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
                   DESCRIPTORS
                                                b.IDENTIFIERS/OPEN ENDED TERMS
                                    COSATi Held, Group
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

-------
           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.

-------
                          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:

-------
                                                                             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

-------
                                                                             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):

-------

                                                                            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

-------
                                                                             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.

-------
                                                                             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

-------
                                                                             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

-------
                                                                               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)

-------
                                                                             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]

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                                                                             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.

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                                                                             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.

-------
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-------
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-------
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-------
                                                                             32
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                                                       200
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                                                       200
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                                                                                                 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

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                                                                                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.

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                                                                              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.

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                                                                             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  ).

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                                                                             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.

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                                                                             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
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                                                                    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.

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                                                                            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.

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                                                                            66

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 transport in aggregated porous  media:  Theoretical  and  experimental evaluation.
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 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
 and J.F. Malina,  Jr.  (Eds.).  Water Resources  Symposium No.   13, Center  for
 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.

 Sims, R.C. 1986.  Land treatment: A waste management alternative, p.151. In Loehr,
 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
to the ecology of microbes in soil. p.231-247. In R.C.W.  Berkeley,  J.M.  Lindi,
J. Melling, P.R.  Rotter,  and B.  Vincent (Eds.). Microbial adhesion  to  surfaces.
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                               •
Symons, B.D.,  R.C. Sims,  and W.J.  Grenney.  1988.  Fate  and transport of organics
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Taylor, J.M, J.F. Parr, L.J. Sikora, and G.B. Willson, 1980.  Considerations  in
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U.S.   EPA.  1986.  Permit guidance  manual  on hazardous  waste  land  treatment
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U.S.   EPA.  1986.  Waste-soil treatability studies for four  complex industrial
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U.S.  EPA. 1988a.  Treatment potential  for 56  EPA  listed  hazardous chemicals  in
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-------
                                                                            73


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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

-------