8413
.8413
.8413
.7150
.7150
.7150
.6238
.6238
.6238
.3873
.3873
.3873
.1459
.1459
.4822
.4822
.4822
.2286
.2286
.2286
.4951E-01
.4951E-01
.4951E-01
.3960
.3960
.1527
.1527
.1527
.2166E-01
.2166E-01
.2166E-01
.3156
.3156
.3156
.9587E-01
Resid
-.4253E-01
-.5253E-01
.5253E-01
.4253E-01
.3253E-01
-.1253E-01
.1747E-01
-.3253E-01
-.1125
-.4088E-01
-.2088E-01
.5088E-01
.1867E-01
-.1133E-01
.2867E-01
.2502E-01
.5502E-01
-.1498E-01
.1962
.1962
.1962
.1573
.1373
-.1073
.2411E-01
.2411E-01
.2578
.2778
.2778
.5855E-01
.2855E-01
.1445E-02
.7049E-01
.8049E-01
.4049E-01
.3140
.5603E-01
.3731E-01
.2731E-01
.8731E-01
.9834E-01
.8834E-01
.6834E-01
-.1556
.1456
-.1956
-.4587E-01
-------
81
150.0
150.0
150.0
150.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
210.0
240.0
240.0
240.0
240.0
240.0
240.0
240.0
20.00
20.00
30.00
30.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
30.00
30.00
10.00
10.00
10.00
20.00
20.00
20.00
30.00
6000E-01
7000E-01
1000E-01
1000E-01
8000E-01
9000E-01
5000E-01
5000E-01
2000E-01
2000E-01
2000E-01
2000E-01
1000
1400
8000E-01
4000E-01
4000E-01
4000E-01
2000E-01
1000E-01
1000E-01
8000E-01
7000E-01
8000E-01
3000E-01
4000E-01
3000E-01
2000E-01
.9587E-01
.9587E-01
.8347E-02
.8347E-02
.2514
.2514
.6019E-01
.6019E-01
.6019E-01
.3217E-02
.3217E-02
.3217E-02
.2003
.2003
.2003
.3779E-01
.3779E-01
.3779E-01
.1239E-02
.1239E-02
.1239E-02
.1596
.1596
.1596
.2373E-01
.2373E-01
.2373E-01
.4776E-03
-.3587E-01
-.2587E-01
.1653E-02
.1653E-02
-.1714
-.1614
-.1019E-01
.1019E-01
.4019E-01
.1678E-01
.1678E-01
.1678E-01
-.1003
-.6034E-01
-.1203
.2208E-02
.2208E-02
.2208E-02
.1876E-01
.8761E-02
.8761E-02
-.7963E-01
-.8963E-01
.7963E-01
.6272E-02
.1627E-01
.6272E-02
.1952E-01
The objective function value is . 773754E+00
The number of function calls is : 53
The number of eigenvalue calculations is 6
The linear theory covariance matrix is :
.118E-05
.130E-04 .731E-03
.447E-05 .332E-05 .699E-04
The linear theory correlation matrix is :
1.000
.4422
.4924
1.000
.1467E-01 1.000
95% Confidence Intervals for the Parameters are :
No. Lower Theta Upper
k20 1 .13350E-01 <
C0 2 .92856 <
6 3 1.0577 <
.15514E-01 <
.98253 <
1.0744 <
.17679E-01
1.0365
1.0911
day
-i
-------
82
O
CJ
O
c
O
-t >
D
i_
C
cu
0
c
O
O
cu
u
13
T)
CU
ct:
0.2 -
0.0
0
Fluorene
0.0
io°c
A 20°c Data
T 30°C
50
00 150
Time (days)
200
250
0.20
0
o
o
D 0.00
CO
cu
cr
-0.20
0 40
Fluorene
* 10°C
20°C
" 30°C
n * ^ *
:> ..: . ' " s i
1 : § :
1 . 1 . 1 . 1
0.2 0.4 0.6 0.
Predicted Reduced Concentration,
.0
o
------- |